DRAWING AND DESIGN iv f K t Psi INI i 1 I i j LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class MACHINE DRAWING AND DESIGN FOR BEGINNERS BY THE SAME AUTHOR Machine Design, Construction and Drawing A Text-book for the use of Young Engineers. With 86 Tables and numerous Exercises. Illustrated by over 1400 Drawings and Figures. 8vo, i or. 6d. net. Notes on, and Drawings of, a Four=Cy Under Petrol Engine Arranged for use in Technical and Engineering Schools. Oblong folio, 2s. net. The Elements of Geometrical Drawing An Elementary Text-book on Practical Plane Geometry, including an Introduction to Solid Geometry, etc. Crown 8vo, y. 6d. LONGMANS, GREEN, AND CO. LONDON, NEW YORK, BOMBAY, AND CALCUTTA MACHINE DRAWING AND DESIGN FOR BEGINNERS AN INTRODUCTORY WORK FOR THE USE OF TECHNICAL STUDENTS BY HENRY I. SPOONER, C.E. j it M.I.MECH.E., A.M.lNST.C.E., M.lNST.A.E., F.G.S., HoN.M.J.lNST.E., ETC. DIRECTOR AND PROFESSOR OF MECHANICAL AND CIVIL ENGINEERING IN THE POLYTECHNIC SCHOOL OF ENGINEERING, REGENT STREET, LONDON AUTHOR OF "MOTORS AND MOTORING," "PRACTICAL PLANE AND SOLID GEOMETRY," "THE ELEMENTS OF GEOMETRICAL DRAWING," "MACHINE DESIGN, CONSTRUCTION AND DRAWING," " NOTES ON, AND DRAWINGS OF, A FOUR-CYLINDER PETROL ENGINE" JOINT AUTHOR OF "ELEMENTS OF MACHINE CONSTRUCTION AND DRAWING," ETC., ETC. LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, AND CALCUTTA 1908 Ail rights reserved "t PREFACE SOME students taking a regular course of instruction in Machine Construction and Drawing in a day Engineering School or Technical College supplement the instruction given by working from such a book as the Author's " Machine Design, Construction and Drawing." On the other hand, most evening students, during their first year or two, prefer something more portable and less expensive ; so, conforming to many requests, and encouraged by the flattering way in which his " Machine Design," has been received in this country and in America, the Author has been induced to prepare this book, in the hope that it may serve as an up-to-date and suitable introduction to the subject, and lead up to his more advanced work. In arranging the contents of the book, the Author has devoted the first six chapters to the drawing part of the subject, and, guided by his extensive experience, he has treated it in such a way that an intelligent beginner should find it easy to learn the art of making working drawings of simple pieces. The remaining chapters treat more particularly of matters relating to details and machine parts. These are either shown with suitable proportions for various sizes, or are fully dimensioned with the object of making them useful to the young designer or fit for drawing exercises ; and occasional suggestions are made as to how such drawings can be best taken in hand. To further assist students and instructors in this direction, suitable drawing exercises are given at the end of most chapters. There are further interesting drawing exercises in Chapter XXIV., suitable for more advanced students, consisting of various engine and machine parts, many of which have appeared in past Examination Papers at the Polytechnic, and a few have been selected from recent papers set by the City Guilds in Mechanical Engineering, and by the Board of Education in Machine Construction and Drawing. The Examination Papers for 1906 and 1908 set by the City Guilds and the Board of Education also appear at the end of the book. There are also, at the end of most chapters, sketching exercises given, as many of the figures lend themselves to the practice of this indispensable art. Indeed, too much importance can hardly be attached to the cultivation of that clear freehand sketching, having in itself nearly the accuracy of scale drawing, which is such a help to the chief draughtsman in rapidly conveying his ideas. In fact, even a junior draughtsman is expected to sketch with facility. Judged from an art point of view, there can be no doubt that the standard of mechanical draughtsmanship has been considerably lowered since the days of our grandfathers, and the modern practice of first setting out working drawings in pencil, tracing them, and making photographic prints from the tracings for use in the shops, has still further lowered the standard. For in ordinary practice mechanical draughtsmen are no longer called upon to produce drawings with delicate, beaiitifully joined lines, soft and rich shadows true to geometry, with crisp and dainty surfaces, such as characterized Mr. David Kirkaldy's superb sections of the SS. Persia, exhibited in the Eoyal Academy over half a century ago, and now adorning the office of his famous son, Mr. W. G. Kirkaldy. However, although it rarely happens in ordinary practice 202052 vi PREFACE that finished drawings are made, most draughtsmen very properly like to be able to turn out a drawing nicely tinted and finished off with shade lines ; but in the ordinary way the student must first master the somewhat difficult art of making a finished pencil drawing, with every line sharp and distinct, and the figuring and lettering bold, neat, and accurate; if this is to be done during an ordinary college course, unless a student has a marked aptitude for artistic work, there is little time available for making pretty or show drawings, and if encouraged to do so systematically it is at the expense of progress along more useful lines. Every student should be encouraged to become proficient in making neat and accurate tracings expeditiously, and up to a certain point the observing ones, whilst acquiring this useful art, will be able to become familiar with many interesting details and with the usual methods of figuring and lettering drawings ; but only very exceptional workers could survive a long course of tracing, for it tends to blunt the perceptions and stifle the powers which are required to make good draughtsmen and clever designers. Indeed, tracing has been defined as "a diabolical invention for destroying draughtsmen during the process of their incubation." Now, although mechanical draughtsmen are no longer called upon to produce highly finished drawings, they are expected to be able to transfer to paper any ideas of their chief's or their own, with quickness combined with neatness in such a way that every detail is clearly defined to scale and accurately dimensioned. It is not usual for writers to refer to such minor details as machine and lever handles, so that young draughtsmen are often left to their own resources to guide them in such matters, therefore a chapter (XIII.) dealing with them has been included. In recent years much attention has been given to roller and ball bearings, particularly in motor-car work : so the construction of these, and the principles which govern their design, are explained in Chapter XVIII. In Chapter XIX. the recent and important improvements in spur gearing are described, and although the greatly improved helical gears have made mortise wheels practically obsolete, the consideration that we shall for some years to come still be using some of the old plants led the Author to include mortise wheels in this chapter. In Chapter XXVI. will be found over one hundred questions relating to the subject, suitable for examinations or for home work pui-ppses. The Author is indebted to the technical press of England and America for some of the information he has found so useful, and whenever he has drawn from such sources or from technical works, or the Proceedings of scientific and professional societies, he has endeavoured to suitably acknowledge it. In his own training and in writing this book he feels particularly indebted to " Der Konstruckteur," which the genius of Eeuleaux gave to the engineering world, and to Professor Unwin's " Machine Design." He has also made references to Professor Goodman's admirable and well-known work, " Mechanics Applied to Engineering." The best thanks of the Author are also due to the engineers and firms who have kindly permitted him to use their copyright illustrations, or have supplied him with information relating to their specialities. And he cannot refrain from expressing his hearty appreciation of the patient industry of his friend, Mr. E. G. Davey, A.M.I.Mech.E., who made the drawings for most of the illustrations in the book from the Author's rough sketches. HENRY J. SPOONER. THE POLYTECHNIC SCHOOL OF ENGINEERING, REGENT STREET, LONDON, W. November, 1908. CONTENTS ( The numbers refer to articles, not pages) CHAPTER I DRAWING INSTRUMENTS, MATERIALS, ETC. PAGES Hints upon the Selection and Use of Drawing Instruments, Mate- rials, etc. 2. Drawing Board. 3. Working Position of Board. 4. T-Square. 5. To test a T-Square in order to see that its Edge is Straight. 6. To test whether the Blade is Square with the Stock. 7. Set-Squares. 8. To test a Set-Square. 9. To test the 60 Angle. 10. Drawing Paper. 11. Whatman's Hot-pressed Paper. 12. What- man's N.H.P. Paper. 13. Quality of " Drawing" Paper. 14. Pencils Different Kinds and Qualities. 15. Degrees of Hardness, etc. 16. How to sharpen the Pencil. 17. Compass Pencils. 18. The Conical- pointed Pencil. 19. Drawing Pins. 20. Horn and Metal Centres. 21. Indiarubber. 22. Measuring Rules. 23. Drawing or Ruling Pens. 24. Indian Ink. 25. Liquid Indian Ink. 26. Colours, etc. 27. Saucers for mixing Colours. 28. Brushes 1-9 CHAPTEE II PRINTING, TRACING, SHADING, ETC. 29. Printing, etc. 30. Working Drawings. 31. Shade Lines. 31a. Shading by Lines. 32. Workshop Drawings. 32a. Tracing. 33. Tracing Exercises. (Also refer to page xvi.) 10-15 CHAPTEE III SCALES, AND DRAWING TO SCALE 34. Introduction. 35. Engineer's Scales 16, 17 CHAPTEE IV HOW TO DRAW STRAIGHT LINES AND SIMPLE FIGURES 36. Introduction. 37. Straight Lines drawn with the Assistance of the T-Square. 38. Defects in Lines. 39. Straight Lines drawn with the Assistance of a Set-Square. 40. Dotted Lines. 41. Rectangles. 42. To draw a Rectangle of given size. 43. Exercises upon the Use of Centre Lines. 44. Figure Symmetrical about Two Centre Lines. 45. Another Case of a Figure Symmetrical about Two Centre Lines 18-24 CHAPTER V CIRCLES, ARCS, AND LINES 46. Introduction. 47. Definitions, Circles and Tangents, etc. 48. To describe a Circular Arc through Three given Points. 49. To draw a Tangent to a Circle through a fixed Point in its Circumference. 49a. To draw a Tangent to a Circle through a fixed Point without it. 49b. To inscribe in a given Angle a Circle of given Radius. 50. To describe a Circle of given Radius to touch a given Line and a given Circle. 51. To draw a Circle to touch Three given Straight Lines. 52. To describe an Arc of a Circle of given Radius to touch a given Arc and a given Straight Line. S3. Exercises 25-28 CHAPTEE VI HOW TO COMMENCE A WORKING DRAWING 54. Introduction. 55. Plan and Elevation. 56. To draw the Plan and Elevation of a Rectangular Block. 57. End Elevations and Sections. 58. Drawings of a Cast-iron Bench Block. 59. To draw a Section of a Wrought-iron Beam or Joist. 60. British Standard Beam Sections. 61. Sectional Shading or Lining for Various Materials. 62. Drawings of a Stuffing Box Gland. Exercises 29-38 vin CONTENTS CHAPTEB VII STUFFING BOXES, LEATHER COLLARS, ETC. ttata 63. Introduction. 64. Stuffing Boxes with Metallic Packing. 65. Soft . Metallic Packing. 65a. Soft Packing for Stuffing Boxes. 66. Leather Packing Collars. 67. Leather Collar v. Hemp Packing. 68. Size of Leathers. 69. Friction of Leather Collars. Exercises 39-44 CHAPTER VIII SHAFTING, CRANK SHAFTS, CRANKS, JOURNALS, ETC. 70. Shafting, its Strength, etc. 71. Torsional Strength of a Shaft trans- mitting Uniform Torque. 72. Example. 73. Combined Torsion and Bending, the Twisting and Bending Moments unvarying. Shaft or Axle subjected to Bending Moment only. 74. Example. 75. Shaft subjected to Combined Twisting and Bending. Rankine and French Formulae. 75a. Example. 76. Guest's Equivalent Bending Moment. 77. Hollow Shafts. 78. Hollow and Solid Shafts of Equal Strength. 79. Example. 80. Cranks. 81. Built-up Cranks. 82. Petrol Motor Crank Shafts. 83. Petrol Motor Crank Shaft (Drawing Exercise). Exercises 45-54 CHAPTEB IX COUPLINGS, CLUTCHES, ETC. 84. Introduction. 85. Drawing Exercise : Butt-Muff Coupling. 86. Fair- bairn's Lap-Box Coupling. 87. Flange Couplings. 88. Strength of Bolts. 89. Pulley Flange Coupling. 90. Claw Coupling. 91. Pro- peller and Crank Shaft Coupling. 92. Proportions of Marine Coupling. Exercises 55-62 CHAPTER X KEYS AND PIN KEYS, ETC. 93. Introduction. 94. Saddle or Hollow Key. 95. Key on Flat. 96. Sunk Key. 97. Two Keys. 98. Key Boss. 99. Staking on. 100. Cone Keys. 101. Pins. Standard Taper Pins. 102. Feathers. 103. Strength of Keys. 104. Example. Exercises 63-69 CHAPTER XI RIVETED JOINTS PACKS 105. Introduction. 106. Proportions of Rivet Heads, etc. 107. Rivet Materials, etc. 108. Drilling and Punching Rivet Holes. 109. Caulking and Fullering. 109a. Sections of Wrought Iron and fiteel Rolled Bars. 109b. Comparative Cost of Bars and Plates. 110. Forms of Joints. The Butt Joint. Proportions. Margin. Diagonal Pitch. llOa. Chain Riveting, Board of Trade Rule. llOb. Combined Lap and Butt Joint. HOc. Butt Joints with Double Straps. Treble Riveted Butt Joint. Butt Straps. Quadruple Riveted Butt Joints. llOd. Intersecting Riveted Joints. Junction of Four Plates. llOe. Connections for Plates at Right Angles. Boiler Ends and Shell. HOf. Flue Connections. Tee Ring. Bowling Ring. Bolton Hoop. Adamson's Joint. Davey-Paxman Joint. HOg. Connecting Parallel Plates. HOh. Strength of Riveted Joints, (a) By Rivet shearing. (6) By tearing of the Plates, (c) By Plastic Flow, (d) By Plate break- ing in Front of Rivet. HOi. Efficiency of Joint. 111. Maximum Value of d in relation to (. Crushing Action in Lap and Butt Joints. 112. Best Diameter of Rivet in relation to Thickness of Plate. Size of Rivets suggested by the National Boiler Insurance Co. 113. Efficiencies of Riveted Joints. 114. Graphic Method of Designing Joints. Exercises 70-85 CHAPTER XII BOLTS, NUTS, SCREWS, ETC. 115. Introduction. 116. Forms of Screw Threads. Whitworth's. Seller's. Square Thread. Buttress Thread. Acme Thread. Knuckle Thread. 117. Proportions of Threads. The Standard British Thread. Core Diameter. Pitch. British Standard Fine Screw Threads. Engi- neering Standards Committee's Definitions. Pitch and Core Diameter of Square Threads. Acme Standard. Depth of Thread. 118. Whit- worth Bolt as a Drawing Exercise. 119. Various Types of Bolts. Bright and Black Heads. Dimensions of Standard Bolts. Approxi- mate Widths across Heads for Drawing Purposes. 120. Dimensions of Bolts and Nuts. 121. Bolt and Screw Heads. Cheese Head. Tommy Head. Cup Head. Tee Head. Wodged-shaped Head. Hook Head. Eye Bolt. Boss Head. Lifting Eye Bolt. Conical Head. Bolt with Intermediate Head. Combined Bolt and Stud. Ordinary Stud. Forcing or Lifting Screw. Adjusting Screw. Saddle-piece. 122. Special Nuts. Spherical seated ones. Flanged Nut. Flanged Cap Nut. Thumb Nut. 123. Extra Thick Nuts. 124. Locking Nuts and Arrangements. Lock Nuts, etc. 125. Other Locking Arrangements. CONTENTS IX PAGES Perm or Ring Nut. 126. Wile's Lock Nut. The use of Taper and Split Pins. 126a. Capstan Nut or Castle Nut. Standard Proportions. 127. Foundation Bolts. Lewis Bolt. 128. Loose Collars. 129. Set- Screws. 130. Washers. 131. Screws with Multiple Threads. Double Thread. Treble Thread. Divided Pitch. 132. Square Threads v. Vee Threads. 133. Working Stress of Bolts and Studs at Root Section, (a) For Face Joints. (6) For Rougher Joints with Packing. Exercises ,86-101 CHAPTEE XIII MACHINE AND LEVER HANDLES 134. Introduction. Lever Handles. Balanced Machine Handles. Star Ball Type. Capstan Type. Unbalanced Machine Handles. Exercises 102-105 GHAPTEE XIV PIPES AND PIPE CONNECTIONS Introduction. 135. Cast-iron Steam Pipes. 136. Copper Pipes, etc. Ordinary Copper Pipe with Gun-metal Flanges. Copper Pipe with Stronger Flanges. Copper Pipe with Brazed and Riveted Flanges. Copper Pipes with Loose Flanges of Steel or Wrought Iron. 137. Wrought-iron and Steel Pipes, etc. Flanged Wrought-iron Pipe. Electrically Welded Flanges. Mild Steel Solid Drawn Pipe with Cast-steel Flanges. Welded Pipe with Riveted Flanges. Rolled Steel Flanges shrunk on. 138. Circumferential (or Longitudinal) Strength of Thin Pipes, Boilers, or other Cylindrical Vessels. 139. Example. 140. Steam-Tubing and Fittings. Bulged Socket. Ordi- nary Socket. Hexagonal Socket. Nipple Connection. Perkin's Joint. Perkin's Joint with Copper Washer. 141. Jointing. India- rubber and Lenticular Packing. Wire Gauze and Red Lead. Copper Rings. Metal-to-metal Joints. 142. Special Joints. Flexible Lens Joint. Union Joint. 143. Use of Expansion Joints. Expansion Coefficients for Pipe Metals. 144. Pipe Hangers and Pipe Bearers. Defective and Efficient Supports. Ground Roller Supports or Bearers. 145. Expansion Joints, etc. Copper Horseshoe Expansion Joint. Copper Expansion Loop. Copper Expansion Cushion. Copper Corru- gated Expansion Joint. Messrs. Crane & Co.'s Malleable Cast-iron Expansion Bends. Gland and Stuffing Box Expansion Joint. 145a. Drawing Exercise: Gland Expansion Joint. 146. Proportions of Standard Pipe Threads. 147. Spigot and Socket Joints. Proportions of Spigot and Socket Lead Joints. Proportions of Spigot and Socket Turned and Bored Joints. 148. Joints for Hydraulic Pipes. Empi- rical Proportions. Working Stress, etc. Bolts, their Strength. 149. Drawing Exercise : Hydraulic Stop Valve, Hemp or Asbestos Packed. 150. Drawing Exercise : Hydraulic Stop Valve, Leather Packed. 151. Drawing Exercise : Body of Steam Stop Valve. 152. Drawing Exercise: Steam Equilibrium Admission Valve. 153. Thick Cylinder Castings. Crystals of the Metal. Confused Crystallization. Lines of Crystallization. Lines of Weakness. Fillets. Bottoms of Hydraulic Presses. Faulty and Correct Forms. 154. Faults in designing Cylinders, etc. Weakening Effect of Holes. Cylinders cast together. Thickness of the Partitions. Exercises . . . 106-124 CHAPTEE XV COTTERS AND COTTERED JOINTS 155. Introduction. Proportions of Cottered Joints for Uniform Strength. 156. Clearance of Cotters. 157. Taper of Cotters. 158. Proportions and Strength of Cottered Joints. 159. Various Cottered Joints. Wrought-iron Standard and Cast-iron Bed Plate. Steel Rod and Piston. Piston Rod and Cross Head. Round Rod End and Cotter. Wrought-iron Rod. Steel Cotter. Cottered Bolt. Cottered Founda- tion Bolt, Round End. Cottered Joint for Rough Bars. Bolt cottered into Casting. Cotter without Gib. 160. Use of Gib. Cotter with Double Gibs. Gib and Cotter with Set-Screw. Exercises . 125-129 CHAPTEE XVI PIN OR KNUCKLE JOINTS, PITCH CHAINS, ETC. 161. Introduction. 162. Forked Knuckle Joint. 163. Strength of Knuckle Joint Pin. 164. Suspension Links. Hammered Eye. American Form. Berkley's Form. Fox's Form. Arrangements of Links and Pin Fastenings. Riveted. Split Pin. Nut and Split Pin. Multiple Link Chain. 165. Gearing Chains. Single Flat-link Gearing Chains. Double Flat-link Gearing Chains. Primary Fault. 166. Form of the Wheel Teeth for Chains. Exercises 130-133 CHAPTEE XVII BEARINGS, JOURNALS, HANGERS, ETC. 107. Introduction. Simplest Form of Bearing. Bushed Solid Bearing. Journal with Solid Collars. Bearing in Two Parts. Collar Bearing. b CONTENTS Thrust Block. Footstep or Toe Bearing. Area of Bearing. 168. Effective Area of a Bearing. 169. Various Bearing Adjustments. Bearing without Top Brass. Five Different Arrangements of Crank Shaft Bearings with Adjustment in Direction of Maximum Pressure. Examples of Arrangements for dealing with more Complex Cases of Varying Pressure. 170. Plummer Blocks or Pedestals. Bearing Block, or Solid Pedestal. 171. Ordinary Plummer Block or Pedestal. 172. Seller's Self-adjusting Pedestal. 173. Drawing Exercise : 3" Plummer Block or Pedestal, 174. Drawing Exercise : Crank Shaft Bearing for 4|" Shaft. 175. A more Advanced Exercise. 176. Brasses, or Steps. Materials used. Various Forms of Steps and Arrangements of the Supporting Surfaces. Fitting Strips. Stop Pins, etc. 177. White Metal Bearings. Babbit's Anti-friction Metal. Perkins' Anti- friction Metal. 178. Hangers. Adjustable Hanger Bearing. Seller's Type. 179. Wall Brackets, Two Examples, for Light and Average Work. 180. Light Wall Bracket (Drawing Exercise). 181. Wall Boxes for Plummer Blocks or Pedestals. Fire-proof Plates. Wall Openings.- 182. Footstep, or Pivot Bearings. Ordinary Form. Foot- step with Hemispherical Seat. Footstep with Multiple Discs. Footstep Collar Bearing. Moment of Friction. 183. Schiele's Pivot. Friction compared with that of a Flat Pivot. Moment of Friction. 184. Materials used for Bearings. Babitted Bearings. Gun-metal. Phosphor Bronze. Hard Steel. Exercises 134-149 CHAPTEE XVIII ROLLER AND BALL BEARINGS 185. Introductory Remarks. 186. Rollers for Bridge Ends, etc. Their Length and Number. 187. Anti-friction Wheels. Their Friction compared with that of Plain Bearings. 188. Roller Bearings. Simplest Form. Spinning. 189. Ring Cage Roller Bearing. 190. Solid Cage Bearing. End Thrust. 191. Flexible Rollers for Bear- ings. Hyatt's Form. Kynock's Form. 192. Conical Roller Thrust Bearings. Different Types. Use of Balls to reduce Friction due to End Thrust. 193. Cylindrical Roller Thrust Bearings for Heavy Work. 194. A Roller Bearing arranged as a Drawing Exercise. Swivel Seatings. 195. Ball Bearings. Two-point Contact. Grooved Races. Three-point Contact. Four-point Contact. Spinning Motion. Stribeck's Races. Housings. 196. Journal Hub Ball Bearings. Form of Constraining Surfaces. Three-point Contact. True Rolling. Four-point Contact. Cup and Ball Two-point Contact. 197. Ball Thrust Bearings. Three-point Contact. Spinning and Grinding. Four-point Contact. Hoffmann's Ball Thrust Washers. 198. Ball Journal Bearings. Simplest Form. P^ffect of Differences of Tempe- rature. 199. Compound Ball Bearings. Single Compound and Double Compound. Exercises 150-159 CHAPTEE XIX TOOTHED GEARING PAGES 200. Introductory Remarks. 201. Relative Speeds. 202. Technical names of Teeth Details. 203. Pitch, etc. Definitions. 204. Dia- metral, or Manchester Pitch. Diametral Pitch Number. Outside Diameter of Wheel. Circular or True Pitch. Distance between Axes. 205. Module, or French Pitch. Definition. 206. Example. 207. Form of Teeth. Cycloid. Involute. Back Lash. Epicycloid and Hypocycloid. Method of drawing Curves of Teeth. 208. Setting out Cycloidal Teeth. Use of Templets. Willis' Odontograph. Influence of Size of Rolling Circle on Form. 209. Rack and Pinion : Case (a) Rack working with Single Pinion. Case (b) Rack working with Set of Wheels. 209a. Arc of Action. Arcs of Approach and Recess. Path of Recess. Path of Approach. 209b. Obliquity of Action, etc. Angle of Obliquity of Action. Path of Contact. 209c. How Form influences Durability. 210. Proportions of Various Teeth, etc. Machine-moulded Wheels. Machine-cut Wheels. Common Pattern- moulded Wheels. Fairbairn's Proportions. Adcock's Proportions. Mortise Wheels. Mortise Bevel Wheels. Browne and Sharpe's Pro- portions. Length of the Teeth. Browne and Sharpe's Dimensions of Machine-cut Wheels. 211. Gee's Buttress Teeth. Back Lash. 212. Knuckle Gearing. Hollows and Rounds. 213. Breadth of Teeth, Rules for. 214. Rims of Toothed Wheels. 215. Shrouding or Flanging of Wheel Teeth. Single Shrouding. Double Shrouding to Pitch Line. Double Shrouding, whole Length. 216. Bevel Wheels. Pitch Surfaces. Mitre Wheels. 217. Drawing Example : Cast-iron Mitre Bevel Wheel. 218. Strength of Wheel Teeth. Safe Load on One Pair of Teeth. Safe Load on Two Pairs of Teeth. Factors of Safety. Table of Safe Loads P, and Factors of Safety for Cast-iron Teeth 1" Pitch and Breadth of 2-5 times the Pitch, when the Pressure is distributed uniformly over the Breadth of the -Teeth. 219. Arms of Wheels, their Shape and Strength, etc. Various Sections of Wheel Arms. 220. Naves or Bosses of Wheels. Rules for their Strength. 221. Rims of Wheels. 222. Mortise Wheels. Hornbeam and Birch Cogs. Bevel Mortise Wheel. Details of Mortise Wheels. Mortise Wheels practically superseded by Improved Wheels with Iron Teeth. Exercises 160-179 CHAPTEE XX BELT GEARING 223. Fast and Loose Pulleys. Belt Gear for Slow, Forward, and Quick Return Motion. Fast and Loose Pulleys for Shaft of a Machine. Fast and Loose Pulley Arrangement for Relief Tension. Fast and CONTENTS XI Loose Pulley without Bushing. 224. Rims of Pulleys or Riggers for Belting. Various Sections of Pulley Rims. Thickness of Rims. 225. Proportions of Pulley Arms. Pulley with Straight Arms. Pulley with Curved Arms. Pulley with Double Curved Arms. Elliptical and Segmental Sections of Pulley Arms. Number of Arms. 226. Split Pulleys. Two Patterns of Cast-iron Split Pulleys. Wrought-iron and Steel Split Pulleys. Medart's Split Pulley. Mac- beth's, the Universal, and Mackie's Split Pulleys. 227. Thickness and Length of Bosses or Naves of Pulleys. Rules for. Exercises 180-184 CHAPTER XXI PISTONS AND CYLINDERS, ETC. 228. Function of a Piston. Difference between Cylinder and Piston, and Pump Barrel and Bucket. Pump Barrel and Plunger. Different Materials for Pistons. 229. Pistons without Packing, Two Forms of. 230. Piston Packings. A Good or Ideal Piston defined. Necessary Ring Pressure against Cylinder Walls. Undue Wear. Lubrication of Pistons. Packing Spring Rings. Ramsbottom's Rings, their Proportions. Piston Rings which give Approximately Uniform Pressure on Cylinder Walls. Junk Ring. Various Forms of Springs for Piston Rings. Clayton's and Goodfellow's, Mather & Platt's, and Mudd's Pistons. 230a. Allen's Pistons, with Rings in Three Pieces. 231. Pump Bucket Packings. Various Forms. Proportions of Packing. 232. Piston Ring Joints. Various Forms of. 233. Guard Rings and Devices. Various Forms of. 234. Connection of Piston to Piston Rod. Various Forms of Fixings. 235. Proportions of Cast-iron Pistons. Dimensions of Cast-iron Pistons up to 16" Diameter. Table of Values of Piston Coefficients. 236. Cast-steel Pistons. Suitable Proportions for Cast-steel Pistons. 237. Cylinder for Steam Engine (Drawing Exercise). 238. A more Advanced Exercise. 239. Pistons for Internal Combustion Engines. Gas Engine Type. Petrol Engine Type. 240. Piston for Petrol Engine (Drawing Exercise). 241. Pair of Cylinders for Petrol Engine (Drawing Exercise). 242. Piston Rods. Exercises .... 185-197 CHAPTER XXII CROSS-HEADS AND GUIDES 243. Cross Heads. Function of, described. 244. Forces acting at the Cross Head. Objections to Short Connecting Rods. 245. Position of Gudgeon or Cross Head Pin in relation to Sliding Surface. Correct and Defective Arrangements. 246. Types of Cross Heads for Stationary Marine, and Locomotive Engines, and for Small and Large Engines. Facing with White Metal. 247. Cross Head Gudgeon Pins. Five Different Arrangements. Bollinckx's Pin (and for Mus- grave Pin, see p. 212). 248. Cross Head for Horizontal Engine (Drawing Exercise). 249. Cross Head for Marine Engine (Drawing Exercise). Exercises . . 198-206 CHAPTER XXIII CONNECTING RODS 250. Length of Connecting Rod. Conditions which decide the ratio of Length to Crank. 251. Strength of Connecting Rods. Locomotive and Marine Practice. Shape of Rod Section. Reference to Rods for Petrol Engines. 252. Connecting Rods for Internal Combustion Engines. Round, Rectangular, and I Sections. Empirical Rules. 253. Connecting-rod Ends. Little Ends and Big Ends. Big Ends of Plain Strap Pattern. Plain Strap Pattern with Screw Adjust- ment. Solid End with Side Adjustment. Solid End with Cotter and Set-Screw. Proportions for a Strap Connecting-rod End. Solid Ends lighter than Other Forms. Brasses for Rod Ends. Two Types of Marine Connecting Rods. Examples of Little Ends. 254. Con- necting-rod End for Marine Engine (Drawing Exercise). 255. Con- necting-rod End, Forked Type (Drawing Exercise). 256. Petrol Engine Connecting Rod (Drawing Exercise). 257. Connecting Rod of Petrol Engine (Joist Type). 258. Connecting-rod Brasses. Pro- portions of. 259. Locomotive Coupling-rod Ends. Type of Coupling- rod End for Four-wheeled Coupled Engine. Type of Ends and Joints for Rods coupling Six or more Wheels. Exercises . . 207-219 CHAPTER XXIV MISCELLANEOUS DRAWING EXAMPLES 260. Cast-iron Bracket. 261. Lathe Bed Bracket. Adjustable Bearing for Boring Machine. 262. Bed Plate and Standard for Vertical Steam Engine. 263. Bed Plate and Brackets for Dynamo. 264. Expansion Slide Valve for Compound Vertical Engine. 265. Some Details of a 4 Horse-power Single Cylinder Petrol Engine. 266. Adjustable Loose Lathe Headstock. 267. Slide Rest for 9J" Lathe. 268. Cylinder with Meyer Expansion Valve for 20 Horse-power Horizontal Steam Engine 220-231 XII CONTENTS CHAPTER XXV PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES p 269. Cast Iron. Iron Ores. Fluxes. Slag. Pig Iron. Effect of Carbon, Sulphur, Silicon, Phosphorus, and Manganese in Iron. Graphite. Fusibility. Effect of mixing Different Kinds of Iron. White and Grey Iron. The Seven Varieties of Pig Iron. Pigs suitable for conversion into Wrought Iron. Pig Iron suitable for Engine Castings. Forge Irons. Mottled Pig. 270. Chemical Composition of Cast Iron. Bloxham's Nos. 1, 2, and 8 Foundry Cast Iron. Swedish Lily. Foundry Glengarnock. Ebbw Vale. Ferro-Manganese. 271. Strength of Cast Iron. Average Ultimate Tensile Strength. Com- pressive Strength. Ratio of Tensile to Compressive Strength. 272. Wrought Iron. Reverberatory Furnace. Refining. Puddling. Fet- ling. Blooms. Shingling. Faggot or Pile. Merchant's Bars. Best, Double Best, and Treble Best Qualities. Selected Scrap Iron for Heavy Forgings. Yorkshire and Staffordshire Irons. Charcoal Iron. 273. Cold Shortness and Red Shortness, Cause of. The Weldable Property. 274. Strength of Wrought Iron. Hard and Steely Qualities. Toughness or Ductility of the Metal. The Elastic Strength. Percentage of Elongation. Length of Specimens. Wire Drawing and Cold Rolling. 275. Steel. Preliminary Remarks. Percentage of Carbon. Effect of Impurities. Low Carbon Steel. The Weldable Property. Property of Hardening. 276. Bessemer Steel. How made. Lining of the Converter. Spiegeleisen. Forming Ingots. Thomas-Gilchrist Process. Basic and Acid Steel. 277. Siemens-Martin or Open Hearth Steel. How made. Control of the Operation. Dephosphorization of Pig Iron. 278. Mild Steel. Relation between Ultimate Strength and Elasticity. Strength, etc., compared with Yorkshire Plates. 279. Steel Castings. Crucible Steel Castings. Whitworth's Fluid Compressed Steel. English and Continental Castings compared. Steel Castings for Motor-Car Work. 280. Motor-Car Steels. Static and Dynamic Tests. Resistance to Shock and Endurance of Fatigue. High Limit of Elasticity. Tough and Ductile. Unaffected by Long-continued Vibration. 281. Copper. General Remarks. Elasticity and Strength. Worked Cold. Forged. Strength when drawn into Wire. Strength of Copper Bolts, Ordinary Copper, and Copper Castings. Effect of Boron in Copper. Elmore's Process. 282. Tin. Strength of. Cost of. Used for Coating Con- denser Tubes. Sheet Tin. 283. Lead. Constituent of Certain Alloys. Bilge Piping. Engine-room Floors. Tensile Strength. 284. Zinc. Alloyed with Copper. Used to Galvanize Iron. 285. Gun-metal, or Bronze. Hardness of Alloy in Relation to that of its Constituents. Effect of Chilling Castings of. Tensile Strengths of Gun-metal for Different Ratios of Copper to Tin. Elastic Limit. Strength in Compression. General Effect of Tin and Zinc in Alloy. Gun-metal for Heavy Bearings. Admiralty Bron/e. 286. Phosphor Bronze. Constituents. Hardness. Strengths of Different Qualities. Effect of Remelting. Red Shortness. Drawn into Wire. Strength of. Used for Bearings, Propeller Blades, Pump Rods, etc. Table giving Particulars of the Ultimate and Elastic Strength, etc., of the Principal Materials used by the Engineer 232-241 CHAPTER XXVI MISCELLANEOUS Table giving the Greatest Working Pressures, p, per sq. inch of Projected Area on Various Bearing Surfaces. Thurston's Rule relating to Pressure and Velocity. 287. Over One Hundred Questions in Machine Construction, etc., suitable for Examinations and Home Work 243-246 Board of Education Examination Papers in Subject II., Machine Con- struction and Drawing. 1906 : Stages 1 and 2. 1908 : Stages 1 and 2 247-257 City and Guilds of London Institute : Technological Examinations in Mechanical Engineering. Ordinary Grade. Part II. (Second Year's Course) for Years 1906 and 1908. THE 1906 C.G. PAPER Instructions. Section A. Machine Drawing. Drawings of Pump, or, Alternative Question, Drawing of an Eccentric Sheave and Strap. Section B. Pattern Making 258 Section C. Foundry Work 259 Section D. Fitters' and Turners' Work. Section E. Smiths' Work . . 262 The Drawing for all Candidates in Sections B, C, D, and E was the Bearing Bracket 259 THE 1908 C.G. PAPER Section A. Machine Drawing. Drawings of a Ring Bearing, or, Alter- native Question, Adjustable Cross Head 263 Section B. Pattern Making 264 Section C. Foundry Work. Section D. Fitters' and Turners' Work. Section E. Smiths' Work 265 The Drawings for all Candidates in Sections B, C, D, and E were the two views of the Slipper for a Cross Head. Figs. 5 and G 264 TABLES NO. PAGE 1. STANDARD TAPER PINS 66 2. SIZE OF RIVETS SUGGESTED BY THE NATIONAL BOILER INSURANCE Co 83 3. DIMENSIONS OF WHITWORTH'S 55 THREADS, HEXAGONAL BOLTS, NUTS, AND HEADS (BRIGHT) 91 4. EXPANSION COEFFICIENTS FOR PIPE METALS (KEMPE) : 110 5. PIPE THREADS. NUMBER OF THREADS. DIAMETERS OF SCREWED PART, CORE, AND OF BLACK TUBE 114 6. PROPORTIONS OF (LEAD) SPIGOT AND SOCKET JOINT (BATEMAN) 115 7. PROPORTIONS OF TURNED AND BORED SPIGOT AND SOCKET JOINT 115 8. PROPORTIONS OF VARIOUS TEETH 168 SA DIMENSIONS OF MACHINE-CUT WHEELS (BROWNE AND SHARPE) 169 9. SAFE LOAD P, FOR CAST-IRON TEETH OF 1" PITCH AND BREADTH OF 2'5" 175 10. DIMENSIONS OF CAST-IRON PISTONS UP TO 16" DIAMETER 191 11. VALUES OF COEFFICIENT K FOR USE IN DESIGNING PISTONS 192 12. COMPOSITION OF FOUNDRY CAST IKON 233 13. ULTIMATE AND ELASTIC STRENGTH OF MATERIALS 241 14. GREATEST ALLOWABLE PRESSURES ON BEARING SURFACES 242 EXERCISES DRAWING EXERCISES To assist in selecting suitable drawing exercises the following particulars are given. The first twelve exercises are fairly progressive, the order in which the others are taken may be varied at pleasure. The break in the continuity of progression was made as it appeared to be more convenient to group similar parts together as far as practicable. By the time the student has worked the twelfth exercise he or his instructor will experience no difficulty in selecting suitable ones to follow. As the student progresses he will be able to make use of the various figures, whose proportions are given in terms of a unit, for further drawing exercises. In the exercises at the end of most chapters suitable exercises of this kind are suggested. 'NO. OP EXF.RCISK No. OF Flo. 1 61 2 63 3 65 4 68 5 70 to 72 6 74 7 92,93 8 96A 9 97 to 99 10 170 to 172 11 185 12 234 to 237 13 312, 313 14 310, 311 15 343 16 347 to 349 17 352, 353 18 354, 355 19 355A 20 355B 21 421 22 424 to 426 23 431, 432 Eectangular block 32 Cast-iron bench block 34 Wrought-iron beam 86 Standard beam 36 Stuffing box gland 37 Marine type stuffing box 40 Built-up steel crank 51 Petrol motor crank shaft 53 Butt-muff coupling 55 Single riveted lap joint, j" plate, f " rivets ... 74 Joint described in Exercise 7, p. 85, but with both the straps wide ones 76 1" hexagonal bolts 90 Tightening or Gripping handle 104 Balanced handle 104 Gland and stuffing box expansion joint .... 113 Hydraulic pipe joint 117 Hydraulic stop'valve with hemp packing . . . 118 Hydraulic stop valve with leather packing . . . 119 Body of steam stop valve 120 Steam equilibrium admission valve 121 3" Plummer block or pedestal 138 Crank shaft bearing 140, 141 Wall bracket . 146 No. OF i EXERCISE No. OF FIG. 24 458 to 461 25 505, 506 26 628 27 630 28 631, 632 29 638, 639 30 660, 661 31 662, 663 32 679 to 681 33 682 34 689, 690 35 691, 692 36 701, 702 87 703, 704 38 709 39 710, 711 40 712, 713 41 716 to 718 42 719, 720 43 721, 722 Roller bearing 154. Mitre bevel wheel 178 12" cylinder for steam engine 194 4" piston for petrol engine 195 Pair of 4" cylinders for 20 H.P. four-cylinder petrol motor . 196 Cross head for small engine 200 Locomotive cross head, four-bar type .... 203 Locomotive cross head, two-bar type .... 203 Cross head for horizontal steam engine . . . 202, 205 Cross head for marine engine 202, 206 Connecting-rod big end (solid type) 209 Connecting-rod big end (locomotive type) . . . 210 Connecting-rod little end (stationary solid type) . 212 Connecting-rod little end (locomotive type) . . . 213 Connecting-rod big end, for marine engine . . 213, 214 Connecting-rod big end, for vertical steam engine (forked type) 213, 215 Connecting rod for petrol engine 213, 216 Locomotive coupling - rod end, for four-wheel driving 218 Locomotive coupling-rod ends and joints, for six or more driving wheels 219 Cast-iron bracket 220 XVI EXERCISES DRAWING EXERCISES contd. No. o EXERCISE 44 45 46 47 48 49 No. OF Fio. 723, 724 728,726 ! 727 728 to 735 736, 737 738 50 739 to 742 51 743 52 744 to 75^ 53 54 Cast-iron lathe bed bracket 220, 221 Adjustable bearing for boring machine .... 222 Bed plate and standard for vertical steam engine . 223 Bed plate and brackets for dynamo .... 224, 225 Expansion slide valve for compound vertical engine 226 Some details of a 4 H.P. single-cylinder petrol engine 221 and 227 Adjustable loose lathe headstock 228 Slide rest for 9j" lathe 229 Cylinder, with Meyer expansion valve for 20 H.P. horizontal steam engine 229-231 1J" bracket bearing 248 End of a connecting link of an air compressor . . 248 No. OF EXKKCISE 55 56 57 58 59 60 61 62 63 64 05 66 Adjustable footstep bearing 252 Lift valve 252 Joint in girder work 253 Piston-rod end and cross head 253 Tool holder for a planing machine 255 A steam engine governor 256 Bearing bracket 259 Pump 260 Eccentric sheave and strap ... ... 261 Lever 262 Ring bearing 263 Cross head for horizontal steam engine 264 TRACING EXERCISES To assist in selecting figures suitable for tracing purposes, the following particulars are given. The first eight or nine exercises are fairly progressive ; the order in which the others are taken may be varied at pleasure. In tracing from the book the corners of the tracing paper may be attached to the page by gum or postage-stamp paper. Set-squares may be used for lines at right angles : No. OF EXKRCISK 12 SO. OF EXERCISR No. OF FIG. 1 38 2 40 3 61 4 63 5 70,71 6 96A 7 97 to 99 8 234, 235 9 310, 311 10 343 11 347, 348 Square figure 22 Figure, symmetrical about two centre lines ... 23 Projections of a rectangular block 32 Projections of a bench block 34 Projections of a stuffing box gland 37 Petrol motor crank shaft 53 Butt-muff coupling 55 Hexagonal bolt 90 Balance machine handle 104 Gland and stuffing-box expansion joint .... 113 Armstrong's hydraulic pipe joint 117 13 14 15 16 17 18 19 20 21 No. OF FIG. 385 to 387 414,415 416,417 431,432 691,692 743 Forms of suspension link eyes 131 Bearing block 136 Adjustable cast-iron bearing 137 Wall bracket 1*6 Connecting-rod end (locomotive type) Pictorial view of a lathe slide rest 229 Eye bolt 248 Crank 250 Eye bar 253 Eccentric and strap 261 EXERCISES IN DESIGNING, SKETCHING, AND DRAWING At the end of most chapters suitable exercises are suggested in the above, and the pages in which these appear are given below Circles, arcs, and lines 28 How to commence a working drawing 38 Stuffing boxes, leather collars, etc 43 Shafting, crank shafts, cranks, journals, etc 54 Couplings, clutches, etc 62 Keys and pin keys, etc 68 Biveted joints 84 Bolts, nuts, and screws, etc 101 Machine handles, etc 105 Pipes and pipe connections .... Cotters and cotter joints Pin or knuckle joints, pitch chains, etc. Bearings, journals, hangers, etc. Roller and ball bearings Toothed gearing Belt gearing ........ Pistons and cylinders, etc. Cross heads and guides 124 129 133 149 159 178 184 197 204 MACHINE DRAWING AND DESIGN FOR BEGINNERS CHAPTER I DRAWING INSTRUMENTS, MATERIALS, ETC. 1. Hints upon the Selection and Use of Drawing Instruments, Materials, etc. The student, having decided to study and practise any kind of mechanical drawing, requires to know what instruments and materials are necessary for the work, and the kind to be obtained, in order to produce satisfactory drawings ; but, unfortunately, he often becomes possessed of inferior materials, and a cheap " set " of instruments of foreign manufacture, which are often badly made and for practical purposes almost useless ; in trying to use these he handicaps himself considerably at a time when he ought to have for his use the best instruments that can be made. It is only necessary to visit any drawing-class and examine the work done and the instruments used, to trace the connection between cause and effect in this matter ; indeed, if a student who has been studying mechanical drawing for some time fails to make proper progress, it is almost invariably due to the use of faulty instruments. The compass small board, a T-square, a pair of set-squares, paper, pins, pencils, and indiarubber. The old-fashioned parallel ruler cannot be relied upon, in fact it is obsolete, but parallel rulers of the roller form are very useful for many purposes. The more expensive instruments are fitted with needle-points, which are preferred by some skilled draughtsmen, but unless they are manipulated with great care and are well fitted with ; 'bolt and nut" arrangement, with shoulders to preveut the points entering too far into the paper, the ordinary conical points are preferable. The latter, in any case, are best for beginners, who lack the light hand necessary for manipulating needle-points properly. 2. Drawing Board. -This instrument is used for holding and supporting a sheet of paper flat, whilst a drawing is being made upon it. Care should be exercised in its selection, or trouble may be occasioned by its becoming twisted and out of truth, after very little use. There are many kinds of drawing boards, but the " Battened " form is the best, and need only be described. Fig. 1 shows 1 A few shillings will now buy a small set of very well-made instruments of the Knglish type, with which much useful work can be done. Of course, they must not be compared with the heavier and better instruments turned out by the best English makers, which every student should endeavour to provide himself with, even if he has to buy them separately from time to time. B MACHINE DRAWING AND DESIGN FOR BEGINNERS one of these boards. They should be made of well-seasoned pine, ploughed and tongued together, and grooved half-way through upon the back as shown, being fitted with chamfered battens or ledges of mahogany or oak, to prevent the surface from twisting. The battens are fixed at their centre, to the back of board with screws ; and fitted with brass slots let into recesses, and held by cheese-head screws to admit of expansion and contraction of the board with variations of temperature and moisture. The left-hand edge of the board usually has an ebony strip (which is smoother and harder than the end grain of the soft wood) inserted in it, for the stock of the T-square to slide upon. This strip is sawn through about every inch of its length to admit of expansion and contraction ; and projects' from j 1 ,/' to J" beyond the end of the board, which is usually varnished. The surface of the board may be slightly rounding, viz. convex, from the top to the bottom edge ; so that a hollow is not formed under a sheet of paper pinned or stretched upon it. The dimensions of a board most suitable for the exercise work of students is about 24" X 17", which takes the half of an "imperial" sheet of paper, or a "medium" sheet. But for drawing office work, a "double elephant" (40" x 26J") is generally used, and for specially large work " antiquarian " (53" X 31") is used, these dimensions allowing about 1" margin between edge of paper and board. Drawing boards for ship work are usually made 100" x 31" of 1J" pine. 3. Working Position of Board. The drawing board when in use should be tilted to an angle of about 15, FIG. 1. Battened drawing board. FIG. 2. Two forms of blocks for tilting board. with the aid of wooden blocks, two forms of which are shown at A and B (Fig. 2). placed under each batten. FIG. 3. English shape T-square. Two blocks are used for each board, one being 4. T-Square. This instrument is used for drawing long linea perpendicular to an edge of the drawing board ; and Fig. 3 shows the " English shape," which is best for general purposes. It is made of well-seasoned pearwood, maple, or mahogany. Those of pear wood are the cheapest and answer very well for rough use in a school, but the mahogany ones, with the working edges of ebony, with the pores of the wood stopped with shellac and alcohol and polished (not varnished), are generally used for office work, and should always be used by those who can afford them. An enlarged section of the ruling edge, which should be about j 1 ,." thick, is shown at A on Fig. 3. DRAWING INSTRUMENTS, MATERIALS, ETC. 6. To test a T-square in order to see that its Edge is Straight. A line should be drawn, using a finely sharpened chisel-pointed pencil (as shown in Fig. 9), hold- ing the pencil quite close to the edge to be tested. Then turn the square over (not end for end), and bring it up to the line, and see if the edge now coincides with it. If so, the edge is straight. 6. To test whether the Blade is Square with the Stock. Draw a line BC, Fig. 4, upon a sheet of paper fastened to the board, parallel to the left-hand edge ; at the middle of the line assume u point A, and mark off above and below it AB = AC. Take B and as centres, and a radius so as to intersect at a distant point C, close to right-hand edge. Join AD. Then place the stock of the T-square against the left-hand edge of the board, and, sliding the square along that edge, see if the edge of the blade corresponds exactly with the line AD. If it does so, the blade is square with the stock. 7. Set-Squares. These are right-angled triangles. They are made of various materials such as pearwood, mahogany, and other woods, vulcanite, transparent celluloid or pellucid, aluminium, and steel, and are used for drawing short lines perpendicular to, parallel to, or at the angle of the square to one another, in conjunction with a straight edge, T-square, or another set-square. Two set-squares are generally used, the usual angles and most useful sizes for which are shown in Fig. 5. Set-squares of pearwood are cheap and useful (if the angles are correct) for students' use, but they are easily soiled, and often -X-D Flo. 4. Testing T-square. FIG. 5. The two set-squares. warp and become untrue. They are not to be compared with those made of transparent celluloid, which on the whole should be preferred. 8. To test a Set-Square. A set-square may be tested to see whether the right angle is correct by placing it against the edge of a T-square, as shown at E, Fig. 6, and drawing a fine line GH against the vertical edge. Without moving the T-square, turn the set edge over, as at F, and bring it up to the line GH to see if it coincides with it. If not, it should be altered until it docs. 9. To test the 60 Angle. From a point G on the line AB. Fig. G, describe a semicircle CD, radius about 12", and at G, the centre of the semicircle, erect a per- pendicular GH. From point C with radius of circle cut the semicircle in J. Join JC, then the angle JCG is 60, and it can be used for testing the 60 angle. If J be joined to D, the angle ADJ will be 30, which can be used for testing the 30 angle of the set-square ; but it follows that if the right angle (90) is correct, and the 60 angle also, the remaining angle must equal 30, as the three angles of every triangle equal 180, or two right angles. Again, if the angles are correctly formed, the long slant edge (hypotenuse) is exactly twice the length of the short edge (base). The 45 set-square may be tested by bisecting the angle HOD in L and joining LG. Then angle LGD is 45. Or, again, if the right angle of the square is correct, and the two edges adjacent to it are of equal length, the angles will be 45. 10. Drawing Paper. Two kinds of paper are generally used for drawing purposes, viz. "Cartridge" paper and "Drawing" MACHINE DRAWING AND DESIGN FOR BEGINNERS paper. " Cartridge " or " Machine-made " drawing paper is used for making details and full-sized working drawings upon. Some of it is sufficiently transparent to be used for tracing paper for large details. It is much cheaper than " drawing paper," and can be obtained either in sheets of various sizes or in rolls up to 62" wide and 60 yds. long, rendering it extremely useful for diagrams, etc. This continuous paper, as it is called, can also be had mounted on canvas to withstand rough usage. The better quality is of a white colour, and the inferior is of a yellowish tint. The unmounted cartridge paper has two surfaces, a rough and a smooth one ; the smooth surface is the proper side to draw upon, and is usually the front side when the water-mark l can be read correctly on holding the sheet between the eyes and the light. Cartridge paper does not usually take tints of colour evenly, but with good paper and care, a very fair effect can be obtained in light tints. But this paper is most suitable for line drawings. It can be obtained in the following sizes, which vary slightly with different makers : FIG. 6. Testing set-squares. DIMENSIONS OF DRAWING PAPERS. Demy Half-imperial .... Medium 22 Eoyal 24 Super-royal ..... 27 Elephant 28 Imperial Columbier . . Atlas .... Double elephant Antiquarian inches. 20 x 15| 22 x 15 x IT] X 19 X 19 X 23 X 22 X 23' x 30 34 40 53 26 26| 31 Emperor 66 x 47 DIMENSIONS OF CARTRIDGE PAPERS. inches. Copy 20 x 16i Demy 22J x 17?, Koyal 25" x 20 Cartridge 26 x 21 Elephant ". 28 x 23 Double crown 30 x 20 Imperial 30 x 22 Double demy 35 1, x 22 i 11. paper I. Whatman's Hot-pressed Paper. For drawings that are to be finished in ink, without colour, the " Hand-made " drawin" known as Whatman's "Hot-pressed," H.P., "Smooth" or "Rolled" surface, is most suitable. The best qualities only are water-marked. DRAWING INSTRUMENTS, MATERIALS, ETC. 5 This paper should also be used for drawings when very fine lines are a necessity, and but little colour is required. 1 12. Whatman's N.H.P. Paper. For drawings which are to be coloured or shaded, or are to stand frequent erasing of lines, Whatman's N.H.P. (not hot-pressed) or rough surface is to be preferred. Its surface will take a fairly fine line, and tints can be laid very evenly upon it. The proper side of the paper to draw upon is that upon which the water-mark of the maker's name can be read correctly when the paper is held between the eyes and the light. This side is generally a little smoother than the opposite one. 13. Quality of " Drawing " Paper. Drawing paper, either hot-pressed or not hot-pressed, is made in various thicknesses, namely, thin, medium, thick, extra thick, and extra extra thick. The medium quality is that generally used for ordinary work. These papers can also be had in continuous lengths, and mounted on union, or white or brown holland ; it is then sold in rolls, or by the yard. The two sizes of paper most used in drawing offices are " imperial," 30" X 22", or " double elephant," 40" X 26|", but if a smaller sheet is required an " imperial " one is usually halved. 14. Pencils Different Kinds and Qualities. The student should only use blacklead pencils of a good quality, such as Stanley's, Faber's, or Hardrnuths' prepared lead, or Cohen's Cumberland lead ; inferior makes should never be used for drawing purposes. The following are the requirements of a good pencil for mechanical drawing : It should be moderately hard, of even colour throughout, and durable enough to retain a working point for a long time. It should be easily sharpened, not liable to roll off the board and injure its point, and the lines drawn by it should be easily rubbed out. The ordinary round cedar-covered blacklead pencil, shown at A, Fig. 7, of good quality, is a serviceable pencil, but it easily rolls off the board. To retard the rolling action, some pencils are made hexagonal (Fig. 7, B), whilst Messrs. Stanley & Co. sell a pencil of specially prepared lead, the wooden cover of which is made elliptical, as shown at C, in which this latter defect is removed. The lead of the pencil is rectangular in section and should be fixed in cover, as shown, 2 in order that the wood may properly support the lead, and enable the pencil to be held firmly and the point seen easily when in use. Many draughtsmen use the small solid lead (about ^, of an inch diameter, shown at D, and made by Messrs. Faber, Hardmuth, and others), fitted in a holder, forming what is known as an artist's ever-pointed pencil, Fig. 8. A holder of this kind can be used for years in skilled hands, but the beginner is apt to strip the screw thread when adjusting Fio. 7. Sections of blacklead pencils. Fio. 8. Artist's ever-pointed pencil. the lead, and the instrument becomes worthless, but with proper care the pencil can always be maintained at one length, and be easily sharpened, preferably on a smooth file or piece of glass paper ; the lead can then be used up to quite short lengths, which are then available for use in the pencil compasses, thus maintaining an even colour of line throughout the drawing. All the best quality modern instruments are fitted to hold these leads, but many of the older and cheaper forms are fitted with pencil holders of various sizes, and it is difficult to obtain a cedar-covered pencil of sufficient hardness to fit them ; these pencils are also more clumsy and difficult to sharpen. 1 Unstre tched paper takes a finer ink line than when the paper is stretched. 2 Such pencils are occasionally to be seen with the thick part of the lead coinciding with the thiu part of the cover. 6 MACHINE DRAWING AND DESIGN FOR BEGINNERS 15. Degrees of Hardness, etc. Pencils are made in various degrees of hardness, varying from BBBB (the softest) to HHHHHH (the hardest) in wood, and No. 1 to 6 in the solid lead. Usually No. 1 = BB. No. 2 = HB. No. 3 = H. No. 4 = HH. No. 5 = HHH. No. 6 = HHHH. Nos. 4 and 5 will be found most useful for ordinary work. 16. How to sharpen the Pencil. For line drawing the pencil should be sharpened to a flat or chisel point, as shown in Fig. 9 ; this gives a strong point, which retains its sharpness longer than a round one, and it can be worked closer up to the squares, and is more easily sharpened, with the added advantage that the lines are more equal in quality. Needless to say, it is used with its flat side laid against the edge of the T or set square. To make a flat or chisel point to a wood-covered pencil, the wood is first cut away, and the best way to do this is to hold the pencil, as shown in Fig. 10, between the thumb and first finger of the left hand, and to rest it upon the second finger, which should be turned upwards, while the penknife (which should be sharp) is held in the four fingers of the right hand, which should be turned down- FIG. 9. Chisel-pointed pencil. wards, the thumb of this hand being placed under the pencil to steady it, as shown. A little practice will enable the student to cut a good point with precision and facility, as he has perfect control over the knife, which, should it slip, moves away from the hand. The lead part is best sharpened by Fio. 10. Knifing pencil point. Fio. 11. Filing pencil point. rubbing it upon a smooth file, as shown in Fig. 11, after which a stroke or two upon a piece of paper gives it a good finish. A 6" smooth hand file, or a 4" or 5" triangular saw file, should be preferred. If a file is not available, a piece of fine emery DRAWING INSTRUMENTS, MATERIALS, ETC. 7 paper or cloth, " F " or " FF," or glass paper, " 0," fastened to a strip of hard wood about 6" long, 1" wide, and " thick, is a good substitute, or small blocks, containing about 16 surfaces of glass paper, especially made for pencil sharpening, may easily be obtained. The latter are very useful for giving the pencil a finer point than can be made with a knife .alone, and when the surface is worn the damaged thickness can ,be torn off and a fresh surface exposed for use. However the point may be produced, a few strokes on a piece of blotting or soft paper will give the point a beautiful working edge. Short pieces of pencil under 3" in length should not be used for line drawing unless fitted into a rigid holder, as sufficient command cannot be obtained over them. 17. Compass Pencils. The points of compass pencils should be made narrower than for straight-line purposes, and must be carefully adjusted so as not to draw a thick line; indeed, the beginner is more likely to do better work with a conical-pointed lead in his compasses. It is not enough to start with a good point, its sharpness must be maintained, and this requires constant attention. As soon as the lines appear to be too thick, one or two strokes of the pencil upon the sharpener will restore the point. 18. The Conical-pointed Pencil. For the making of freehand sketches, dimensioning, or descriptive writing upon a pencil drawing, it is desirable to use a softer pencil than that used for line drawing (such as a No. 3 or 4, or H or HB), and to sharpen it to a long conical point, as shown in Fig. 12. A B A B C V ~ T FIG. 12. Conical-pointed pencil. FIG. 13. Three different forms of drawing pins. FIG. 14. Horn and metal centres. Several pencil sharpeners are sold for this purpose, but they do not produce a good long point, such as draughtsmen pride themselves upon, and which can be readily made as previously explained. The point should on no account be moistened when used, as marks made by it in that condition are very difficult to erase. 19. Drawing Pins. To secure the paper to the drawing board either drawing pins or paper clips are used, or, if the drawing is a very important one, the paper should be stretched ; particularly is this necessary if the drawing is to be highly finished by shading and colouring. There are many kinds of drawing pins, three of which are shown in Fig. 13. That at A consists of a brass head, with milled edges, with a steel pin screwed or riveted into it. This form projects too much above the surface of the paper, the height of the head preventing the T-square from lying flat upon the paper, and the edge of the T-square is injured by coming into contact with it. The pin-point is often badly fastened into the head, frequently unscrewing from it, and the shape of the point does not enable it to hold well into the board. The one shown at B is formed of a disc of brass or electrum, turned circular to the section shown, and has a steel pin ; the head is about T ' 8 " thick at the centre, and the upper surface is convex, and thinned towards the edge, which is rounded and milled, so that the thumb-nail can be used for removing it from the board. The pin shown at C is similarly made, only its upper surface is flat and bevelled instead of being rounded. The two latter forms are those generally used in drawing offices, and they are recommended ; the most useful sizes are f g " to f" diameter. 20. Horn and Metal Centres should be used for preventing the centre point of the compasses from making a large hole in the paper whenever a number of circles are described from the same centre. They consist of small discs of transparent horn or of electrum, as shown at A and B, Fig. 14. 8 MACHINE DRAWING AND DESIGN FOR BEGINNERS 21. Indiarubber. The ordinary dark coloured native or bottle indiarubber is best for removing pencil marks when the best blacklead has been used, especially if the drawing is to be coloured, as it does not injure the surface of the paper when carefully used, and if the rubber becomes dirty or sticky with use it can easily be restored by boiling in clean water for a short time. Fine vulcanized grey or white indiarubber is very largely used, especially for blacklead pencil marks upon machine-made paper, the lines of which are hard to erase, but care should be taken that the rubber is soft and not too highly vulcanized or gritty, or the surface of the paper will be injured and rendered unfit for colouring purposes. 22. Measuring Rules. A 12" steel rule, divided into inches, with divisions of 8ths, IGths, 32nds, and 64ths on one edge, and lOths and lOOths of an inch on the other, will be found useful. The more simply a rule is marked the better for ordinary use, especially when foreign measures are concerned. It is much better to use separate rules than to crowd a number of different divisions on a single one, which often lead to serious errors being made. This steel rule should be plated with nickel, or an alloy of platinum, the former prevents rust, and the latter rust and also discoloration. Care should be exercised in placing the points of the compasses upon a steel rule in a normal direction, or they will be injured. Fig. 15 shows how, by inclining the compasses to the rule, the sides of the points may be made to rest in the cuts or divisions without injuring the points. The figure also shows how the compasses and rule should be held if the right hand is to have complete command over the former in adjusting the points to take off any required dimension. An edge of the rule may also be directly placed on a line and a dimension pricked off by sliding the pricker down the divisions of the rule, but this requires great care. The accuracy of the steel rule and its durability make it superior to any other at the command of the draughtsman. As the student and draughtsman are now so frequently called upon to set out work with metric measurements, there is no reason why the back of the steel rule should not be divided into centimetres and millimetres. 23. Drawing or Ruling Pens. In most full sets of instruments there are two ruling pens, a large one and a smaller one, called a fine ruling pen. The best type of these pens is jointed, so that when the screw is taken out one of the nibs can be moved away from the other about its hinge or joint for cleaning purposes. The cheaper pens are made without this joint, and there is a difficulty in cleaning them. This is best done in any case by drawing an edge of a damp duster between the nibs and not by scraping them with a knife or file. All pens must be frequently cleaned when in use, and should never be put away without being completely freed from ink and dirt. They should also be sufficiently unscrewed to prevent the nibs remaining in contact when not in use. 24. Indian Ink. It is well known that ordinary writing ink is unsuitable for use on drawings, as, although it is more or less indelible, it has not the blackness and body that are considered necessary, to say nothing of the corrosive action of such inks on steel, which alone would preclude its use in the ordinary drawing pen. In addition to these objections it runs too freely FIG. 15. Application of compasses to rule. DRAWING INSTRUMENTS, MATERIALS, ETC. 9 from the pen and blurs when touched by a brush in colouring. The only ink that satisfies all the draughtsman's requirements is known as Indian ink ; this ink, when properly used, produces a clean, dense, jet-black Hue, and, being free from acid, it does not corrode the instruments : it can be had either in a solid or liquid form. The quality of Indian ink (lifters very much, but if good the stick will have a brownish glazed appearance at the end after being used. 25. Liquid Indian Ink. Some makes of this ink are very good, but the majority are very indifferent. It is often purchased by students because it is cheap in first cost (6d. or Is. per bottle) and saves the trouble of mixing. But as a rule it is not so black, is liable to dry xip and deteriorate in quality after being opened, and the lines drawn with it lack the beautiful jet-like appearance so characteristic of good Indian ink ; it cannot be used for shading purposes with much success, and the bottles are liable to get upset. 26. Colours, etc. The best water colours only should be used for tinting mechanical drawings ; these may be obtained in cakes, hexagonal sticks, or small pans, and as very few will suffice for the student to begin with, it is of no advantage to purchase inferior ones. If cake or stick colours are used, they are ground up with water in a saucer until of the required depth of tint. Moist water colours in pans are to be preferred for students' use and for drawing office work. The pans in which the colours are placed are of china or porcelain, covered with a suitable wrapper, which should not be removed, but cut through three sides at the top of the pan with a sharp penknife, to form a lid to protect the colour when not in use. The most useful colours and the materials they are used to represent are given below. The first four will suffice if only ordinary metals are to be indicated ; the others are required when the other materials of construction are to be shown in colours. Prussian blue to represent wrought iron and dimension lines Payne's grey cast iron Crimson lake centre and datum lines Gamboge, or Indian yellow brass and gunmetal Yellow ochre stone Burnt sienna ,, wood Sepia leather Light red brickwork Indigo lead lead Burnt umber ,, packing French ultramarine water Prussian blue and crimson lake steel 27. Saucers for mixing Colours. Saucers for mixing colours in are of various kinds; but the most useful ones for students or office use are the cabinet nests of white china, which are sold in sets of five and a cover. They vary from 2|" to 3f" diameter, the largest size being most useful. With these saucers, colour left over from a previous wash can be remixed and used up. Dust can always be kept out by piling them up together and putting the cover on. 28. Brushes. For colouring drawings the student will require at least two brushes, the most suitable being a "middle swan" and a "small goose," preferably of red or brown sable hair. He will also require a camel-hair water brush of about " large swan" size, for transferring water to the saucers, etc. c CHAPTER II PRINTING, TRACING, SHADING, ETC. 29. Printing, etc. The following style of lettering, which should be neatly written with an ordinary writing pen, is most suitable for notes or remarks on a drawing : abcdefghij klm nopqrstuvwxy z In drawing office practice it is usual to stencil x headings and titles, etc., in plain letters, such as the following, the size varying from J" to }", according to the size of the drawing ; for example, the heading or title on medium or royal size sheets would be in good proportion if made with f " or " letters, or with -|" and " letters for imperial and double elephant respectively ; and such titles as plan, elevation, etc., with J" or ^ 6 " letters : ABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567890 Although most of this printing is done by stencilling, students should endeavour by practice to do it neatly by freehand, to enable them to proceed when stencil plates are not available. The quality of printing and writing upon a drawing greatly adds to or detracts from its appearance. 30. Working Drawings of machinery are made in such a way that the form and size of every detail are clearly shown for the guidance of those in the works. The rule is to make them to as large a scale as possible, generally full size for all small details, and J and \ full size for larger ones. Such drawings are first carefully set out in pencil and then inked in, all parts cut by section planes being cross-hatched with sectional lines indicating the materials they are made of, in accordance with the shading shown in Art. 61; or, alternately, they are coloured 2 to indicate the materials, as explained in Art. 26. The edges of surfaces that are to be machined are usually coloured with a narrow band of a deeper tint. The next step is 1 A good deal of practice is necessary to enable the beginner to do this neatly. He usually commences by making the stencil brush too wet, which causes the ink to flow between the stencil plate and paper. The best expedient is to recess a piece of Indian ink in a thin block of wood, and, after wetting the brush, rub it over the ink and wood till it is dry enough to use on the plate. It is best to start from the middle of a title when stencilling, so as to get it quite symmetrical with the drawing. This can easily be done by counting the letters which come each side of the centre, allowing one for each interval between two words. * Drawings from which tracings are to be made for reproduction by photographic printing are, of course, always section-lined and not coloured. PRINTING, TRACING, SHADING, ETC. 11 to ink in with red ink l the centre lines, and the dimension lines with Prussian blue. 2 The arrowheads and the dimensions should be now neatly written with an ordinary writing or mapping pen, care being taken to make the dimensions bold and neat, so that they can be easily read from the drawing. The value of a drawing for workshop purposes greatly depends upon the clearness and accuracy of the figures or dimensions and the skilful way in which they have been arranged. Often an occasional duplication of a dimension on different views will save much time in the works. In cases where original drawings are not likely to be much used, it is the practice of many engineers not to ink them in. This, of course, necessitates more careful finishing in pencil. Indeed, the beginner should not be encouraged to do any inking in work until he has become fairly proficient in the somewhat difficult art of making a good pencil drawing. The particulars as to the scale to which the drawing is made must always be clearly shown upon that drawing, not in order to enable workmen to " scale it," as sufficient dimensions should always be given to entirely obviate this. If there is any probability of the drawing being sent abroad where a different system of measurement is used, or to where it will be exposed to variations of temperature, the scale should always be drawn upon the drawing. Sometimes the scale of a working drawing has to be reduced to make it suitable for attachment to a specification, or some such purpose ; in such a case, proportional compasses may be advantageously employed, the best practice being to locate the centres of the circles and curves and to ink the latter in direct, and then to proceed with the straight lines, avoiding the use of pencils as much as possible. SHADE LINES AND LINE SHADING. 3 31. Shade Lines. The appearance of finished drawings (which are usually made to a small scale) is improved, and the true form ^of parts made more intelligible in a single view, by the use of shade or dark lines, which give an appearance of relief to the various parts. Shade lines indicate the intersection of two surfaces, one of which is in the shade and the other illuminated. In arranging the shade lines, the parallel rays of light are conventionally assumed to come from the left and from behind (over the left shoulder) towards the object, their plans and elevations making angles of 45 with the vertical and horizontal planes respectively, their real inclination to the ground being 35'15 nearly. 4 Thus, applying these rules to the body shown in Fig. 16, we have the back and right-hand edges ab and be, also ef and fg of the projecting piece of the plan as shade lines ; whilst the rules applied to the elevation give us the bottom and right-hand edges, hi and ic', as shade lines. But, it should be explained, the line hi would not be a shade line if the body was actually resting on a horizontal surface, as the two surfaces would be in contact, and the upper not projecting beyond the lower. For these reasons jk is not a shade line, but g'k is. These rules applied to a case where there is a recess or hole, ats in Fig. 17, give us the front and left-hand edges, be and ab, as shade lines, the upper surface being in the light or illuminated, and the front and left-hand sides of the hole in the shade. In dealing with curved surfaces shade lines are never used to denote their contour or outlines. Thus, in Fig. 18 the only 1 This may be prepared by rubbing down a little colour from the cake of crimson lake. 2 This may also be made by rubbing down a cake of the colour required, but most draughtsmen have the use of bottles of specially prepared red and blue inks. 3 Articles 31 and 31a may very well be passed over by the student until he has reached and read Chapter VI. ' The cosine of the angle being obviously the <\/2 -i- Vs. MACHINE DRAWING AND DESIGN FOR BEGINNERS EXAMPLES OF SHADE LINES AND LINE SHADING. FIG. 24. PRINTING, TRACING, SHADING, ETC. 13 shade line on the elevation of the vertical cylinder is de, the line representing the solid's base, fe, being a boundary line of a curved surface, is not a shade line. Now, the plan of the cylinder has a curved outline, and the rule relating to such cases is to make the shade line begin at the points a and I, at which the projections of the rays touch this outline, and let it gradually increase in thickness till its full strength is reached at c. Similarly, for the hole, the shade line increases in thickness from ra and n to g. The rules we have given relating to the rays of light we shall see are also concerned in the art of Shading, but, strangely enough, although generally followed by artists, many English engineers prefer to take the rays of light as shown in Fig. 24, where the rays in plan are parallel to those in elevation ; this makes no difference to the elevation, but in plan the shade lines come in front, as shown, instead of at the back. 31a. Shading by Lines. By shading a projection of an object its true form can often be rendered intelligible in a single view. For example, the shaded view of a cylinder explains itself. But, on account of the time and labour involved, shading by tinting is only rarely used, even in finished machine drawings. However, a similar effect can be easily produced by a few shading lines, 1 which are or should be drawn in accordance with the rules followed in shading proper. To commence with a simple example, that very often in many forms appears on machine drawings, we have in Fig. 19 a' vertical hexagonal prism, with its front face in the light or illuminated. Such surfaces parallel to the vertical plane would receive flat tints, and the nearer the surface is to the eye the lighter such tints would be, and the shading lines would be equally spaced (between V and c'), the spacing being increased on the lighter surfaces parallel to the plane of projection, and in the surfaces in the shade also receive flat tints, but the nearer such surfaces are to the eye the darker such tints are, or the closer the shade lines. Thus Surfaces in the light inclined to the plane of projection have given them graduated tints (represented by graduated lines, as shown between a'b', Fig. 19), and as such surfaces recede from the eye the tints are made darker, or the lines closer together, as shown. Surfaces in the shade inclined to the plane of projection also have given them graduated tints (or lines), and as such surfaces recede from the eye they are made lighter, or the lines further apart, as between c' and d", Fig. 19. When two such surfaces are unequally inclined, the one upon which the rays impinge most directly is made lightest. Curved Surfaces. The above rules in the main are followed in shading curved surfaces. Thus in Fig. 20 we have the plan and elevation of a vertical cylinder upon which the light falls from a' a" to e'e", but most directly at the generator whose plan is b ; this, therefore, as we have seen, should be the lightest part, but succeeding generators from b'b" to d'd" approach the eye, and according to what we have seen should therefore be increasingly lighter. So, in order to meet both these considerations, it is the practice to bisect Id in c, and make the surface between b'b" and c'c" the lightest ; in fact, it is usually untinted, and remains white. Obviously, the darkest part of the cylinder is at e'e", so that the shade and shading increase in depth from c'c" to e'e", and diminish from e'e" to ff. A horizontal cylinder, with its axis perpendicular to the vertical plane, is shown in Fig. 21, and the student will see that similar lines are used in arranging the shading. The case of a vertical hollow semi-cylinder is shown in Fig. 22, and, for reasons we have explained, the lightest part of the cylindrical surface is between the generators b'b" and c'c", and the darkest at the generator e'e", the part between e'e" and ff" being in the shade. Fig. 23 is a hollow horizontal semi-cylinder whose axis is parallel to the vertical plane, and the shading shown should now speak for itself. . ' These are only used in connection with rounded surfaces on machine drawings. 14 MACHINE DRAWING AND DESIGN FOR BEGINNERS 32. Workshop Drawings. The original drawings are kept in the drawing office for reference purposes, and copies only, produced in various ways, are used in the workshops. The most direct way of copying a drawing is to trace it on a sheet of tracing paper or tracing cloth, and, if more than one copy is required, the tracing is used to produce blue prints by sun-printing. There are several photo-copying processes used for reproducing copies, or blue prints, by heliography, or sun-printing as it is called, in which the tracing is placed in front of, and in close contact with, a sensitized sheet of paper, both being clamped in a glass frame and exposed to the actinic l rays of light which, falling upon the tracing, pass through the transparent portions, decomposing the sensitized paper below, leaving the opaque lines upon the tracing undecomposed and transferred to the sensitized sheet. This sheet is then removed from the frame, and washed in water or certain solutions to remove the sensitizing matter and thereby develop the lines. The various processes in use are the Ferro-cyanide, Ferro-yallic, Platinotype, Zincographic, and Ferro-prussiate. The sun-printing process has the drawback of being somewhat slow, since it is mainly dependent upon the character of the natural light, and as this varies a great deal, so does the time taken to make the prints ; but since the invention some years ago of the electrical photo-copying apparatus, in which electricity is used to produce the requisite light, engineers have had at their command a simple, handy apparatus which makes them independent of the weather, and in which prints may be made in two or three minutes. Perhaps the best-known apparatus of this kind is the one invented by Messrs. Shaw and Halden, and manufactured by Messrs. J. Halden of Manchester. In using the apparatus the tracing and sensitized paper is laid upon a vertical semi-cylindrical glass plate, and a cover or jacket is then laid over the back of the sensitized sheet and firmly clamped by engaging with a rod. The cylinder is then turned into position, and the arc lamp lowered gradually down its interior, the speed of lowering being arranged to suit the exposure required of various sensitized papers. 32a. Tracing. No small amount of skill is required to expeditiously make a good tracing. The beginner cannot do better than commence by drawing a number of straight lines and arcs of different thicknesses on tracing paper and cloth with his drawing pen and bow pen respectively. The ink may be introduced between the nibs of the pen by a pointed quill, or by a writing pen, care being taken to wipe the outside of the nibs, to prevent any ink from them touching the edge of the square, straight edge, or set square, for should the ink get in contact with these instruments it runs on to the paper and spoils the tracing. Care must be taken to preserve uniformity of thickness in the lines where required, and to make arcs and curves flow into straight lines without any apparent break, in other words, to satisfy the geometrical condition for tangential contact. If the ink does not freely run on the tracing paper or cloth, a little powdered chalk may be rubbed over the sheet, or a drop or two of ox-gall may be added to the ink. In commencing a tracing, be careful to pin the tracing paper over the drawing and on to the drawing board in such a way that the sheets are taut, and the principal line of the drawing is square with the working edge of the board. As a general rule it is best to draw all the lines that are in the direction of the length of the board first. In working down from top to bottom in doing this, many lines will probably be missed, but they will be picked up by working down a second, and even a third time if necessary. The transverse lines can then be drawn in the same way, and then any connecting arcs drawn, and the circles, if any, described. 1 The action, as in photography, of the sun's rays iu their chemical, as distinct from their illuminating and heating, effects. PRINTING, TRACING, SHADING, ETC. 15 Usually the first tracing made by a beginner is not much of a success, but by persevering in the way indicated he should soon become proficient. Great care, of course, has to be taken in writing the dimensions, to ensure absolute accuracy. 33. Tracing Exercises. Beginners will find that the figures given for tracing in the B. of E. Examination papers at the end of the book, are the most suitable to commence on. After a little practice on these, he will be able to attempt the tracing of most of the drawing exercises given in the book, of course working on the simpler ones first. CHAPTER III SCALES, AND DRAWING TO SCALE 34. IF we wish to draw the elevation of a machine whose height 1 is, say, 5', and length 12', upon a sheet of paper whose surface does not exceed two or three square feet in area, it is evident it would be impossible to make this drawing of the machine full size. Now, suppose we make a line 3" in length on the drawing represent a foot on the machine, then a line 5" X 3" = 15" long would represent the height of the machine, and one 12" X 3", or 36" long, its length; and we should speak of the scale as being one of 3" to the foot, and tlie fraction of the scale, as it is called (or representative fraction as it is sometimes called), would be 3 inches _ 3 1 Ifoot = 12 = 4 In the same way : If inch represented 1 foot the scale would be ^ * yy -*-2 " " " " ^ v * 11 a 3 4-1 it ^2 " " 6j >t it H 2 And if 1 inch represented 1 yard, the scale would be ,- -- ^ 5 = ^T> L X \-& X o OD 1 1 lTx 1 millimetre represented 1 centimetre, scale would be ^ I decimetre -^^ 1 . 1 metre ro ^J 1 The dimensions of machines, details, etc., are usually written in feet and inches. The former being indicated by the suffix ', and the latter by the suffix ". Thus, 5' reads 5 feet, and 5' 8|" reads 5 feet 3| inches. Further, 0'783" reads decimal (or point) seven eight three of an inch, equal to ^jjjj, of an inch. When metric measure- ments are used the following abbreviations, m., dm., cm., mm. respectively represent metres, decimetres, centimetres, and millimetres. Angles are measured in degrees, minutes, and seconds. Thus 45 reads 45 degrees, and 20, 40', 50" reads twenty degrees, forty minutes, fifty seconds. SCALES, AND DRAWING TO SCALE 17 Of course, whenever practicable, the drawing is made the same size as the thing to be drawn ; the drawing is then spoken of as being full size. If the size of the object will not admit of its being drawn full size, then as large a scale as is practicable should be selected. This applies more particularly to detail drawings, where every minute feature must be clearly shown. The great size of some work necessitates its being set out in detail on large specially prepared boards, whilst, on the other hand, the details of watches, clocks, and small instruments can only be satisfactorily shown when drawn larger than their true size. In every case, whatever scale is decided upon, care must be taken to draw all parts of the object to the same scale, and thus get an exact, although a reduced or enlarged, representation of it. Scales should always be constructed and drawn at the foot of important drawings that are not fully dimensioned, so that the various parts may, with the aid of a pair of dividers, be scaled off, and so that any alteration in size, due to the shrinking of the paper, will affect both scale and drawing alike. These scales must be constructed and divided with great care and accuracy, and should be tested by measuring the same lengths from different parts of the scale. In drawing them, a very sharp pencil should be used, and when inked in the lines should be very fine. 35. Engineer's Scales. Although most of the drawings made by the beginner will be full-size or half-size, for which any ordinary rule can be used, yet after some practice he will be called upon to make them to a smaller scale, such as ^ or J full size, or even less, so that he will require an instrument with these scales marked on it. Such instruments are called Scales, or Drawing Scales, and they can be had made of various materials, such as cardboard, vulcanite, boxwood, ivory, and steel. The ordinary lengths are 6" and 12", and they are made thin, and some are divided to the edge to enable a distance to be marked off from it with pencil or pricker ; but a more accurate method is to take the distance off with dividers, as shown in Fig. 15, care being taken to lay the sides of the points on the scale or rule so as not to damage the points. (Refer to Art. 22.) Vulcanite scales should be avoided, as they expand and contract greatly with changes of temperature. On the whole, the best materials for them are boxwooil and ivory. They are arranged with eight single reading open divided scales, two on each edge. The scales are 3", 1J", 1", f , J", f", J ', and J" to the foot, or ' !, T ' 5 , ,,, jt,, h, is, and 9 ^ full size respectively. CHAPTER IV HOW TO DRAW STRAIGHT LINES AND SIMPLE FIGURES 86. IT is a waste of valuable time for the beginner to attempt to draw views, even of the simplest machine details, without some previous practice in drawing in a workmanlike way lines and circles (which are the component parts of such figures), and a few representative symmetrical figures. So the student is advised to carefully practise drawing the following progressive exercises, and after a few hours' practice he should be able to draw simple figures neatly and with accuracy. 37. EXAMPLE. Straight Lines drawn with the Assistance of the T-Square. The student should patiently practise with his pencil and T-square in the following way : Commence by pinning the paper flat on the drawing board ; this can best be done by first pinning one corner until the under-side of the pin-head is in close contact with the paper. Then place the back of the right hand upon the paper near this pin, and draw it diagonally across the sheet to the right-hand bottom corner, drawing the paper taut by the friction exerted. Hold this corner down by the thumb and fingers of the left hand, and insert a drawing pin in it as before described. The back of the right hand may then be placed at about the centre of the sheet, which is drawn diagonally to the right-hand top corner and pinned. Do the same with the remaining corner and the sheet will be as flat as it is possible to have it without damp stretching. The T-square can now be placed in position and held firmly by the left hand in such a way as to keep the stock in contact with the edge of the board, and the blade tight on the paper, as shown in Fig. 25. The pencil should be held between the first two fingers and thumb of the right hand, and kept in contact with the edge of the T-square, resting the third and fourth fingers on the square as the stroke is made. The student must now aim at producing lines equal in thickness throughout their length, and, as the thickness and quality of a line depend upon the sharpness of the pencil and amount of unvarying pressure exerted upon it, he will understand that only practice will enable him to draw them with certainty and facility. Each line should be drawn the full length of the T-square, and several of each kind should be drawn ; in fact, they should be drawn again and again till they can be freely produced at least equal in quality to those shown in the following figure (26), where it will be seen that A is a very fine line, suitable for centre and construction lines. This should be drawn with a very sharp chisel-pointed pencil, and should be so fine that a light touch of. the indiarubber will clean it out. At B is a line sensibly thicker than the previous one, and suitable for the finished lines of a very small drawing. is thicker, and suitable for ordinary drawing purposes. D is more suitable for working drawing of single objects, drawn to a large scale, and E is a suitable line for shade lines on drawings ; this line is best drawn with three strokes of the pencil, as the pressure necessary with a point thick enough to produce it with one stroke would in most cases break the lead. When lines thicker than E are to be drawn, a good finish can only be given them by three strokes of the pencil ; the two outside ones should be sharp and distinct, and the HOW TO DRAW STRAIGHT LINES AND SIMPLE FIGURES 19 distance between them decided by the thickness of the required line. In making the third stroke, the pencil should be turned sideways, so as to fill the space between the outer lines. 38. Defects in Lines. The main defects in lines which should be avoided are : Varying thickness, caused by varying the amount A B C- D. FIG. 25. Showing how the T-square and pencil should be held. Fra. 26. Thickness of lines. of pressure exerted upon the pencil. Want of sharpness, the sides of the lines having a blurred appearance, caused by softness of lead or want of sharpness in the pencil. Uneven colour, due to unequal quality of the lead or paper, or uneven pressure upon the pencil. 39. EXAMPLE. Straight Lines, drawn with the Assistance of a Set-Square. The student should remember the instructions given for the previous example, and should now practise drawing similar lines with the assistance of one of his set-squares. The larger one had better be used, and the lines drawn its full length, at first to the right-hand side of the square as shown in Fig. 27 (and at A, Fig. 28) and afterwards to the ;left as shown in Fig. 29 (and at B, Fig. 28) in the direction indicated by the arrows. It will be seen that the left hand in each case is firmly holding the set-square and T-square together and on to the board in such a way that the stock of the T-square is kept closely in contact with the edge of the board. The remarks upon the previous exercise respecting the quality of the lines apply equally to this one, and the necessity of practising the drawing of these lines from both sides of the set square will be understood by the student after his first attempts, as he will find that to steadily move his hand about with ease, in the required ways, needs considerable practice. 40. Dotted Lines. Dotted Lines are used on drawings either to indicate the line upon which a section has been taken or to mark the position of any existing part which is unseen; for the former, dot-and-dash lines, as at A (Fig. 30), are used, whilst for the latter chain-dotted lines, B, should be used. In the former case, A, they look best when the dots are equally spaced, and the short lines or dashes are equal in length, and about four or five times the lengths of the spaces ; and in the latter case, B, when of equal length and equally spaced, the lines being made three or four times the length of the spaces, as shown. Obviously, if the dots are made shorter, they take a longer time to draw. The thickness of the lines, and the lengths of the spaces and dots, should be regulated by 20 MACHINE DRAWING AND DESIGN FOR BEGINNERS the size of the drawing. A glance at some of the following lines, A to E (Fig. 31), will give the student some idea of what is con- sidered good proportion, showing how they should vary in form with the thickness ; and the student should patiently practise drawing FIG. '27. Using set-square with downward stroke of pencil. B FIG. 28. Diagram showing use of Bet- squares. FIG. 29. Using set-square witli upward stroke of pencil. D FIG. HO. Dotted lines : different forms. A B c- D- E- Fia. 31. Examples of dotted lines : different thicknesses. such lines until he can space them with a fair amount of neatness and facility. 41. Rectangles. The student should now be in a position to draw some simple figures. Having practised on lines drawn in HOW TO DRAW STRAIGHT LINES AND SIMPLE FIGURES AC D B FIG. 32. Construction of a rectangle. First step. AC OB Fio. ii3. Construction of a rectangle. Second step. Fio. 34. Construction of a rectangle. The complete figure. the direction of the T-square, and at right angles to it, figures whose sides are made up of such lines should be easily drawn. So, by carefully working the following progressive exercises, which are very fully described, the student should make an important step in the practice of mechanical drawing. 42. EXAMPLE. To Draw a Rectangle whose Length (2") and Breadth (!") are given. Draw, with the aid of the T-square, a very fine indefinite line AB, about 2" long, Fig. 32. With the aid of a rule and a pair of dividers prick off (Art. 22) the length CD equal to 2", and between these two points draw a good finished line as shown. Then, with the aid of a set-square, draw from C and D very fine distinct lines perpendicular to CD and a little longer than the given breadth (l^")- 1 Now, prick off as before the point E (Fig. 33) from C, making CE equal to \\", the given breadth, and with the aid of the T-square, draw the finished line EF parallel to CD. The rectangle is com- pleted by re-drawing CE and DF (Fig. 34), with the aid of the set-square, per- pendicular to CD, being careful to regulate the thickness of the lines, so that they are the same throughout the figure, and removing with indiarubber the ends of the construction lines AC and DB, and those above E and F, leaving the rectangle completed as shown, care being taken not to remove the sharp corners formed by the intersection of the lines. NOTE. The student should always aim at constructing a figure by drawing the least number of lines possible ; in other words, a line should not be gone over twice if once will suffice. As an illustration of this advice, with reference to the rectangle just drawn, many students would first have drawn the complete figure in fine lines, and then pencilled over each line to make it of the required thickness. Such a practice usually produces a poor result, as it is difficult to exactly cover the previous lines, and, further, it takes a longer time. 43. Exercises upon the Use of Centre Lines. 2 First Case. Figure Symmetrical about a Single Centre Line Whenever a figure has more than one line each side of its centre, and is symmetrical about that centre, it is best drawn by commencing with the centre line. To illustrate this, let us proceed to draw the figure shown in the dimensioned sketch (Fig. 35). Commence by drawing a very fine line AB (Fig. 36), with the aid of the T-square ; then with dividers prickoff upon it two points C and D, 2" apart. Through these points, with the aid of a set-square, draw two fine indefinite lines EG and FH. Then, with the dividers, prick off on one of these lines, say from C, the points J and K (Fig. 37), the opening of the dividers being ", equal to a half of the breadth (1|") of the given figure, and with the aid of the T-square draw through these points the finished full 1 The student, after a little practice, will be able to estimate these distances and lengths to within a quarter of an inch, so that such lines need not be drawn much longer than their required length, to minimize rubbing out, but in no case should they be drawn too short at first, as any attempt at joining a length on is usually noticeable, and should be avoided. 2 Centre lines should be very fine continuous ones, undotted, as at A, Fig. 26 ; then any part of them can be used to measure to or from. MACHINE DRAWING AND DESIGN FOR BEGINNERS i ( . t -1* y 2" > ' i* 4, V * Fio. 35. Eectangular figure, symmetrical about a centre line. The complete figure. A 2"- B G H FIG. 36. Rectangular figure. First step. E J N F L | = |00 I C P K G oicn i D Q M H 1 B t ' Wf- i G II ~3 . i" i *- '" > 2 A F E H t Nl- 1" FIG. 38. Square figure. Use of two centre lines. J D FIG. 37 Kectangular figure. Second step. Fio. 39. Square figure. Construction lines. HOW TO DRAW STRAIGHT LINES AND SIMPLE FIGURES 23 lines KM and JL. In a similar way mark off N and P from C, with the dividers open to g", and through these points draw, in a similar way, the lines NO and PQ. a 1 c "I --IN ^ , d .1 'I u. I oi" >l FIQ. 40. Figure symmetrical about two centre lines. FIG. 41. First step Fio. 42. Second step. Fia. 43. Third step. The figure should now be completed by going over the lines KJ and LM with the pencil, taking care to give the lines the same thickness and finish as the others, and the figure will be now complete as in Fig. 35. The projecting parts of the construction lines should now be rubbed out, as in the previous exercise, with indiarubber, the centre line AB being left projecting about a \" beyond the figure upon each side. NOTE. The appearance and finish of the figure depends upon the lines being perfectly uniform in thickness and colour, and the student should constantly bear in mind the instructions previously given respecting the production of such lines. 24 MACHINE DRAWING AND DESIGN FOR BEGINNERS 44. Second Case. Figure Symmetrical about Two Centre Lines. The figure No. 38 consists of two concentric squares which are symmetrical about two centre lines, at right angles to each other. So, first draw any two indefinite centre lines AB and CD, perpendicular to one another (Fig. 39), and intersecting at E ; then, with rule and dividers, prick off from E, along the centre lines EF, EG, EH, and EJ, distances equal to half the side of the outer square, viz. 1", and complete the square as in the previous case. The inner square should be drawn in the same way, the construction lines removed, and the required figure completed as shown in Fig. 38. 45. EXAMPLE. Another Case of a Figure Symmetrical about Two Centre Lines. The figure to be drawn in this exercise consists of a rectangle, with a trapezoid at each end (Fig. 40). It will not be necessary to explain every step in the construction of the figure, as the student should by this time be familiar with the method of working from centre lines, and might now attempt to draw the figure in what appears to him the best way, with a hint that the small ends ab and ed of the trapezoid should be drawn before the sloping sides. The figures 41, 42, and 43 show the steps in the construction. These should speak for themselves now. Of course Fig. 40 shows the finished figure. But the student should not trouble about writing dimensions on his drawings yet. CHAPTER V CIRCLES, ARCS, AND LINES 46. As ordinary mechanical drawings mainly consist of combinations of circles, arcs, and lines, the art of correctly and neatly drawing a few of them in various positions in relation one to the others should be cultivated by the beginner ; for if such lines are faulty in form and finish, or do not satisfy the geometrical conditions of proper contact, they spoil the appearance and detract from the value of any drawing upon which they appear. As the student will have a great deal of work to do with the compasses, he cannot do better than carefully read the remarks upon their manipulation, etc. (Art. 17), before attempting this chapter. A few of the more important definitions and problems relating to circles and arcs are given here to help beginners, but for more complete information on these matters refer to the author's " Geometrical Drawing," pp. 61, etc. 47. Definitions. The radius of a circle is & straight line drawn from the centre to its circumference. A diameter of a circle is a straight line passing through its centre, and terminated on both sides by the circumference. An arc of a circle is any part of the circumference. A chord is a straight line joining the extremities of an arc. A segment is any part of a circle, bounded by an arc and its chord. A semicircle is half a circle, or a segment cut off by a diameter. A sector is any part of a circle bounded by an arc and two radii drawn to its extremities. A quadrant, or quarter of a circle, is a sector haying a quarter of a circumference for its arc, and the two radii perpendicular to each other. A sextant, or sixth of a circle, is a sector having a sixth of the circumference for its arc, and the two radii making an angle of 60 with each other. An octant, or eighth of a circle, is a sector having an eighth of the circumference for its arc, and the two radii making an angle of 45 with each other. A tangent is any line perpendicular to a radius at its extremity in the circle. A tangent touches the circle in a point, as at P, Fig. 44 (which is called the point of contact), where the line AB touches the circle, and it is perpendicular to the radius OP. Point of Contact. When two circles touch one another, they do so in a point only, called the point ofoontact, and the straight line which joins their centres passes through this point. Thus, Fig. 45 shows two circles, A and B, touching one another in the point P, which is the point of contact. It is only when this condition is satisfied that a part of one circle can be made to flow into a part of the other ; the thick line in the figure shows how this condition must be satisfied. To enable the student to correctly treat cases where circles are in contact with one another, and with straight lines, he should carefully study the following problems before attempting the exercises at the end of the chapter. 48. To describe a Circular Arc through Three given Points. Let ABC (Fig. 46) be the given points. Join AB and BC, and bisect the lines AB and BC in G and D, and through these points draw perpendiculars intersecting in F. Then, with F as centre and radius FB, describe the required arc ABC. 49. To draw a Tangent to a Circle through a fixed Point in its Circumference. Let B (Fig. 47) be the fixed point in the circle. Join B to the centre A, and through B draw CD perpendicular to AB. Then CD is the tangent required. 49a. To draw a Tangent to a Circle through a fixed Point without it. Let the circle in Fig. 47 be the given one, and P the point. E MACHINE DRAWING AND DESIGN FOR BEGINNERS Join the centre A with P, the fixed point without the circle, and bisect AP in E. With E as centre, radius EA, describe the semi- circle AFP, cutting the given circle in F. Join PF. Then PF is the required tangent. It is evident that in a similar way a tangent the other side of PA could have been drawn. FIG. ii. Circle and tangent. Fio. 45. Point of contact of two circles. FIG. 46. An arc described through three points. NOTES. 1. The student will notice that if F be joined with A, the angle PFA will bo a right angle, being an angle in a semicircle (Euc. III. 31). And FA will be a normal to the tangent at F. 2. The Euclidean geometry does not allow a tangent from a fixed point to a given circle to be drawn without first finding the point of contact as above, and the C B ~~D FIG. 47. Tangents to a circle. F' A F FIG. 48. Circle touching two given lines. FIG. 49. Circle of given size touching a fixed line and circle. same remarks apply to the cage of a common tangent to two circles, but for practical drawing purposes a tangent may be drawn from an external point to a circle, or a common tangent to two circles directly by carefully adjusting the straight-edge; and should the actual point of contact be required, a perpendicular to the tangent from the centre fixes it. 49b. To inscribe in a given Angle a Circle of given Radius (say 1-5"). Let EAF (Fig. 48) be the given angle. Bisect the angle CIRCLES, ARCS, AND LINES by the line AB, and draw CD parallel to AF and 1'5" from it, intersecting AB in C. With C as centre, radius T5", draw the circle touching the sides of the angle in E and F. The exact points of contact can be found by drawing from C the lines CE and OF perpendicular to AE and AF respectively. 1 The dotted lines refer to a case when the angle is obtuse, and the same letters apply. NOTES. 1 . This is a problem often met with in mechanical drawing, when two lines are to be connected by an arc of a circle of given radius. 2. For most practical purposes a common tangent to two given circles (such as E'E, Pig. 48) can be drawn with a sufficient degree of accuracy by offering the edge of a square to the two circles and drawing a line to touch them, the points of contact being found by drawing perpendiculars from the centres to the tangent. 50. To describe a Circle of given Eadius to touch a given Line and a given Circle. From C (Fig. 49), the centre of the given circle, draw any line CE, cutting the circle in F ; from F mark off FE, equal to the given radius, and with centre C describe the arc ED. At any point H in AB draw GH equal to the given radius EF, and perpendicular to AB. Through G draw GD parallel to AB, and cutting the arc DE in D. Then, with D as centre, radius EF, describe the required circle. NOTE. D is equidistant from line and circle. 51. To draw a Circle to touch Three given Straight Lines. Let the given lines be AB, AC, and CD (Fig. 50), intersecting in A and C. Bisect the angle BAG by the line AE. The centre of the required circle must be somewhere in this line. Bisect the angle ACD by the line CF ; the centre must also be somewhere in CF. Therefore it is in G, the intersection of AE and CF. From G draw GH perpendicular to AB and cutting it in H. With centre G, radius GH, describe the required circle or arc. 2 Then perpendiculars from G, such as GH, give the points of contact. NOTE. This problem sometimes occurs when a small bevel wheel is drawn. 52. To describe an Arc of a Circle of given Radius (say 1") to touch a given Arc and a given Straight Line. Let AB (Fig. 51) be the given line, and G the centre of the given arc. Draw GC, any line passing through the centre of the circle G, and cutting the arc in C. Mark off CE equal to the given radius of 1", and with centre G, radius GE, describe the arc EF, and draw F'F parallel to AB and 1" from it, intersecting EF in F, which is the centre of the required arc. With F as centre, radius FH, a perpendicular to AB, describe the required arc. Draw through G and F the line GK, cutting the circle in K. Then the points of contact are H and K. If the arc were to touch the given circle externally, F' would be its centre, and I and J its points of contact. The working is similar, and can be easily followed on the figure. NOTE. This problem occurs when a wheel with arms is drawn. HB is then the side of an arm, and tho arc OK a part of the rim. 1 AE and AF are two tangents to the circle from A, and they are equal to one another (Euc. III. 17). - Three other circles can be drawn to touch the given lines, and one of them will obviously be contained by the triangle made by producing DC and ISA till they meet. Fio. 50. Circle touching three straight lines. FIG. 51. Arc touching straight line and arc. 28 MACHINE DRAWING AND DESIGN FOR BEGINNERS 53. Having studied the preceding problems, the student should be able to work the following exercises without further help. They should be carefully constructed from the dimensions shown, and not merely copied. Having pinned down a sheet of paper, the T and set squares should be carefully dusted, and the pencils and lead of the pencil bows to be used sharpened, and the latter adjusted so that the pencil and steel point are of equal length ; the exercises can then be proceeded with. EXERCISES. 1. Assume any point P in the given circle (Fig. 52), and draw a tangent at the point. '2. Through the fixed point P (Fig. 53) draw a tangent to the given circle. 3. In the angles ABD and CBD (Fig. 54) inscribe arcs of 1J" radius. 4. Describe a circle of lj" diameter to touch both the line AB (Fig. 55) and the given circle. 5. Describe a circle touching the three given lines, BA, AC, and CD (Fig. 56), and mark the points of contact. (!. Describe a 2J" circle to touch both the given circles (Fig. 56A). FIG. 52. Fio. 53. B Fio. 54. FIG 55. CHAPTER VI HOW TO COMMENCE A WORKING DRAWING 54. WE will assume that the student has carefully read the preceding pages, particularly those from Art. 34 onwards, and that he is about to attempt a drawing of some simple object. Now, before he can do this intelligently, it is obvious that lie should have a fair acquaintance with elementary projection, such as is taught him in his geometry class, so, if on joining a class in Machine Construction and Drawing he has not had some training in solid geometry, he will doubtless be recommended by his instructor to take up the study of that subject concurrently with his course in drawing. In most schools or Institutes this can be easily done, as the geometry and machine drawing classes are often so arranged that they can be attended the same evening or day. However, for the benefit of those who may not be able to attend such classes, or have not the help of a teacher, we will proceed to briefly explain how an object may be drawn in plan and elevation, for the shape and proportions of most simple solids can be completely shown by drawing two views only, namely 55. Plan and Elevation, called their projections. The terms " plan " and " elevation," as applied to the representation of an object, are fairly well understood in a general way. Thus we speak of the elevation of a house, meaning the view we get by looking at its front, back, or sides. By such a view we see its height and breadth, and the height of everything shown is found on this elevational view. Again, we speak of the plan of a plot of ground. This view, of course, shows its length and breadth, and the distance it may be from some landmark. In the same way the plan of a house or any object is the view we get by looking down on it from above. All this and much more can better be made clear by referring to an example; and as first steps cannot be made too easy, the subject frequently presenting considerable difficulties to beginners, the tyro cannot do better than take a sheet of drawing paper and any rectangular solid, such as a box or a book, and work out the following simple exercise : Let BACD (Fig. 57) be the sheet of paper. Draw across it any line XY (this may be done in the ordinary way with the T-square), and place the bottom (EFGK) of your box on the paper, so that one of the long edges, EK, is resting on XY. Then bend the part of the paper BD about the line XY, as shown, until it touches the back of the box EKIJ. If, when the paper is in this position, a pencil point be drawn round the box, marking the lines EFttKIJ, we shall have on the horizontal plane (XYCA) a plan EFGK of the box, and on the vertical plane (XYDB) an elevation EKIJ. Now, let us suppose that we are to draw the plan and elevation of the box in its present position in the ordinary way. Begin by drawing XY (Fig. 58) with the aid of the T-square; then construct EKIJ (the eleva- tion), a rectangle, making EK equal to the length of the box, and EJ equal to its thickness, remembering that EK must rest on the ground line (XY), as the box is resting on the ground (horizontal plane), and that as it is touching the vertical plane, the plan, which may now be projected (carried down) from the elevation, must be drawn showing the back EK of the box touching XY. Of course, all the lines on the plan and elevation are drawn with the assistance of the T-square and the set- square S. The student will notice that in this case the plan might have been drawn first, and the elevation projected from it. That is to say, this is a case where either the plan or elevation may be first drawn. (Cases will occur directly where this is not a matter of choice.) It will now bo seen that in Fig. 58 we have repre- sented the form and position of a body which possesses three dimensions (namely, length, breadth, and thickness) upon a plane having only two dimensions, namely, length and breadth. The student should now bend the paper (Fig. 58) about its XY so that the two parts are at right angles, as in Fig. 57, and then imagine that MACHINE DRAWING AND DESIGN FOR BEGINNERS the box is in its place, as it is shown in that figure, for beginners frequently fail to make much progress owing to their inability to exercise their imagination in this way. As a further exercise we may draw the plan and elevation of a rectangular block in such positions as shown in Fig. 60, where it will be seen that the two views are separated by the distance aa', and to enable the student to see what bearing this change of position has upon the previous case we will proceed to work a little problem which shall be a distinct step in advance of the previous study, but, nevertheless, one that ought to be readily understood. The problem may be stated thus : 56. To draw the Plan and Elevation of a Rectangular Block 9" long, 6" wide, and 3" thick, when a 9" X 6" Face is horizontal, and 1" above the H.P. (or Ground), and one of its Sides is parallel to the Vertical Plane, and 8" from it. (Scale, half-size.) First draw across the paper a line, and mark it XY 1 (Fig. 59). Then fold or bend the paper about this line, as in the previous study, and as shown in Fig. 59, and place the block on something 1" thick ; it will then be the right height above the ground, or horizontal plane. If we now move it till its back face is parallel to the vertical plane, and 2" from it, the block will be in the required position. The figure clearly shows this position, and at this stage it will be instructive to compare this problem with the previous study (assuming that the box and the block are the same size). It will be noticed that the plan in Fig. 59 is the same shape as the plan in Fig. 58 (this must be so, as both solids are horizontal), but is 2" dis- tant from XY (that is, 2" from the V.P.), and similarly with the eleva- tions, they are the same shape. The one in Fig. 59, being 1" above XY, shows that it is 1" high. Of course it will be noticed that the lines (projectors) connecting the block with its elevation are perpendicular to the V.P., and also the lines connecting the block and the plan are perpendicular to the horizontal plane. The 1 This is the ground-line, as it is called ; it is invariably marked XY in geometry. FIG. 57. Relation of plan to elevation. FIG. 58. Projecting one view from the other. HOW TO COMMENCE A WORKING DRAWING 31 figure also shows by dotted lines the paper folded (constructed) back into its proper (normal) position, and the dotted elevation shown will be seen to be in the same straight line with the plan, perpendicular to the ground-line (XY). Thus, when the projections of an object are drawn, we always have the plan and elevation in the same straight line perpendicular to the ground-line. To make this second study complete, let us suppose that we, knowing exactly how the views will appear in shape and position, wish to draw in the ordinary way the projections of the block to satisfy the problem. The first thing to do is to draw XY, the ground-line (Fig. 60). Then, as in this case we can first draw either projection, let us start on the plan. Eemembering that the block is 2" from the V.P., we draw a line ab parallel to XY and 2" below it, and on this line we construct the plan, which of course is a rectangle, whose length is 9" and breadth 6". Then from each end of this plan draw a projector perpendicular to XY ; be- tween these projectors draw a'b', the bottom of the elevation parallel to XY and 1" above it, and on this line complete the rectangle, whose breadth is 3" (the block's thickness), which forms the elevation. The projectors are best drawn undotted, but much thinner than the lines that form the projections. 1 This completes the projections, and the student would do well to repeat the operation explained in the previous study, and try to imagine that the solid itself is standing over the plan, and in front of the elevation, as shown in the figure. NOTE. Before leaving this study, we might notice that the line a'b' on the elevation represents the bottom of the block, a horizontal surface, and a surface perpen- dicular to the vertical plane. The student will directly better understand that the projections of all surfaces perpendicular to a plane are straight lines on that plane. Thus the line ab on the horizontal plane is the plan of a vertical side. 57. End Elevations and Sections. -Let us suppose we are looking at the rectangular block (Fig. 61) in the direction of the arrow B, the view we then get is called an end elevation, and it may be shown as at E, where the figure is obviously constructed with the assistance of the plan, the 3" height being marked off with the dividers. It is generally more convenient to place 1 In an ordinary mechanical drawing the projectors are not allowed to remain ; any that may have been drawn aa a matter of necessity or convenience being rubbed out. a' b' t, ELEVATION 3 i' 1 " a f i b PLAN Q" 1 FIG. 59. Block in position, between folded drawing paper. Kio. 60. Projections of a rectangular block. MACHINE DRAWING AND DESIGN FOR BEGINNERS G SECTION ON LINE C.D. "lO ELEVATION |, ^-A END F ELEVATION r \ V \ \ /. m i/z UJ V ^ C (_? /END ELEVATION ^.1 t R x * D / s * 9 ' s I" . pl ! AN L "'"S'H b FIG. 61. Projecting sections and end elevations. this view by the side of the elevation, as shown at F ; the view is then projected from the elevation as shown, the 6" breadth being marked off with the dividers or found by using the arcs fm and hn. If we were to cut through the solid with a vertical saw-cut along the line CD in plan, the true shape of the cut would be a vertical section (a section on the line CD as it is called) of the solid. This is shown at G in the position which is usually most convenient in relation to the elevation. It is drawn in the same way as the end elevation F. We may now proceed to review the salient points as they would probably present themselves to the student who is about to commence a working drawing. He should begin by making up his mind as to how many views of the object he intends to show, bearing in mind that the drawings should clearly represent the object in such a way that its true dimensions and the form of every detail are shown. So long as this is satisfactorily accomplished, as few views as possible should be drawn. Two views at least are always required, and theso may be an Elevation (which shows length and height) and a Plan (which shows length and breadth). Or the front elevation and an end elevation may be used to obtain a similar result. But three views, namely, a Front elevation, an End elevation, and a Plan, are generally shown, with sufficient sectional elevations and sectional plans (part section and part elevation, and part section and part plan respectively) to make the external and internal form or construction of the object quite clear. The use of dotted lines, as in the end elevation at MM 2 KK 2 (Fig. 63), for indicating the position of unseen parts, should as a rule be avoided as far as possible ; but a judicious use of a few of them may save the making of another view, provided always that they do not impair the clearness of the view upon which they are placed. Dotted lines should not be used for unseen parts in highly finished coloured drawings, but only for working drawings. In cases where the object to be shown is symmetrical about the centre line, it is usual to show one half of the view in elevation, and the other half in section, as in the sectional elevation of the coupling (Fig. 98, Chapter IX.). The section may extend slightly beyond the centre line, or may finish at it ; in either case a black line is used to terminate the section. This saves the making of a separate sectional view. Although it is obviously desirable to limit the number of views of an object, as previously explained, care must be taken not to carry this too far ; as in the case of a complicated object, say a casting, much time is often spent by the pattern-maker and others in trying to read a drawing, where an additional view or section would have enabled the trained eye to see at a glance a mental picture of the required object. It is usual to arrange elevations above plans, or sectional plans, when convenient ; but in all cases the views must be arranged so that the relation between two adjoining ones may be readily recognized, and so as to facilitate their being properly projected one from another. Haying decided upon the number of views to be shown, it is usual to take a spare piece of paper, and to roughly sketch upon it the views decided upon in their relative positions one to another, and to mark upon each the overall sizes, as in Fig. 63. HOW TO COMMENCE A WORKING DRAWING 33 The size of the i off fquare, and from : be allowed to enable the drawing to be cut off clear inside the adhering edge. From 1J" to 3" is usually allowed between the border lines and the right- views, and from 1" to 2" horizontally between separate views. These amounts must be added together, and subtracted from the length of the sheet; and then the dimensions of the longest line of horizontal lengths of the various views must be added together. By comparing this with the space remaining for them upon the sheet, the scale to which the views can be drawn may be decided upon. After a scale has been assumed for the horizontal line of views, the longest line of vertical dimensions must be checked against this in a similar way to see if the scale is suitable. All drawings forming one set should have equal outer margins, and as far as possible equal margins between the views. Having arranged the positions of the views upon the sheet, and the scale to which they are to be drawn, the next thing to be done is to draw the cutting off and border lines upon the sheet, and then the centre lines of the various views. The positions of these can be readily ascertained from a rough sketch used to adjust the spaeings, and they should be carefully marked out ; and after this has been done, the various views may be commenced. Of course, these remarks are for the guidance of the young draughtsman. The beginner will always have plenty of paper to practise on, and need not trouble about the spacing out. It is impossible to lay down any fixed ride as to what view should be first completed ; in fact, it is usually the practice to work upon two or three views at the same time, drawing some part upon all views first, and then adding another pait to these, and so on. But generally any known portion, such as the size of a shaft, stroke of a part, leading centres or outline is first drawn ; and always the view from which the greatest number of parts of other views can be projected, or the greatest amount of information obtained (frequently a section) is then proceeded with; an axiom being to put in outside sizes of work definitely first, and to fill in all smaller details, as bolts, rivets, studs, nuts, keys, cotters, etc., afterwards. In the case where a part has a circular form, the circles should lie drawn first, and the other views projected from them, and when a number of similar parts, as rivets, bolts, and nuts, occur, it is best to put in the small circles of the entire number first, with one setting of the compasses, and then the similar lines of each. This will take less time than if each one is completed singly, and ensures a more uniform result. It is also usual to show upon working drawings, bolts, nuts, pins, rivets, studs, keys, cotters, rods, shafts, spindles, springs and levers in elevation, even when the section plane passes through their axes. The reason being that it is less trouble to show them in elevation than in section, and it renders the drawing more clear. But all these matters can now be more conveniently dealt with as we proceed to explain how drawings of a feM- simple objects may be made, starting with a very easy example and selecting others so that they may gradually present to the student further features and expedients in a progressive way. 58. Drawings of a Cast-iron Bench Block. The sketch, Fig. 62, shows the form often given to a bench block or anvil, such as is often used in an engineer's fitting shop. Cast Iron is used for the block in preference to Wrought Iron, as it is much cheaper in first cost, and, being harder, is not so easily injured by a blow. The flat surfaces may be planed, but it is sometimes used rough as cast. In this and the following exercises, the views and scale selected are so arranged as to enable the object to be drawn upon a half-imperial sheet of paper, viz. 22" x 15". As a drawing example, the four views of the block shown in Eig. 63, viz. a front elevation, a plan, an end elevation and a section on the line no taken transversely through the centre of the hole and looking to the right (the left-hand portion being removed), are to be drawn full size. So commence by placing a sheet of paper on the drawing board and pin it down taut and flat, as explained in Art 37. This being a beginner's exercise, we need not trouble very much about spacing out the views of the block we wish to draw, as previously F FIG. 62. Isometiic view of bench block. 34 MACHINE DRAWING AND DESIGN FOR BEGINNERS explained. M; ,. t I 1 i _!-'- i 21 "13 V M / K The student who has followed the previous exercises will by this time be fairly able to manipulate his instruments correctly, and by the exercise of a ELEVATION . END ELEVATION . little intelligence he will easily draw the plan and elevation of the block ; so, bearing in mind the hints pre- viously given as to which view to draw first, it will be seen that this is a case where the plan should be first set out. Then start by drawing the centre lines jk and cd, intersecting in y (Fig. 63), in suitable positions. The length of the block should be first set out by pricking off yj and yk with a 4" opening of the dividers, the scale being full size. The T-square is then drawn down to about 3^" below jk, and the 60 set- square is placed upon it and brought into position so that the pencil will be in line k. The line is then lightly drawn downward, nearly l to the T- square ; and the set-square is then slid along the T-square, and a line drawn through j in a similar manner. Next prick off with the dividers c and d, 3" on each side of y. The T-square is then raised to the lower mark D, and the finished line DF is drawn carefully, once and for all, between the two vertical lines previously drawn. The T-square is then raised to the upper mark C, and a similar finished line CE drawn through 'it. Then rub out the extra portions of the lines at Next draw the vertical centre line I in of the H SECTION ON LINE H.O. FIG 63. Four views of a cast-iron bench block. CD and EF and rule the vertical lines in, similar to the finished horizontal ones. 1 As we do not know exactly where to stop, we always rule it lightly and too long, and rub out what we do not require after its desired length lias been obtained. This is much better than to rule a line too short, and to join a piece on to make it of the required length, as the joint always shows. HOW TO COMMENCE A WORKING DRAWING 35 hole in the block, which will be 2^" from the centre of the block ; and take the dividers and set them carefully to %", and prick off points in the sides of the square from the intersection of the centre lines of the hole, and pencil in the sides JKLM of the square in the same way as the outline of the plan was done. The elevation may now be proceeded with by first drawing an indefinite line PQ, a suitable distance from CE, and a similar line NO at the top, 4i" from it. The side lines PN and OQ may now be projected from the plan and drawn their finished thickness. The arched opening KT may now be drawn; first mark up centre line ba, the height (1") of the arch above the bottom of the block, and set the pencil compasses to an opening of 2" (the radius of the arch), and describe the arc ET as shown. Then project up the centre line of the hole from Im, drawing no, and making it about " longer top and bottom than the elevation. From J and K in plan project points on to the bottom of the block and line of arch, as LI and MI ; through these points draw vertical finished dotted lines as shown, from bottom to top of the elevation, to indicate the position of the hole. To commence the end elevation project two indefinite lines TJV and WX from the top and bottom of the elevation respectively, and draw the centre line ef in a suitable position. Then mark off 3" each side of this line and draw the finished sides UW and VX, completing the outline as before. To indicate the position of the square hole on this view set off eM and eK, J" each side of e, and draw the dotted lines MM 2 and KK 2 . The dotted line SiS 2 and L 2 L 3 are projected from the elevation, and indicate the position of top of the arch part and the intersection of the arch with the side of the square hole respectively. The section on line no is drawn in a similar way about a centre line gh, the bottom GH being projected preferably from DF of the plan, and the sides YG and ZH from UW and VX respectively. Of course, the height GY is 4", the same as that of the elevations. As we are looking at the section from the left, we shall see the right-hand side of the section. The parts actually cvit through by the section plane should be section-lined as shown, and as described in Art. 39. And the section lines on both right- and left-hand side of the hole should be drawn sloping in one direction only, as it is one piece of metal. The section lines used to indicate cast iron are continuous ones (Fig. 69) ; as shown, they are drawn with the 45 set-square resting upon the T-square. The distance between them, or pitch of the lines, is a matter of taste, and should vary with the size of the part to be sectioned; in this case lines ^th of an inch apart may be used. They can be drawn by judging the distances by the eye after a little practice, or a line can be drawn at right angles to the slope of the section lines, across the figure to be sectioned, and equal spaces set off upon it by ticking them off from a scale of equal parts, or by using a pair of dividers. To finish the drawing, carefully clean off any matter or lines not required, but the centre lines should be left, projecting about |" beyond the boundary of the view they are shown upon. The dimensions need not at present be shown on the drawing. The title of the drawing should be neatly written (printed) by hand, at the top of the drawing, making it clear and brief. >. I /^~^o B If the beginner has any difficulty in realizing what the section on line no, or any other section, shows, he is strongly recommended to make a kind of perspective sketch of the object, somewhat FlQ - &* like that shown at " A " in Fig. 64, or better, if he will take the trouble to cut the object out in yellow soap, or mould it with putly or modelling clay. It need not be to scale, but should be roughly proportionate in size. This model he can cut in the desired position to enable him to realize what shape Ihe section would be. If he uses a sketch, and has difficulty in deciding how the part cut by the section plane will appear, let him place the section line upon his sketch in the desired position, as no. Then rub out the forward portion (that to be removed) up to the section line, as MACHINE DRAWING AND DESIGN FOR BEGINNERS shown at "B," and then try to complete the sketch "B," obtaining the data necessary to enable him to do so from the other views of the object. For instance, knowing the block to be rectangular with parallel sides, he can add to " B " the lines YG and HG, Fig. " C." Then he knows from the elevations that the holo goes right through parallel to the sides, so he can draw the lines KK, and MM,, indicating the cut hole. Of course this is only a sketch, but a student should have no difficulty in identifying it with the section on line no, as given in Fig. 63. 59. To draw a Section of a Wrought-Iron Beam or Joist. Fig. 65 is a finished drawing of the section of the beam, drawn in a conventional way to a scale of one-half full size, and fully dimensioned. After studying the previous exercise, each step the student should take in making this simple drawing should be obvious ; indeed, all that he should require is a hint or two to FIG. 65. W. I. beam. Finished section. -B SECTIONAL WEIGHT PERF1 FIG. 66. Section of W. I. beam. First step. FIG. 67. Section of W. I. beam. Second step. FIG. 68. Section of maximum size standard beam. enable him to go about it in a workmanlike way. The section being symmetrical about a centre line, this line should be drawn first, as ab (Fig. 66), and the rectangular outline of the section drawn as shown in the figure. It will be noticed that the only lines in this figure that can be drawn in a finished state right off are AB and CD. The next step is to describe the arcs, 1 having previously found their centres as indicated at c and d, Fig. 67 (these centres can, with ordinary care and a little practice, be found by trial). The drawing then appears as shown in Fig. 67. All that now remains to be done is to carefully join the arcs aiid complete the outline* with lines of uniform thickness throughout. The figure may now be cross-hatched or section-lined. The conventional lines in this case (as the material is wrought iron) are alternately thick and thin as shown in the Fig. 65. (Refer to Art. 61.) These sections are now standardized. (Refer to Art. 60.) 60. British Standard Beam Sections. The form given to the beam section in Fig. 65 is conventional, it being a convenient oiie for drawing purposes. Formerly there was a great want of uniformity in the relative thickness of flanges and web, and also ' It will be noticed that the radius of the arcs is three-fourths the thickness' of the metal. It should be explained that the actual radii vary with dift'erent makers, and in most cases the flanges are slightly taper in thickness (as shown in Fig. 68) ; but for drawing purposes the above proportions may be used, and the flanges raado of uniform thickness. HOW TO COMMENCE A WORKING DRAWING CAST IRON BRASS WHITE METAL WOOD FIG. 09. Conventional sectional lining for various materials. of the radii of the fillets and edges, to say nothing of the amount of taper given to the flanges; 1 but in 1904 the Engineering Standards Committee published their Report on the Properties of British Standard Sections, 2 in which all the sections commonly used by ship and bridge builders, etc., are standardized. Fig. (i8 gives the standard dimensions for the largest beam section, which is shown here as an example of a standardized section. 8 61. Sectional Shading or Lining for Various Materials. Fig. 69 shows the sectional shading that is very generally used to indicate the materials used in engineering work. They speak for themselves. *62. Drawing of a Stuffing Box Gland. (Scale, full size.) Figs. 70 and 71 show, in elevation and plan, a gun-metal stuffing box gland (fully dimensioned) for a 2" piston rod or valve spindle. 4 In commencing a drawing of these views, the student will first set out the centre lines ab and cd, as the object is symmetrical about these lines. Now, as matter of practice, as has been previously explained, whenever one of two views of a body or part of a body is circular in form, that view should be drawn first. So mark out centre lines for the holes A and B (Fig. 72), and describe the four circles in plan to the dimensions shown, giving the lines their finished thickness. Then, with 1" radius, arcs may be drawn about the centres of the stud holes A and B with a light line, also arc DJ, of 2^" radius, about centre K, then tangents such as CD can be drawn, and the plan completed (as in Fig. 71) by going over the arcs EF and GH, etc., making them uniform in thickness with the other lines. The elevation presents no diffi- culty, and should be easily drawn 3 4 c 1 ; i \ \ ! T P P 1 \ \ I \ 'MOO >-'- i 3 2 ELEVATION. FIG. 70. now. 1 Largely due to the many Continental sections on the market made to metric measure- ments. - Published by Crosby, Lockwood & Son, price 3s. net 3 For further information relating to section of bars, etc., refer to Chapter XI. * For particulars relating to stuffing boxes, etc., see Arts, from 63. 38 MACHINE DRAWING AND DESIGN FOR BEGINNERS At this stage, a good exercise on the above would be to draw a section of the gland made by a plane, cutting it in halves through the line db (Fig. 71). Obviously, its outline would be similar to the elevation (Fig. 70). EXERCISES. DRAWING EXEKCJSE. 1. Make a drawing of the beam section, Fig. 08. Scale, quarter full site. SKETCHING EXERCISES. 2. Show by sketches the sectional shading or lining used to indicate the following materials : cast iron, wrought iron, and steel. 3. Sketch the sectional shading or cross-hatching used to indicate brass, white nietal, and wood. CHAPTER VII STUFFING BOXES, LEATHER COLLARS, ETC. 63. IN cases where a reciprocating or rotating rod or spindle passes through a cylinder or casing containing a fluid, it becomes necessary to use a stuffing box : to prevent leakage of the fluid. Thus, every one is familiar with the stuffing box of a steam engine piston or valve rod, also of pump rods, and possibly, with the stuffing boxes used on the casing of a centrifugal pump where the shaft passes through it. Another interesting application that attention may be called to is the sliding expansion joint of a long steam pipe. In Fig. 73 is shown a sketch of a stuffing box for a horizontal rod, lettered to show suitable proportions of its parts. 2 G is the gland, SS the studs, B the lack-bush or neck-brass (which, made of brass or gun-metal, is softer than the rod, and therefore preserves the latter to a large extent from injury by wear; but when necessary the worn bush is easily replaced by a new one), SB is the stuffing box, and OB oil box. PROPORTION OF PARTS. d = ID + \" with 2 studs. / = l\d to d = ID + i" with 3 studs. g = lid, or l\d with oil box. a = t> + 3d + i" h = a + \" b = D + d + k = 2d. c = fe p = D + 4rf + I" e = 5dto 7d. j = p + 2d + i" It is not practicable to give any very definite rules for the proportions of stuffing boxes, as they differ with circumstances, and some parts do not vary in the same proportion as others ; but the proportions given above may be taken as a guide in cases where the designer has not practical experience to fall back on. In Fig. 74 is shown an ordinary marine type stuffing box (which has been dimensioned for a drawing exercise). The depth of the packing space S, which holds the stuffing, depends upon the pressure of the steam. In this case it has been dimensioned for a pressure up to about 150 Ibs., but for a pressure of about 50 Ibs. it may be made 3" less. 3 Further, it may be explained 1 Invented by Sir Samuel Morton. 2 Most of these proportions are due to Uuwin. 3 Boxes that are not very get-at-able are often made very deep for the pressure they are worked at, so that they might run longer without repacking, and the same remark applies to boxes for valve rods. 40 MACHINE DRAWING AND DESIGN FOR BEGINNERS that it is the practice of some engineers to make the medium-pressure and low-pressure boxes the same depth as the one for the high-pressure rod, for uniformity's sake. It will be noticed that a supplementary packing, P, is used to prevent leakage of oil and water. ORDINARY MARINE TYPE STUFFING BOX. FIG. 73. Stuffing box for a horizontal rod. FIG. 74. 64. Stuffing Boxes with Metallic Packing. The use of high pressure steam in modern practice has been the cause of a good deal of attention being given to the improvement of stuffing boxes. Although some patent vegetable find asbestos packings work very well when in good hands, with proper attention paid to ensure efficient lubrication, too often in vertical engines using high-pressure steam the lubricant only reaches the top layers of packing, keeping them soft, whilst the lower ones get hard and charred. So, for some time metallic packings have been growing in favour where high-pressure steam is used, and, although in the opinion of some engineers they have so far not been completely successful, they bid fair to entirely supersede all others, at least for the high-pressure, and perhaps even for medium-pressure, cylinders. There are a large number of different arrangements in use, differing but little in principle, so the following example should answer the student's purpose. In Fig. 75 is shown the type of stuffing box that important piston- and slide-rods are fitted with in the Royal Navy, the wedge-shaped rings, GM, of gun-metal, and WM, of white metal, in contact with the rod, are made in sections scraped and fitted together, the latter being fitted with springs, S, so that any slackness due to wear in working may be taken up, to prevent movements of rings in the gland, as there is no means of adjustment when under way. Although the metallic packing effectively STUFFING BOXES, LEATHER COLLARS, ETC. 41 ROYAL NAVY TYPE. bears the impact and contact of the hot steam, it generally requires to be supplemented by a few turns of soft packing placed so that it is removed from the destructive action of the high-pressure steam to stay any small leakage of steam which passes the metallic packing. Such an arrangement is shown at SP in this box. The neck and gland bushes are bored large enough to allow the packing to float in the box when slight lateral movements of the rod occur. 65. Soft versus Metallic Packing. No part of an engine requires more careful attention than the stuffing boxes, for if fitted with soft packing they can easily be screwed up until a very large amount of unnecessary friction is the result. They work at their highest efficiency when a faint leakage of vapour is allowed to pass out with the rod ; this lubricates the packing and keeps it soft. The success in the use of metallic packing depends largely upon its being in careful hands after the designer has done his part ; particu- larly is this the case where the pressure on the rings can be adjusted by hand. In the best practice, with excellent workmanship and experienced attendants, it gives little trouble, the wear of the piston-rods being very small. So, for high-pressure it is considered greatly superior to the old- fashioned soft packing, although the first cost is much greater. 65a. Soft Packing for Stuffing Boxes. Any pliable packing that can be used in the packing space of an ordinary stuffing box is called soft packing, although the packing may be metallic, such as the split-rings of coiled copper or brass gauze, invented by Girdwood, for high-pressures. But the ordinary soft packing is spun yarn (a loose kind of hemp rope) steeped in melted tallow, and this can only be satisfactorily used for comparatively low pressures. 66. Leather Packing Collars. For the rams of hydraulic machines, under certain working conditions, the most perfect packing 1 is the \J-leather, or double cup-leather collar (invented by Benjamin Hick, of Bolton, and used by Bramah), which is shown in position in sectional elevation in Fig. 76 ; it is placed either in a groove in the press, as shown, or in a packing box, as shown in Fig. 77. The action is very simple, for when the water enters the press or cylinder it leaks past the part A (Fig. 77), and enters the space S (the hole in the collar is made slightly smaller than the ram, so that it is a close fit, and the outer part also 1 Indiarubber and gutta-percha cups, also lignum vita? and brass spring rings, have been used for packing, but on the whole, when the conditions are favourable, it is found that the leather packing cannot be improved on, particularly when it is of a close-grained flexible qualify, from the mid'lle of the back of the animal. A paper in Cottier's Magazine of July, lllOli, stated that " leather treated with paraffin has given good results. There is no doubt that the method of preparation of the leather is an important factor in its imporviousness to water, and I have within recent years tried Vim leather, which has given better results than any I have heretofore used. The manufacturers of Vim leather claim that their peculiar process of tanning preserves the fibre, and brings the fibre into closer contact. . . . For light pressures the leather is supplied without any filler, but for high pressure the leather is filled with a lubricant which primarily hardens the leather, and renders it more impervious. ... It is claimed that Vim leather will absorb 45 per cent, of lubricant, as compared with 15 per cent, by oak-tanned leather." G Fio. 75. Metallic stuffing box. 42 MACHINE DRAWING AND DESIGN FOR BEGINNERS slightly larger in diameter than the groove for the same reason); the pressure water then forces one part of the collar against the ram and the other against the side of the groove, and the pressure between these parts increases with the pressure of the water, automatically making the friction proportional to the load on the ram, whilst with soft packing in a stuffing box the gland must be screwed down tight to prevent leakage at the highest pressure the machine is worked at, the friction being nearly the same for the smallest load. In the case of a double-acting ram or piston, such as is used in the cylinder of a hydraulic crane, two cup leathers (Fig. 78), are used. One of these leathers is shown in Fig. 80 in sectional elevation. In Fig. 79 is shown a simple cup-leather arrangement which has been found to answer well in hydraulic capstans; and FIG. 80. Cup leather. FIG. 76. Leather collar in groove. FIG. 77. Leather collar with gland. FIG. 78. Piston fitted with cup leathers. FIG. 79. Cylinder (in section) of hydraulic capstan. FIG. 81. Hat leather. in cases where the pressure water acts on one side only. The form of this collar (Fig. 81) resembles a hat, hence its name. It is used for keeping valve spindles and rods watertight. 67. Leather Collar versus Hemp Packing. Leather collars can be efficiently used only when they are not exposed to heat, and when they are effectively lubricated, as they soon become injured if neglected or worked in contact with water charged with gritty matter. Further, it Is not practicable to use them when the ram or plunger cannot be conveniently taken out of the press to renew them. And for this reason they are not used for lift and accumulator rams, which are kept tight by ordinary hemp packing, as most pump plungers are, even where the pressures run up to 2000 Ibs. per square inch, or more. In using hemp packing the gasket of hemp should be plaited very tight and well greased, for if the plaiting be done carelessly portions are liable to be torn off when it is first used and to find their way into the valves. At first the friction with this packing is considerable, but after it has become consolidated the friction is greatly reduced. A slight leak past the packing serves to STUFFING BOXES, LEATHER COLLARS, ETC. w >\ lubricate it. But when the pressure is great and the conditions are favourable for the use of leather collars, no other kind of packing can compare with them, notwithstanding that they are more expensive. 68. Size of Leathers. Mr. Welch, in a communication to the Institute of Mechanical Engineers, 1876, gives the thickness t for U -leather collars for great pressures as t = 0-156rf 028 (1) where d = the diameter of the ram or plunger ; and for the other proportions he gives the depth D as equal to the width W (Fig. 82). But W is more commonly made as small as practicable, and D from I. 1 ,- W to 2 W, although, as the friction appears to be independent of the depth D, and the wear takes place" near the top, it would appear that D is often made unnecessarily large. It also should not be overlooked that the deeper the collar the more the leather is strained in making it. 69. Friction of Leather Collars. No very conclusive experiments on the friction of leather collars appear to have been made since those that were carried out by Mr. John Hick, of Bolton (a descendant of the inventor), many years ago, 1 from which he deduced that if F = the total friction of the leather collar, P = the pressure in Ibs. per square inch, D = the diameter of ram in inches, C = 0'0314 if collars are in good condition and well lubricated, C = 0-047 if collars are new or badly lubricated, Then F = P x D X C . . (2) 7T But the total pressure on the ram = PD 2 ^ So let x = the fraction 'of ram total pressure exerted in overcoming friction then FIG. 82. Proportions of U-leathers. 'J = PDC Hence x = 4C (3) EXERCISES. DESIGN, ETC. 1. A hydraulic ram, 20" diameter, is fitted with a U-leather collar, the water pressure being 800 Ibs. per square inch. Assuming that it is badly lubricated, estimate (a) the total friction of the collar, (b) the fraction of ram pressure exerted in overcoming friction. What would you expect this fraction to be with collars in good condition and well lubricated? 1 For an account of some interesting experiments carried out by Professor Martens, of Berlin, in which he found that the efficiency of leather collars at high pressures is nearly constant, refer to Engineering, Sept. 20th, 1907. 44 MACHINE DRAWING AND DESIGN FOR BEGINNERS SKETCHING EXERCISES. 2. Make a freehand sketch in good proportion of a stuffing box for a 3" horizontal piston rod. 3. Sketch a cast-iron busted gland suitable for a horizontal piston rod. What is the object of making the gland of cast iron ? 4. (a) Sketch a stuffing box for quite a small valve spindle, (b) A gland suitable for vertical stuffing box. 5. Sketch an ordinary marine type stuffing box. G. Make a sectional sketch of the Royal Navy type of metallic stuffing box. 7. Make a bold sketch of a U-leather for a hydraulic press. Show how the collar is got into its groove if the press is not fitted with a gland. 8. Sketch a packing box fitted with a hydraulic hat leather. 9. Show by a sketch how small pump plungers are kept water-tight by leather packing. DRAWING EXERCISES. 10. Make half-size drawings of the stuffing box (Fig. 73) for a 4" piston rod. 11. Make working drawings of the ordinary marine type stuffing box, shown in Fig. 74. Scale 3" = 1'. CHAPTER VIII SHAFTING, CRANK SHAFTS, CRANKS, JOURNALS, ETC. 70. Shafting, its Strength, etc. Every young engineer knows that a bar arranged to rotate about its axis, and in so doing to convey or distribute motive power, is called a shaft, and that shafts are supported by and rotate in what are called bearings, the supports of vertical shafts being either footstep or collar bearings. He also knows that the parts of the shaft which fit in the bearings are known as journals. And that when a shaft is too long to be made in one piece, or when it is necessary to connect two shafts or lengths of shafting together (ordinary mill shafting being made in lengths not exceeding 20', and in diameters which advance by quarters of an inch), a coupling is used. Now the journals of a shaft are always circular in section, but the shaft or axle, 1 although its most economical section (the one that is always used by preference for the simple transmission of power) is circular, may be made square, or some other section to meet the requirements of a particular case. 2 Now the exigencies of space forbid our going into these matters in such a way as to prove the truth of every equation used, so that the beginner without some previous training in practical mechanics, or the assistance of a teacher, could follow it ; and, this being so, frequent reference will be made in foot-notes to such books as students will either possess or have the use of, so that they may plod through their difficulties if the assistance of a teacher is not available. In calculating the diameter of a shaft the simplest cases that occur are the following : () Shafts that Transmit a Uniform Twisting Moment or Torque, 3 and are so short that the bending action due to their own weight can be neglected. In these it is only necessary to equate the torque (twisting moment) to the moment of resistance to twisting. (&) Shafts where Combined Torsion and Bending occur, the bending being due to their own weight, to the thrust on a crank, or the weight of wheels, the pull of belts, etc. 71. Case (a). Torsional Strength of a Shaft Transmitting Uniform Torque. In books on practical mechanics it is proved 4 that if d = the diameter of the shaft in inches, T = the twisting moment or torque in Ib.-inches, as measured in either of the Figs. 83, 84, and 85, f s = the maximum shear stress the shaft is subjected to (called skin stress), X = Number of revolutions per minute, 1 The term axle is frequently used when it would appear that thaft would be more appropriate, but it is not easy to lay down any fixed rule in this matter, as the terms are rather indiscriminately ueed, although, strictly, the term should only be used for shafts subjected to bending only. 2 As for example, in some motor gear shafts, along which the change wheels are moved. 3 This term is now commonly used as a synonym of twitting moment. * In Lineham's " Mechanical Engineering," p. 417, there is a simple proof. 46 MACHINE DRAWING AND DESIGN FOR BEGINNERS Then the twisting moment T = modulus of section for torsion x f s Thatis T = rf3 iV' = M ' ' ' ' 3 /R-Tr A J 7 / J JL-L And .'. d = A/ -^ Ji K.11 also 51T (5) (6) 72. EXAMPLE. A short wrought-iron shaft is to transmit a uniform torque of 20,000 Ib.-ins., and the skin stress /, has been fixed at 7500 Ibs. per sq. inch. Find its diameter. By equation (5) d = V /5>1 *~ = 2"386 Am. d = 2-386", say 2J" the nearest |" 73. Case (ft). Combined Torsion and Bending, the Twisting and Bending Moments unvarying. The counter-shaft (Figs. 86 and 87) shows an example of this kind, when used to drive a machine of uniform resistance. I. M V////A N f f Y/////M R 1 1 RJJ * FIGS. 83, 84, 85. Measurement of twisting moment T. |T, + t, FIG. 80. Let T = Twisting moment in inches and pounds. B = Bending moment in inches and pounds. T<, = An equivalent twisting moment, equal in its effect to combined twisting and bending. B,. = an equivalent bending moment, equal in its effect to combined twisting and bending. Now, most students know how to find the greatest bending moment, B (which of course is either at M or N), in such a case as SHAFTING, CRANK SHAFIS, CRANKS, JOURNALS, ETC. 47 the above, where the positions of the pulleys in relation to the bearings and the tensions of the belts are known. Obviously, the twisting moment, T, equals (Tx d.+ O39", but two smaller ones, as shown at P, are better, as they do not weaken the part between the pin and shaft. 82. Petrol Motor Crank Shafts. The stages in the manufacture of a slofcted-out motor-car crank shaft are shown in Fig. 96 (taken by kind permission from Messrs. Willans and Eobinson's pamphlet), but the operations vary little in the manufacture of this type of \Z II 10 19 18 _i7 |6 |5 .4 |3 2 .1 |0 lnr.he.fj I I I I I I I I I I I ll I I I I I I I I f I "F ot. " 7 si- Thickness of Arms 2". FIG. 96*. Petrol motor crank shaft. Offset type. shaft, whether it be for a marine or motor car. The drawing should speak for itself. The greatest care need be exercised in selecting material for crank shafts, but this particularly applies to motor-car work, where the dimensions must be kept down, and, therefore, in the best practice no expense is spared to secure material of the very highest quality. Experience has proved that one of the finest steels for this purpose, if not the finest, is oil-tempered vanadium steel, which shows a unique combination of high static strength (and especially a high yield-point) with high resistance to shock and fatigue ; indeed, it is claimed for it that it is the best steel yet produced for dealing with the severe strains 1 to which crank shafts are subject. 83. Petrol Motor Crank Shaft (Drawing Exercise). We have shown in Fig. 96A a petrol motor crank shaft of the offset type. It is fully dimensioned and may be drawn to a scale of half full size. ' The crank shafts of internal combustion engines during the suction stroke of the piston are subject to a reversed torque. 54 MACHINE DRAWING AND DESIGN FOR BEGINNERS EXERCISES. DESIGN, ETC. 1. A shaft of 15" diameter is fitted with a crank of 40" radius in such a way that the bending action may be neglected. The maximum thrust on the crank end is 149,000 Ibs. Find the skin stress of the shaft. Ans. 9000 Ibs. per sq. inch. 2. A steel shaft of a crane transmits a torque due to a force of 2 tons acting in the pitch circle (36" diameter) of a wheel fixed to it, and the maximum shear stress is 9500 Ibs. per sq. inch. Find the diameter of the shaft. NOTE. Crane shafts, being very short, are usually designed for strength alone, and not torsioual stiffness. The wheel being close to the journal, neglect effect of bending action. Am, d = 3'51, say 3J". 3. The driving ptilley of a machine is 30" diameter, and the effective tension of the belt is 150 Ibs. What horse-power is given to the machine when the pulley makes 120 revolutions per minute ? Arts. H.P. = 4$. 4. The upright shaft of a turbine transmits 30 H.P. at 250 revolutions per minute, and the skin stress is 10,000 Ibs. per sq. inch. Find the diameter of the shaft. Am. d = 1-56", say If. 5. The trunnions of a mixing machine have an effective length of 10", and the weight which comes on each one is 1J tons. What should their diameter be if the skin stress is not to exceed 5500 Ibs. per sq. inch ? NOTE. In this arrangement you are to assume that the trunnions are only subjected to bending. Am. d = 3-145", nay d = 3J". DRAWING EXERCISES. 6. Make a set of drawings of the built-up crank (Figs. 92 and 93). Scale 1" = 1'. SKETCHING EXERCISES. 7. Make a sketch , fixed at right angles to each other ; one of these is usually either a saddle key, or a key on the flat, whose function is to cause the shaft to be gripped in three places, and so prevent rocking on the shaft. 98. Key Boss. In heavy work the weakening effect of the keyway in the boss of a wheel cannot be neglected, so the thickness, t, of the boss is maintained, or slightly increased, as shown in Fig. 124, by arranging what is called a key boss, AB. The drawing should speak for itself. 99. Staking On. In Figs. 125 and 126 are shown two examples of what is called staking on. Should the solid boss of a wheel have to be passed over an enlarged end of a shaft, it is usual to fit it to the shaft by using four keys bedded on flats on the shaft, 1 as in Fig. 125. Where the strains are very great, and the shaft is square, Fig. 126 shows the most reliable way of fixing a wheel. Four temporary keys are first fitted in the spaces, K, and the wheel truly centred, after which the permanent keys are accurately fitted. Only those parts on which they bed need be machined. The keys are numbered and marked, so that the job can easily be re-erected. 100. Cone Keys. For light work, where a frictional drive is practicable, instead of staking a wheel on a shaft, as explained in the previous article, cone keys may be used. The three keys are cast in one piece, with wrought-iron dividing plates ; they can be bored to the size of the shaft, and turned with the usual key taper to fit the hole in the pulley boss, before parting them into the three pieces, which, after trimming, are ready for use as saddle keys, as shown in Figs. 127 and 128. 101. Pins. For light work it is often convenient to use taper pins, instead of ordinary keys. Thus, in Figs. 129 and 130, the boss of a lever is shown pinned on to a shaft or spindle. The holes, after drilling (for all such pins), should be rimered out to a total taper of i" in 1', and the mean' diameter of the pin, d, may be 1 D. In Fig. 131 a small pulley or hand-wheel is 1 For light work, cone keys are used in this way. (Art. 100.) KEYS AND PIN KEYS, ETC. 65 shown fixed this way, but in this case the hole can only be drilled on the slant, as shown. When the materials of the boss and shaft are the same, or very nearly alike in character and hardness, they can be drilled for the reception of a cylindrical pin, as KEY BOSS. FIG. 124. STAKING ON. CONE KEYS. FIG. 125. FIG. 126. FIG. 127. FIG. 128. in Fig. 132 ; the diameter, d, of the pin may be -J- D to \ D, according to the length of the boss. In Figs. 133 and 134 are shown two lengths of pipe, connected by taper pins and a dowel. This is a joint which is largely used for railway signalling APPLICATIONS OF TAPER PINS. FIG. 129. j FIG. 133. FIG. 130. FIG. 131. FIG. 132. FIG. 134. rods, which are alternately in tension and compression, also for ventilating machinery, the rods transmitting a twisting n/tirirm 66 MACHINE DRAWING AND DESIGN FOR BEGINNERS The following Table 1, gives the standard dimensions for taper pins : TABLE 1. STANDARD TAPER PINS. Taper J" per foot. No. of pin. Tutsi length of pin. Largest diameter of pin. Smallest diameter of pin. No. of pin. Total length of pin. Largest diameter of pin. Smallest diameter of pin. Inches. Part of an inch. Part of an inch. Inches. Part of an inch. Part of an inch. 1 0-156 0-135 6 3-25 0-341 0-279 1 1-25 0-172 0146 7 375 0-409 0-331 2 1-5 0-193 0-162 8 4-5 0-492 0-398 3 1-75 0-219 0-183 9 5-25 0-591 0-482 1 2 0-250 0-208 10 6 0-706 0-581 5 2-25 0-289 0-240 102. Feathers. When a wheel or some part of a machine is to be secured to a shaft, in such a way that it must rotate with it, but is free to be moved in the direction of the axis of the shaft, a feather is used. Now, this feather or sliding key is a parallel strip which is usually fixed to the shaft, the groove in the wheel boss or sliding piece being made a working fit. Or, alternatively, the feather is fixed to the sliding piece, and slides in the feather way of the shaft. Figs. 135 and 136 show one arrangement of the former, the feather being very slightly dovetailed where it fits the shaft, and the metal of the shaft each side of it being lightly caulked down to secure it. Figs. 137 and 138 show an alternative way of fixing the feather by two countersunk screws, as at A (one only shown), or by forging on the feather two pins to pass through the shaft with countersunk riveted heads, as at B (one only shown). VARIOUS FORMS OF FEATHERS. 1 BI t- 1 ._j_ j L I -1- - , 1 i 1 I 1 FIG. 135. Fio. 136. FIG. 137. w^sws Fio. 138. FIG. 139. FIG. 140. FIG. 141. Figs. 139 and 140 show the feather fixed to the boss by dovetailing, the feather being a driving fit in the boss, whilst Fig. 141 shows how it is fixed by two screws through the boss. Sometimes by forging two pins on the feather it is fixed to the KEYS AND PIN KEYS, ETC. 67 VARIOUS FORMS OF FEATHERS. p JQ FIG. 143. FIG. 144. boss by riveting, in a similar way to that shown at B, Fig. 138. Other alternative arrangements are shown in Figs. 142, 143, and 144. In Fig. 142 the feather is made with a lug, F, which is attached to the side of the boss by means of a screw. To make a job of this the workmanship must be very accurate. Figs. 143 and 144 show loose feathers fitted to the bosses; in the former the feather is made with a projecting pin, which is placed in the hole to prevent any end movement, and the same purpose is served by the gib-heads of the feather in the latter. In both of these the shaft must admit of the boss and feather being passed over its end. 103. Strength of Keys. When keys are made in accord- ance with the empirical proportions 1 marked on Figs. 118 to 123, they very rarely give trouble or fail unless they are made exceptionally short in proportion to their other dimen- sions. Nevertheless, as cases occur (particularly with large crank shafts) where the part secured by the key takes off only a small proportion of the power transmitted by the shaft, it will be instructive to show how they should be treated, with the help of Fig. 145. Now, let L = length of the key. B = breadth T> t = mean thickness = -g f s = safe shear stress of shaft per square inch. /,' = safe shear stress of key per square inch. f c = safe compressional stress -of key and shaft per square inch, say = 2/ s . F = safe shear force acting on key = LB/,'. F = also safe load in compression on sides = / T = moment of resistance to twisting of shaft = d 3 y^/ = also -=- Then, if the crushing resistance of the key is to be equal to its shearing resistance, ~L\tf c = LB/,', that is B/, = tyfc. But ft may equal 2 x /,', therefore, the key to be equally strong to resist crushing and shearing would have to be square, which is about its section 1 The following proportions of sunk keys are recommended by Box : where D = diameter of shaft, B = the breadth of key, T = thickness of key, d = depth sunk in the shaft measured at the side of the key, then B = (D -=- 4) + 0-125, T = (D -i- 11) + 0-16, and d = (D -i- 40) + 0-075. FIG. 145. Shearing resistance of keys. 68 MACHINE DRAWING AND DESIGN FOR BEGINNERS when it takes the form of a feather, and is not a tight fit top and bottom. But for ordinary keys we have seen that B = 2t, and, if the full strength of the shaft is to be transmitted by the key, we must not overlook the wedge action, which considerably relieves the sides of the crushing effect. Hence it is usual in designing a special feather to take into account the crushing effect, but in dealing with a key to take into account its shearing resistance. So, let us assume that we wish to determine the length L of the key shown in Fig. 145, in terms of the other quantities, where t = mean thickness and the materials of the key and shaft are the same, that is/, = /,'. Then for equal 1 strengths of shaft and key Or, when the shaft and key are of the same material, we have L = ^ ................. (17) oi> 104. EXAMPLE. The full strength of a 3" steel shaft is to be transmitted through a steel key. Find the dimension of the key. From the empirical proportions, Fig. 122 and 123 Then by (Eq. 17)- ~ L - = = 4-04 Ans. L = say, 4" EXERCISES. DESIGN, ETC. 1. The coupling of a 4" steel shaft has to transmit the full strength of the shaft. What should be the dimensions of a steel key for this purpose ? 2. A 12" lever is fixed to a 1J" shaft by means of a taper pin passed through its boss, as in Figs. 129 and 131), the mean diameter of the pin being I". What pull on the end of the lever would cause a shear stress on the pin of 9000 Ibs. per sq. inch ? and what skin stress in the shaft would this correspond to ? 3. A treadle lever 30" long is fitted to a break shaft 1J" diameter, the maximum load on a treadle being 200 Ibs. A key f s " wide is used to fix the lever to the shaft. What should tlie length of the key (and that of the lever boss) be, if the shear stress is not to exceed 8000 Ibs. per sq. inch ? 4. A lever is fixed to a 2" shaft by a taper pin, as in Figs. 129 and 130 ; the mean diameter of the pin is J". Find the ratio of the shearing stress of the pin to the skin stress of the shaft. 5. A lever is fixed to a 3" shaft by a taper pi a, as in Figs. 129 and 130, and the skin stress of the shaft is the same as the shear stress on the pins. What must be the mean diameter of the pin ? 1 After looking through the above, the case where those strengths are unequal should be easily worked. Obviously the strength of the key is proportional to its length. KEYS AND PIN KEYS, ETC. 69 6. An inch pipe has an outside diameter of !.", and it is arranged as a shaft, with a lever fixed to it, as in Figs. 129 and 130. What should the size of the pin be if its shear stress be 50 per cent, greater than the skin stress of the pipe ? SKETCHING EXERCISES. 7. Show by sketches three different ways of keying wheels to a shaft, and explain under what conditions each would be used in practice. 8. Show by a sketch how the boss of an important wheel is strengthened where the keyway is cut by a key boss. 9. Make sketches showing how wheels are staked on to round and square shafts. Under what conditions is staking on necessary? 10. What are the conditions which allow a wheel to be fixed to shaft by cone Tteyil Make a sketch of the arrangement. 11. Levers, hand-wheels, and small pulleys are sometimes pinned on to a shaft or spindle. Show two ways of doing this. 12. Lengths of metal tubing are sometimes connected by a dowel and taper pins. Show how this is done, and mention any application of this joint you are acquainted with. 13. What is a feather? In what important respect does it differ from a key? Sketch three or four characteristic examples at feather*. CHAPTER XI RIVETED JOINTS 105. ONE of the most simple and efficient fastenings, which has been extensively used for a great variety of purposes from very ancient times, is the rivet. As a fastening, it somewhat resembles a bolt, but ditfers from it in two important respects ; for a bolt can be used as a temporary fastening, and can be withdrawn by unscrewing the nut ; but a rivet is a permanent fastening and the parts held together by it can only be separated by chipping off a head. Further, a bolt is used satisfactorily when the straining force acts in the direction of its axis, giving it a tensional load, but it is not considered safe to load a rivet in this way, its proper function being to resist shearing in a direction normal to its axis. Rivets are made in special machines, from special round iron or steel bar, 1 with heads either cup-shaped, as in Fig. 146, or pan-shaped, as in Fig. 147, formed while red hot by dies of these shapes, and their finished forms before use (showing the length of rivet required to form the head) are shown by the dotted lines. In riveting plates, whenever practicable, riveting machines are used,: the rivet is made red hot, passed through the plates and pressed between two dies by hydraulic or steam pressure. The heads are then usually made cup or spherical shaped, as in Fig. 146, and are said to be machine riveted. When machines are not available, the rivets are hand riveted. For this job a full gang consists of three men and a boy, the latter to heat the rivet and bring it from the furnace to the holder up, who inserts it into the rivet hole and presses against the rivet with a tool called a dolly, cupped to receive the head of the rivet, while the other two men on the opposite side hammer the other end down with riveting hammers and finish it off by a blow or two from a sledge hammer, a snap- headed tool being interposed to give the head the cup shape in Fig. 146. In confined positions where it is not possible to snap the heads, they are finished by hammering 2 to the conical or conoidal form shown in Fig. 148, which has not quite the strength of the cup head. In many classes of work, such as the skin of ships, 3 the seatings of girders, etc., the heads must not project; the plates are then countersunk, as shown in Fig. 147 (which shows a full counter-sunk head), and the heads finished off flush with the plate, or with a slight fulness or projection, as shown dotted. Fig. 149 shows a form that is sometimes given to this head to prevent its sharp edge springing away from the plate. Fig. 151 shows the half-countersunk head. Fig. 150A shows how, by slightly counter- sinking the holes, the head can be a little strengthened ; it is usual to somewhat reduce the size of the heads, as shown, when this is 1 See Art. 106. 1 Rivets up to 1" or 1}" in diameter may readily be closed with hammers of 8 to 10 Ibs. weight ; but if the head is to be formed in a die or swage, a heavier hammer, say 16 Ibs. weight, is necessary. Skilful riveters on bridge work can rivet up from 200 to 250 per day when the size is jj", and from 90 to 100 if 1". On vertical members about 75 per cent, of these may be done, and for boiler work about twice as many. ' Lloyds' Registry have fixed the size and shape of rivet heads for this purpose for diameters from j" to 1J". RIVETED JOINTS 71 done. For drawing purposes an approxi- mation to the ordinary cup head is easily made by using a radius of | the diameter, as shown in Fig. 150A, and striking the head from a point on the centre line ^D from the shoulder. 106. Proportions of Rivet Heads, etc. These proportions vary somewhat in prac- tice, as they have not yet been standardized, 1 but those shown on Figs. 146 to 150 may be taken to be average ones ; they are in terms of D, the diameter of the hole. The dotted lengths for forming the heads should be taken to be approximate. They vary from 1'25 to 1'7 times the diameter, the actual length required depending upon the completeness with which the rivet tills the hole, and upon whether the head is formed by hand or by machine ; the former requires about JD less length than the latter, as the machine compresses and swells the rivet till it completely fills the hole, thus making a very perfect job. 2 Great care must be taken in dealing with long rivets, as when they are some 6 1 In some firms it is the practice to make the rivet diameter for sizes above |" smaller than the holes by ,'B". 2 Muchinu work has been for some years largely superseding hand riveting. The machines perform their work much more rapidly and economically. They were first used for bridge work on the famous I'onway Tubular Bridge. Rivels can only be made to solidly fill the holes by freeing them from the oxide and slag, which can be done by heating them to a bright red singly, and passing them through a fine spray of water, the chilling action causing the slag and oxide to shell off, leaving a peifectly clean rivet. PROPORTIONS OFRIVETS,ETC. 148. CONOIDAL HEAD 146. CUP OR SNAP HEAD. 147. FULL COUNTERSUNK HEAD. HAMMER FINISHED. I50A. PROPORTIONS FOR DRAWING PURPOSES. K-I-S2 149. FLUSH COUNTERSUNK 150. SNAP COUNTERSUNK LSI. HALF COUNTERSUNK HEAD 72 MACHINE DRAWING AND DESIGN FOR BEGINNERS to 8 diameters in length, they often contract enough to draw off their heads, so, to avoid this in very long rivets, the head end should be cooled before placing the rivet in its hole. 107. Rivet Materials, etc. With iron plates, soft ductile iron of a strong, tough, good quality, with a tensile strength not exceeding 54,000 Ibs., and giving an elongation of not less than 25 per cent, in 8" is used for the rivets. Formerly such iron for rivets was largely used with steel plates, but there is now no difficulty in getting a soft low-carbon steel suitable for rivets, with a tensile strength not greater than 54,000 Ibs. per square inch, and an elongation in 8" of 30 per cent., and such rivets are generally used now with steel plates. And for boiler purposes the Board of Trade is satisfied with steel plates of an ultimate tensile strength / ( of 28 tons per square inch, with an ultimate shear strength f, of 23 tons per square inch for rivet steel. 108. Drilling and punching Rivet Holes. Many years ago the general practice was to punch all rivet holes for girder, bridge, and boiler work, with the result that the spacing and alignment of the holes were very imperfect, 1 and this want of accuracy became more pronounced when two plates, each with a row of punched holes, were brought together to be riveted, and led to the objection- able practice of more or less forcing the holes into agreement by hammering a conical drift into them ; even then a fairly large proportion of the rivets would be forced into position in such a way that their sectional area was materially reduced at the joints just where the shear occurred. But the use of multiple-drilling machines and high-speed tool steel has enabled engineers in increasing numbers to considerably reduce this evil by drilling the plates, and it looks as though the barbarous practice just referred to, if not punching generally, will be almost or entirely superseded. Certainly, in the best boiler work all the holes are drilled, and most of them when the plates are together in position. It should be further explained that when plates are punched, particularly steel ones, the metal round the hole is injured by the lateral flow of the metal under the pressure of the punch. This injury, however, may be entirely removed in either of two ways, for if the plate is annealed after punching it is restored to its original condition, or, if the hole is punched j 1 ,;" smaller than is required and rimered or drilled out to size, the injured material is removed 2 and the plate is ready for use. 109. Caulking and Fullering. Joints in boilers, tanks, etc., are made fluid-tight by caulking. Fig. 152 shows how this is ordinarily done; T being a narrow, blunt chisel-like tool, called a caulking tool, about j\" thick at the end and 1|" in breadth, the edge ground to an angle of 80. It is moved after each blow along the edge of the plate, which is usually planed to a bevel of about 75 to 80, to facilitate the forcing down of the edge. It will be seen that the tool burrs down the plate at B, forming a metal-to- metal joint, care being taken not to damage the plate 3 below the tool, or spring the joint open. Usually both edges A and B are caulked, and the rivet heads also, if they leak, as at C. Fig. 153 shows how, in certain classes of boilers, the nipple or tube connections are caulked with a similar tool. A more satisfactory way of making the joints staunch and tight, known as fullering, which has largely superseded caulking, is shown in Fig. 155. The fullering tool, having a thickness at the end equal to that of the plate, is used in such a way that the greatest pressure due to the blows occurs at A, near the point, giving a clean finish, with less risk of damaging the plate. Fig. 154 shows a tool introduced by Mr. Webb, which combines features of caulking and fullering. 1 The late Mr. J. Stansfield devised a multiple-punching machine, which he most successfully used in the construction of the flouting docks designed by his firm. ' The great bridge which spans the Hooghly, made on the Thames some years ago, had the rivet holes for it, over a million in number, treated in this way. 3 Too often this work is done by untrained youths, who are apt to bungle in overdoing a job that requires mucli care und not a little skill, if the efficiency of the joint is not to be impaired. RIVETED JOINTS 73 109a. The sections of wrought iron and steel rolled bars, 1 etc., used by the engineer are shown in Figs. 156 to 168, which should speak for themselves. FIG. 152. Ordinary caulking. Fio. 153. Caulking boiler connections. FIG. 154. Combined caulking and fullering. FIG. 155. Fullering. SECTIONS OF WROUGHT IRON AND STEEL ROLLED BARS. SQUARE FLAT ROUND CHISEL HIGHBACK FIG. 156. Sections of rolled bars. *a-ar U- ^ft IEQUAL IUNEQUA mm BANGLE ANGLE GHBACK ^^^ ^^i FIG. 157. FIG. 158. FIG. 159. Tee. FIG. 160. Channel. FIG. 161. Zed. FIG. 162. Bulb plate. d+3 w 9t^ l-Sf iza Arafe&jsss HW "W 2 it\ i 9 - /= W (the width of the angle 1 When the angle bar is in the form of a ring, it must be of very good quality to stand bending and welding. 2 As far away from the thin edge as practicable. Usually, the front end is first riveted to the shell, the back end is afterwards offered on and the rivet holes marked. This enables any slight creep that may have occurred in building up the shell (and perhaps'lengthening it ,'/') to be dealt with without putting an initial strain on the end plate. FIGS. 192 and 193. Single and double riveted lap. FIGS. 194 and 195. Double riveted lap and treble riveted butt. 0' TNI UNIVERSITY OF RIVETED JOINTS 79 ring), but generally it has to be nearer the centre of y. Fig. 198 shows how, by flanging an end plate, the angle bar can be dispensed with, but only plates of very good quality can be thus flanged, particularly to a small radius. The radius of the inner surface JUNCTIONS OF PLATES AT RIGHT ANGLES. FRONT END OF BOILER BACK END OF BOILER FLANGED END PLATE , AND SHELL. AND SHELL. BOILER END, FLANGED END PLATE. BOILER END, BOILER ENO, FLANGED END PLATE 4 FLUE. CORRUGATED FLUE. CORRUGATED ' FLUE NGCD END PLATE/ FIG. 201. '" ^ \J_^ ~ N^l-/ FIG. 196. FIG. 197. FIG. 198. should not be less than 4<, but in exceptional cases it is made as small as 2. Figs. 199 and 200 show how boiler flues are FLUE CONNECTIONS. TEE RING. FLUESTIFFENING RINGS. ADAMSON'S RING -A PAXMAN'S JOINT FIG. 202. FIG. 203. FIG. 204. FIG. 205. Fio. 20G. FIG. 207. FIG. 208. connected to end plates, the former the oldest, and probably the best, connection. When the end is flanged, as in Fig. 200, the 80 MACHINE DRAWING AND DESIGN FOR BEGINNERS root of the flange is often too weak to bear the strains arising from the expansion and contraction, and sooner or later grooves and becomes fractured. An additional angle plate, giving two thicknesses at the flange, has been tried, but without success. So, on the whole, makers have found that the old rings, which are strong, and easily made and repaired, are the best. The connection of flue to the end plates is usually the same at both ends, and Fig. 201 shows the connection of a corrugated flue to a flanged end plate. llOf. Flue Connections. Fairbairn's experiments show that the function of a flue joint should be to connect two sections or lengths of a flue in such a way as to give it longitudinal flexibility and circumferential rigidity, and Figs. 202 to 205 show some typical flue connections, but Fig. 202, the Tee Ring, is too rigid longitudinally for ordinary plain flues, and the rivet heads are exposed to the fire, as they are in the Bowling Eing or Bolton Hoop, Fig. 203, which has the advantage of being very flexible longitudinally. 1 Adamson's joint, Fig. 204, is a good one, being very rigid circumferentially, it has a proper amount of flexibility longitudinally ; the ring plate A (about |" to J" thick) projecting a little beyond the flanges for caulking purposes. Fig. 200 shows how this flue is connected to the end plate. In the Davey-Paxman joint, Fig. 205, there are rivet heads inside the flue, but they are clear of the run of the burning gases. When a flue section is very long, it may be stiffened either by an angle ring, or solid ring; the former (shown in Figs. 206 and 207) is kept clear of the flue by distance pieces D, and riveted to the flue ; the pitch of the rivets being about 7". Fig. 208 shows the latter arrangement, with a solid ring instead of the angle ring. There are several variations of the above to be occasionally met with. llOg. Connecting Parallel Plates. The lower part of the fire-boxes of vertical boilers, locomotives, and certain other boilers, are connected to the external shells as shown in Figs. 209 to 212. The simplest and most popular, particularly for locomotives, is 209 ; it is easily riveted and caulked. This joint is also used round the opening for the furnace door. In Fig. 210 a channel iron is used, but this requires the finest material and workman- ship to forge the corners, and the rivets are not so get-at-able. The principal objection to the Z-bar in Fig. 211 is that the inner rivets cannot be caulked. Fig. 212 is much used for vertical boilers, but is unsatisfactory, as the sediment lodges in the recess S and causes corrosion. llOh. Strength of Riveted Joints. Let us first consider what may happen if we take a simple joint, such as the single riveted lap of Figs. 170 and 172, and assume that it has been tested till it fails. For this purpose we may deal with a strip representing a length of the joint equal to the pitch of the rivets, and it will be convenient in working examples to assume that we are dealing with steel plates, and rivets of a quality generally used for boilers. Other values from the Tables can be substituted as required. Then Let p = pitch of rivets. S = strength of a strip of the joint of length p. 1 Notwithstanding the exposure of the heads, some engineers, on the whole, prefer this joint to Adamson'e. FIRE-BOX CONNECTIONS. UlJg Fio. 209. FIG. 210. FIG. 211. Fio. 212. RIVETED JOINTS 81 Let d n = diameter of rivet before riveting, or nominal diameter. d = diameter of rivet after riveting. ft = tensile strength of material of plates per square inch = 28 tons for steel. f s = shearing strength of rivets per square inch = 23 tons for steel. 1 f c = crushing strength of plates and rivets at the hole = say, 46 tons per square inch. t = thickness of plates. ,, (| = efficiency of joint. The joints may fail (a) By rivet shearing, as in Fig. 213. FAILURES OF RIVETED JOINTS. A Qf Then S = d^f f and /, = ^ as the rivet is in single shear. (ft) By the tearing of the plates between the rivets, as in Fig. 214. Then S = (p - d)tf t , and /, = _ (e) By the plastic flow of the material of the plate or rivet under compression, as in Fig. 215. a Then, 2 S = dtf e , and / = T -PITCH- Js FIG. 213. PITCH- MAR PITCH- FIG. 214. FIG. 215. |s FIG. 216. (d) By the plate breaking in front of the rivet, as in Fig. 216. This rarely happens, as, when the distance of the edge of the plate from the rivet, called the margin, is equal to d, there is an abundance of strength. 3 As a rule, when a joint is tested to destruction, it fails either as in (a) or (ft), so, when these are equal in strength we have Whence, f. = (p - ird?f p = -rri' + d for single riveted lap joints (18) 1 Allowed by Board of Trade. A treble riveted lap-joint, d = 0'95", t = 077", failed by rivets shearing, giving /, = 23-0 and/, = 28'6 (plate and rivets of steel), when tested by Kirkaldy. 2 The area of the plate resisting the pressure of (lie rivet is the projected area of the rivet, namely dt. 3 Considering the plate in front of the rivet as a short beam of length il, depth M, and breadth t, encastre at the ends, and equating the shearing strength of rivet to the bending strength, M = !,d nearly, where M is the margin. M 82 MACHINE DRAWING AND DESIGN FOR BEGINNERS 1101. EXAMPLE. What should be the pitch of a single riveted lap joint with steel plates and rivets, d = |", and t - *" for equal strength in shearing and tearing ? Also find the efficiency of the joint. 22 X 9 X 23 3 _ ^ E 1- < 18 ) P = 28 X 16 X | X 28 + 4 = 172 Ans. p = 172" or If" bare. (In practice this would be made I}".) sec. area of plate at rivet (p d)t p d Efficiency of joint = - - = -^ L . -*L- . ........ nSA 1 ) sec. area of strip ft p 1-72 - 075 .-. j) = -- -- ---- = 0'564 or D(r4 per cent. 1*7^ 111. Maximum Value of d in Eelation to t. Crushing Action. When joints fail by crushing, as in Fig. 215, the crushing stress has been found to be both high and irregular, but the usual practice of taking it to be about twice the shearing stress appears to be a safe one for ordinary purposes. That is, f c = 46 tons per square inch l for boiler steel. In the case of boilers, the greatest stress on the bearing surface will occur during a hydraulic test, and this will seldom reach one-third the ultimate strength, 2 so, probably, joints as they are ordinarily made are not much injured by compression, unless the stress gets rather near the ultimate strength. Indeed, this seems to be borne out by the behaviour of joints that have been tested to destruction. f 2 So, if the ratio J ~ = - , as we have seen it may do, then, if the shearing strength is to equal the resistan- e to crushing / * d??f t = dtf c , whence d = -$*- or (the maximum value of d in terms of t is) d = 2'54 ................. (19) A larger rivet will crush, and we can infer that the crushing effect need not be considered when in lap joints d is less than 2 - 54, as it usually is. Now, if we had been considering a rivet in double shear, as those are in Fig. 183, then we should have to remember that the strength of a rivet in double shear is not quite twice that of one in single shear. 3 The Board of Trade consider 175 should only be taken ; so, following this rule, the above equation becomes l-75d" |/. = dtf t , whence d = or (the maximum diameter d in terms oft for double shear) d = 1'455< ................. (20) 1 In the case of boilers, with a factor of safety of 4}, this amounts to the working value of/, being 10 tor a per sq. inch nearly, which in the opinion of some engineers should not be exceeded ; indeed, 8 or 9 tons only is usually allowed in bridge work. * The testing pretsure used by the Boiler Insurance Companies ranges from 1J to 2 times the working pressure. 3 This is probably due to absence of absolute symmetry about the line of force in the joint, and to the want of absolute uniformity in the quality of the materials. RIVETED JOINTS A larger rivet will crush, and, therefore, on these lines the enishiny effect need not be considered when in butt joints d is less than 1'455. 112. Best Diameter of Rivet in Relation to Thickness of Plate. It can be easily proved that if the d be less than t there will be danger of the punch crushing, so this consideration alone would limit the smallness of all punched holes in relation to the thick- ness of the plates, but it is a Board of Trade rule that d shall not be less than t, and if this condition be satisfied the relation of d to t is to some extent arbitrary and may be varied considerably within certain limits, experience dictating what is expedient in different thicknesses and classes of work, the relationship varying somewhat with the kind of work, 1 material, and joint. But it can be shown that the size of d is fixed when the thickness of plate and efficiency of joint are given. As a guide, where experience is not available, the following should be useful : According to Unwin d = l~2\/t to 1'4\/F ............... (21) Box's Eule is d = (1 \t) + ^' ...... ........... (22) Kennedy's Rule 2 for lap joints is d = 2\,t .................... (23) T 5" In girder work, when the rivets join several plates of total thickness T, the diameter of rivet d may = - +- o o The diameter d is taken to the nearest .}.". But the rivet must be small enough when red hot to freely enter the hole ; so it is made from 0'03" to O06", (or d n = d - 0'04"~say) smaller than the hole. TABLE 2. SIZE OF RIVETS SUGGESTED BY THE NATIONAL BOILEK INSURANCE Co. Thickness of plate. Diameter of rivet. Finished size. Thickness of plate. Diameter of rivet. Finished size. inch. inch. loch. inch. 8 8 11 7 8 4 n ff t 1 1 7 1 6 8 I 1 :i 1C M H A I i; H i i M II 1 lu girder work ]" rivets are generally used for plates under J", and |" rivets for J" to j" plates ; and whatever sized rivet is used, the pitch can be adjusted to obtain an equality of shearing and tearing resistances when required. But in boiler work the pitch is restricted by the pressure of the steam, as the joint must be staunch enough to be steam tight, and we are confronted with the anomaly, that as we increase the pressure we must reduce the diameter of the rivet. - Obviously, this size of rivet would be inconveniently largo for thick plates and for treble riveting, but Kennedy rightly says that they (the diameters) should bo made as large as possible. 84 MACHINE DRAWING AND DESIGN FOR BEGINNERS 113. Efficiencies of Eiveted Joints. In ordinary practice well-designed joints for boiler work should have the following efficiencies : Single riveted = 50 to 55 per cent. Double riveted r/ = 65 to 70 per cent. Treble riveted i/ = 80 to 85 per cent. 114. The Graphic Method of Designing Joints, 1 due to Schwedler, is in many cases very helpful; a simple example will suffice to explain the principle. Figs. 217 and 218 show a joint for a tie bar; such a joint would fail either by tearing across AB, or by shearing the four rivets. Then, for equal strength, a width SCHWEDLER'S GRAPHIC METHOD. M of plate w, having a strength equal to that of one rivet, must be provided, as shown. To determine w we have wtf t = d* ^f, for single shear. N Whence w = ^f' (24) Then, if around each rivet a circle of x radius be drawn, and flowing lines from these circles be drawn along the bar, it will be seen that each rivet has a portion of plate of equal strength allotted to it. And if S equals the strength of the solid bar, the strength of the joint will be S dtf t , the strength of the net section at AB. When the rivet lines CD FIGS. 219, 220. and AB are close enough together, Kirkaldy found that the FIGS. 217, 218. plate tears along DMNOPC, and that the further they are apart and the more easy flowing the lines of the strips w, the more likely is rupture to occur at AB. Obviously, the other things being the same, the smaller the rivet the greater will be the efficiency at this part ; indeed, in some special cases the end rivets It have been made smaller than the others to increase the efficiency of the joint. Figs. 219 and 220 show at M and N two other joints (butt ones, with cover straps) of this type, also commonly used in bridge work. EXERCISES. DESIGN, ETC. 1. A single riveted lap joint, J" plates, I" rivets, both steel,/, and/, (the ultimate strength in shear and tension) being 23 and 28 tons per sq. incli respectively, find the most efficient pitch, also find the efficiency of the joint. Ana. p = 1J", q= 53 per cent. 1 For further information relating to the designing of riveted joints, refer to the author's " Machine Design, Construction and Drawing," p. 145. RIVETED JOINTS 85 2. Examine the joint described in exercise 7 below, and determine whether it would fail by the rivet shearing or the plate tearing, both being of steel. 3. A tie bar of rectangular section, 8" X '", is to be lengthened, a butt joint, with double straps, and nine rivets each side of the butt, arranged to give the strongest joint, being used. Sketch the joint, and determine the diameter of the rivets, the thickness of the straps and its efficiency, when f t and/ t = 23 and 28 tons per sq. inch respectively. 4. 1" diameter stays are to be used for the fire-box of a boiler ; their working stress is not to exceed 4500 Ibs. per sq. inch at their net section. The steam pressure being 140 Ibs. per sq. inch, what distance apart should the stays be pitched? DRAWING EXERCISES. 5. Set out a double riveted lap joint, J" plates, rivets j", distance between rivet lines 1|", zigzag riveting. Scale full size. 0. Draw two views of a double riveted (zigzag) lap joint, fj" plates, V e " rivets, distance between rivet linos Ij", pitch 3". Scale full size. 7. Set out a treble riveted butt joint, double straps, one strap being double riveted only, as in Fig. 185. The distances of the three rivet lines each side of the butt (or centre of joint) are 1^", 2j|" and 5f s " ; plates ,' e ", rivets J", inner pitches 3J", outer pitches 6J". Scale full size. SKETCHING EXERCISES. 8. Explain, with the assistance of sketches, in what respect the operation of fullering differs from caulking. 9. Make freehand sketches, in fairly good proportion, of the principal sections of bars used by the engineer. 10. Show by sketches how riveled lap joints, also butt joints, with single butt strap*, become distorted when subjected to tensional strain. What defect in the form of the joint is the cause of this distortion ? 1 1 . Make a sketch of a combined lap and butt joint. What advantage lias this joint over an ordinary lap one ? 12. Make sketches showing how the ends of a cylindrical boiler are connected to the shell, both by angle rings and by flanging. 13. Show by freehand sketches three different forms of flue connections or joints, and point out their relative merits. 14. In how many different ways may a riveted joint fail ? Illustrate your answer by sketches. CHAPTER XII BOLTS, NUTS, SCREWS, ETC. 115. IT will now be convenient to give some attention to the pair of elements forming the fastening, which in the science of kinematics * is called a screw-pair, the simplest form of which is the common bolt and nut shown in Fig. 234. A fundamental feature of bolts and screws is that parts connected by them can be easily disconnected when required, and when it is reali/ed what a great variety of work these interesting fastenings are used for, some idea can be formed of the multiplicity of forms and kinds that are in actual use ; but for our purpose we shall give attention to a few of the most important only. Now, to completely specify some special form of bolt or screw it may be necessary to mention eight features, namely, (a) shape or form of the thread, (b) pitch or number of threads to the inch, (c) shape of head, (d) outline of body, barrel or stem, (c) size or diameter, (/) direction of threads (as right-hand or left-hand), (g) length, (h) material, as iron, brass, etc. 116. Forms of Screw Threads. Figs. 221 to 233 show the best known threads used by the engineer. Fig. 221, a vee thread FORMS OF SCREW THREADS. FIG. 221. Whitworth's. Fio. 222. Seller's. Fio. 223. Vee. FIG. 224. Square. FIG. 225. Buttress. FIG. 226. Acme standard. FIG. 227. Round or knuckle. slightly rounded at the top and bottom, is Whitworth's, the standard British thread. Fig. 222 is also a vee, with the top and bottom slightly flat ; it is Seller's, and the standard thread of America. Fig. 223 shows a plain vee of angle f>CF, used for most screws made of wood and for small brasswork. Fig. 224 is the square thread, Fig. 225 the buttress thread. Fig. 226 is the Acme thread, a square thread with a slight taper, to facilitate its being rapidly engaged and disengaged when used with a split nut, as in the screw-cutting lathe. In Fig. 227 is shown the round top and bottom or knuckle thread, largely used for railway Science of pure motion. BOLTS, NUTS, SCREWS, ETC. 87 carriage couplings and hydrants, a very strong screw, not easily damaged when exposed to rough usage, but only suitable (for reasons that will be understood later) for special purposes. 117. Proportions of Threads. It is not easy for the young engineer to imagine what a hopeless want of uniformity existed before the labours of the late Sir Joseph Whitworth 1 led to screw threads being standardized in this country (1857-61). The question of further standardizing screw thread and limit gauges engaged the attention of the Engineering Standards Committee in October, 1902, and a committee on Screw Threads and Limit Gauges was appointed. This committee issued an interim report in April, 1905, and their final report in 1907. A report on British Standard Nuts, Bolt-heads and Spanners was also issued in August, 1906, by the Engineering Standards Committee, and we shall refer to these reports where they affect current practice as we proceed. In the old days it rarely happened that screws of the same nominal size made in different parts of the country had even the same pitch, therefore the all-important factor of- interchangeability in the construction and repairing of engines and machines, which is now a fundamental feature of all good work, did not exist. Even now, when the screw threads proposed by Whitworth are universally used, screws varying in diameter, pitch, and number of threads from standard proportions, called bastard screws, are to be occasionally met with in old work. Fig. 228 shows the shape of our Whitworth Vee thread. The angle between the threads being 55, and -jl of the full depth of the triangle ale being rounded off at the top and bottom, to a radius of - 137329p, as shown. But the full depth is 0'96 the pitch, so that the actual depth of the thread is $ x 0'96p = 0'64p, or, to be exact, 0'640327p. And if d = diameter of the screw at top of the threads, Fig. 230, and d\ = diameter at bottom of the threads (the net diameter), then the diameter di = 0'9rf - 0'05, nearly ..... .......... (25) and if n = number of threads per inch, Then 2 p = 1 = Q'OSd + 0'04, nearly .............. (26) 7l> A series of finer pitches 8 (to supplement the Whitworth series) suitable for bolts for connecting rod ends, and pistou-rod heads, is now in use, known as the British Standard Fine Screw Threads (B.S.A.). For screws up to and including I",' the pitches being based upon the formula p = -y^-. where d = full diameter of thread. And for sizes above 1" and up to 6", p = -y/r-- Definitions. The following definitions are due to the Engineering Standards Committee : Effective Diameter of a Screw. The effective diameter of a screw having a single thread is the length of a line drawn through the axis and at right angles to it, measured between the points where the line cuts the slopes of the threads. Core Diameter. Twice the minimum radius of a screw, measured at right angles to the axis. Full Diameter. Twice the maximum radius of a screw, measured at right angles to the axis. 1 Bamsden, in 17GG, was one of the earliest to attempt to obtain extreme accuracy in originating screw threads iu his dividing engine. The famous mechanician, Maudslay, subsequently took the mutter in hand, and his labours did not cease until he had practically evolved the screw-cutting lathe. 2 According to Briggs the relation of pitch und diameter of the Whitworth system is approximately p = 0-1075(1 - 0-OU75(P + 0-024 3 Refer to author's " Machine Design, etc.," p. 193. 88 MACHINE DRAWING AND DESIGN FOR BEGINNERS Crest. The prominent part of the thread, whether of the male screw or of the female screw. Root. The bottom of the groove of the thread, whether of the male screw or of the female screw. Slope of Thread. The straight part of the thread which connects the crests and roots. Angle of Thread. The angle between the slopes, measured in the axial plane. In Fig. 229 is shown Seller's thread, which we have explained is the standard shape adopted by America. The triangle being equilateral, the angle is therefore 60, \ the full depth of the triangle being cut off top and bottom, as shown, to form PROPORTIONS OF SCREW THREADS. WHITWORTH'S THREAD SELLER'S THREAD ^ -^^^- #A ~ U f 106/3 FIG. 229. flats parallel with axis. So that the actual depth of the thread d' = $d, or d' = f x 0'866p = 0'65p. The proportions of the Square thread (Fig. 224) are shown in Fig. 231, the pitch for standard screws being twice that for vee threads, or, the pitch, for square threads p = - = 0-lGrf + 0-08, nearly 71 (27) And, if di = diameter at bottom of threads, as in the other cases, Then di = 0'85d - 0075 (28) With this thread the thrust is very nearly parallel to the axis of the screw, and therefore there is no bursting strain on the nut, which is an important advantage. But the thread is more costly to produce than the vee thread, more particularly as it cannot be satisfactorily cut with dies. The figure shows the usual proportions of the thickness and depth of the threads. Fig. 232 shows a modified form of the square thread known as the Acme standard, or 29 screw thread. It is used in machine tools where a disengaging nut is required, as previously explained. The depth of the thread is (refer to Fig. 232) d' = \p + O'Ol (29) BOLTS, NUTS, SCREWS, ETC, 89 And the width of the point of the tool for a screw or tap thread = 0'3707p 0'0052 width of flat on top of the thread = 0'3707p (30) This angle of 29 has also been generally adopted in cutting worms for gearing. Refer to Chapter on Spur Gearing. The usual proportions of the buttress thread are shown on Fig. 233. This thread to a certain extent combines the important feature of the square thread already explained with the strength of the vee thread, but it has the disadvantage that it can only be efficiently used in one direction, namely, that which causes the thrust to act parallel to the axis, as shown by the arrows. In PROPORTIONS OF SCREW THREADS. WHITWORTH SCREW. SQUARE THREAD pitch =p VS. -0 ACME SCREW THREAD pitch BUTTRESS THREAD. FIG. 230. FIG. 231. Pio. 232. FIG. 233. cases where there is little work to be done by it during a reversed motion, as in some presses, and when used on the breach blocks of large guns, the effect of the oblique thrust is negligible, and this is often the best form of thread for the purpose. 118. Drawing Exercise. From a drawing point of view by far the most important detail is the bolt and nut, as any want of accuracy in presenting it mars the appearance of what otherwise might be a very good drawing, and offends the trained eye. Further, as the detail so often occurs on drawings, a real effort should be made to set it out in the usual conventional way shown in Figs. 234, 235, and 237. Commence with the Plan, Fig. 237, by drawing the circumscribing circle (with a radius 1 equal to d, the diameter of the bolt) and the bolt circle (radius "), and from the latter draw projectors, cutting the former in a and b, join ab, and draw the chamfer circle, touching ab in c. The hexagon is then completed with the 60 set-square, making each of the other sides just touch the chamfer circle. Projectors from the corners e, f can now be drawn, and these, with projectors from a and b, give the indefinite elevation of the bolt body, and edges of nut and head. The thickness of the nut (= d) can now be set off, and with radius 1 2d, and centre on centre line, the arc/K can be drawn, and a line through these points gives M and N, which are used, as shown, to draw the arcs on the side faces ; 2 the elevation of the nut is then completed by drawing the chamfers at 30, to just touch the arcs. The head is drawn in the same way, making its thickness equal to 0'9d, whilst the point or end of the bolt is usually rounded with a radius = d. The screw threads are easily drawn in the conventional way shown, the slope being fixed by 1 As we have explained, for drawing purposes (for 1" bolts and under) it is convenient to make the diameter across the angles = 2 A little practice will enable the student to draw these with consideiabl for the former till its true position is found. considerable accuracy and facility, by feeling for the centre and radius, assuming tentative positions N PROPORTIONS OF HEXAGONAL BOLTS FOR DRAWING PURPOSES. BOLT WITH SQUARE HEAD AND NUT. EQUILATERAL TRIANGLE: TO OBTAIN APPROXIMATE DEPTH OF THREAP. SLOPE OF THREAD EQUALS HALF THE PITCH FIG. 234. | JJ*~. marking up the pitch ; the thick lines of course represent the bottom of the threads, and their diameter may be found by making the small equilateral triangle, of side equal to the pitch, wliich gives the ap- proximate depth. Fig. 236 shows a bolt with square head and nut and square neck to prevent the bolt rotating whilst screwing up ; the proportions given in the table (No. 3), with the ex- ception of the diameter across the angles, apply to these. 119. Various Types of Bolts, etc. We may now give some atten- tion to the various types of bolts and bolt heads in general use. Figs. 234, 235, and 237 show the form of the common hexagonal bolt and nut. The proportions of these are now standardized, 1 they are practi- cally those given in Table 3, which are in common use. The practice of some manufacturers in the past has been to make bright nuts and heads, somewhat smaller in diameter than black ones, but this is very inconvenient, as, if for no other reason, it necessitates the use of two spanners for the same size bolt. However, as now standardized both the bright and black have the same maximum dimensions, the minimum dimensions fixed for the latter giving a larger allowance. For ordinary dmwiny purposes the 1 Uefer to Reports on British Standard Screw Threads, published by Crosby Lockwood & Son. 8 J^ I FIG. 235. BOLTS, NUTS, SCREWS, ETC. 91 TABLE 3. DIMENSIONS OF WHITWORTH'S 55 THREADS, HEXAGONAL BOLTS, NUTS, AND HEADS (BRIGHT). Thickness of nut in each case = diameter of bolt. Square nuts and bolts have the same proportions, with the exception of the diameter across the angles. NOTE. Refer to remarks in Art. 120 relating to this table. Diameter of bolt of screw = d. No. of threads per inch = n. Diameter at bottom of threads = *N " 307. 308. 309. dimensions shown on the handle itself are suitable for a large range of si^es. A handle of another shape is shown in Fig. 320 ; but the remarks made in connection with Fig. 308 equally apply to this. These handles are shown riveted, but they are sometimes stamped from the solid. 104 MACHINE DRAWING AND DESIGN FOR BEGINNERS MACHINE HANDLES. DIFFERENT TYPES. Fios. 810, 311. Balanced type. FIGS. 312, 313. Tightening handle. -e EM Hh-^-lrF / 572 F Steel . . ... 0-00000600 32-212 F. 0-00000955 32 212 F Wrought iron .... 0-00000656 32-212 F. Conner . 0-00001092 32-572 F. 1 The author, in testing pipes fitted with such joints, hag often, at pressures of some 4000 or 5000 Ibs. per sq. inch, squeezed water through the pores of the metal, whilst the joints have remained tight. " Taking the form of an annulus of soft copper, usually made by cutting rings from thick solid drawn copper pipes, the sections of the rings being grooved in various ways, so that the sharp edges when in contact with the flange bases easily make a metal -to-metal joint. Some firms, such as the Combination Metallic Packing Co., make a speciality of these, and stock a variety of sections and sizes ; but this type of packing should only be used when the flanges are very strong and rigid. * This is the best practice for very high-pressure steam pipes. The copper exhaust pipes for petrol engines are frequently made with sharp elbows, where they should be arranged with easy bends. PIPES AND PIPE CONNECTIONS 111 Thus, with steam at 240 Ibs. per sq. inch, with a range of temperature from 32 to nearly 380 F., the expansion per 100' would be, for cast iron or steel, O'OOOOOG X 380 x 12 x 100 = 2'756", say 3". In some cases the range may be, for pipes beyond the superheater, some 600 F. Then, with wrought-iron pipes (taking the coefficient at 0'000009) we get O'OOOOOQ x 600 X 12 x 100 = 6*48", say 6" expansion (above the length when cold) per 100'. It is usual in good boiler practice to make the branch pipes (which connect the boiler stop valves to the main steam-pipe), at least 12' long, to give the necessary relief. 144. Pipe Hangers and Beaters. Fig. 341 shows a simple way that heavy pipes are sometimes supported in, which is obviously defective, as any movement of the pipe in the direction of its length would probably cause the clip to heel on one of its supports, and slightly lift the pipe out of position. The hanger should be fitted with a roller, as shown in Figs. 341A to DEFECTIVE SUPPORT. PIPE HANGERS AND BEARERS. EFFICIENT SUPPORT. GROUND ROLLER SUPPORTS OR BEARERS. 341c. Steam pipes should not rest on the ground, but be supported at suitable intervals by cast-iron roller-bearing blocks resting on a bed of concrete or stone, as shown in Figs. 341D and 341E, or if some distance from the ground, by a roller standard, Fig. 34lF. 145. Expansion Joints, etc. We have explained under what conditions expansion joints become necessary, and we have in Fig. 342 a length of copper pipe (or of lap-welded or weldless steel pipe, with riveted flanges) bent into the form of a horseshoe, which may take the place of a short length in a pipe ; it offers little resistance to the ends A and B being moved closer together or further apart, by expansion and contraction. Fig. 342A shows a loop arranged for the same purpose ; but these expansion joints are only reliable when they are very little stressed by such straining actions, particularly when made of copper, as that metal has a low elastic limit, and less spring than wrought iron or mild steel. The same remarks apply to the cushion expansion joint shown in Fig. 342n, and also to the corrugated expansion joint, Fig. 342c (which is a development of the latter) ; these can only be safely used to serve very short lengths of pipe that for some reason or other have to be straight. The difficulty with these joints is that there is MACHINE DRAWING AND DESIGN FOR BEGINNERS sure to be some one part or corrugation that is a little weaker to resist compression or tension than the others, with the result that it takes up all the work, and the joint ultimately fails l at that part, and when two or more such joints are used in one length of pipe, EXPANSION JOINTS. COPPER EXPANSION LOOR COPPER HORSE-SHOE EXPANSION JOINT. CORRUGATED COPPER EXPANSION JOINT. COPPER EXPANSION CUSHION. Fio. 342. FIGS. 342A, 342s. FIG. 342o. FIG. 342D. llessrs. Crane & Co.'s malleable cast-iron expansion bends. one joint alone may take up nearly the whole expansion ; for this reason more than one such joint per length of pipe should never be used. The battery of expansion bends shown in Fig. 342D, is manufactured by Messrs. Crane & Co. The three bends have a total sectional area about equal to that of the main pipe, 2 their smaller diameter giving greater flexibility. On the whole, perhaps by far the most satisfactory expansion joint is the well-known gland and stuffing-box arrangement shown in Fig. 343, which should always be fitted with guard-bolts A, B, to prevent the two parts being blown apart, should any movement of either end of the pipe take place. These bolts sometimes are also used as studs for the stuffing box. When the skin of cast iron is removed by machining, the metal quickly oxidizes, so, to prevent rust joints being formed, the working surfaces in the best work are gun-metal, the parts being bushed and sheathed, as shown in Fig. 343. 145a. Drawing Exercise. Fig. 343. Draw the sectional elevation. A plan and two end elevations. Scale, half full- size. 146. British Standard Pipe Threads. The Engineering Standards Committee have recommended that the Whitworth thread (Art. 117) should be employed for all iron or steel tubes and couplers or sockets ; also for tubes made from copper, brass, or similar metal, and for these latter materials where the outside diameters agree, and the thickness of the metal permit, the same pitcties be adopted. The committee has formulated full particulars of pipe threads for nominal lores of J" to 18", which are now known as the 1 The anthor gave these joints (the corrugated ones) a trial some years ago, but they were so unsatisfactory that he had to replace tbem by joints of the gland and stuffing-box type. * Kefer to author's "Machine Design, Construction and Drawing," footnote, p. 196. PIPES AND PIPE CONNECTIONS 113 British Standard pipe threads, 1 and this standardization will doubtless be greatly appreciated by all who have to do with pipe threads from various manufacturers. Table 5 gives a few ordinary particulars relating to pipe threads. GLAND & STUFFING-BOX EXPANSION JOINT. I- 9, Fio. 343. The Report issued by the Committee contains their recommendations, and a large amount of valuable information relating to these screw threads, in addition to the Tables. It is published by Messrs. Crosby Lockwood & Son, at 2. Gd. net. Q 114 MACHINE DRAWING AND DESIGN FOR BEGINNERS TABLE 5. PIPE THREADS. The Number of Threads per Inch have not been altered by the Standard Committee. They are as follows : Nominal bore of tube. Number of threads per inch. Nominal bore of tube. Number of threads per inch. r 28 l"to 6" 11 i" a d |" 19 7" to 10" 10 *" to r 14 11" to 18" 8 The bores advance by J" from j" to I", by j" from 1" to 4", by J" from 4" to 6", and by inches from 6" to 18". Diameters of Screwed Part, Core, and of Black Tube. Nominal bore of tube. A pproximate outside Diameter top diameter. of thread. Diameter of core. Nominal bore of tube. Approximate outside Diameter top ~. diameter. of thread. Diameter of core. Black tube. Black tube. Ins. Ins. Ins. Ins. Ins. Ins. Ins. Ins. 1 0-383 0-337 li HJ 1-650 1-534 0-518 0-451 It Iff 1-882 1-766 | 0-656 0-589 1^ 2A 2-116 2-000 1 0-825 0-734 2 2|" 2-347 2-231 g 0-902 0-811 2i 2| 2-587 2-471 | 1-041 0-950 24 3 2-960 2-844 ! 1-189 1-098 2| 31 3-210 3-094 1 1-309 1-193 3 3! 3-460 3-344 147. Spigot and Socket Joints. Cast-iroii pipes, used for the conveyance of low-pressure water or gas, which have to be embedded in the ground, are connected by spigot and socket joints, which have a certain amount of flexibility at the joints, allowing the pipe to accommodate itself to slight settlements of the earth. The proportions and details somewhat differ, but Fig. 344 shows a typical example of the joint for cast-iron pipes as used by Mr. Bateman at the Glasgow Waterworks, and his proportions for various sizes are shown in Table 6. The joint is made by first driving a few coils of gasket or yarn into the socket and then filling the remaining space with lead, which is done by putting a clay band round the outside of the socket and running in the molten lead, which, when cold enough, is caulked or stemmed tightly into the socket, and the clay is removed. The socket is sometimes grooved, as at G, Fig. 345, to better prevent the lead being blown out. Fig. 344A shows a form of turned and bored spigot and socket joint ; the taper of the bored part is jfa" per inch of length ; the joint is made iiuid tight by painting the turned parts with red lead or PIPES AND PIPE CONNECTIONS 115 liquid Portland cement before putting them together with a blow or two to drive the spigot home. The socket is then filled up with cement, as shown. TABLE 6. PROPORTIONS OF (LEAD) SPIGOT AND SOCKET JOINT. BATEMAN. (Fig. 344.) Bore in inches. Length of each pipe-ft A B c D E F G u T 1 2 6 3 3 , i I I , f a 9 3 3 1 | I 1 I i 4 9 3 3 | I i I I 1 i 5 6 9 9 3i 31 3 1 i 1 1 1 ; if II f i 7 9 3i 5? ? 1 J f il I | 8 9 4 4 i li 1 \>- I i i 9 9 4 4 i: ll 1 1 ' 1 _^. 12 9 4 4 if 1 li | 15 9 44 44 | If IJ, a ij 11 18 9 4 4* g 1? IT 1} i i 1 :: 20 9 4 4j g l| ll ij 11 u H | 24 12 5 5" | If u i a U li 1 33 12 55 5 j 2 If 4 if 1^ to 1^ 1 to 1} i TABLE 7. TCHNED AND BORED SPIOOT AND SOCKET JOINT. (Fig. 344A). Pore in inches. Length of each pipe-ft. , 1! C D E f c , H I T ( 2 6 3 3 1 , j j [ 1] 3 9 3 3 | j . 1 1 I l| 1 I 4 9 3 3 1 j i i 3 l] 1 a 5 G 7 8 9 9 3i 9 3l 9 4" 9 4 3i 3$ 3| 4 i J ! 1 1 | li if j i ; I; 1 * \ I; lj 1 i 12 9 4} 4} i l| i 1 !' f 1 1| I 1 But recent practice favours a shorter turned part, as shown in Fig. 346, its length being some f to J-", which much increases the flexibility of the joint. 116 MACHINE DRAWING AND DESIGN FOR BEGINNERS 148. Joints for Hydraulic Pipes. Many years ago the late Lord Armstrong introduced the simple and efficient joint, Figs. 347 and 348, for high-pressure water pipes, and it is now generally used for hydraulic mains. Fig. 340 shows in detail how the joint is SPIGOT AND SOCKET JOINTS. ORDINARY SOCKET & SPIGOT JOINT, MADE WITH LEAD I*. 4 TURNED & BORED SPIGOT & SOCKET JOINT, MADE WITH CEMENT Fw. 344. FIG. 344A. LEAD JOINT, SOCKET GROOVED TURNED & BORED, SHORT FLEXIBLE JOINT formed. The empirical proportions of the ordinary cast-iron pipe joint in terms of t and tl generally used are shown on Figs. 347 and 349. The practice of some engineers is to make the face ab of the flange flush, which enables the joint to slightly yield under a lateral load. The usual practice is to subject the metal of the pipe to a working stress of 2800 Ibs. per sq. inch, and the bolts at the core section to 7700 Ibs. per sq. inch, allowing an extra thickness k = \" for corrosion, inequalities of the casting, etc., of the former. But we have seen (Eq. 32, Art. 138) that for a thin l cylin- drical vessel subjected to internal pressure, we have PD = 2//,, PD or t = -^. Then for, say, a 5" pipe, and P = 700 Ibs. per sq. inch, the thickness 2 x 2246 - = ' 625 + ' 25 = ' 875 = *" . And the above is equivalent to the simple rule of t = -^ + j" for a pressure of 700 and a stress of 2800 Ibs. per sq. inch. 1 Strictly speaking, these pipes could hardly be culled thin cylinders, but it is usual to consider them so for this purpose, aud any error duo to this is well covered by the J" allowed. FIG. 345. S^^^^$$$$ FIG. 346. ,_ 700X5 , ARMSTRONG'S HYDRAULIC PIPE JOINT T ^ en >o FIG. 347. HYDRAULIC UNION FIG. 348. HYDRAULIC UNION FOR COPPER PIPES. FIG. 349. FIG. 350. FIG. 351. 118 MACHINE DRAWING AND DESIGN FOR BEGINNERS Bolts. Equating the total pressure acting on a section of the pipe, to the strength of two bolts, we get PD a -. = 2^ x 7700, where d is the core diameter of the bolts. HYDRAULIC STOP VALVE, HEMP PACKED (Drawing Exercise). C,,G. Two - FIG. 352. Fio. 353. Then 700 x 5 2 2 x 7700 = 1-066. But di = 0-Qd - 0-05 (Eq. 25, Art. 117). .-. d = J 9 (rfi + 0-05) = J^(l-066 + 0-05) = 1-24, say 1J". HYDRAULIC STOP VALVE, LEATHER PACKED '(Drawing Exercise). ->! Scr*fld 4$ ffereads ber i\fich . 4- - 2 ~ *ft FIG 354. FIG. 355. 120 MACHINE DRAWING AND DESIGN F"OR BEGINNERS Figs. 350 and 351 show two forms of Hydraulic Union Joint, the packing rings being either of leather, gutta-percha, or soft copper. BODY OF STEAM STOP VALVE (Drawing Exercise). 149. Hydraulic Stop Valves (Drawing Exer- cise). Two sectional views of an 1^" hydraulic stop valve l are shown in Figs. 352 and 353. Instructions. Make full-size separate scale drawings of its following details, showing at least two views of each one : Xut B, gland C, bush D, seating E, and cap F. 150. Another Drawing Exercise. Figs. 354 and 355 are two sectional views of a 7" hydraulic stop valve, which, as will be seen, is somewhat more complicated, being arranged for leather pack- ing, but the details are so fully dimensioned that an apt student should experience no difficulty in drawing the two views and adding a plan. Scale, one-quarter full size. 151. Steam Stop Valve, Body of (Drawing Exer- cise). Three dimensioned views of the body of a steam stop valve 2 are shown in Fig. 355A. Instructions. Set out the views to a scale of full size. Advanced students should bo able to complete the valve by fitting it with a suitable spindle, gland, hnndwheel, etc. 152. Steam Equilibrium Admission Valve (Draw- ing Exercise). In Fig. 355n we have two sectional views of a steam equilibrium admission valve, which were given in the 1907, Stage 2, B. of E. paper. Students were supplied with the following: Instructions. () Draw a part sectional elevation of the stuffing-box cover and the valve seating, looking in the direction indicated by the arrow K. The part of the elevation to the left of the centre line is to be a section along HG, and the part to the right an external elevation of the valve seating and cover. The valve ' and the outer casing are to be omitted in this view. (!>) Draw a part sectional plan, the part above the horizontal centre line is to be a horizontal section of the valve and seating through EF, and the part below a plan of the cover. The outer casing is again to lie omitted. Scale^ full size. Neither dotted lines nor dimensions need be shown. N.B. Take the vertical centre line in the direction of the longer dimension of your drawing paper. FIG. 355A. 1 This drawing example was given in the B. of E. Exam. Stage 1, 1907. It is arranged for hemp or asbestos packing. 2 In the 1907 C. G. Exam, in Mechanical Engineering pattern-makers were asked to make a pattern of this valve. STEAM EQUILIBRIUM ADMISSION VALVE (Drawing Exercise). 122 MACHINE DRAWING AND DESIGN FOR BEGINNERS 153. Thick Cylinder Castings. When a casting is cooling from its molten condition the heat passes out in the most direct way, that is, in a direction normal to the surface, as shown in the sections of solid and hollow columns, A and B, Fig. 357, and the crystals of the metal (a group of which is shown in Fig. 356) arrange themselves in that direction, 1 so that when two cooling surfaces are at right angles to each other, as at C, Fig. 357, and the passage of heat is equally rapid in both directions, solidification occurs in such a way that confused crystallization results, and a line XY of weakness 2 is produced bisecting the angle, whilst in A and B the lines of crystallization all radiate from the centre, and no interference occurs. The section A (Fig. 358) is a variation of C (Fig. 357), and B is a representative case where sharp angles give lines of weakness, C showing how the use of fillets and rounding the corners results in a satisfactory casting. The first very large hydraulic presses were made to raise the gigantic tubes of the THICK CYLINDER CASTINGS. FIG. 358. FIG. 356. Britannia and Conway tubular bridges, the form of the bottom ends of the presses being that shown in the figure D (Fig. 358), but, to the astonishment of the engineers, the bottoms came out, conical in form, the fracture occurring at BS and TU. The same thing occurring when they were made thicker, Mr. Edwin Clerk 3 decided to try the hemispherical form E of uniform thickness, which decision was based on a true knowledge of the cause of failure, and resulted in complete success. But this form is not always convenient in practice, so, as a compromise, the bottom at the inside is usually rounded as in A, Fig. 359, which shows a form that answers well. When the cylinder is so long that a core bar must be passed through its bottom to be supported at that end, the hole is bored and plugged with a slightly tapered plug driven from the inside as in B, Fig. 359. For cylinders over about 12" diameter a back plate and U-leather are sometimes used with the plug, as shown in C, Fig. 359. The metal used in these castings must not only be strong and tough enough for the purpose, but it must also be of close texture, 1 The molten metal coming in contact with the mould is cooled, and forms a thin lining to the mould, the inner surface of which consists of the tops of crystals (belonging to the cubic system) of the metal in groups projecting into the body of the molten metal, and growing in size as cooling and solidification proceed, at the same time arranging themselves so that their longer dimension is at right angles to the cooling surface. For this reason castings (particularly iron ones) always have, or should have, a round or Hat fillet at the corners or angles. 2 This weakness is apparently partly due to irregular crystallization, and partly to the separation of tho more fusible constituents of the iron and their accumulation in that part. 3 Mr. Edwin Clerk and his brother Latimer (two of the author's old chiefs) were resident engineers for the bridges under Robert Stephenson, the former of them afterwards becoming so famous in connection with hie canal lifts and floating docks. PIPES AND PIPE CONNECTIONS 123 or the water will ooze through it when under great pressures. 1 And to ensure the castings being sound these cylinders are always cast with a head of substantial volume on the uppermost end a in the mould, so as to produce a sufficient fluid pressure on the metal in the mould, and cause the metal to remain fluid long enough to exert this pressure till solidification of the casting occurs. 154. Faults in Designing Cylinders, etc. When the boiler- maker cuts a manhole in a boiler he is careful to surround it with a ring plate of sufficient section to strengthen the ring of the boiler whose continuity has been destroyed by the cutting of the hole ; so CORRECT "FORM FAULTY "FORM i FAULTY CORRECT FIG. 359. FIG. 360. Use of strengthening boss. FIG. 36). Thick partition. in cylinder design, wherever a pipe connection is to be made to a cylinder, a loss A, Fig. 360, must be provided to make good the metal that has been cut away in drilling the hole, otherwise the cylinder will be materially weakened, as shown at B, Fig. 360. When cylinders are cast together, the same want of skill is sometimes met with, the metal, t, between them being made the same thickness as the cylinder C, Fig. 361, instead of being twice that thickness (as it should be), as shown at D. For, obviously, when adjacent cylinders are simultaneously worked there is twice the circumferential tension at D that there is at E. EXERCISES. DESIGNING, ETO. 1. The length of a cast-iron steam pipe is 120', and the working pressure 160 Ibs. per sq. inch. How much will it expand in being heated from 32 2. A copper steam pipe is worked at 130 Ibs. per sq. inch, and it has a length of 90". How much will it expand iu being heated from 32 F. ? 3. Make a rough sketch design for a 6" Armstrong hydraulic joint, pressure 800 Ibs. per sq. inch ; give the principal dimensions. F.? 1 When this occurs, there is always the possibility of the stress being increased in the internal layers, owing to the presence of the pressure water, and rupture of the press may happen at a pressure sensibly below the one it was designed for. A slight leakage will often take-up (or rust-np) after a few days by rusting of the pores. This is usually the bottom end of the cylinders. 124 MACHINE DRAWING AND DESIGN FOR BEGINNERS SKETCHING EXERCISES. 4. Sketch in fairly good projx>rtion three examples of cast-iron flanged joints for steam pipes. 5. Show by sketches three examples of how copper steam pipes arc fitted with gun-metal flanges. (!. Show by sketches (a) a mild-steel solid drawn pipe with cast-steel flanges; (fc) a welded irun pipe with riveted Uunges. 7. Show by neat sketches the following joints used for tubing : ordinary socket, Perkin's, 1'erkin's joint with copper washer, and Emery's joint for connecting a steel tube to a gun-metal nozzle. 8. Sketch the following : boiler tube and ferrule, boiler stay-tube with backnuts, boiler tube with Admiralty ferrule. What is about thu ordinary diameter and thickness of the last-mentioned tube ? 9. Show by sketches the usual form of union joint. Under what conditions of working are these joints used ? 10. Sketch three different expansion joints suitable for steam pipes, and say which you would prefer, and why. 11. Sketch an ordinary spigot and socket joint suitable for a cast-iron water pipe. Why is this type of joint most suitable for horizontal pipes '< 12. Show by a sketch how you would form the bottom of a hydraulic cylinder so that there would be no danger of the bottom being forced out. In some cases it is necessary to cast the cylinder with a hole through the bottom ; why is this ? Show how such holes are afterwards plugged up. 13. Explain, with the assistance of sketches, some of the faults occasionally met with in the design of cylinder castings, particularly for hydraulic work. 14. Why is it necessary to east hydraulic cylinders with calling head* f Make sketches of the usual forms of heads, and say which you prefer, and why. DRAWING EXERCISES. 15. Make working drawings of a spigot and socket joint, made with lead, for a 6" pipe. Fig. 344. 16. Make sectional elevation and end view of a turned and bored spigot and socket joint for an 8" cast-iron pipe. Fig. 346. 17. Make a sectional elevation, and a sectional end elevation, of an Armstrong hydraulic pipe joint for a pressure of 700 Ibs. per sq. inch, and diameter 4". You should show the detail of the joint full size. The other views half full size. NOTE. The information given in Art. 148 will enable you to easily determine the leading dimensions. 18. Make a sectional elevation, plan, and sectional end elevation of u gland and shilling-box expansion joint for a (>" steam pipe. Scale half full size. (Kefcr to Fig. 441.) CHAPTER XV COTTERS AND COTTERED JOINTS 155. WHEN two rods are to be rigidly connected one to the other in such a way as to transmit a force in the direction of their length only, the most convenient joint for the purpose is the Cottered or Keyed joint, one form of which is shown in Figs. 362 and 3f)3, where the end of the rod B takes the form of a socket or box, into which the end of the rod A fits and is held in position, by the Cotter G, a taper or wedge-like flat bar, which is driven through the socket and rod. The joint, as arranged in the figures, is a type suitable for connecting round bars to form a long pump rod for a well or mine, or some such purpose ; but we shall see directly how it can be varied and adapted to the requirements of a number of interesting cases, and of these the best known is the joint which is used to connect the piston rod to the cross head of an engine, Fig. 367. It can be shown 1 that when the joint (Figs. 362 and 363) is in tension its various parts will have practically the same strength when their proportions are as follows : PROPORTIONS OF COTTERED JOINTS FOR UNIFORM STRENGTH. d = 0-82rf 2 " D 2 = l-75d b = l-31d t = * D = 2-42rf l = lt = from Q-75d to d D 3 = I'U t- 2 = 0'42rf 156. Clearance of Cotters. An important feature of the cottered joint is the clearance. Obviously, if the cotter in Fig. 362 is to draw the rod end A into the socket of B, there must be some clearance at in and p in the socket to allow the cotter in being driven to enter further into the socket, and there must be the same amount of clearance in the rod at K. In this type of joint the cotter when fitted is driven home, and the clearance is usually from j' 6 " to J". 157. Taper of Cotters. Now, it is not difficult to prove that with surfaces slightly greasy the total taper 2 must not exceed 9, if the cotter is not to slip back after being driven into the joint. This corresponds to a total taper or draught 3 of 1 in 7. But of 1 For proofs refer to author's " Machine Design, etc.," p. 225. - Un win's "Machine Design," vol. i. p. 219. 3 This draught is the trigonometrical tangent of the angle of taper, when one side of the cotter is square with the bar, as in Fig. 379, or twice the tangent of half the angle when the cotter is tapered both sides, as in Fig. 380. 126 MACHINE DRAWING AND DESIGN FOR BEGINNERS COTTERED JOINT FOR TENSION AND COMPRESSION RODS. course, for safety's sake, the taper is made a good deal less than this, usually about j" to the foot to J" to the foot. But when any special arrangement for keeping the cotter from slacking is made, its taper may be as large as the 1 in 7. 158. Proportions and Strength of Cottered Joints. The young designer has, in these joints, good opportunities of proportioning the parts from suitable data ; indeed, a little time could be most profitably spent in that way, 1 although in actual practice the empirical proportions we shall directly refer to are largely made use of, but even these, from an examination of several examples from ordinary good practice, seem to vary more than they should. Of course, in calculating the dimensions in a given joint the nearest -j 1 ,." is always used. 159. Various Cottered Joints. Figs. 364 to 382 show repre- sentative examples of cottered joints, with the proportions in general use. Figs. 364 and 365 show two views of the bottom end of a wrought-iron standard cottered to a cast-iron bed plate, the unit being d, the diameter of the rod, in each case. Fio. 362. Via. 363. Fig. 366 shows a low-pressure piston cottered to the rod of a tandem engine, d (the unit) being the mean diameter of the taper part. In Fig. 367 the socket of a cross head is thickened to give the requisite "bearing surface for the cotter, 2 and Fig. 368 shows another arrangement of a cottered standard. Fig. 369 shows a cottered joint arranged for thrust and tension, the proportions being suitable for wrought-iron rods and steel cotter. A modified form of this joint is shown in Fig. 370, the socket being reduced in diameter below the part where the cotter bears upon it. The .proportions are for all parts of wrought iron or steel. A simple cottered bolt is shown in Fig. 371 with the usual proportions. In Figs. 372, 373, and 374 we have two arrangements of foundation bolts and cast-iron washers ; 8 in each case the bolts may be enlarged at the upper ends for the screwed part to a diameter d' = - . For other examples of foundation bolts, see Figs. \) y 288 to 290 (Art. 127). The Figs. 375 and 376 show a cottered joint used for rough bars, the unit being the side S of the square bars. Fig. 377 shows a stud or bolt cottered in a casting, the hole usually being a cored one. 160. TTse of a Gib. Fig. 378 shows what would happen if a cotter AD was driven to draw the strap CB on to the rod EF. The friction between the cotter and strap at H would cause the latter to be sprung away, as shown dotted at B. To prevent this a gib G, Fig. 379, is used, but the hole in this case must be parallel (unlike the one in Fig. 378, where it has the same taper as the cotter) 1 See the author's " Machine Design, etc." (p. 225), for an examination of the strength to resist various forms of rupture. 2 The end of the rod is sometimes tapered (as in Fig. 366) both for piston rods and valve spindles, and, to facilitate the withdrawal of the rod, a small transverse hole through the socket may be drilled so that a taper pin can be used to wedge out the rod. 3 When the cottered ends are round, as in these cases, it is usual to cast a snug or projection on the washer to prevent rotation of the cotter and bolt in screwing up. VARIOUS COTTERED BOLTS AND JOINTS, ETC. ^^ Unit = c. *--> i i I * KM i kv 0) 2H> FIG. 366. Steel rod and FIG. 367. Piston rod and cotter. C.I. piston. cross head. FIGS. 364 and 365. W.I. standard and C.I. bed plate. in -I-5-* 1 FIG. 368. Rod and cotter either both W.I. or steel. FIG. 369. W.I. rods, steel cotter. FIG. 370. W.I. rods, steel cotter. FIG. 371. Cottered bolt. 128 MACHINE DRAWING AND DESIGN FOR BEGINNERS and the taper given to the gib as at MN. Two gibs are sometimes used, as in Fig. 380 ; the taper is then either equally divided between them as shown, or only one gib need be tapered. FURTHER EXAMPLES OF THE USE OF COTTERS. FIG. 372. Foundation bolt. Rod and cotter both either W.I. or steel. FIGS. 373, 374. Foundation bolt. Rod and cotter both either W.I. or steel. x j ^ 1 1 cr ~[ 1 t h- s -, ..__ __. : 2 H h* '1 -'6* r t IT| > ! i UNIT= s 3 FIGS. 375, 376. Cottered joint for rough bars. FIG. 377. Bolt cottercd into casting. FIG. 378. Cotter without gib. FIG. 379.- Use of gib. FIG. 380. Cotter with double gibs. FIGS. 381, 382. Gib and cotter with set-screw. COTTERS AND COTTERED JOINTS 129 EXERCISES. DRAWING EXERCISES. 1. Make working drawings of a cottcred joint for a 8" round steel bar with steel cotter. It is to be suitable for a tensional and coinpressional condition of the bar, and to be of the form shown in Fig. 370. Scale full size. 2. Draw three views of a 1J" foundation bolt, with bottom end cottered and fitted with cast-iron washer (Figs. 373 and 374), both ends to be enlarged so that they are equal in strength to the body of the bolt. Scale full size. 3. Make suitable views of a cottered joint for rough 2" square bars. Scale full size (Figs. 375 and 376). 4. The upper part of a machine is supported by four 3" wrought-irou round standard, cottered into a cast-iron bed plate. Set out a suitable joint showing two sectional views (Figs. 364 and 365). SKETCHING EXERCISES. 5. Make a freehand sketch of a cottered joint suitable for connecting lengths of a long pump rod. 6. Show by a sketch how a piston rod can be fixed to a piston by a cotter. 7. Make a sketch of a piston rod cottered to a cross head. S. Show by a sketch any application of a cotter with double gibs (Fig. 380). 9. Sketch a bolt cottcred into a casting. Under what circumstances would you use such a bolt? . S CHAPTER XVI PIN OR KNUCKLE JOINTS, PITCH CHAINS, ETC. 161. PIN or knuckle joints are used (a) in structures, the pin connecting two or more bars or rods (such as the members of a braced girder, suspension chain, or roof principal) whose axes intersect in the axis of the pin, a special form being the forked knuckle joint, and another important form the eye joint of sus- / "V I T J Fios. 383, 384. Forked pin or knuckle joint. pension links ; (b) in machinery, to connect two rods or parts so that one may have a small angular movement about the other, the best known case of this kind being the joint connecting a valve rod to the rod of an eccentric ; (c) for the joints of gearing and elevator chains. 1 The following is an example of (a) : 162. Forked Knuckle Joint. Two views of this joint are shown in Figs. 383 and 384, and the dotted parts show how two other members It and S (usually split ones) are also sometimes con- nected by the joint, the opening of the fork being increased to accommodate them. The proportions of the joint in terms of d, the diameter of the rod, may be as given on the figures. No part of the joint will then be weaker than the rod when it is either in tension or compression ; indeed, the pin could in some cases be made somewhat smaller, as we shall see in the next article, but making it the same size as the rod provides a margin of strength to resist the bending action which occurs when the pin is a somewhat loo.se fit or becomes worn. 163. Strength of Knuckle Joint Pin. If there 1 The pin joint of an engine cross head is also a special joint of this kind, but it is convenient to treat this separately. PIN OR KNUCKLE JOINTS, PITCH CHAINS, ETC. 181 is no bending 1 action, the pin will fail in double shear, and then, if d = diameter of the rod, tensional strength of rod per sq. inch, f s = the shear strength of the pin per sq. inch, = say 0'8/<, = diameter of the pin, f t = the Then rf 2 ' = 2 or ! = (33A) 164. Suspension Links, or plate-link chains are used in structures of the suspension bridge type, but the same type of chain only with short links and suitable pins has for years been increasingly used as gearing chains, when a positive and powerful drive is required. Figs. 386 and 387 show the forms and proportions of eyes (in terms of W) found by experiment to be strongest by Sir FORMS OF SUSPENSION LINK EYES. UNIT = W FIG. 385. Hammered eye, American form. FIG. 386. Berkley's form. FIG. 387. Fox's form. G. Berkley and Sir C. Fox respectively. It was found that if d is less than 0'66W the link crushes in the eye. In Fig. 385 is shown the hammered eye largely used in America. Figs. 388 and 389 show a chain arranged with two thin links, D and E, and a thick one F (double the thickness of the others) between them. Of course, the length I depends upon the flexibility required ; it is sometimes as large as 25'. These figures also show the three different methods of fastening the pins. A multiple link chain is shown in Fig. 390. Of course, in this case, for uniform strength, the total thickness at M must equal the total thickness at N, or 3t = 4*i. 165. Gearing Chains. The development of the motor-car and the popularity of the chain-drive have given a great impetus to the production of efficient pitch chains suitable to run at high speeds. For many years engineers have used chains for various special purposes in the transmission of power, but the possibilities of this system of transmission for many purposes, 1 Unwin shows that where bending occurs and the joint is subjected to stresses reversing in sign, a skin stress of 5400 due to bending will not be exceeded if the diameter of the pin = 0-0224 ,/P, where P = axial force iu the rod. 132 MACHINE DRAWING AND DESIGN FOR BEGINNERS when a positive drive with no slip is required, and where ordinary gearing would be inconvenient, have only been in recent years grasped. It frequently happens that two shafts can be advantageously connected by a pitch chain, where their distance apart ARRANGEMENTS OF LINKS AND PIN FASTENINGS. BEARING CHAINS. \ /' 1 A 1 I *ii 1 <- 1 t 1 FIG. 394. Double flat-link gearing chain. PIN OR KNUCKLE JOINTS, PITCH CHAINS, ETC. 133 166. Form of the Wheel Teeth for Chains. In Fig. 391 we have shown a sprocket or chain wheel. Now, if we had a perfectly flexible chain, the path of any point in the chain (such as the centre of a pin) as it left the wheel would be an involute l of a circle, and the actual curve of the tooth would be formed by drawing a parallel to the involute, distant from it half the diameter of a pin. But the links being solid, in most cases one pin P of a link (as the latter leaves the wheel) moves in an arc PQ about the centre M of its other pin. So, to set out the teeth, first find the centres ac, MN, etc., of the pin positions round the wheel, which form the corners of a polygon whose sides equal in length the pitch of the chain, the number of sides of course being equal to the number of teeth. Then, with centres a and c and radius ac, describe arcs intersecting in b (these are the paths of the pin centres), and with the same centres, radius equal to ac ', describe arcs intersecting in d, which give the sides of the teeth, and the teeth can be completed, as shown, by giving them a suitable length. EXERCISES. DESIGN AND DBAWING EXEBOISEB. 1. Slake working drawings of tlie knuckle joint (Figs. 383 and 384) for a 2" rod. 2. Hake a working drawing of the end of a suspension link to take a load of twenty tons; the width of the link is 8". You may make use of the propor- tions recommended by Berkley, and use a working tensile stress of five tons per square inch. What shear stress is the pin subjected to, and what crushing stress ? 3. Draw two views of a 15-teeth sprocket wheel for a single flat-link gearing chain, whose pins are T V' diameter, and whose links have a pitch of 1". Figs. 391 and 393. SKETCHING EXERCISES. 4. Sketch three forms of eyes for suspension links, and give their usual proportions in terms of the width of the links. 5. Sketch a forked pin or knuckle joint. Figs. 383 and 384. 1 See the author's " Geometrical Drawing," p. 160. CHAPTER XVII BEARINGS, JOURNALS, HANGERS, ETC. 167. THE parts of a shaft, spindle, or rotating piece which are supported by the bearings are called Journals. The simplest form of bearing is a cylindrical hole in the frame of the machine, such as is shown in Fig. 395, which is often met with in rough crane work. We have in this case a Solid Bearing, in the sense that it is not split, but in one piece. When end movement of a shaft or spindle of a machine J is to be prevented by the bearing, the journal is usually fitted with solid collars, as shown in Fig. 397, but of course this necessitates making the bearing with a cap, as shown in Fig. 398. Solid cast-iron bearings, if of ample proportions and made of hard tough cast iron, are used in some classes of work with most satisfactory results, and with very little wear. And, should the wear become excessive, they can be restored and fitted with gun-metal bushes, but in this case it is not always easy to bore them true to the original centres, so this is an additional reason for bushing them, as in Fig. 396, although it adds to the first cost. TYPES OF BEARINGS. Y ?m YFRAMEf \S-tZ& 1 o I p - L " FIG. 395. Solid FIG. 396. Bushed Fio. 397. Journal FIG. 398. Bearing FIG. 399. Collar FIG. 400. Thrust FIG. 401. Footstep FIG. 402. Area bearing. solid bearing. with solid collars. in two parts. bearing. block. or toe bearing. of bearing. In each of the cases we have referred to the direction of the pressure on the bearing is perpendicular to the axis of the shaft. But two other typical cases occur when the main pressure is parallel to the axis. In the first, a Thrust Bearing either of the form Fig. 399, called Collar Bearing, or Fig. 400, with more than one collar, called a Thrust Block, is used. In the second, we have the case of the vertical shaft, where the end pressure is taken on what is called either a Footstep, Toe, or Pivot Bearing. In all of these cases the direction of the pressure on the bearing is indicated by an arrow in the figures. 1 In the case of line shafting the end movement is prevented by loose collars, as shown in Figs. 86 and 558. BEARINGS, JOURNALS, HANGERS, ETC. 135 168. Effective Area of a Bearing. The total load or pressure any bearing will support is the product of the working pressure allowable per sq. inch, and the projected area, the projection being taken in the direction of the load, on a plane at right angles to it. Thus, in the Footstep Searing, Fig. 401, the projection is a circle, 1 and the area of the bearing surface will therefore be D 2 ? and in the TJirust Block, Fig. 400, the area will be the sum of the areas of the collars, or A = -rC^i 2 D 2 )N, where N is the number of the collars. Then we have the important case of the ordinary Horizontal Shaft, Fig. 395, and Fig. 402 shows the projection of the bearing surface, 2 its area being L x D, and this time the working pressure p equals the total load W, or p = T ^. i-t X \J VARIOUS BEARING ADJUSTMENTS. FIG. 403. FIG. 404. FIG. 405. FIG. 406. FIG. 407. 169. Various Bearing Adjustments. In arranging bearings so that adjustments due to wear may be most effectively made, attention must be paid to the direction of the load on the bearing. Thus, in Fig. 403, the load is vertically downwards, and if it always acts in this direction a top brass, or step is not required ; indeed, often the bearings for line shafting are fitted in this way, and with wood or shell caps to hold the lubricators and keep the dirt out. But in the crank shaft bearings of engines and similar machines the pressure acts alternately in opposite directions, and then two brasses are used, the dividing plane being perpendicular to the direction of the maximum pressure. Figs. 404 to 408 show five arrangements of this kind which speak for themselves, whilst 1 Obviously this area is independent of any curvature that may be given to the ond of the shaft. - Of course, the real pressure between a journal and its bearing varies from point to point, and p is a kind of mean value of the actual pressure. Strangely enough, Mr. Box, in his well-known work on Mill Gearing, takes the area to be half the area of the journal, or A = -. This must be remembered should the student refer to Box's table of pressures. FIG. 411. FIG. 412. FIG. 413. 136 MACHINE DRAWING AND DESIGN FOR BEGINNERS in Figs. 409 to 413 five arrangements for dealing with more complex cases of varying pressure are shown. It will be noticed that in Fig. 412 the wedge end of the bolts for side adjustment W has its larger end at the top ; the objection to this is that, should the nut work loose, the wedge is apt to work down and cause the packing piece to jamb the shaft. For this reason the arrangement shown in Figs. 411 and 413 is to be preferred. For the matter of that, there is much to be said against the practice which is so common, where large engines of the stationary type are concerned, of taking up the wear by means of wedges acting on the three or more brasses forming a bearing, for unless the greatest care is taken in the design, construction, and adjustment, no advantage will accrue from such refinements, 1 and the results are likely to compare unfavourably with the use of the simple ordinary two-part steps used by the locomotive and marine engineer. 170. Plummer Blocks or Pedestals. The simplest form of Pedestal is the cast-iron Bearing Block shown in Figs. 414 and 41"), which BEARING BLOCK, OR SOLID PEDESTAL. UNIT d+i FIG. 414. Sectional elevation. FIG. 415. Sectional end elevation. in this or some form varied to suit special jobs is largely used in some classes of rough work. Of course the oil hole is made in the part of the block which is highest when fixed. Suitable proportions are marked on it, the unit being d + ". An improvement on this form is shown in Figs. 416 and 417, the bearing being fitted with a cap, so that, by filing the packing piece, or when none used, the top AB of the block, or the bottom of the cap, wear can be taken up. This form also allows of a shaft with collars being used. Figs. 418 and 419 show how this type of bearing is arranged to form part of the frame of a machine. 1 Refer to Spooner's and Davey's ' Elements of Machine Construction and Drawing," p. 49. BEARINGS, JOURNALS, HANGERS, ETC. 137 171. Ordinary Plummer Block or Pedestal, Unit = D + ". An ordinary Plummer Block is shown in Figs. 420 and 421. The actual forms and proportions of these vary somewhat (for the same size shaftings) with different makers, but they all have the same essential parts, namely, the block B, cap G, brasses or steps S, and bolls E. FRAME BEARING. Fios. 416, 417. Adjustable cast-iron bearing. FIGS. 418, 419. The advantage of fitting the blocks with brasses of the shape shown is that they can have their fitting edges turned, and the block and cap bored to correspond. But for the heaviest work the old-fashioned brasses, Figs. 427o and 427n, with backs of octagonal form, 138 MACHINE DRAWING AND DESIGN FOR BEGINNERS ORDI NARY PLUMMER BLOCK OR PEDESTAL. UNIT 1-65- cannot be surpassed, as with them, when properly fitted, the whole of the bottom surface of the lower brass is supported by the block, and the flow of the brass under pressure and jarring is prevented. Of course the brasses are filed at the joints a and b (Fig. 420) to take Up wear when necessary, but this has to be done with great care, or the shaft is held tight when the cap is bolted down. 172. Seller's Self-adjusting Pedestal. We have explained that cast-iron bearings run remarkably well when properly proportioned ; indeed, with a length of four diameters and efficient lubrication, such bearings show little sign of wear after a lengthy run of the shaft at high speeds, so long as the pressure does not exceed 50 Ibs. per sq. inch, and there is perfect alignment of the shaft. To secure this Mr. Seller designed his Pedestal, Figs. 422 and 423, in which it will be seen that the seats A and B of the cast-iron steps are spherical, and that so long as the pedestal has been fixed the right height and in the correct position, the steps can adjust themselves to a slight extent to the position of the shaft. The centre cup C is for ordinary lubrication, but the side cups T are fitted with a mixture of oil and tallow, which at ordinary temperatures is solid, but melts should the bearing be heated up to about 100 F., and in so doing protects the shaft from injury ; the drippings falling into the side cups D. 173. 3" Plummer Block or Pedestal (Drawing Exercise). The parts of a 3" pedestal are shown separated in Fig. 427, and the student should now be able to assemble them. Instructions. The following views of the complete block may be shown. (1) Elevation, (2) Plan, (3) Section on Line AB, (4) End Klevation. Each view is to be property projected and completed. Then write upon each part the name of the material of which it should bo made. Show chipping and facing pieces to block and brass, and lighten out brasses to save material nnd minimize labour ; show long holes in block for adjustment, and how you would make the oil channels. Scale, half fall size. FIGS. 420, 421. ; 174. Crank Shaft Bearing (Drawing Exercise). Parts of an adjustable bearing for the crank shaft of a horizontal engine are shown in Figs. 424, 425, and 426. The adjustment for horizontal wear is made by screwing up the wedge pieces, as explained in Art. 169. Instructions. Elementary students may draw the bearing complete, placing the various parts in their proper positions, and showing the left-hand half of view Z in section on line AA and the right-hand half in elevation. Project from it an end elevation, as seen when looking in the direction of the arrrow X. The plan need not be drawn, but dimensions for other views taken from it. Scale, quarter full size. BEARINGS, JOURNALS, HANGERS, ETC. 139 175. As a more advanced exercise Studentt may draw the bearing completely put together, showing the left-hand half of view Z in section on line AA, and right- hand half in elevation, also a complete plan, and a vertical section on line MM, when looking in the direction of the arrow X. Scale, quarter fall size. SELLER'S SELF-ADJUSTING PEDESTAL. WITH CAST IRON 176. Brasses, or Steps. We have seen, Art. 169, that certain bearings are fitted with brasses (or steps, as they are sometimes calldd) ; but the names do not really indicate the material, as they are usually made of gun-metal or an alloy of that type, such as phosphor or. manganese bronze. There are several ways of forming them and fitting them to the supporting surfaces of the bear- ings, of which they form part, shown in Figs. 427A to 427L. The unit for the proportions is usually t, the thickness of that part of the brass which supports the load, and this may be for average thicknesses, t = O'OSD + 01". The brasses shown in Figs. 42?A, 427c, 427l, 427M, 427o, and 427s, are usually fitted by turning the fitting-strips (on backs) and boring the block or bed which receives them. Eotation of the brasses in the block and cup is prevented by either a stop- pin, as in Figs. 427A and 427B ; by stop lugs, as in Figs. 427c and 427D ; by rectangular chipping strips, as in Figs. 427u and 427i ; and by (for Figs. 427i, 427M, 427o) the top of the upper brass being flat, the cap keeping them in position, or, should the back of the upper brass be also round, the cap is fitted with lugs which hold the packing pieces tight, and prevent rotation. 177. White Metal Bearings. Many bearings are now fitted with white metal, or Babbit's anti-friction metal. 1 There are several ways of doing this. Fig. 427Q shows the metal run into the grooved bed of the bearing when the shaft is in position. In Figs. 427.W, 427N, the metal has been run into the brass, caulked, and the hole bored in the usual way, whilst in Fig. 427R the spiral grooves, and in Figs. 427o, 427p, the round holes, are filled with the white metal. 2 Another method is shown in Fig. 427s, longitudinal strips of the white metal being fitted and driven into the grooves. Owing to the contraction of some of these alloys in 1 An alloy of copper, tin, and antimony. The employment of these so-called anti-friction, soft, white metals is in the nature of a makeshift, and is largely due to the heatiny troubles which are met with when ordinary bronzes are used. Another very important anti-friction metal is Perkins'. It is an alloy of tin and copper in the proportion of 5 to 16, and is whitish in colour, but, unlike the white metals referred to, is very hard a'nd exceedingly brittle, and the author's experience is that it makes admirable piston rings and slide-valve faces for very high steam pressures with or without lubrication, when exceptional care is taken to prevent fracture, the rubbing surfaces becoming very smooth and mirror-like. * These expedients are employed to prevent flow of the soft white metal under pressure. This metal must always be encased by a metal such as bronze or cast iron, strong enough for the purpose to prevent such flow. Fio. 422. FIG. 423. DRAWING EXERCISE. DRAWING EXERCISE. Centf-e i-f Shq*f - *- - Z^n ... . .8*1 4**' 4- iTZiddle far of HZettl. (2 ifeus). _ .zr"-_ Akij_ 05- Jtal^ Sectfoa D.D. _ ^alfSectroKZ .._>talf l CUju&fittg Screw -for Vledqts. Waiktr & Locking fiiz.v r 4 v (- - S*\ ?w M/ ^ \\^RXCE.V' N\^V,\V,\; ---{- -1- --L: 1 . ' THREE POINT FOUR POINT CONTACT STRIBECK'S RACES. CONTACT |G i i \ K. <" ^i \ (5 i MiT i I D-frrf-H-F -1-H FIG. 462. FIG. 468. FIG. 464. FIG. 465. Fia. 466. FIG. 467. Fio. 468. Fw. 469. surfaces, and it is called a two-point bearing, because contact occurs at two points, A and B, and the parts C and D, which are in rolling contact with the balls, are called races, each race being a solid ring. Now, to prevent any tendency of the balls to get out of position sideways, it might appear that the best form of the races would be grooves whose radius is just equal to that of the balls, as shown in Fig. 463, but, obviously, with such an arrangement the friction becomes excessive ; so, to avoid this, the three- or four- point contact is used. Figs. 464 and 465 are two examples of three-point contact ; in each case one of the races is cylindrical and the other grooved, both sides of the groove making the same angle with the axis of the bearing, so that mn, Fig. 464, the two points of contact of the ball against the sides of the race, shall be the same distance from the axis (this also applies to Figs. 465 and 466). It can be easily understood that when the ball is pressed between the sides of the groove the pressure will slightly flatten the ball where the contacts occur, instead of the contacts being geometrical points, as they would be if the ball and race were inelastic. Now, this being so, it can be conceived that the ball has a rolling motion in the groove combined with a slight spinning 1 motion 1 We have referred to this spinning or grinding action in Art. 188, 156 MACHINE DRAWING AND DESIGN FOR BEGINNERS BALL BEARINGS. THREE POINT CONTACT. 4.W VARIOUS CONTACTS. FOUR POINT CONTACT CUP AND BALL TWO" POINT CONTACT about the axis mn. Of course, with this form of bearing, the only resistance it can offer to end motion (in the direction of the shaft's axis) is the sliding friction between the balls and the cylindrical surface ; on the other hand, care must be taken to make the angle large enough or the balls may bind or wedge between the races and probably become fractured. In Fig. 466 is shown a four-point contact arrangement. Although this bearing is chiefly used to support a pressure normal to the axis of rotation, it will also resist to a certain extent end thrust, but two firmly fixed, bearings of this kind should not be used on the same shaft, especially when it is a long one, as any change of length of the shaft due to differences of temperature tends to force the balls against the sides of races with possible damage to them or the balls. Such a bearing, however, can be used on the same shaft with others made a loose fit in their respective housings so that they do not restrain end motion. The angle 6 should be not less than 30, and this also applies to in Fig. 466. Fig. 467 shows the form of races (first suggested by Professor Stribeck), which are now largely used, they are struck with a radius of about % to y times that of the balls. With this form a greater load can be carried with less friction. Figs. 468 and 469 show how one of the rings or races R may be fitted with a removable piece P, accurately fitted, and held in position by the screw shown, to allow of the balls being introduced or withdrawn. 196. Journal Hub Ball Bearings. Form of Constraining Surfaces. In arranging the constraining surfaces care must be taken that the balls have no effective tendency to leave their proper path ; thus in Figs. 470 and 471, the tendency of the balls to leave the races is reduced to a minimum, as the races are so formed that true rolling occurs. When a load W (Fig. 470) on the three- point contact bearing is supported, the reactions Q and R (whose relative magnitudes are shown in the triangle of forces) at a and d on the hub and cone respectively, create small areas (as we have seen) on the ball and cause it to roll witli a motion akin to that of a cone, whose sides dC and baG should intersect in a point (C) OK the axis CF, as shown, if true rolling is to occur. To avoid any tendency of the balls to wedge between the cup and cone, the angle at A should not be less than 30. Fig. 471 shows the arrangement for a four-point contact bearing. It has the advan- tage of being more compact than the preceding one. Of course, FIG- 471. FIG. 472. the angle at A, and the corresponding one opposite, should not be less than 30, and the lines abC and edC (passing through the contact points) must intersect in the axis, as shown at C, and just explained. The well-known cup-and-ball two-point contact is shown in Fig. 472 : it is extensively used for the wheels of cycles and very light cars, etc. ; each ball runs in a pair of concave races, whose radius should not exceed some y the radius of the balls, to prevent side motion, for with this arrangement the balls are not in a stable condition, the actual positions of their contacts with the races being indeterminate. Of course, any tendency of the balls to roll further out from the axis or nearer to it is resisted by the increasing slope of the sides of the races, so the bearing automatically adjusts itself into a position of equilibrium, but to prevent wedging it is advisable to well lubricate the bearing. Obviously, this bearing is capable of resisting a small side or end thrust, but we shall directly see that for heavy vehicles, where very considerable side thrusts occur, a more satisfactory bearing is used. FJS. 470. ROLLER AND BALL BEARINGS 157 197. Ball Thrust Bearings. The simplest way of taking the end thrust or pressure of a shaft is to arrange balls between two rings or discs whose planes are normal to the axis of motion, but this necessitates the use of a retaining cage, as we shall directly see. If this is to bs avoided, one or both of the rings or discs may be grooved to constrain the balls to move in a circular path. Fig. 473 shows one way of doing this, the lower or bearing ring being flat and the upper ring grooved, giving a three-point contact. As explained in the previous article, if spinning or grinding of the balls is to be prevented, the sides of the grooves must be so shaped that a line baC, through the points of contact a and b, must cut the surface Cm of the ring in a point C in the axis of motion, as the motion of the balls is akin to that of a cone, as previously explained. The pressures on the balls due to a weight W is shown by the triangle of forces, WQR. One of the rings may be coned, as in Fig. 474, at DE. Then, if DE be produced till it cuts the BALL THRUST BEARINGS. THREE POINT CONTACT THRUST. iw THREE POINT CONTACT THRUST. BEARING RING. \ 'BEARING RING. FOUR POINT CONTACT THRUST. BALL THRUST WASHER TWO POINT CONTACT WITH CAGE. FlO. 473. FIG. 474. FIG. 475. FIG. 476. axis in C, a line Gab must cut the ball in a and b, the contact points with the sides of the groove, giving a three-point contact. In this case W is resolved into the normal force P acting on the ball and a force H perpendicular to the axis, P being resolved into E and Q, the other two pressures on the ball. If both rings be grooved, we get four points of contact, as in Fig. 475, which should speak for itself. Professor Goodman has called attention to the fact that " although these forms of thrust bearings are right in principle, they are not found to work well in practice, probably because the exact conditions are upset when any wear or change of load takes place. A series of tests of some bearings of this type showed that the balls began to peel and score and the races to grind at very low loads and speeds." Hence, we find in the best practice that flat or slightly hollow races are used, giving a two-point contact, as shown in Fig. 476, which represents one of Messrs. Hoffmann's ball thrust washers l designed for the spindles of drilling machines, feed and elevating screws, worms and mandrils of lathes, etc. The balls are held in the gun-metal retaining case or ring 2 whicli keeps them in position and prevents them falling out when the bearing is dismantled. The diameters of the holes in the top and bottom hardened steel washers which form the ball races are made five thousandths of an inch above standard size, so as to allow the shaft to revolve freely inside the stationary race. 198. Ball Journal Bearings. The simplest form of a single-row ball bearing is shown in Fig. 477. It can only be used when a 1 Those bearings carry no journal pressure, but only end thrust. To equally distribute the load over all the balls, one of the washers is sometimes fitted with a spherical buck which allows it to swivel into its exact position when the load is applied. : The thickness of the ring is about one-half to two-thirds the diameter of the balls, and holes are drilled for the reception of the balls, the top and bottom edges of the holes being slightly burred over to keep the balls in position. 158 MACHINE DRAWING AND DESIGN FOR BEGINNERS journal load has to be carried ; great care must be taken to fix tbe shaft and bearings, so that the former may be free to expand and contract, due to differences of temperature, without putting any end thrust whatever upon the bearing. The most satisfactory way of fixing the internal race ring is to make it conical, as in Fig. 478, and to hold it on to a corresponding conical part of the shaft (or sleeve) by means of a nut or collar screwed upon the shaft, or, if this cannot be done, a split conical sleeve should be drawn into the conical part of the race ring by a collar nut or back nut to grip the shaft and race, a set-screw being used to prevent the collar-nut working off, as shown in the figure (478). HOFFMANN'S BALL BEARINGS. 199- Compound Ball Bearings. When a bearing is constructed by combining the thrust and journal bearings we have referred to, it is called a Com/pound Bearing. If arranged as in Fig. 479, it is a Single Compound Bearing, but of course this can take the thrust in one direction only, 1 and is therefore suitable for such arrange- ments as footstep bearings of vertical shafts, for clutch shafts of motor-cars, where conical clutches are used and there is an end thrust, etc. Eeferring to the figure just above and to the right of the journal balls, a spring will be seen ; it is slightly in compression, and keeps the balls properly in contact with their races, it also allows of any slight contraction or ex- pansion of the shaft. In certain applications of this bearing the spring is dispensed with, and a distance piece used to fill space occupied by it. It is absolutely necessary to firmly clamp the cone upon the shaft, and the simplest way of doing this is shown, it being a slight variation of the one explained in the previous article. When it is required to remove the bearing from the standard housing, the small locking screw FIG. 477. Single row journal bearing. FIG. 478. Journal bearing. FIG. 479. Single compound. is removed and the disc nut unscrewed at the right-hand end of the housing, where the bearing can be withdrawn. The balls, being held in ball retaining cages, will not drop out. Students may refer to the author's " Machine Design, etc.," p. 283, for data for designing ball bearings. 1 It is often convenient to use two of these tingle compound bearings on the same shaft, in cases where there is thrust in both directions, instead of a double compound one. ROLLER AND BALL BEARINGS 159 EXERCISES. DRAWING EXERCISE. 1. Make working drawings (four views) of the roller bearing shown in Figs. 458 to 461. Scale full size. SKETCHING EXEBCISES. 2. Make sketches showing the difference between a rintj cage and a solid cage for a roller bearing. 3. Show by sketches two ways of arranging a roller thnift bearing. In one case the bottom bearing plate is to be flat, and in the other conical. 4. Make a sketch of a cylindrical roller thrust bearing. Why are the rollers in such bearings usually staggered? 5. Explain what is meant by a roller or ball spinning. Illustrate your answer by sketches. Do you consider ball bearings require lubricating? If so, why, and what lubricant would you use ? 6. Show by diagrammatic sketches the difference between three-point and four-point contact in ball bearings. What conditions must be satisfied if spinning is not to occur ? 7. Show by a diagrammatic sketch the difference between three-point and four-point contact in ball thrutt bearings, and define the conditions which must be satisfied if there is to be true rolling contact on each of the races. CHAPTER XIX TOOTHED GEARING 200. Introductory Remarks. Toothed wheels have been used for the transmission of motion and power since the days of Archimedes, about two centuries before the Christian era, but it remained for geometricians of comparatively recent times to investigate and solve the problems which have enabled the engineer to shape the teeth of wheels so that practically the same uniformity of motion 1 can be transmitted from one to the other as if they were plain cylinders (or cones) rolling on one another by frictional contact ; in fact, in every pair of spur wheels we have two imaginary cylinders 2 (and in every pair of bevel wheels two imaginary cones) provided with certain projections or teeth, and intermediate depressions or tooth spaces, so that the teeth of one wheel enter the spaces of the other, but, when these teeth are properly formed, the velocity of one wheel in relation to that of the other, that is, the angular velocity ratio, is inversely proportional to the diameters of the imaginary cylinders 3 and cones, as we shall see directly, and these cylinders and cones are represented by circles (called pitch circles) on the wheels, as shown in Figs. 480 and 481. /, / v_A/'\^ I X 201. Relative Speeds. If the pitch circles, Fig. 480, roll on one another / I y 9 V ~^~) s\ i / they have the same velocity, that is, travel the same distance in a given time ; s*?r>s si~J JL s * D 71 _ . _| _ therefore NDn- = ndw, or -, = where N and n are there volutions per minute / of wheels A and B respectively. But the angular velocity is proportional to the revolutions ; therefore the angular velocities are inversely proportional to the diameters of the pitch circles. 202. Technical Names of Teeth Details. An inspection of Fig. 481 will enable the student to understand the meaning of the technical names of the FIG. 480. different parts of wheel teeth, as we shall frequently have to make use of them. The diagram should speak for itself. 203. Pitch, etc. Fig. 481 shows that the pitch of a wheel is the distance, centre to centre, of two adjacent teeth, but there are 1 As the inertia of heavy moving parts resists alteration of velocity, any variation in the uniformity of the motion causes the driven wheel to alternately fall back and overtake the driving wheel (a jerky action, technically called back lash), with loss of power, vibration, and noise. Wheels correctly designed, made, and fitted, will bear evidence of uniform contact from the point of each tooth to some distance below the pitch circle. 2 The pitch surfaces. ' This condition of com fancy of Telocity rniio may to some extent be secured by hving the teeth small and numerous. TOOTHED GEARING 161 two ways of measuring it, namely, along the arc, and along the chord, and among the earlier authorities there used to be a great difference of opinion as to which of these is correct. But, if the diameters of wheels are to be exactly proportional to the number of teeth, the pitch must be measured by the length DEFINITIONS. / f tne arc > or a ' on o tae curved pitch line, and this, the , ^PQ/MT- obviously correct way, was adopted by Willis, Rankine, and ~f ~~ "V*f*i . others, and is now the accepted mode. This being so, the relationship of circular pitch, 1 diameter, and number of teeth is expressed by the equation DTT = Njp, where D = the diameter of pitch circle in inches, p = pitch in inches, and N = the number of teeth. 2 * G\* C > *o<^ ^PA FIG. 481. mu -r> N DTT , , T DTT Then D = -^- , p = ^ , and .N = 7T N p 204. Diametral, or Manchester Pitch. The use of this pitcli has been much extended since the advent of the motor-car in this country, as it has been largely used in connection with its gear wheels (the other pitch used for these wheels is the French Module), thereby avoiding inconvenient fractions in their pitch diameters, as with the diametral pitch system the diameters of the pitch circles can always be made suitable. In the practice of Messrs. Browne and Sharpe, and Messrs. Sharp, Stewart, & Co., of America, the dimetral pitch equals the number of teeth divided by the diameters of the pitch circle. 3 So that it is a ratio and not a measure like the circular pitch. To further explain, let D = the diameter of pitch circle, pa = the diametral pitch, N = number of teeth, p = circular pitch. Then And diametral pitch number D' N = Dp* 1 Pd Pd The addition to diameter for increased number of teeth = Xum ^ to _. tejd&*d 2 Pd Outside diameter of wheel = (- D. And circular or true pitcli = PJL 1 Circular pitch must not bo confused with diametral pitch. When the word " pitch " is alone used, circular pitch is referred to. - It is the practice of some engineers to make one of a pair of equal wheels with an additional tooth called a hunting cog. Then eacli tooth of one wheel will encounter each tooth of the other equally often, and the wear will be equalized. Any pair of wheels will have a hunting cog if the teeth of both cannot be divided without remainder by any number except 1. In other words, the numbers must be prime to each other. 3 But the diametral pitch which is perhaps more commonly used in this country is the reciprocal of this, OT^J- Then the circular or true pitch p = irp,,. Y 162 MACHINE DRAWING AND DESIGN FOR BEGINNERS Distance between axes, or centre distance Sum of the number of teeth EXAMPLE. A 12 pitch wheel (diametral, or Manchester pitch), 8" diameter, will have 12 x 8 = 96 teeth, and the true or circular pitch 1 h = 0-2618". MODULE OR FRENCH PITCH. 205. Module, or French Pitch. This pitch, which we have just referred to, is the one in general use in France, the country from which so many of our finest motor-cars have come, so that the business relations between the two countries in connection with this remarkable industry, to say nothing of the inherent advantage of the system, are leading to an increasing use of it in this country. The module is the diameter of the pitch circle in millimetres divided by the number of teeth, and it equals the length of the face part (M) of the tooth, as shown in Fig. 481 A. For other relationships Let D = diameter of pitch circle in millimetres. D 2 = diameter of circle tipping teeth. M = module in millimetres (face length orjieight above pitch line). N = number of teeth. = circular pitch in millimetres. = thickness of teeth on pitch line. = clearance at top of teeth. Then root length = M + x. p T FIG. 48lA. And And x = 1-5708M 1 *~ * M = M(N + 2) M 206. EXAMPLE. A wheel with 60 teeth and Mod. 10 pitch will have a diameter of pitch circle = 10 x 60 = 600 mm., and an outside diameter of 10(60 + 2) = 620 mm., whilst M, the face or height of the teeth above pitch line = - 6 ,. (l = 10 mm. 207. Form of the Teeth. Geometricians have shown that there are only two curves, namely the cycloid and the involute, 1 which completely fulfil the condition of giving the perfect uniformity of motion referred to in Art. 200. Teeth of the cycloidal type are generally used in ordinary work, as they cause less thrust on the bearings than involute ones, the thrust being perpendicular to the line of centres at the instant of crossing it. On the other hand, the thrust of the latter is constantly in the direction of the common tangent of their bases. However, they have many advantages over the former, which make them suitable for use in some cases, particularly where the distance apart of the centres requires to be variable, as in rolling mills, or where great strength and practically no back lash are important factors, as in motor-car gears. 1 Refer to the author's " Machine Design, etc.," p. 297. TOOTHED GEARING 163 OF DRAWING _ We will now deal with cycloidal curves so far as they apply to the simple problems of forming the teeth of wheels. Now, if a circle be constrained to roll on another, any point in the moving circle (called the rolling circle) will describe a curve. If the rolling circle roll outside the other, as shown in Fig. 48lB, which should speak for itself, 1 or as at P on circle B, Fig. 482, the curve PP 2 generated or described will be an epicy- cloid 2 (used for the faces of the teeth on wheel B), whilst if it roll inside circle A, as at P 3 , the curve P 3 P4 is called an hypocycloid (used for the Hanks of the teeth on wheel A). It is a peculiar, and in this con- nection useful, fact that, if the rolling circle be half the diameter of the circle it rolls on, the hypocycloid is a straight line, in fact, a diameter of the pitch circle. This is shown both at P 3 P 4 and Q 3 Q 4 in Fig. 482. It is often convenient to use this particular form of the curve for the nanks of the teeth, as they then become radial, as at B, Fig. 487. If, on the other hand, the rolling circle rolls on a straight line, the curve genera ted is a cycloid, used for the curves of the teeth of racks. Now, let us suppose that A and B, Fig. 482, are the pitch circles of two wheels which are to gear together, we may, for present purposes, arbitrarily select CURVES OF TEETH. FIG. 481s. Generation of cycloidal curves by rolling circles. 1 Refer to author's " Elements of Geometrical Drawing," p. 182. 2 For much useful information relating to these curves, see the author's " Elements of Geometrical Drawing," p. 177. 164 MACHINE DRAWING AND DESIGN FOR BEGINNERS any size rolling circle to generate all the curves, but it will be better understood directly that, for USE OF TEMPLETS IN SETTING OUT CYCLOIDAL TEETH. VUSEOFNEEDLE Fio. 482. FIG. 483. 208. Setting out Cycloidal Teeth, Use of Templets, etc. In setting out these curves or drawings of practical reasons, this rolling circle must not in any case be smaller in diameter than the radius of the pitcli circle of the smallest wheel in the train, in this case B ; and if condition be satisfied for any number of wheels in a train, it is a fundamental fact that any two will correctly gear together, if the teeth be made of the same pitch. It will be observed that in all cases the part of the tooth below pitch line works only with the part above pitch line in its fellow, and vice versa. This being so, it is obvious that we may elect to use a certain size rolling circle for the flanks of one wheel of a pair, and the same circle for the faces of the other, and this will enable us to have radial flanks in each wheel, which has been done in Fig. 482, the hypocycloid P 3 P 4 , and the epicycloid PP 2 , being generated by circles of the same diameter, equal to the radius of pitch circle A. Also the hypocycloid Q 3 Q 4 , and epicycloid VV 2 , are generated by circles whose diameter is the radius of the pitch circle B. tooth forms the draughtsman TOOTHED GEARING 165 who has studied practical geometry experiences no trouble, for after geometrically finding a few points l in each curve, he draws a fair line through them, and then finds the centres and radii of circular arcs that closely approximate to the cycloidal curves, and uses them to describe the teeth ; or Willis' Odontograph 2 can be used with advantage to find the centres of arcs which will closely approximate to the true cycloidal ones, so that all wheels of the same pitch will truly gear with one another. When this instru- ment is not used a portion of the pitch circle may be drawn to full size on paper (or on a smooth chalked board), and a templet, WY, Fig. 482, may be made, formed of wood, say ^" thick, shaped to the arc, and laid upon it. In the same way a segmrat of the rolling circle, JK, may be made, and a needle driven obliquely through the edge of it, as shown in Fig. 483, its point being made to just coincide with the arc at P. Then, by placing one hand on the templet, and with the other moving the segment (being very careful to prevent slipping), a clean fine line or groove 3 is made on the paper from P to P 2 . In this case the same size rolling circle generates f - /4 _.Ui/ xy/v /Qj t^f \ Fid. 488A. being the same. Conversely, the general effect of reducing the size of rolling circles is (a) to decrease the arc or number of teeth iu gear at once, and thereby decrease the power the wheel can transmit, also to increase the obliquity of action for a given length of tooth ; (b) to increase the thickness of the teeth at the root, and thereby increase the power the wheel can transmit, by increasing the strength of the teeth ; (c) to increase the wearing surface, and therefore the durability of the wheel. It will thus be seen that the best size rolling circle in any given case is in the nature of a compromise, and the relative value of each of these factors can only 168 MACHINE DRAWING AND DESIGN FOR BEGINNERS be determined by trial in each case. But for trains of wheels such as are used for screw-cutting lathes and machine tools, the smallest wheel usually has 20 teeth, therefore the rolling circle for all the wheels may have a diameter equal to the radius of the 20-teeth one. Whilst for rough crane work the smallest pinions sometimes have a minimum of 11 teetli ; on the other hand, the more important wheels used for transmission of power should never have less than 24 teeth, which corresponds to the line of contact (or obliquity) making an angle of 15 with the common tangent to the pitch lines * (or circles). 210. Proportions of Various Teeth, etc. In Table 8 we have given the various proportions of wheel teetli in ordinary use. It will be noticed that in some respects they vary between pretty wide limits, so it will be as well to explain why this is so. Commencing with the clearance, obviously, a wheel cast from a wooden pattern, which has perhaps been stored in a damp place and has warped out of shape, and in the mould has, by irregular ramming, been still further distorted, will require more clearance both at the top and bottom and sides of its teeth 2 than one whose teeth have been shaped or machined accurately to form and size. Thus we have (in the second column of the table) a clearance of 0~55p 0'4:5p = Q'lp in the ordinary wheels made from wood patterns, which are almost of the proportions Fairbairn adopted (third column) in his extensive practice, whilst we see that machine- moulded wheels (fourth column) have only 0'52p 0'48p = 0'04j clearance, and that machine-cut wheels have practically no clearance 8 (eighth column) ; but of course these are only used under ideal conditions, where it is possible to make a pair of wheels TABLE 8. PROPORTIONS OF VARIOUS TEETH. Common Machine- Farts of teeth. Refer to Fig. 481. pattern- moulded Fairbairn's proportions. moulded wheels, Adcock's proportions. Mortise wheels. Mortise bevel wheels. (Kne 6 ; lid Sbarpe). wheels. say Pitch of teeth. p P P P P P P Diametral Height above pitch line F . Depth below pitch line R . Thickness of teeth t . . . 0-33p 0-45p 0-35p 0-40p 0'48p 0-2p 0-Sp 0-48p cog, o-6 ; iron teeth, 0'4/j 0'25p to 0'3p 0-3p to 0-35/j cog, o'6p ; iron teeth, Q-4p 0-318^ 0'368p 0-5p l-SJlp't Width of spaces S . . . 0-55p O52p 0'52^* 0-4/; Q-4j> 0-& 1-67&, Total length 1 0-75i> 0-7p 0-5p Q-&f 0-55p to 0-05// 0-686 )-l57pj Width of teeth 1 . . . . 2pioBp 2p to 3p - which shall always be in contact on both the working faces and the backs. But it more often happens that the teeth have from eV" * ii-i" clearance, according to size, etc. When the clearance is small, even with well-formed teeth there is often liability to 1 Refer to the author's " Machine Design, etc.," p. 297. * Refer to Plate No. 24, author's " Elements of Machine Construction and Drawing." ' Good machine-cut wheels can now be had at prices very little above those for wheels with ordinary cast teeth, aud the timi; saved in fitting up soon repays the extra cost. TOOTHED GEARING 169 ADCOCKS PROPORTIONS damage by the cross bearing of teeth due to wear of bearings or settlement, or by small objects falling into the wheels when at work. As to the length of the teeth, we have seen that the most suitable is a matter for judgment and experience. It is true that long teeth increase the arc of contact 1 (Art. 209a), and are indeed generally required to always remain in working contact at least in one place, when the pinions are small. But there can be little doubt that in mill-gearing, and similar cases where there are no small pinions, the length of the tooth can be reduced with a proportional increase of strength ; indeed, the trend of modern practice has been for some years in this direction, particularly in the Lanca- shire district, and the length of half the pitch recommended by Adcock 2 has been proved by experience to be a perfectly satisfactory one, particularly for uncut cast gears. But the appearance of these short teeth to the uneducated eye militates against their more general use. The table shows (also Fig. 489) that Adcock made the face length 0'2p, and the root length Q'3p, which allows bottom clearance enough (O'lp) for good fillets 3 at the root, as shown in the figure. TABLE SA. DIMENSIONS OP MACHINE-CUT WHEELS (BROWNE AND SHARPE). FIG. 489. Pitch number. Diametral pitch. No. of teeth Thick- Circular ness of Height above Depth Mow Total length Pitch number. Diametral pitch. No. of teeth Circular Thick- ness of Height above Depth below Total length 1-5-Pj " ~ Diam. pitch circle = 0-5 p. line'= Fv. line. of teeth. l-S-Pj "Warn, pitch circle = 0-5p. line=Pj. line. of teeth. J 2 6-283 3-142 2-000 2-314 4-314 4 0-25 0-785 0-393 0-250 0-289 0-539 1-333 4-189 2-094 1-333 1-543 2-876 5 0-2 0-628 0-314 0-200 0-231 0-431 l' 1 3-142 1-571 1-000 1-157 2-157 6 0-167 0-524 0-262 0-167 0-193 0-360 li- 0-8 2-513 1-257 0-800 0-926 1-726 7 0-143 0-449 0-224 0-143 0-165 0-308 lt 0-667 2-094 1-047 0-667 0-771 1-438 8 0-125 0-393 0-196 0-125 0-145 0-270 If 0-571 1-795 0-898 0-571 0-661 1-233 9 0-111 0-349 0-176 0-111 0-129 0-240 2 0-5 1-571 ! 0-785 0-500 0-578 1-078 10 0-100 0-314 0-157 0-100 0-116 0216 2| 0-444 1-396 0-698 0-444 0-514 0-959 12 0-083 0-262 0-131 0-083 0-096 0-180 4 0-4 1-257 0-628 0-400 0-463 0-863 14 0-066 0-224 0-112 0-071 0-083 0-154 2} 0-364 1-142 0-571 0-364 0-421 0-784 16 0-062 0-196 0-098 0-063 0-072 0-135 3 0-333 1-047 0-524 0-333 0-386 0-719 18 0-055 0-175 0-087 0-056 0-064 0-120 8| 0-286 0-898 0-449 0-286 0-331 0-616 20 0-050 0-157 0-079 0-050 0-058 0-108 1 Refer to the author's " Machine Design, etc.," p. 299, for arc of contact, etc., of involute teeth. 2 The Engineer of September 17th, 1869, also M. Longridge, has shown that oven shorter teeth, from 0'35 to 0'4p, are better calculated to resist wear and tear. This matter has also been ably treated by Prof. Archibald Sharp, C.E., B.SO., WH. s.c., in his paper, "A New Method of Designing Wheel Teeth," Proa. Inet. C.E., vol. cxiii. p. 241. 3 This materially increases the strength of the tooth, particularly when subjected to shocks. In cases where it is not considered necessary to use an ample fillet, the root length of 2p may be correspondingly reduced. The table shows that Fairbairu in his extensive practice used a fillet of O'Oop radius. Z 170 MACHINE DRAWING AND DESIGN FOR BEGINNERS 211. Gee's Buttress Teeth. 1 In cases where a pair of wheels run always in the same direction the teeth may be strengthened by making their backs in the form of a buttress, as shown in Fig. 490, the driving faces of the teeth being of the usual form. In this way it is claimed that they can be made 35 per cent, stronger than ordinary teeth. The back faces may be described by smaller rolling circles or by involutes of considerable obliquity, 2 but whatever curve is used for them, there is an obvious increase of obliquity which makes this form of gearing quite unsuitable for use in cases where back lash 3 is likely to occur, as severe stresses upon the teeth, rims, and journals are caused by the wedging action of the back of the teeth. 212. Knuckle Gearing. A very strong but imperfect form of teeth known as knuckle gearing, or Hollows and Rounds, is shown in Fig. 491. It is sometimes used for rough crane work and other slow-moving machinery exposed to much rough treatment ; and the teeth are formed by circles struck alternately within FIG. 490. and without the pitch circles. As might be expected, the velocity ratio is variable, as the teeth come into and go out of contact. 213. Breadth of the Teeth. When a tooth is engaged with its fellow, and is transmitting power, we have in some positions of the teeth in relation to one another approximately line contact, and therefore there is a limit to the allowable pressure per inch of breadth B (Fig. 492) on the face of the teeth apart from the strength of the teeth, which experience has proved should not be much exceeded. Fairbairn agreed with Tredgold's opinion and fixed this at 400 Ibs. per inch of breadth for cast iron, and in ordinary cases this might well be taken as the limit. 4 Obviously the condition of loading of a tooth is that of a cantilever supporting a load at its free end, and therefore its strength is directly proportional to its breadth, while the pitch and form remain constant. But, should the axis of the shaft to which one of the wheels is fixed get out of its normal position, due to wear of the bearings at one end or to any settlement, it may happen that the load instead of being distributed over the whole width of the tooth is supported at one of the corners ; or it may happen in a case where the clearance between the teeth was very small, causing them to bear on opposite corners, with a straining action enough to cause failure. Of course, other things being the same, the shorter the shaft the more serious this effect ; for these FlG 492 reasons, it is only when there is a great probability of maintaining contact across the teeth that the usual arbitrary breadth of 2 limes the pitch may be exceeded to the extent of 3 to 3^ times the pitch. Box was of opinion that the breadth of 2J times the pitch makes the breadth of the teeth for a wheel of small pitch too 1 Kefer to the Engineer and Machiniit'* Asuittanl-. These teeth were first suggested by Willis, in 1838. See Willis's " Mechanism," 2nd edit. p. 142. '' If all the curves be involutes, a large bnge-circle for the working sides mn is required, Fig. 490, and n small base-circle for the opposite sides. 3 Refer to Art. 200, footnote. 4 Although this 400 Ibs. per inch of breadth should not be exceeded in a general way, uncut cast-iron teeth of very good design, well lubricated, have satisfactorily run with a load of 800 Ibs. per inch. KNUCKLE|GEARING. TOOTHED GEARING 171 broad, and one of large pitch too narrow, and recommended that the following formula should be used to fix the breadth, namely, breadth of teeth B =j> 2 x 1-8 4- Vp. This gives for 1" pitch, B = I 2 x 1-8 = 1-8" ; and for a 4" pitch B = 4 2 x 1-8 = 14-4". 214. Rims of Toothed Wheels. Figs. 492 to 495 show the sections of toothed wheel ritns in general use; the unit in each case is the pitch. Usually the thickness of the rim is made equal to that of the teeth, therefore 0'48p has been assumed in these cases. RIMS OF TOOTHED WHEELS. For light work the section Fig. 492 is most suitable, and Fig. 495 shows a useful section generally used in heavy machine-moulded wheels. 215. Shrouding or Flanging of Wheel Teeth. The strength of the teeth of wheels can be.considerably increased by extending the width of the rim and carrying it outwards from the shaft, as shown in Figs. 496 to 498, the object being to reduce the effective length of the teeth as a cantilever, and thereby increase the break- ing strength. Obviously, the amount of this increase will depend upon the form of the tooth to which it is applied, and the arrangement of the shrouding. In the case of a pinion gearing with a large wheel or rack, there is a great inequality of strength, the tooth of the pinion being much thinner at the root than that of the wheel or rack, and therefore it is much weaker. In many cases the one is only 07 the thickness of the other, and therefore has only half its strength ; 1 but it can be shown that when this is so, by shrouding the pinion up to its pitch line, as in Fig. 497, the FIG. 492. FIG. 493. FIG. 491. FIG. 495. SHROUDING OF WHEEL TEETH. PROBABLE FRACTURES. fS i ^. ' \v KTO. 49(j. Single shrouding. FIG. 497. Double shroud- FIG. 498. Double ing to pitch line. shrouding. Whole length. FIG. 499. FIG. 500. FIG. 501. teeth have about the same strength. Further, as the teeth of the pinion are more often in contact than those of the wheel, they sooner become reduced in thickness by wear, and this should be borne in mind. The teeth of some large wheels are broader at the root than at the pitch line, and in form sensibly approximate to a parabola ; when this is so it can be shown that they are practically equal in strength throughout their length, and the shrouding would be useless if the opposite teeth were The strength varies as the square of the thickness. 172 MACHINE DRAWING AND DESIGN FOR BEGINNERS of the same material ; but such wheels are sometimes shrouded if they gear with a pinion of stronger material, a cast-iron wheel and steel pinion, for instance, the wear being greatest in the former. And occasionally they are shrouded for appearance' sake only. Another consideration which influences the designer is, that it may be more convenient to replace a pinion than a wheel, so that when the wheels may be subjected to unavoidable shocks, they sometimes shroud both wheel and pinion up to the pitch line, 1 as shown dotted in Fig. 497, or even shroud the wheel and leave the pinion plain, 2 as in Fig. 498. Of course, when teeth are shrouded right up to their points, as in this figure, failure must occur by shearing, probably along a line, dbc, Fig. 501, near the pitch line ; 3 shrouding in this way about doubles the strength of the wheel, but, needless to say, only one of a pair can be made in this way. It is sometimes only convenient to shroud one side of the pinion, and gear it with a plain wheel or a wheel shrouded on the opposite side, as shown dotted at A, Fig. 496. 216. Bevel Wheels. 4 We have seen, Art. 200, that in every pair of bevel wheels we have two imaginary cones (or pitch surface), Figs. 502, 503, and 504, rolling on one another with a common vertex a, which is the intersection of the axes of the two shafts. When the wheels are the same size and the shafts are at right angles, as in Fig. 502, we have what are called mitre wheels. Fig. 503 shows two unequal level wheels with shafts at right angles, and Fig. 504 a case where the shafts are not at right angles, but intersect at an obtuse angle O. 5 The pitch point p is in the common generator ap of the cones, in each case. Obviously, when the angle between the shafts, the velocity ratio, and the diameter of the pitch circle of one of the wheels are given, the pitch cones can be easily set out. Figs. 505 and 506 are views of a mitre bevel wheel, and the few following hints bearing on the drawings of this wheel may be of interest to the young student. 217. Drawing Example. Cast-iron Mitre Bevel Wheel. To draw the two views shown in Figs. 505 and 506, which are fully dimensioned, first draw the axis AL, and from any point A, set off the pitch line AP inclined 45 to it ; a parallel to AL, and distant from it the radius of the pitch circle, will cut this line in P, the pitch point ; through P draw DE at right angles to AP, and set off E and D the root and point of the tooth from P on this line. The length of the tooth may be now set off from P, on line PA, and the thickness of the rim EG from G, and finish these parts by lines from the vertex A, as shown, making the end of the tooth at F at right angles to the pitch line AP. From K, set off the length of the boss for L, and HL for the thickness of the web part. The centre N can then be found by bisecting the angles at H and L. The vertex B of a cone whose side is DG produced till it cuts the axis AB, can now be found and the arcs DS, PQ, and ET, forming part of the development of the back cone, described, and upon these the true shape of the teeth is set out, as shown. The circular arcs, of radii 2|" and 1|" forming the teeth, give very close approximations 6 to the true curve, and the drawings can now be easily finished 1 Wheels gearing together that do not much differ in diameter may for ordinary cases be shrouded up to the pitch lines. = Other expedients are making the teeth of different thickness, and the use of frictioual slipping devices. 3 Figs. 499 and 500 show at dbc the probable lines of fracture for the other methods of shrouding. 4 Formerly, in large machine shops the long lengths of line shafting, arranged parallel to one another at short intervals in the length of the shop, were often driven from a main shaft which ran along the side of the shop, by means of bevel wheels ; but since electric motors have been so largely used, each to drive a single line of shafting, bevel wheels for such purposes have been discarded. 5 We have seen that when two shafts are not quite in the same straight line, aud one drives the other through a Hooke's joint, there may bo an ununiformity in the motion, and perhaps excessive wear. But bevel wheels can sometimes be nsed instead, making a much better mechanical job. 8 Each arc passes through three points in the actual cycloidal curve, this curve being first geometrically set out (or by the xise of the odontograph or templets), as previously described. See author's " Elements of Machine Construction and Drawing," Plate No. 24. MITRE BEVEL WHEELS. . PITCH CONESl^j PITCH CIRCLE. TOOTHED GEARING MITRE BEVEL WHEEL. N? OF TEETH 30, PITCH OF TEETH 2'.' BREADTH OF TEETH 5". DIA 1 ? OF SHAFT 3'.' 173 ic. C>riCLE. x BEVEL WHEELS. ARCE END. TEETH. SMALL END. FIG. 504. ELEVAT FIG. 505. SECTIONAL SIDE ELEVATION. FIG. 506. 174 MACHINE DRAWING AND DESIGN FOR BEGINNERS without further help, but it should be explained that as the teeth curves on the elevation are foreshortened, they are drawn in the conventional way shown by the dotted arcs. 218. Strength of Wheel Teeth. Having considered how to obtain the best form for the teeth of wheels, we may now proceed to see how their size for any given case may be determined, and this is to a large extent a question of strength, which depends upon (a) the strength of the material, (6) the forces which act on the teeth due to the power transmitted, (c) the way in which the teeth resist fracture under the action of the load which conies upon them. First, with regard to (a) the material, cast iron on account of its cheapness and because it may be readily cast in any form, is used for ordinary wheels ; second, (b) with small pinions, such as are used in rough crane-work, only one tooth of each wheel can be relied upon to engage at once ; indeed, for the matter of that, owing to slight inaccuracies, and the possibility of the presence of dirt between the teeth, it is probably never absolutely safe to rely upon there being more than one pair of teeth in actual working contact at once, 1 whatever the size of the wheels. So, assuming this to be the case, we have the force P (acting in the pitch circle of the driving wheel) acting as a load on the end of a tooth (as in Fig. 488A), and we may regard the case as one of a cantilever loaded at its end. And, lastly, (c) the tooth, if in contact throughout its breadth with its fellow, may break at its root, and the full strength of the tooth is available, or, should the load P on a tooth act at one corner only, owing to faulty construction or erection, or to settlement or wear of a bearing, then the tooth may break along a line ab, Fig. 495, making about 45 with its root. 2 We may now examine the strength of a tooth, assuming what we may call the normal case of one pair of teeth in full contact, taking the proportions we have in the Table (8) for machine-moulded wheels, as being fairly representative of good modern practice, 3 we have the length of the cantilever I = 0'7p and its breadth b say 2'5p, whilst if we allow for 25 per cent, wear of the teeth, 4 the thickness t becomes 0-48^ - Q-12p = 0'36>. Then, equating greatest bending moment ufi to the moment of resistance to bending, we get PI = Z/, where Z, the modulus of the section, is -= , and /, the safe skin stress ultimate skin stress .. 36,000 n ~ nn -,-, i, = -f f 3rr - = (say for this example 6 ) - - = 3600 Ibs. per sq. inch. factor of safety 10 .-. The safe load P on one pair of teeth (of 1" pitch) = - -^TOT - - = 278 Ibs. ... . (34) And for Two pairs of teeth in contact P = 2 X 278 = 5561bs ................ (35) 1 Some writers get over this difficulty by assuming that each tooth takes about two-thirds the full load, but surely it must be either une tooth or tteo teeth in contact, and to be on the safe side we shall assume the former. The student will readily be able to make the proper allowance for any other assumption. 2 It can be shown that its strength to resist failure in this way is about equal to that of the tooth with a breadth of about l-4p, or approximately twice the length of the teeth. By some, a greater breadth than this is not reckoned to add to the transverse resistance of the tooth ; but it is necessary for durability, so that the maximum breadth that can be relied upon under all conditions is twice the length. 1 These proportions are frequently used both for cut and uncut teeth. Wheel teeth are now made of better form and proportions than they were years ago, with an improvement in the uniformity of loading and strength. 4 The allowance recommended by Tredgold, and adopted by Fairbairn and Unwin. See Fairbairn's " Millwork," vol. ii. p. 43. 5 See Anderson's " Strength of Materials," p. 188. A cast-iron bar, 1" long and 1" square, loaded at its end as a cantilever, breaks with about o'OOO Ibs. Then we may take, to find the equivalent skin stress/, 0000 = *& , or/ = ^ x .f = 36,000, and with FS (factor of safety) = 10, we get / = ^~- = 3600. TOOTHED GEARING 175 The student should now be in a position, in any given case, to decide which of the above values would be applicable. Now, the factor of safety part of the equation requires some further consideration, for only those who can intelligently decide upon its allowable value in any given case can succeed in steering clear of the mistakes which can so easily be made, due to the apparent want of agreement that exists in the works of various authorities ; so that when the failure of a wheel occurs it is not difficult to justify its proportions by reference to some accepted authority. And this is possible, because frequently the conditions of running that are assumed are not sufficiently defined, or are so involved that none but the expert can grasp their true significance and value in a given case. This can be better understood by an inspection of Table 9, which has been calculated from the equations 34 and 35, for the cases of one pair and two pairs of teeth in contact and for a range of value of the factor of safety used, which satisfies most conditions of running in practice. TABLE 9. SAFE LOAD P, FOR CAST-IRON TEETH OF 1" PITCH AND BBEADTH OF 2'5 TIMES THE PITCH. WHEN THE PRESSURE is DISTRIBUTED UNIFORMLY OVER THE BREADTH OF THE TEETH, 1 THE ULTIMATE SKIN STRESS BEING TAKEN AT 36,000 LBS. Kind of vunning. No. of case. One pair of teeth In gear at once, P = Two pairs of teeth in gear at once, P =: Skin stress/ in Ibs. (F.S.I Factor of safety used. Without shocks .... 1 463 926 cooo G Very slight shocks . . . 2 278 556 3000 10 Moderate shocks .... 3 139 278 1800 20 Excessive shocks .... 4 93 185 1200 30 VARIOUS SECTIONS WHEEL ARMS. It will be noticed that the above values are for breadth of 2'5p, but of course for any other breadth (when P is distributed uniformly over it) the value of P will be directly proportional to the breadth. 219. Arms of Wheels, their Shape and Strength, etc. Only very small wheels (called plate wheels) are made with a disc connecting their rims to their naves. The number of arms that a given wheel should have is more or less arbitrary, their number increases with the size of the wheel, usually wheels under 4' having four, from 4' to 8' six, and 8' to 16' eight. Pulleys, or quite light wheels, have arms of elliptical section, Fig. 507, and the cross section, Fig. 509, is largely used, whilst the H section, Fig. 510, is more often used for heavy wheel's; the tee section, 514, is commonly used for level wheels, and the other FIGS. 507. 508. 509. 510. 511. 512. 518. 514. 1 Refer to author's " Machine Design, elc.," p. 310. 176 MACHINE DRAWING AND DESIGN FOR BEGINNERS sections, Figs. 511 and 512, are more often adopted for built-up wheels ; and when these wheels have steel arms the hollow sections, Figs. 508 and 513, are generally used. Obviously, when the arms, rim, and nave are cast in one piece, the arms are fixed at both ends, but if the arins are in any way attached to the rim, they are usually treated for strength purposes as being fixed at the nave only ; indeed, for the matter of that, to make allowance for the contraction in cooling stresses, it is usual to assume that all arms are fixed in this way. 220. Naves or Bosses of Wheels. We have, in Figs. 515 to 521, forms of the naves or bosses of wheels which correspond to some of the arms shown in Figs. 509 to 514, the letters A, B, etc., being common to both sets. When the wheels are large and heavy the initial stresses due to contraction in cooling may seriously reduce the strength of the nave ; to avoid this they are made in two parts and bolted together. Figs. 522 and 523 show the nave part of such a wheel. Or the nave is sometimes slotted across between the arms in two or more places, according to the size of the wheel, 1 and iron plates are fitted to the openings, a ring of wrought iron E being shrunk on each side of the nave to bind the segments firmly together. NAVES OR BOSSES OF WHEELS. R FIG. 515. FIG. 516. FIG. 517. FIG. 518. FIG. 519. FIG. 520. FIG. 522. FIG. 52;j. There is apparently no very satisfactory rule in general use for the thickness T, and length of the nave of a wheel. For spur wheels Box's rule is T = (p x 7 4- 9) + (0-125 X D) (36) where p = pitch of teeth in inches, and D = diameter of wheel in feet. Unwin's rule is T = 0-4V//E + I" where E is the radius of the pitch circle in inches. A pretty general arbitrary practice (when a designer in a particular case has not experience to guide him) is to make them with a diameter at least twice that of the shaft at its smallest section (usually at the journal), or, if d be the diameter of this part, and the 1 Refer to author's " Machine Design, etc.," p. 317. TOOTHED GEARING 177 shaft is increased in size at and near the wheel to resist bending, then T, the thickness of the nave, is made \d. For a parallel shaft the wheel seating is usually \'\ld to 1'lScZ in diameter, the length of the nave being from l'5d to l'75d. 221. Rims of Wheels. A few typical sections of wheel rims principally for fly wheels, are shown in Figs. 524 to 536. The rinis, Figs. 530, 531, and 533 are for belt drives, whilst 529 is for a band saw wheel, the arms being staggered to allow for contraction RIMS OF SOLID AND BUILT-UP FLY WHEELS. fflffllffl FIG. 524. FIG. 525. FIG. 526. Fro. 527. FIG. 528. FIG. 529. FIG. 530. Fia. 531. Fio. 532. FIG. 533. FIG. 534. FIGS. 535, 536. Cottered dowel. in cooling and to give lateral stiffness. The other sections are for fly wheels proper. Obviously, Figs. 528 and 534 are simple forms whose moments of inertia can be readily found. Fig. 532 is a section suitable for attaching arms in built-up wheels, and Figs. 535 and 536 are two views of a built-up rim with cottered joints. 222. Mortise Wheels. When wooden teeth are mortised and fixed into rims of cast-iron wheels designed to receive them, as shown in Figs. 537 to 553, we have what are technically called Mortise Wheels. The wood commonly used for the cogs is hornbeam, which, owing to its strength : and stringy toughness, is unsurpassed by any other for the purpose, although birch is occasionally used for cheapness' sake. The taper part or tenor of the well-seasoned cog is driven tight 2 into the rim of the wheel, and usually secured by a pin of iron (drawn) wire, the hole for which is so placed that when the pin is driven in it tends to draw the cog still further into the wheel. Fig 540 shows a cog with short tenon for fitting opposite an arm. 3 An alternative way of securing the cog is shown in Fig. 544, dovetailed wooden keys being driven between the projecting ends of the tenons. A variation in the form of the key (used on the Continent) is shown in Figs. 545 and 546, whilst in 547 we have a saw-cut in the end of the tenon, so that the end may be spread when the pin is driven. Fig. 551 shows how the arms are formed near the rim to allow of the cogs being fitted at these parts. It will be noticed that the cog A, Fig. 541, is symmetrical about a centre line through the tenon, whilst cog B (Fig. 542) is flush at one of its sides C, which means that the other, the working side, has more material available for wear. When the wheel is wide, two or more cogs are used to make up the breadth, as shown in Fig. 539. The usual proportions are shown on some of the figures. When cogs are used there is little or no clearance required between the cogs and iron teeth with which they gear, generally the cog is 0'6p in thickness. Figs. 552 and 553 show sections of the rim of a bevel mortise wheel, Fig. 548 showing how 1 A cantilever bar of this wood, 1" square, 1" long, breaks with about 1800 Ibs. at its free end (about three-tenths the breaking weight of cast iron). 2 After the rough cog has been fitted and driven into the rim, a line is scribed round the cog a uniform distance from the surface of the rim, and the cog knocked out, when it is shouldered with the wood chisel, so that when it is driven in again it can be driven right up to the shoulder, as in Figs. 537 to 543, or show a uniform clearance, as in Figs. 545 to 547. Refer to author's " Machine Design, etc.," p. 322. 3 Refer also to Sheet 39, author's " Elements of Machine Construction and Drawing." 2 A DETAILS OF MORTISE WHEELS. UNIT = PITCH =p FIG. 537 FIG|538. r IG.539. A_ / \ B C FIG. 547. FIG. 548. cogs near the arms are secured by screws. 1 Mortise ivluels are used with the object of intro- ducing an elastic medium to reduce the effect of shocks due to any defect in the form of the teeth, and to reduce the noise that is commonly made when ordinary iron teeth are running together. When the iron teeth of wheels that are to gear with mortise wheels are machine moulded, the teeth only, as a rule, require filing to clear them of the sand and make them smooth, but in cases where the wheels are cast from patterns, the teeth must be machined or pitched and trimmed, the rough surfaces being chipped true to their geometrical form, and filed smooth ; the wooden teeth then easily wear to the exact form of the iron teeth they gear with, without their surfaces being destroyed by the rough surfaces of the .casting. But the steady improvement in the construction of wheels with iron teeth, which has been taking place for some years (particu- larly since the introduction of improved helical gearing), has caused mortise wheels to be com- paratively little used ; indeed, it is not often that their adoption is now really necessary, mainly owing to the great improvements that have been made in the cutting of helical gears, a description of which is given in the author's " Machine Design, etc.," p. 326. 1. Set out the velocity ratio 3 and EXERCISES. DESIGNING, ETC. pitch circles of a pair of spur wheels, The smaller wheel has thirty teeth, and the pitch is 1J". Be careful to give the exact distance between their axes. Scale 3" = 1'. 1 Refer also to author's "Elements of Machine Con- struction and Drawing," Plate No. 40. FIG. 550. FIG 551. FIG. 552. FIG 553. TOOTHED GEARING 179 2. A toothed wheel has fifty teeth, whose diametral (or Manchester) pitch is No. 4. Set out its pitch circle and give the outside diameter of the teeth. Scale 3" = 1'. What is the circular or true pitch of the teeth of this wheel ? 3. The circular pitch of the teeth of a wheel is 22 millimetres, and the number of teeth 120. Set out the wheel pitch circle, and give the diameter of the pitch circle, and the outside diameter. If it gears with another wheel half its size, what is the difference between the axes ? Scale 1J" = 1'. 4. The pitch circles of a pair of wheels in gear are 4" and 2J" in diameter, and the rolling circle ia 1\" diameter. Determine the arc of action, and the arcs of approach and recess of the teeth described by the rolling circle. 5. Referring to the previous exercise, measure the obliquity of action of the teeth, assuming that the faces of the teeth are 7 3 S " long on your drawing. 6. Assuming that a wheel with teeth of 1" pitch, whose breadth is 2Jp, safely transmits 140 Ibs. at the pitch line when subjected to moderate shocks. What should bo the pitch of the teeth of a wheel to transmit 30 H P. under similar conditions at a speed of pitch line 1800 feet per minute ? .4ns. 1'98". Say, pitch = 2". DBAWIKG EXERCISE. 7. Set out the mitre bevel wheel shown in Figs. 505 and 506. Scale half full size. SKETCHING EXERCISES. 8. Sketch two cycloidal teeth, roughly in good proportion, pitch = 4", and mark on them the names and proportions of the various parts. You may make the length of the teeth 0'7 pitch. 9. Sketch a pair of Gee's buttress teeth in gear, and explain what advantage is claimed for this form of teeth. What is their principal disadvantage ? 10. Show by sketches how the teeth of wheels are shrouded. What is the object of shrouding ? Describe the kind of wheel which most requires shrouding. 11. Sketch four typical sections of wheel arms, and explain for what type of wheel you would use each one. 12. Show by sketches how the nave of a wheel is strengthened by shrinking on wrought-iron rings. 13. Make a sketch of two teeth of a mortise wheel in fairly good proportion, and show how the cogs are secured. Also show an alternative way of securing the cogs, and give the principal proportions. What ia the object of using a mortise wheel ? 14. Make sketches showing how cogs which come near the end of an arm in a mortise wheel are secured : (a) when the wheel is solid ; (b) when the wheel ia made in halves. 15. Show a section of the rim of a mortise bevel wheel, with a cog in position, and mark on the tketch the principal dimensions. 16. Show by sketches two ways of connecting by toothed wheels, shafts that cross one another but are not in the same plane. 17. Sketch a light fly wheel with daggered arms. What advantages are claimed for this arrangement of the arms ? 18. Sketch four or five representative sections of fly wheel rims. What advantage can be claimed for a simple rectangular section? CHAPTER XX BELT GEARING 223. Fast and Loose Pulleys. There are some interesting and important details of these that should receive attention. In Fig. 556 the shaft A of a machine projects from the frame bearing B, and is fitted with the fast and loose pulleys F and L, the former being driven on to the feather K, which fixes it to the shaft, and the latter (bushed with gun-metal) is kept in position by the washer W, which is held on to the end of the shaft by the hollow brass screw S, whose ball end is drilled and countersunk to admit oil for the bearing; an alternative fitting here being a Stauffer's grease-box. A cheaper but less efficient arrangement for lubricating is shown at x, Fig. 558, but the tendency of the oil is to flow out of the hole away from the journal due to centrifugal force, whilst, if it is admitted from the axis, as in Fig. 556, in flowing outwards it passes over the journal. Fig. 557 shows a part of the rim of the driving wheel, whose width must of course be at least equal to both that of F and L, the fast and loose pulleys, Fig. 556. Fig. 558 also shows how a screw D is sometimes used to keep the bush in position ; a more usual way is to slightly countersink each end of the hole in the boss and to burr the bush over, the latter being in all cases a driving fit in the boss. The loose collar C, which keeps the pulley in position on the shaft, is fixed to the shaft by the set-screw E. When the loose pulley is not bushed, the boss is made much longer, as shown in Fig. 559. This figure also shows how set-screws T are sometimes used with feathers, to avoid driving the pulley on in fixing. < In cases where the belt is running on the loose pulley the best part of the time, it is advantageous to make this pulley somewhat smaller in diameter than the fast pulley l (Fig. 55?A). This relieves the tension of the belt and the pressure on the journals when the belt is running idle. In this arrangement it will be seen that the bracket A has a sleeve S projecting from the boss B, upon which the loose pulley L works, the hole throughout the boss and sleeve being larger than the shaft, to clear it, so that the latter runs perfectly clear of the loose pulley when the belt is on the fast pulley F, which is coned at its edge C to allow the belt to easily mount the larger pulley. Of course in this case the belt, which is driven from the main shaft, is always running. Figs. 554 and 555 are two views of a belt gear for slow forward and quick return motion, which should speak for themselves. 224. Rims of Pulleys or Riggers for Belting. As lightness and rigidity are two essential features of these wheels, the rims are made as thin as practicable, the inside of the section tapering slightly, as shown in Fig. 566 (which gives suitable proportions), so that the pattern may be easily drawn from the mould, and a stiffener or strengthening rib S (Figs. 560 to 564) is generally used to assist in making them rigid. "With wide pulleys the stiffeners are sometimes on the edges, as in Fig. 563, and when they have double sets of arms these are usually placed somewhat near the edges, as at S, Fig. 564 ; but the inner surface 1 Refer to author's " Machine Design, etc.," p. 875. FAST AND LOOSE PULLEYS, ETC. w 554 & 555. BELTGEAR FOR SLOW. FORWARD, SrQUICK RETURN MOTON. 556 & 5 57, FAST 8t LOOSE PULLEYS FOR SHAFT OF A MACHINE. 558, DETAILOF BUSHING -LOOSE PULLEY DRIVEN Sh|AFT. COLLAR 557 A, FAST 8c LOOSE PULLEY ARRANGEMENT FOR RELIEF TENSIONV 559,FAST&LOOSE PULLEY WITHOUT BUSHING. SOLID BELT 565, PULLEY WITH 56 7, PULLEY WITH DOUBLE SEGMENTAL CURVED ARMS. of the rims should be turned as near the arms as possible to balance the wheel (the im- portance of this increasing with the square of the speed), so this should be a guide in designing them. The thick- ness (t) of the rim at the edge after turning may be about t = 0-6T + 0-0003D, for pul- leys where B does not exceed p to t = 0-7T + 0-0005D for wider pulleys, where T is the thickness of the belt, B is the breadth of face in inches, and D is the diameter of the pulley in inches. The width of belt pulleys is usually at least |" greater than that of the belt, or, say, width of belt = 0'9B. 225. Proportions of Pul- ley Arms. The arms of pul- leys are either straight, as in Fig. 565, curved, as in Fig. 566, or double curved, as in Fig. 567. The object of curving is to prevent fracture when the casting cools, but with straight arms, suitably proportioned and with proper precautions taken in cooling, there should be no trouble from contraction. This being so, they should be preferred, as they are lighter and stronger, and their patterns are less costly. The section of the arms tapers off from the boss to the riin in the way shown in Fig. 565. The usual practice is to make the breadth and thickness at the rim two- thirds the amounts at the boss. Fig. 566 shows how the curved arms may be set out. The number of arms is fixed in a somewhat arbitrary way, the usual practice being to have four for pulleys up to about 24" diameter, six from about 2' to 8' or 9', and eight for larger sizes, ten being sometimes used for very large wheels. But the breadth of the pulley should properly WITH CURVED ARMS. BELT GEARING 183 T)T'\ be a factor in fixing the number of arms, and Professor Unwin gives the number of arms N = y^ + 3, the breadth B and diameter D being in inches, and the nearest whole number being taken. The shape of the rim section is either elliptical or segmental, of the proportions shown in Fig. 568. 226. Split Pulleys. Some shafts are bossed at their ends, and then, to avoid using cone keys, the pulleys are often cast in halves and bolted together in position without dismounting the shaft. Figs. 569 and 569s show two examples of this class of pulleys, 1 Fig. 569A showing how the joint is made when it occurs between arms. The bolt, or bolts, at the rim and boss should have a total net section equal to about 0'28 to 03 times the sectional area of the rim and boss respectively. In recent years there has been a great development in the use of wrought-iron and steel pulleys, particularly for high speeds and large diameters ; owing to their lightness, and freedom from the initial strains due to cooling which exist in cast-iron pulleys ; they have the additional advantage SPLIT BELT PULLEYS. FtG. 569. Cast-iron split pulley. FIG. 5G9B. Cast-iron split pulley. ffl Fio. 569o. Medart's split pulley. FIG. 569D. Wrought-iron split pulley. Macbeth's. Universal. Maokie's. FIG. 569E. of not flying to pieces should they be overrun. Fig. 569o shows a pulley of this type ; the boss is made of cast iron in two parts and the rim in one piece, the ends joined by a cover strip or lapping piece, placed under the rim and riveted to one part and bolted to the other. Both joints can be sprung open wide enough to receive the shaft. The bolt springs in all split pulleys are made to grasp the shaft tight enough to give a frictional drive without keys. Fig. 569c shows a Medart's split pulley, which has a wrought- iron rim, with the arms and boss of cast iron. Fig. 569E shows three well-known forms of steel split pulleys. The arms and rims of this type are made of steel, and the bosses or hubs are either cast iron or cast steel. 227. Thickness and Length of Bosses or Naves of Pulleys. There seems to be no well-established rule for determining the thickness of the boss (sometimes called the eye or hub) or central part of a pulley, as we remarked in Art. 220 in referring to spur wheels. 1 In quite small pulleys bolts at the boss only are required. 184 MACHINE DRAWING AND DESIGN FOR BEGINNERS It seems obvious that it should either vary with both the size of shaft and diameter of pulley, or with both the breadth and diameter of the pulley. Unwin * favours the latter, and says the thickness t of the boss may le as follows : t = 014\/BD + i" for single belt (37) t = 0-18v/BD + " for double belt ............. (38) But Box 2 gives a simple rule, which seems to agree very well with the best practice, and his rule is t in |ths = D in feet + d in inches + 5 (38A) where D and d are diameters of pulley and shaft respectively. The length of the boss is, usually, for &fast pulley about f B, and for a bushed loose pulley equal to B, where B is the breadth of the pulley rim. For details of keys refer to Art. 93. EXERCISES. DESIGN, ETC. 1. A cast-iron pulley, 5' in diameter, is to be designed for an 8" single leather belt ; the arms are to be straight, and seginental in section. How many arms would you arrange for 1 and what size would you make them at the boss and at the rim ? 2. The skin stress in the shaft for the pulley in the previous question is 5000 Ibs. per sq. inch, and half the power transmitted by the shaft is transmitted by the wheel. What size shaft would be required ? and what thickness would you make the metal of the wheel's boss ? SKETCHING EXERCISES. 3. Sketch a belt gear suitable for driving a variable speed machine from a main shaft. 4. Make a sketch of a safety cap for a gib-headed key. 5. Make a sketch of a pair of fast and loose pulleys, suitable for use on the shaft of a machine. Be careful to show how the journal of the loose pulley is lubricated. 6. Sketch a bolt gear for a slow forward and quick return motion, suitable for driving a screw-worked planing machine. 7. What is the object of curving pulley arms? When the arms are made straight, what precautions should be taken in designing and in casting? 8. Sketch a cast-iron split pulley, showing (a) The joint when it occurs through the arms. (6) The joint when it occurs between arms. DRAWING EXERCISE. 9. Make working drawings of the pulley with curved arms (Figs. 566 and 567). Give t a suitable value for a single belt. 1 " Machine Design," vol. i. p. 487. 2 Box's " Mill Gearing," p. 98. CHAPTER XXI CYLINDER. PISTON, ETC BUCKET PUMP PLUNGER PUMP. GLAND PISTONS AND CYLINDERS, ETC. * 228. Function of a Piston. A piston is a cylindrical body fitted to a hollow cylinder in such a way that although free to slide in it under the action of fluid pressure, as in a steam engine (Fig. 570), or if acting against fluid pressure under the action of a force, as in a pump (Fig. 571), practically no escape of the fluid from one side of the piston to the other takes place. Usually, when a piston is used as part of a pump, and it is provided with a valve or valves, which allow the fluid to pass from one side to the other of the piston during one of its strokes, it is called a bucket. Ordinarily the piston is attached l to a rod called the piston rod, which passes through a stuffing box in the cover of the cylinder in which the piston works, and is used to connect the piston to some piece outside the cylinder. If the piston be reduced in size or the piston rod increased, until they are the same size, we have what is technically called a plunger, as shown in Fig. 572, which forms an important part of the feed pump. Small pistons (and large ones for the engines of cargo ships), where weight is of little importance, are made of cast- iron. But in engines for large passenger ships, and all large warships, the pistons are made of cast steel, while in torpedo boats they are made of forged steel. 229. Pistons without Packing. For some purposes a plain cylindrical piston, Fig. 573, accurately fitting the cylinder, answers very well, particularly in cases where the resistance due to the packing would be objectionable, as with the piston used in the steam engine indicator, which is without packing, but is grooved, as in Fig. 574, to diminish leakage, 2 and to some extent lubricate the rubbing surfaces, sometimes used in pumps, and when the piston is sufficiently long there is very little wear. 1 Occasionally, in small engines, the piston and rod are forged in one piece. 2 The grooves present an abrupt change of section to any fluid passing by them, and impose a resistance to the flow which is, no doubt, in part due to the decrease of fluid pressure which occurs at each groove. There is very much to be said in favour of solid pistons, and there seems no satisfactory reason why, with more accurate work, suitable fits, large bearing surfaces, and highly finished surfaces, they should not be more generally used, particularly for vertical engines. 2 B FIG. 570. FIG. 571. FIG. 572 This type of piston is 186 MACHINE DRAWING AND DESIGN FOR BEGINNERS 230. Piston Packings. A plain or solid piston (one without packing), let it be ever so well proportioned or fitted, sooner or later becomes leaky, so, to prevent this, the pistons of heat engines are packed with metallic spring rings, many forms and arrangements of which are in use ; indeed, of pistons of steam engines alone, there are endless varieties, due to efforts made in endeavouring to produce a perfect piston to stand the high speed and pressures in common use now. Notwithstanding these efforts it is safe to assume that the last word has not been said in piston design. A good or ideal piston should be designed and constructed in such a way that it is sufficiently strong, keeps steam-tight for a considerable length of time, has comparatively few parts, its bolts and nuts being secured against working loose, and the piston as a whole to work silently with as little friction as possible ; steam must not pass the rings at their joints, or find an easy passage beneath the rings and add its pressure to the normal spring of the rings against the cylinder walls, for if this occurred, the 3 or 4 Ibs. per square inch between the rubbing surfaces, which is found to be all that is required when the rings fit the cylinder accurately, would be increased to some ten to fifty times that amount, with consequent undue wear and great loss of power. Indeed, the pressure of the rings against the cylinder should never exceed what is allowable between rubbing surfaces under the conditions of lubrication and speed which prevail. A skilfully designed piston, worked with ordinary dry steam, should be efficiently lubricated by the condensation of the steam on the rubbing surfaces alone ; but of course all pistons are lubricated with high-flash oil when the steam is superheated. With these points before us it will be convenient to deal with the characteristic features of the best known pistons by grouping their like parts and features together. Commencing with the packing spring rings, the simplest of these, used for locomotives and other quick-running engines, are Ramsbottom's. They are made either of very tough close-grained cast iron, steel, gun-metal, or Perkins' 1 anti-friction metal; cast iron (which works better than steel on the cylinder surface) being most commonly used for cylinders of all sizes, and steel for locomotives. These rings are made rectangular in section, as shown in the five Figs, (for small and medium size pistons) 575 to 579, to fit separate grooves turned in the solid piston, there being two, three, or more grooves PISTON PACKINGS, ETC. FIG. 573. Fio. 574. FIG. 575. FIG. 57G. FIG. 577. FIG. 578. FIG. 579. FIG. 580. FIG. 581. FIG. 582. Mudd's. FIG. 583. FIG. 584. Buckley's. according to the fluid pressure and depth of piston. In the simplest arrangements the rings are turned solid to a diameter about !> greater than that of the cylinder, and they are cut and the ends shaped to overlap, as in Fig. 602, or a piece is cut out and the 1 Refer to Art. 177. PISTONS AND CYLINDERS, ETC. 187 ends filed to an angle, as in Fig. 599. They are then carefully sprung over the piston into position, 1 and when the piston is placed in the cylinder they press against the bore or walls with sufficient force to make a steam-tight joint. Fig. 579 shows an arrange- ment for admitting steam to the back of the rings (to increase their fluid tightness), which has been occasionally used, but this principle, which answers so well in the leather collar of a hydraulic press, does not appear to be favoured by those who have tried it. The size of these rings may be : thickness from 0-Q25D to 0'03D ; and width O'OSD to 0'06D, where D is the diameter of the piston. Eings fitted in the way described are, when sprung into position, obviously not circular in form, and until they have become well bedded by wear will allow a small leakage to occur. For an ordinary steam cylinder this is of trifling importance, but in an internal combustion engine it would mean a loss of compression, and rings for such cylinders should be, after they are split and the ends drawn together, turned on their outer edge so that they exactly fit the cylinder. 2 Even then there is not an equal pressure between ring and cylinder wall all round, as this can only be secured by making the ring of varying thickness. 3 An approximation to this ideal condition is sometimes secured by making the ring eccentric in form,, the thickest part being opposite the joint, and 1 times thicker than the thinnest part. One of the disadvantages of Eamsbottom's rings is that they cannot be got at for removal without drawing the piston. To overcome this objection, and to allow of larger rings being used than could be sprung over the body of a piston, a junk ring * is used, as shown in Fig. 585, and this ring is sometimes made for large pistons of the form shown in Fig. 587 to overcome the above objection. The figure shows four eccentric rings at their thickest sections. In small engines sometimes the junk ring takes the form of a cover, which is held on to the piston by the piston rod nut, as shown in Fig. 580, or the piston itself is made in two parts A and B, Fig. 581, with the joint at the centre C, the parts being held together by the piston rod, as in the previous one. 5 It will be noticed that these two pistons have their rings backed up by spring rings S behind them, which are fitted in the same way, the pressure they exert on the outer rings makes the latter more effectively steam-tight ; and Fig. 592 shows how the rings may be reinforced by the acting of a spring S and wedge W. For pistons of larger size these spring rings are not very efficient, and the old method (not often used in new work) of dealing with the problem was to press the piston ring against the cylinder wall by a number of dished springs or coach springs S, Fig. 590. The chief objection to this arrangement is that it is not possible to set all the springs so that the pressure on the ring is uniform, and being always in motion whilst the engine is running, the springs tend to wear themselves (as well as the piston) away, and furthermore, in horizontal engines it is important that the piston ring shall follow the sides of the cylinder freely, or, in other words, float, which it cannot do if the springs react from the piston body ; moreover, the range of action of this form of spring is very limited. To 1 In the ease of cast-iron and anti-friction rings, this must be done with great care to prevent them breaking. No matter how carefully they have been jointed, there is often a slight leakage at the joint. To reduce this, the joints in the different rings should be kept as far apart as possible. Stop pins are sometimes used near the ends to keep them in such positions. 2 Of course, this is always done with larger pistons fitted with junk rings. A piece of paper is placed between the junk ring and piston ring or rings, and the whole is screwed up tight, gripping the piston rings so that they can be turned and accurately fitted to the cylinder, after which of course the paper is withdrawn. Of course, with rings for the solid pistons referred to above, they are held in a suitable lathe chuck. 3 Refer to Unwin's " Elements of Machine Design," Part II. p. 255. * The early engineers, in dealing with steam at low pressure*, packed their pistons with hempen rope soaked in tallow, which they called junk, and they used a ring to tighten it up as it became worn, or to allow of its being removed without drawing the piston. And although we now use for steam purposes metallic packing, we retain the name of the ring. 5 In all these pistons the rings must be fitted, either by very accurate turning, by scraping, or by grinding, so that they are steam-tight between flange and ring, although free to move between them. 188 MACHINE DRAWING AND DESIGN FOR BEGINNERS overcome these objections a number of expedients have been employed, thus in the Cameron piston, Fig. 591, we have a corrugated ribbon of steel pressing the piston ring out, the lateral or radial pressure being obtained by the resistance of the spring to being bent into a circle, and by the almost uniform pressure exerted by the corrugations when the ends of the springs are pressed apart, by packing pieces between them, without the spring touching the body of the piston. With this arrangement the piston ring can be comparatively thin, enabling it to conform to the shape of the cylinder when worn. Another arrangement, similar in principle, which is very generally used, particularly for low-pressure marine pistons, is Buckley's, shown in Fig. 584 (fitted to a steel piston). FURTHER EXAMPLES OF PISTON PACKINGS. FIG. 585. FIG. 586. FIG. 587. FIG. 588. FIG. 589. FIG. 590. Coach springs. A flattened helical spring is so placed behind the inner slanting surfaces of two rings that it presses them out against the walls of the cylinder, and also down and up against the flange of the piston and of the junk ring. The same action is provided for in Fig. 586, where a helical spring of circular section is used. In fact, it has long been understood that wear not only takes place between the ring and cylinder walls, but also between the edges of the ring and the flange of the piston and of the junk ring, a very slight amount of play soon developing into a large degree of slackness, due to the continual concussion on change of motion at each stroke. Thus we have, in Fig. 583, Clayton's and Goodfellow's piston for mill engines, with a spiral spring H made of strong cast iron, and cut out of a ring of the metal, having four or five turns, being coiled inside the piston rings, and so shaped that, by wedging, it acts in the double way just described. Mather & Platt's, Fig. 589, is another piston where this principle in a modified form is employed, the spiral hoop or spring being sometimes made of steel. These forms have on the whole given much satisfaction, the objection some- times raised against them, that no adjustment of the spring is possible, and that therefore it is always exerting its maximum effect, does not appear to be an important one. It should be understood that the chief part of the elasticity of the spring is exerted in pressing the .rings against the junk ring and flange, and that the friction so caused helps to prevent undue pressure on the cylinder walls when first fitted, and there is sufficient of it when the cylinder is worn. Closely allied to these in principle is Mudd's arrangement, shown in Fig. 582, two rings each 2" x 2" (for all sizes of pistons from 18" to 80" diameter) are pressed against the flange and junk rings by a number of helical springs, placed as shown, and separate helical springs (not shown) are applied tangentially at the joints of the rings to press them against the cylinder walls. 230a. Allen's Piston. 1 This invention is a radical departure from ordinary practice of great promise. The rings are each made in three pieces, and their opposing ends are carefully fitted to cast-iron expanding pieces, the inner ends of which fit into holes drilled radially into the piston. Internal springs keep these pieces up to their work, and thus furnish the pressure to hold the rings against the cylinder walls. Should experience prove that pistons of this type are free from internal trouble when worked by 1 'Manufactured by Messrs. Allen and Simmons of Beading. PISTONS AND CYLINDERS, ETC. 189 PUMP BUCKET PACKINGS. superheated steam or gases of high temperature, there will probably be a great future for them and pistons of this type, notwith- standing their cost. 231. Pump Bucket Packings. The buckets of air pumps (and occasionally circulating pumps 1 ) are packed either with wood staves or with cotton or hemp, usually with the latter. When wood is used, lignum vitae is preferred, as it works well with the brass barrel. Figs. 593 and 594 show how small buckets are sometimes fitted ; in the latter we have two rings, each being made up of a number of blocks, breaking joint with those in the other ring. Fig. 595 shows, for larger buckets, another way of breaking joint to prevent leakage ; the staves A have keys B let in them where the joints occur, and two stiff rubber tubes D with a distance ring C are squeezed in to act as an elastic cushion at the back to keep the bucket tight as wear takes place. When wood packing is used it must be very carefully fitted, and there must be clear- ance enough to allow the wood to swell when it is wet. A simpler and very effective packing is the hemp or cotton rope one, Figs. 596 and 597. It will be seen that the flanges of the bucket have been grooved and drilled at PP to allow of the ends of the rope being pegged in and held secure. In Fig. 598 a junk ring is used, but it is not intended to adjust the packing, but merely to keep it in position ; it is screwed down firmly to the bucket. d of the packing is about O'l diameter D + 1'4, and the thickness t of the packing - to -=. 4: U 232. Piston Ring Joints. We have seen that in small rings the joint is made as shown in Fig. 599, and that, when the rings are made to break joint, very little steam passes them. But with large rings, some kind of tongue or stop piece, offering a barrier PISTON RING JOINTS. FIQ. 503. FIG. 51)4. FIG. 505. FIG. 596. FIG. 597. FIG. 508. The depth Z FIG. 599. FIG. 601. FIG. 602. FIG. 603. Fia. 604. FIG. 605. at the joint to the passage of steam, is used ; in Figs. 600 to 605 several of these are shown ; they are made of brass and are screwed to the ring by countersunk headed screws, and the drawings should speak for themselves. 233. Guard Rings and Devices. Every nut and screw about a piston must be so secured that it is impossible for it to work off 1 There is not much necessity to pack these for Marine purposes, as the water usually flows freely into the pump by gravity, and the pump runs too fast to allow of much leakage past the piston if the latter be well filled. Thus the frictional resistances are sensibly reduced when no packing is used. 190 MACHINE DRAWING AND DESIGN FOR BEGINNERS and do serious damage to the cylinder cover, or to the piston itself. Some of the fittings used to secure or lock nuts, etc., are shown in Figs. 606 to 612. One of the simplest is to recess the junk ring, as in Fig. 606, so that the nuts are flush with the top of the ring, and then to prevent rotation of the nut by a brass screw in contact with one of its sides, and screwed firmly home into the junk ring. Figs. 607 to 611 show different forms of guard rings, most of which are held to the junk ring by small studs fitted with split GUARD RINGS AND DEVICES. FIG. 606. FIG. 607. FIG. 608. FIG. 609. FIG. 610. FIG. 611. FIG. 612. pins. Sometimes these studs are made (as they should be) with square shoulders, fitting in square holes in the rings to prevent rotation. Fig. 609 shows how the stud itself is in some cases made with the upper part square, the guard ring GE preventing rotation of the washer W, into which the stud fits. A neat, but rather expensive, arrangement is shown in Fig. 612, where a dove-tailed plate P is placed in the recess 11 and slid into position over a nut towards the left, and held there by the brass screw S, the circle around the holding-down screw showing the clearance for a box spanner. The other devices shown should need no further explanation. 234. Connection of Piston to Piston Rod. Small pistons that are not likely to require removing from their rods are sometimes FIXINGS OF PISTONS TO RODS. 131 ^l-KSi FIG. 613. FIG. 614. FIG. 615. FIG. 616. FIG. 617. FIG. 618. Fio. 619. FIG. 620. FIG. 621. KIG. 622. attached to the latter, as shown in Fig. 613, the rod being accurately turned to fit the hole in the piston and riveted over, forming a PISTONS AND CYLINDERS, ETC. 191 PROPORTIONS CAST-IRON PISTONS. countersunk head. Another simple connection is the screwed one, Fig. 614. The end in this case is also slightly riveted, but only enough to prevent the rod unscrewing. A combined cone and screwed end is shown in Fig. 615, with the set-screw shown to pre- vent unscrewing. Figs. 616 to 619 show forms often used, the one in Fig. 618 having its nut held by a safety washer, one wing A of which is in contact with a flat on the side of the piston boss, and the other B with a side of the nut. The nuts in Figs. 616, 617, and 619 are secured by split taper pins, and these are also used in Figs. 620 and 621, which show how pistons are fitted to tandem rods. Fig. 622 also shows a tandem rod, but the piston is held on in this case by a cotter. It will be noticed that the angle of the taper or conical parts varies considerably ; in practice the taper ranges from about 1 in 4 to as little as 1 in 20. Piston rods are occasionally secured to large pistons, as shown in Fig. 623, by a flange, which enables the piston to be very easily drawn, but the nuts require well locking. 235. Proportions of Cast-iron Pistons. A very simple form of cast-iron piston which is largely used for diameters up to about 16" is shown in Fig. 624, and the following Table 10 gives suitable dimensions. It will be seen that the junk ring takes the form of a cover, which TABLE 1C. DIMENSIONS OF CAST-IRON PISTONS' UP TO 16" DIAMETER. (Fig. 624.) FIG. G23. FIG. 624. Small cast-iron piston. FIG, 625. Large cast-iron piston. Diameter of cylinder D. b c d e r 9 A ' k j 6 8 3 3} 1 A 4 if * I A A A A if 11 , 1 10 3S i A H | i if 2| IJ 12 4 ii! 2 f i 2? Jl 14 4* 3 21 tt i 24 31 o 16 4? f i f 2A 3f o^ 1 Haeder and Powell's "Handbook on the Steam Engine." 192 MACHINE DRAWING AND DESIGN FOR BEGINNERS is held in position by the piston rod nut, as explained in connection with Fig. 580. Fig. 625 shows a section of a large cast-iron piston. This type is often fitted with Ramsbottom rings, as shown in Fig. 587. The thickness t of the ribs and the upper and lower walls may be from about + 04" to j^ + 04", the lower value being for the low-pressure cylinder. To enable the walls to be strong enough between the stiffening webs or ribs W, the number N of the latter should be at least as follows : N = 4 for D = 12" to 24" N = 6 for D = 24" to 40". N = 8 for D = 40" to 60" N = 10 to 12 for D = 60" to 80". And the other main proportions may be as follows : di = 1'5K to 1-7K, T = 1'4K to 1'7K (for values of K refer to Table 11). Diameter of junk ring bolts = O'lC + \" ; pitch of junk ring bolts, about 10 diameters. D The coefficient C = Vp + 1 X gp Where p = half boiler pressure * for high-pressure pistons, quarter boiler pressure for medium-pressure pistons, and boiler pressure -r ratio of low pressure to high pressure piston diameters for low-pressure pistons. The thickness of locomotive pistons usually = diameter x - 28. TABLE 11. VALUES OP COEFFICIENT K FOB PISTONS.* (Admission pressures in Ibs. per sq. inch, absolute.) Diameter of cylinder D. Pressure 15 to 30. Pressure 30 to 55. Pressure 55 to 85. Pressure 85 to 114. Pressure 114 to 112. Pressure 142 to HO. Pressure HO to 200. Pressure 200 to 227. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. Inches. 15 to 23 1 1* i H If 2 2 8 2t 23 to 31 If U 12 2 2J 22 3 S| 31 to 39 1} If 2 2 34 31 8} 4 39 to 47 If 2 2 3 3' 4 4i 47 to 55 2 2* 2f 34 BJ 4* 55 to 63 2 2* ^ 3J 4 4i 63 to 71 2* 3 3| 4 4 71 to 79 2'2 34 3J 44 79 to 86 3 3f 3J :l "*Wl . Elevation Section i?t * 'O"'4 ->- Section of Cylinder on A B Fio. 028. Cylinder for horizontal steam engine. PISTONS AND CYLINDERS, ETC. 195 thrust. The pistons being hollow with open ends, they are commonly called trunk pistons. As the closed end during the explosion stroke is in contact with the burning gases it should be made a shade smaller 1 in diameter than the body, so that when at work it fits the cylinder uniformly from end to end. Fig. 629 shows a piston suitable for a gas engine. The usual average proportions being given in terms of D the diameter. For high-speed engines L = D to 1'6D ; for large engines L = 1*2D to about 1'75 ; whilst for small engines L ranges from 1-4D to 2-25D. It is packed with Ramsbottom's Rings, whose number is usually about -, with a 2i minimum number of three. Fig. 629A gives suitable average proportions for pistons of petrol engines. The gudgeon pin GP should PISTONS FOR INTERNAL COMBUSTION ENGINES. Fio. 629. Gas engine piston. L=l-25tol-5D Fio. 629A. Petrol engine piston. have for both cases such diameters and lengths that the maximum pressure does not exceed 800 to 1000 Ibs. per sq. inch of projected bearing. 2 And they should be checked for bending, 3 when the maximum stress for steel should not exceed 15,000 Ibs. per sq. inch. 240. Piston for Petrol Engine (Drawing Exercise). A plan and sectional elevation of a petrol engine piston are shown in Fig. 630. Instructions. Draw these two views, and a complete elevation. Also show in detail, by separate drawings, the set-screws and gudgeon pin. Scale full size. 241. Cylinders for Petrol Engine (Drawing Exercise). An elevation and sectional elevation of a pair of cylinders for a petrol engine are shown in Figs. 631 and 632. ' About 0-01D" smaller. f> ' s(on Fio. 630. Piston for petrol engine (Drawing Exercise). 2 The area of the gudgeon pin is often twice that of the crank, the latter being subjected to a maximum pressure of 4000 Ibs. per sq. inch. ' See author's " Machine Design, etc.," p. 510. 196 MACHINE DRAWING AND DESIGN FOR BEGINNERS PAIR OF CYLINDERS FOR 20 H.P. FOUR-CYLINDER PETROL MOTOR (Drawing Exercise). perinch. Cylinder and Valve Openings II threads perinch SCALE ...EhJP. I . VTTTf , I , I*, I , I 8 , I, I 7 , I, I 6 , I, I 5 , I FIQ. 631. FIG. 632. Instructions. Drew these views, and from the elevation project a sectional plan ; half of the plan being a section through the exhaust and inlet openings, due to a horizontal cutting plane. Scale fall size. PISTONS AND CYLINDERS, ETC. 197 242. Piston Eods. We have seen that usually piston rods at the piston end are formed with a taper and attached to the piston by a nut or cotter. In some types of engines, such as marine, we have the piston rod forged to the cross head, but when not made in this way the rod usually has a taper end fitted into the cross head, the large diameter of which is rather less than that of the body of the rod, which allows for the re-turning of the rod without interfering with the fit in the cross head. The material l in common use for piston rods is almost exclusively Siemens-Martin Steel, excepting for warships, when crucible or nickel steel is often used. EXERCISES. DESIGN, ETC. 1. Referring to the piston in Fig. 624, determine for one of 16" diameter (by using the dimensions in the table of proportions) what the stress in the rod, and in the screwed portion of the rod, would be due to a pressure on the piston of 140 Ibs. per sq. inch. 2. Make a sketch design of a petrol engine piston (Fig. 629A). Diameter 4J" ; the maximum pressure on the piston may be taken at 200 Ibs. per sq. inch, and the maximum pressure on the gudgeon, 1000 Ibs. per sq. inch. Choose your own working stress for the gudgeon pin. DRAWING. 3. Make working drawings of a cast-iron piston for a 16" cylinder (Fig. 624). Scale half size. 4. Make complete drawings of a petrol engine piston. Diameter 5", length of piston 7", diameter of gudgeon pin 1}". Scale full size. SKETCHING. 5. Show by sketches Mudd's, Buckley's, and Cameron's piston packing. 6. Sketch two different ways of packing an air-pump bucket to make it water-tight. What precautions must be taken when wood packing is used? 7. Show three different ways of arranging the joint in a piston ring to prevent leakage of steam past it. 8. Sketch three different ways of preventing the piston junk-ring screws from working loose. 9. You are to show by sketches how a piston is attached to its rod in the following cases : () By coning the end of the rod and using a nut. (6) By flanging the end of the rod and bolting the piston on to it. (c) In the case of a tandem engine, attaching the piston to a coned part of the rod by means of a cotter. 10. Make a sketch of a small cast-iron piston. 11. Sketch a cast-steel conical piston, suitable for very large engines. What is the object of making a piston conical form? What angle of the cone gives the lightest piston ? 12. Make a sketch of a piston suitable for a petrol engine. 1 Formerly piston rods wero made of ecrap iron forging of the highest quality, but this had a smaller strength, and was, owing to its fibrous character, liable to wear in ridge* or flute'. a CHAPTER XXII CROSS HEADS AND GUIDES 243. Cross Heads. The part of an engine which connects together the piston rod and connecting rod is known as the cross head. It is so formed that it is guided or constrained to move in a straight line by the parts called slides. Cross heads are made in a great variety of forms in either wrought iron, mild steel, cast iron, or cast steel. Some representative examples of types used in stationary engines, locomotives, and marine engines are shown in Figs. 634 to 672. But, before we proceed to touch on these, attention may be given to the forces acting at the cross head. 244. Forces acting at the Cross Head. Fig. 633 is a diagrammatic drawing of a crank and connecting-rod arrange- ment. A being the cross head, AB the connecting rod, BC the crank, and R the reaction of the guide on the cross head, which is a maximum when the angle ABC = 90 ; if the steam cut-off does not occur before that position is reached. Let P = the total pressure on the piston = j?D 2 v, p being the steam pressure per sq. inch, which we may assume to be constant in this case, and we may neglect the inertia forces. Then, the triangle of forces shown (in which ab represents P to a suitable scale) it ac gives us the magnitude of E in terms of P, for p = -j. But, by similar triangles, therefore E _ BD _ BC _ / P ~ AD ~ AB ~ I Jt I P ~L' orE = pr Let n, then 11 = P (39) So, by decreasing the length of the connecting rod we increase the pressure R on the guides, 1 and this explains one of the 1 For other relative positions of crank and connecting rod it can be shown that R = P- sin 8 CROSS HEADS AND GUIDES 199 objections to short connecting rods. And the above shows that for any angle the connecting rod makes with the horizontal E = P tan 0. T be AB Furthermore p ==. = secant .'. T = p secant (40) 245. Position of Gudgeon or Cross Head Pin in Relation to Sliding Surface. We have seen in the previous Article that in every case there is a certain position of the cross head which corresponds to its greatest pressure E on the guides. Now, obviously the best position for the axis C of the gudgeon pin, Fig. 634, in relation to the sliding surface DE of the cross head, is such that it is midway between D and E ; the pressure is then evenly distributed over the sliding surface ; but cases sometimes occur where it is convenient (but not good practice) to fix the gudgeon pin out of the centre. If this is done and C is over B, then it can be shown that the maximum pressure on the slide occurs at E, and that it uniformly tapers off to nothing at D. Or, of course, should C be over A, then the maximum pressure is at D, and there is no pressure at E. Fig. 635 shows a very bad case, the gudgeon pin overhanging the sliding surface, and the force E, acting through C, is tending to tilt the cross head p .vx^x x*\ \\X\\V\\sk\\V \lp R /S/S-"i' /> ^ f '\ / FIG. 634. Correct arrangement. FIG. 635. Showing defective arrangement. about E, causing an upward pressure at D, and a bending action on the piston rod. 246. Types of Cross Heads. We have remarked upon the fact that there seems no end to the number of different forms that designers have given and are giving to cross heads, and it is hardly possible to classify them in such a way as to say that this or that particular design is a locomotive one or a marine one, as the case may be ; but still, for our purpose it will be convenient to group them under the headings of stationary engine, locomotive, and marine. Commencing with the stationary types, we have, in Fig. 636, a simple and inexpensive form for small engines, the sliding surfaces being turned and bored. Although mostly used on cheap engines, there is an increasing tendency to use it in a more complete form, such as shown in Figs. 640 to 643 for important ones. In Figs. 640 and 641 the wrought-iron or steel rod is cottered into a cast-iron head, in which the brasses are held by wrought-iron or mild steel bolts and cap, the connecting rod having a forked end, in which is fixed the gudgeon. The head in Figs. 642 and 643 is fitted with cast-iron shoes S which are adjusted for wear by the cotters C, the gudgeon pin P being fitted with a Stauffer lubricator. Figs. 644 and 645 show an example of a cross head for two-bar guides, containing within itself a means of adjustment, namely, the nuts N and screws S, while the slide bars are fixed and properly arranged to resist the pressure. The head, which is used with a forked connecting rod, is made of malleable cast iron or cast steel, and the side blocks of cast iron. In Figs. 646 and 647 we have a slipper cross head, 1 both the piston rod and the cast-iron slipper being cottered to the wrought-irou head, which is bushed with gun-metal and fitted with a lubricator. A very simple and compact cross head of this type, suitable for small engines, is fully shown in Figs. 637 to 639. In a slightly different form it was an example in the Science and Art Examination Paper of 1893. A different 1 Generally used only on stationary engines when they run in one direction only, BO that the pressure is always on the bottom bar, and the slipper block can be arranged to run in a bath of oil. 200 MACHINE DRAWING AND DESIGN FOR BEGINNERS CROSS HEADS, STATIONARY ENGINE TYPES. r "i 3" v i" 3" i" *Ti Zg-*J?Ml -**-AJU | /?/ y^c-t. |- ^^ Fio. 036. Piston rod head in cast-iron guide. Taper Q- per foot] i Kios. 638, 639. Slipper cross head for small engines (Drawing Exercise). FURTHER TYPES OF STATIONARY ENGINE CROSS HEADS. FIQS. 640. 041. Cast-iron cross head. Fins. I!f2, 043. C.I. adjustable cross head. Fids. 044, 045. Adjustable cross head. CROSS HEADS AND GUIDES 201 -A- type is shown in Figs. 649 to 653, four slide bars S being required ; the forked head is of wrought iron or steel cottered to the piston rod, and the gudgeon pin P, passing through it, forms a neck journal for the connecting rod, and also two end journals J, on which fit the cast-iron slide blocks B. The guide bars are notched at the end E, so that the slide block passes the edge of the notch each stroke for even wear. 1 Figs. 654 to 656 also show a slipper cross head, the cast-iron slipper S being screwed to the wrought- iron head, whilst the gun-metal steps are tightened up by a side cotter, adjusted by the screw A, as shown. A more im- portant and expensive slipper cross head (of the marine type) is shown in Figs. 657 to 659 ; the piston rod and head are in one forging, and the cast-iron slipper block is screwed to a plate A, which is dovetailed into the head. A four-bar locomotive cross head is shown in Figs. 660 and 661, and a two-bar one in Figs. 662 and 663, whilst Figs. 664 and 665 show an original and interesting cross head designed by Mr. W. Adams of the G.E.K. The cast-iron head is made in two parts bolted together by eight J" bolts. It will be seen that the steel slide bar is drilled to allow the oil to reach the under side. The maximum pressure allowed on the sliding block is about 40 Ibs. per sq. inch. Figs. 666 to 668 show still another locomotive cross head, but of the slipper 2 kind, designed by Mr. Stroudley. The wrought-iron head is forged in one with the piston rod. The pin is also wrought-iron but case-hardened, the steps being of gun-metal. 3 The ordinary direct-acting marine engine is usually Fl0 ' 652 - so arranged that the gudgeon pin for the cross head is secured to the forked end of the connecting rod, and it works in a bearing in the cross head, as we have seen in some previous examples, and as shown in Figs. 669 and 670. It will be seen that the steps and slipper block 4 of the cross head in Figs. 671 and 672 (which is largely used), are faced with white metal and the other details of construction should speak for themselves. 247. Cross-head Gudgeon Pins. These pins require to be very accurately fitted, so as to be free from the slightest looseness or 1 This type for a great many years held its own, and was very largely used, notwithstanding the number of parts and the labour involved in fitting up. The almost universal practice now is to make the guiding surface in one with the frame (as shown in Figs. 630, 040, and 041), which reduces the liability of error in erecting, and also the labour. 2 The guide bar U is in this case above the cross head. This, of course, is the best position for it in a slipper arrangement for a locomotive, as the greatest pressure is upwards when the engine is running forward. When running backwards the sliding surface taking the pressure is smaller (as with all slipper cross heads), but, in this case, not very much smaller. 3 The proportions shown are mainly those given by Unwin. ' The shoes of all these 01*088 heads must be so fitted that they are easily taken down, and there is no possibility of their working loose. Wear takes place after a time, and this U usually taken up by fitting thin strips of Muntz metal between the slipper and the body of the head. 2D FIGS. GiU, 647. Slipper cross heiid. FIG. 049. Section 011 line EE. FIG. 651. Section on line H. Fio. 048. Plan. Plan. Four-bar stationary cross head. 202 MACHINE DRAWING AND DESIGN FOR BEGINNERS STATIONARY AND MARINE CROSS HEADS. FIG. 658. Fio. 659. shake, and to be held or secured in such a way that they cannot rotate about their axes. Perhaps the most simple and easy way to satisfy these conditions is to make the pin parallel, and a snug fit at its ends, fitting a feather or feathers F, Fig. 673, to it to prevent any movement about the axis. Fig. 674 is a somewhat similar arrangement, a shoulder 1 S being used instead of the head H of the other, and a pin P is sometimes used instead of the feather. Coning the ends, as in Fig. 677, is a very popular expedient, but in practice it is most difficult to get an exact fit at both ends ; however, by slightly increasing the diameter of the large end, as in Fig. 675, the two conical ends are parts of the same cone, as shown by the dotted lines, and this greatly facilitates the machine work both on pin and head. Fig. 676 shows a pin for a marine cross head ; it is forced into the forked end of the connecting rod by hydraulic pressure, or shrunk into it while the fork is hot ; usually the pin is further secured in the fork by a strong set -screw, as shown. Such gudgeon pins are made hollow if weight is of importance. As will be noticed in Fig. 677, a snug S may be used on the pin instead of a feather, and the gudgeon pin held in position by the plate A pressed on the shoulder of the pin by the three screws. A simple and effective arrangement of fixing, which allows the gudgeon or cross-head pin to be readily withdrawn, is shown in Fig. 678 ; it was devised by Messrs. Bollinckx, of Brussels, and is used on their famous engines. 248. Cross Head for Horizontal Engine (Drawing Exercise). The three views, Figs. 679, 680, and 681, show a cast-iron cross head for a horizontal steam engine. Some particulars of this type are given in connection with Figs. 640 and 641. Instructions. Draw the views shown, completing the section EF. Draw also nn end elevation as seen when looking at the end of the rod. Scale 6 ins. = 1 ft. 249. Cross Head for Marine Engine (Drawing Exercise). Fig. 682 shows in detail the separate parts of a marine engine cross head. Instructions. Draw three views of the assembled cross head. Scale quarter full size. 1 These require to be well filleted, as cross-head pin failures with about half Wohler's value of the stress, have to be attributed to sharp shoulders. Refer to Dr. Stanton's experiments, Proceedings Inst. C.E., vol. clxvi. CROSS HEADS AND GUIDES TYPES OF LOCOMOTIVE CROSS HEADS. 203 FIGS. 660, 661. Four-bar type (Drawing Exercise). Pros. 662, 663. Two-bar type (Drawing Exercise). Fio. 664. Fio. H65. Adams's cross head. One-bar type. Instructions. Work to the dimensions upon the figure, which is n:>t to scale. And (a) Draw the cross head in elevation. (6) Draw the cross head as seen looking towards the cap, the top to be a half end elevation, the lower half a vertical section, taken through the centre of the pin. Scale 3 inches = 1 foot. You are not to draw the parts separated, as shown, but put them together in their proper positions. Section line the various parts for suitable materials. FIG. 668. Stroudley's cross head. Slipper type. MACHINE DRAWING AND DESIGN FOR BEGINNERS TYPES OF MARINE CROSS HEADS. TYPES OF CROSS-HEAD GUDGEON PINS. FIGS. 6C9, 670. FIG. 678. Bollincki. FIGS. 671, 672. FIG. 676. FIG. G77. EXERCISES. DESIGN, ETC. 1. A connecting rod is five times the length of the crank, and the pressure on the piston is 20,000 Ibs. Find, by thr triangle of forces, what is the pressure on the cross-head guide when the crank has moved through 4:">. And what is the pressure when the crank and connecting rod are at right angles to each oilier. 2. A gudgeon pin has a diameter of 3" and a length of 4", and the journal is loaded to 1100 per sq. inch. What skin stress dues this correspond to, and what pressure per sq. inch on the journal ? 3. A piston has a diameter of 30", and when the connecting rod is inclined 15 the pressure on the piston is 80 Ibs. per sq. inch. What would bo the thrust of the connecting rod on the gudgeon at that instant ? CROSS HEADS AND GUIDES 205 DRAWING. 4. Make working drawings of the cross head, Figs. 660 and 661. Scale half-size. 5. Set out the locomotive cross head shown in Figs. 662 and 663. Scale 6" = 1'. 3. Draw the three views of the cross head in Figs. 687 to 639, full size. SKETCHING. 7. Make a sketch of cast-iron cross head suitable for a stationary engine (Figs. 637 and 6H9). 8. Make a sketch of Stroudluy's loco- motive cross head (Figs. 666 to 668). 9. Sketch a slipper cross bead, marine type, arranged to receive tbe gudgeon pin of a forked connecting rod (Figs. 671 and 672). 10. Show by sketches three ways of fixing gudgeon pins to cross heads, and state which one you prefer, and why. CROSS HEAD FOR HORIZONTAL STEAM ENGINE (Drawing Exercise). Half Elevation. Fio. 679. Sectional elevation on line AB. JL Fio. 681. Section on line EF. Fio. 680. Sectional plan on line CD. Lock W'asKr CROS5HEAD FOR MARINE ENGINE. tnd oV 'Rod ItEus. Clip 9oide as offter side (^ -*-!-* I'-! ~ " Fie. 682. Drawing Exercise. For instructions, refer to Art. 249, p. 202. CHAPTER XXIII CONNECTING RODS 250. Length of Connecting Rod. The length of a connecting rod, measured from the centre of the crank pin to the centre of the gudgeon or cross-head pin, varies from about 3'5 to about 8 (or in extreme cases even 9) times the length of the crank, according to the type of the engine ; a ratio of 6 to 1 being very generally used for stationary (and often for locomotive) engines. If we had only to consider the rod in fixing this ratio, in a given case, we should make the latter as short as practicable, because the rods acting as struts, must obviously (for a given load on the piston) be larger in diameter as their lengths increase. But we have seen (Art. 244) that the longer the rod is in relation to the crank, the smaller will be the pressure on the cross-head guides, and there is the further important advantage of a more uniform motion of the piston, the longer the connecting rod. 1 However, in practice there are conditions which restrict the length. Thus, the restricted height of marine engines rarely allows of a larger ratio than 4'5 to 1, a ratio of 4 to 1 being more often used, whilst, on the other hand, in locomotive practice, the ratio is generally about 6 to 1, as we have seen. 251. Strength of Connecting Rod. In addition to the alternate compressive and tensile stresses 2 there is a transverse force applied to the body of the connecting rod due to the oscillation of the crank-pin end. This last factor is important in small and very high-speed engines, but not in large ones running at a moderate speed. The diameter of connecting rods for large stationary engines, for the sake of stiffeners, is always made greater than would be necessary from a consideration of its ultimate strength as a strut, or its transverse strength against bending. Generally, the largest diameter is such that the mean stress there is 800 or 900 Ibs. per sq. inch, and the mean direct stress at the smallest diameter is, as a rule, 1560 to 1600 Ibs. per sq. inch. In locomotive practice, an old rule was to make the diameter of the ends about 0'16 x the diameter of the cylinder, and that of the centre of the rodO'21 X diameter of cylinder ; the former dimension, it will be noticed, is the same as we have given for locomotive piston rods. Molesworth gives the rule, diameter of connecting rod = 0'021DY/p for iron, and d = 0'018D\/^ for steel, which for steel nearly corresponds to the previous rule, when the pressure = 150 Ibs. per sq. inch, for then d = 0'22D. And again, in Marine practice, the diameter d of the connecting rod just below the fork (Fig. 695) is generally made equal to the diameter of the piston rod. Then, if the taper of the rod be produced to the axis of the cross-head pin, di = about 0'75rf. And, if the taper is produced in the opposite direction till it cuts a diameter of the crank (Fig. 695), fairly correct values for the larger end are obtained, 3 if DI = 0'6D, where D is the diameter of the crank pin. Usually the part of the shaft of the rod between the small 1 The motiou of the piston becomes harmonic when the length of the connecting rod is infinite. See Goodman's " Mechanics of Engineering," pp. 133 and 163. - For the magnitude of these, refer to the author's " Machine Design, etc.," p. 514. 3 Bauer and Robertson's " Marine Engines and Boilers," p. 194. 208 MACHINE DRAWING AND DESIGN FOR BEGINNERS end and large end is made with a straight taper. In some cases rods are made taper from the cross-head end to the middle, and for the remainder of the length parallel. 1 The tapering of the rod not only makes the change of size less sudden, but it gives greater strength to the middle of the rod where it is required to resist bending when in compression. Flats are sometimes planed on the taper shaft near the large end and parallel to the plane of motion ; this somewhat reduces the section and weight, but very little decreases the strength to resist bending, as the modulus of the section is very little affected. This principle is carried a step further when the rods are made rectangular or I-shape 2 in section, as they often are for high-speed engines, such as petrol engines, or even locomotives. The rods of beam section have been found to answer well when made of cast steel ; the section of these at the small end may be made equal in area to that of the piston rod (if of the same material). And the more economical section allows of the large end being made sensibly smaller in section than it would be if of round section, so we see that the proportions of connecting rods are to a larye extent fixed by the application of empirical rules, which long experience has proved to be satisfactory ; however, in cases where there is a departure from ordinary practice in any important respect, it is certainly advisable to check the dimensions of the principal parts of the rod, or at least those of the shaft, by determining the maximum stresses, and we will proceed to indicate how this may be done. 252. Connecting Eods for Internal Combustion Engines are usually fitted with big ends of the marine type, and the little ends for small gas engines and petrol engines are fitted with solid bushes to engage the gudgeon pin ; the bushes being easily renewed when necessary. Connecting rods for these engines are practically always in compression, 3 with respect to gas pressures, but at certain parts of the strokes they are in ten-sion due to inertia. And (unlike rods for steam engines) when the ignition is early and the other conditions at their best, the greatest possible thrust on the rod equals the total pressure mi the piston at the commencement of the stroke.* So there is little beyond the determination of maximum thrust in designing these rods further than what we have seen applies to steam-engine rods. Except when the main object of the design is to obtain the minimum weight in a given case, then a very careful and complete analysis should be made, by combining gas pressure and inertia curves, etc. For petrol engines, connecting rods are usually made very light for the work they do. Dr. Lucke 5 gives the following empirical rule for the limiting values of d, the mid-section diameter of round rods, namely, between d = O-OllD-s/p, and d = Q-QUT)\/p (41) where D is the diameter of the cylinder, and p the initial pressure per sq. inch (about 250, say). Or for plain rectangular rods, the mean thickness t, for rods varying from 15 to 25 thicknesses in length, is t = O-OOSDv/p (42) The width at the piston end is usually l'6t, and at the crank end 2'3<. A common practice now is to make the connecting rods of I 1 Long rods with ends equal in size are usually made barrel shape with the diameter at the ends = 0'75IV-3i I p* *i|lf" ' i itt-XLrr I f\l . I . FIGS. 703, 704. Little end, locomotive type (Drawing Exercise). Exercise). Fig. 709. Instructions. Draw the sectional elevation and sectional plan, also an end elevation as seen when looking in the direction of arrow A. Take dimensions for the smaller details from sketches given. Section each part to indicate material used. Scale one half fall size. 255. Connecting-rod End, Forked Type (Drawing Exercise). Figs. 710 and 711 show two views of the little end (forked type) of a connecting rod for a vertical engine. This example was set at the C. and G. Examination in Mechanical Engi- CONNECTING-ROD LITTLE ENDS. FIGS. 705, 706. Solid end, with Mnsgrave brasses. FIGS. 707, 708. Solid end, with side adjustment. neering in 1907, Part II., Ordinary Grade. Students were given the following : Instructions. The figures show two incomplete views of the little end of a connecting rod for a vertical steam engine. Draw to a scale of 3" to 1' : (1) A half sectional elevation, the upper hiilf being in elevation and the lower half in section, on the plane AB. (2) In place of the plan, a section on tlie plane CD of one-half of the rod end. (8) A section on the plane EF of one side of the rod end, and a complete end elevation of the other side. Any omitted detail must be added, together with a suitable oil catcher. 256. Petrol Engine Connecting Rod (Drawing Exercise). Figs. 712 and 713. Instructions. Draw the connecting rod and piston, assembling all the parts shown separately on the figure ns when in use, showing front sectional elevation, side elevation, and a plan. Scale full size. CONNECTING-ROD END FOR MARINE ENGINE (Drawing Exercise). _T Snug _ 2 ffeas._ _Sfrlir Cotter. 1 _ 2 rfJus._ Sec (Tonal CONNECTING-ROD END FOR VERTICAL STEAM ENGINE (Drawing Exercise). r 4% -m -HIWI? < L- i- FIGS. 710, 711. PETROL ENGINE CONNECTING ROD (Drawing Exercise). / V [ 1 1 nfj / ; I i , r 1 " 1 \ L/ ' 6 f ; ! ' T * *-^ \ t-'it Connecting Rod. ^Centre of Crank Pin CONNECTING RODS 217 257. Connecting Rod of Petrol Engine (Joist Type). 1 Figs. 714 and 715 show a lighter form of rod, which is now 258. Connecting-rod Brasses. The total load and the permissible pressure per sq. inch (see Table 14) determine of the brasses. When the crank pins are of large diameter the brasses are made, as we have seen, of bronze, or of cast steel with white metal linings, and the distance x from centre to back of brass, Fig. 695, may be such ,. ^OQj that for solid gun-metal or cast steel lined with white metal much used, the dimensions a = 1-3 to 1-4 And for gun-metal brasses lined with white metal ,- F x = 1-3& to 1-5 a (43) (44) the higher values being for the smaller pins in each case. For circular-shaped brasses, Figs. 697 and 698, and other forms shown on the rod ends, in fixing the dimensions, the proportions shown on Figs. 427A to 427s, Art. 176, may be used as a guide, the unit for this purpose being t = 0-08D + 0125 FIGS. 714, 715. Petrol engine connecting-rod end, joist type. (45) 259. Coupling-rod Ends. The rods used in locomotives to transmit the motion of the crank axle to another or other axles coupling them together, so that a larger proportion of the whole weight of the engine may be available to increase the adhesion on the rails, are called coupling rods ,- they are made of steel or wrought iron, and usually of rectangular or I section, and the ends are now made solid ; as there is not a great amount of wear, the lubrication being very good, so no adjustment for wear is usually arranged, a solid brass bush, with a key or feather to prevent rotation, being fitted to each end, this being easily replaced by a new one when worn out. An ordinary form of coupling-rod end 2 for a four-wheel coupled engine is shown in Figs. 716 to 718. And Figs. 719 and 720 show how the rods are generally arranged and connected when more than two pah's of wheels are coupled together. They are drawings of a pattern adopted by the M. S. & L. Eailway Co. for their goods engines. 1 Refer to Art. 48'2, author's " Machine Design, etc." 2 This example is taken from a past B. of E. Examination paper. AVordseH's Coupling-rod End is illustrated on Sheet '23 of the author's " Elements of Machine Construction and Drawing." 2F 218 MACHINE DRAWING AND DESIGN FOR BEGINNERS LOCOMOTIVE COUPLING-ROD END. EXERCISES. DRAWING, ETC. 1. Make working drawings of the connecting-rod big end. and 686.) Scale full size. 2. motive (Figs. 68:> FIGS. 716, 717. Type of end for four-wheel coupled engine. 14. Make a sketch showing Musgrave's or Halpiu'i ordinary one ? 2. Make plan, elevation, and end elevation, in part section of the loco- ive connecting-rod big end. Figs. 691 and 692. Scale 6" = 1'. 3. Set out a strap connecting-rod big end from the proportions given in connection with Figs. 683 and 684; diameter of crank pin, 2". Full size. 4. Draw the two views of the connecting-rod little end (Figs. 69o and 696), and add an end view. Full size. 5. Draw three views of the locomotive connecting-rod little end (Figs. 703 and 704), half size, and calculate the mean shear stress in bolts ; also the tensional stress in the rod, and in the strap at the bolt hole, assuming that the maximum load on the rod is :<4,000 Ibs. 6. Draw three views of the coupling-rod end (Figs. 716 to 718) partly in section. Full size. 7. Set out three views, partly in section, of the coupling-rod end (Figs. 719 and 720). Full size. SKETCHING. 8. Make a sketch of a plain strap connecting-rod end, witli screw adjustment (Figs. 685 and 686). Why is the strap made thicker at the end and where the brass beds ? 9. Make a sketch of a locomotive connecting-rod big end (Figs. 691 and 692), and explain how, if the other end be like Figs. 703 and 704, the true distance between centres is practically maintained when wear occurs. 10. Make a sketcli of a eolid end for a connecting rod. What are the good points of this type, and what feature limits its use '! 11. Make sketches of two patterns of marine connecting-rod big ends, and explain their relative good features. 12. Sketch two patterns of connecting-rod little ends, and say which you consider makes the best mechanical job, and why. 13. Show by a sketch how you would arrange the ends of a connecting rod so that tightening up for wear at both ends practically keeps the rod centres constant in length. brasses and pin for a connecting-rod little end. What advantage is claimed for this arrangement over the LOCOMOTIVE COUPLING-ROD ENDS AND JOINTS. cl~ I ' foT < fr *#* SECTION ON LINE AA. _ A SECTION ON LINE BB. FIG. 737 SECTION ON LINECC._ w.fh Chaest Head Screws -SECTION ON LINE DP. Fio. 786. Crank Case MISCELLANEOUS DRAWING EXERCISES SOME DETAILS OF A 4 H.P. PETROL ENGINE. Cover 'Bash. 227 *rrrf77777A '/iw nd s CTJ I V////////A d ) M r - | lV * + i 3 1 ^ K W K. 5 UK \ 1 1, **'" -If- Dimintj S ar .-...I. ^_ 1 J .. : -T- 5 ' Secfional flan. Via. 738. ADJUSTABLE LOOSE LATHE HEADSTOCK. "----_- =-- 39* -H *- 2**- * -i 4'/ t ". '- hJ \NO ELEVAT/ON F/c 739 SIDE ELEVAT/ON A'O i VA r/OA/ orB/ifipeL F/G 741 Screwed 11 threads P 1 ( /Ti oer inch \ i j i i * * A ^ , ; ^-1 -^ > "1 j ' T* - 1 jr Screw fyi "D/a. 8-Tftreads per inch Left Hand S - "- 4- ; 4 ^- v-/*"---H -i .. 1 ^ 1 1 C j "\ ! * /" 7 ** J-^r *} SECT/ ON THROUGH BARREL ON A B F/G 742 MISCELLANEOUS DRAWING EXERCISES Figs. 739 to 742 show four views of an adjustable loose headstock for a lathe. Draw to a scale of ^ full size : (1) A section on the plane AB, looking in the direction of the arrow 1. (2) A section on the plane CD, looking in the direction of the arrow 2. (3) An end elevation of the " centre " end. (4) A complete plan. Add omitted detail. 267. Slide Rest for 91" Lathe. Ad- vanced students will experience little diffi- culty in making working drawings from the dimensioned pictorial sketch of the unfinished slide rest shown in Fig. 743. Instructions. Draw two elevations and a plan of the slide rest, showing in section as much of the plan as is necessary to clearly display any important detail. You are to arrange a tool holder on the top slider, and show any other part that may be omitted. Scale half size. 268. Cylinder, with Meyer Expansion Valve, for 20 Horse-power Horizontal Steam Engine. Eight fully dimensioned views of the cylinder and its fittings are shown in Figs. 744 to 751. Instructions. Set out the views shown to a scale of 3" to the foot, and make working drawings of the piston to a scale of half size, and of the main and expansion valves, bushes, etc., to a scale of full size. Yep oj- fool off SLIDE REST FOR 9i" LATHE. g 3 r 5~ 22 8 VertTcial bcfvVeerc centre.* j screws L of Slide FIG. 743. UJ z CJ z UJ u H eo z O N QL O X CL X O CM cc. O UJ Q O LU Z CJ z u LJ H co z O N o: O I ci i o CNJ O L. LJ Q >- O CHAPTER XXV PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES 269. Cast Iron. The crude metal derived from smelting common ores of iron with fuel in a blast furnace is cast iron. A strong blast of air acting on the burning fuel generates an intense heat, which gradually melts the iron. As iron ores are generally found mixed with earthy materials, which make them refractory, fluxes have to be used with the fuel to combine with the earthy materials and facilitate their fusion. When the ore is calcareous the flux employed has to be of an argillaceous nature, that is to say, to contain clay ; on the other hand, if the ore contains clay the flux must be of a calcareous nature. This being so, it is occasionally possible to mix the two kinds of ore in proper proportions to enable the one to act as a flux to the other. When a flux is used it is tipped into the furnace with the fuel and ore, and it unites at a high temperature with the earthy matter of the ore, forming slag, setting the greater part of the iron free, which, as it fuses, falls by gravitation to the bottom of the furnace, and when a suitable quantity has accumulated it is allowed to flow out of a tap-hole on to a sand bed along a large groove in it (called a sow), from which at right angles it enters smaller grooves, or hollows, which form the moulds for the pigs. And these castings are commercially known as pig iron. During the smelting process the liquid iron absorbs and combines with a considerable quantity of carbon from the fuel, and is more or less contaminated with the impurities of the ore fuel and flux, hence the presence in cast iron of carbon, sulphur, silicon, phosphorus, and manganese. A portion of the carbon is chemically combined with the iron, while the remainder exists in the iron in the form of graphite, but the presence of carbon in the iron, whether in combination with it or not, determines its behaviour, giving to it its fusibility, which .enables it to be remelted again and again for foundry purposes, and rendering the iron more liquid in the fluid state, and tougher and softer when in the solid state ; the degree of fusibility depending upon the percentage of carbon which it contains, but an excess of carbon weakens the iron, and therefore the skill, experience, and judgment of the founder have to be exercised to secure by a suitable mixture of different sorts and qualities of iron the requisite degree of strength, softness, hardness, toughness, and closeness of grain for various kinds of castings. Strangely enough, the best results for both strength and elasticity are obtained by mixing a number of carefully selected different kinds of iron in the cupola ; this gives higher tensile strengths than the average of the different samples when cast separately. When practically all the carbon is combined with the iron, the fracture of a freshly broken piece will have a silvery white colour, and the cast iron is white, and is found to be very brittle and hard. When only a little carbon is combined, and most of its particles crystallize separately, a fracture is grey in colour, and the iron is weaker and more fusible. Silicon apparently influences the form the carbon takes in cast iron, also the rate of cooling. The more slowly a casting cools the more graphite forms and the softer the iron. Usually, for commercial purposes, cast irons are divided into seven varieties. The greyer cast irons, containing the most graphite or free carbon, used for foundry purposes, are classed as N"os. 1, 2, and 3. The whiter and harder cast irons, Nos. 4, 5, 6, and 7, are used only for conversion PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES into wrought iron, No. 4 being occasionally used to close the grain and harden the metal of foundry mixtures. As the greyest iron, No. 1, is wanting in strength, most castings are composed of mixtures of Nos. 1, 2, and 3 in varying proportions, according to the judgment of the founder. No. 3, Scotch iron, is most generally used for engine castings, as it can be depended on for closeness of grain and strength, and it runs sufficiently fluid to make any casting. But generally, the stronger and larger the casting the smaller the proportion of No. 1 used. On the other hand, a larger proportion of No. 1 gives greater fluidity and causes the metal to run very thin and expand at the moment it solidifies, so that intricate forms and sharp corners of the mould are filled better. Nos. 5 and 6, called forge irons, often present a mottled appearance, as if a grey iron and a white iron had been melted and imperfectly mixed, hence it is often called mottled pig. No. 7, called white forge, is very hard, and silvery white in appearance. 270. Chemical Composition of Cast Iron. The proportion of carbon in cast iron varies in different varieties from about 3 to about 4'6 per cent., 1 and its effect, etc., is explained in the previous article. Mr. Bloxam, the famous authority on cast iron, gives the following as the composition of the kinds of iron in the foundry to which reference has been made : TABLE 12. CHEMICAL COMPOSITION OF VARIOUS KINDS OF FOUNDRY CAST IRON. Btexhwn. Swedish Lily. Foundry Glengarnock. Splegels. No. l(Grey). No. 2. No. 3. Ebbw Vale. Ferro-Manganese. Iron 90-24 1-02 2-64 3-06 1-14 0-39 0-38 89-31 1-79 1-11 2-17 1-48 1-17 1-60 89-86 2-461 0-87/ 1-12 2-52 0-91 2-72 4-603 0-070 0-006 0-015 1-276 3-677 2-400 0-602 1-010 1-777 3-734 0-215 0-064 0-088 8-958 C-588 0-187 0-081 0-059 65-150 Combined carbon . . . Graphite Silicon .... Sulphur Phosphorus .'.... Manganese .... Whilst the ore is being smelted in the blast furnace a glassy slag is formed by the alumina, silica, and lime in the ore and flux ; by aid of the heat, this floats on the molten metal and is run off near the bottom of the furnace. Part of the carbon of the fuel combines with the iron, the remainder combining with the oxygen in the air and ore, forming carbonic oxide and carbon dioxide, which pass out of the furnace at the top. 271. Strength of Cast Iron. Probably no metal used by the engineer varies so much in strength and soundness as cast iron, and, as this material is so largely used in the construction of the machines and structures he is responsible for, no efforts on his part to get a sound knowledge of its physical properties should be spared. Cast iron of an inferior quality may have an ultimate tensile strength of 5 tons per sq. inch, or even less, but such exceptionally poor qualities have no value where strength is required ; they 1 For the methods employed in estimating the proportion of carbon in iron, see an article in Technics, April, 1904, by H. C. H. Carpenter, B.A., PH.D., on " The Estimation of Carbon in Iron-carbon Alloys." 2 H 234 MACHINE DRAWING AND DESIGN FOR BEGINNERS may be used for balance weights, foundation blocks, or for purposes where weight alone is of consequence. On the other hand, a tenacity of 14 or 15 tons per sq. inch is sometimes reached, and in very exceptional cases 17 or 18 tons, and even 19'6 has been reached, 1 but the average ultimate tensile strength of cast iron is about 7 tons per sq. inch. Further, as the limit of its elasticity, as determined by short specimens of ordinary quality, is found to be only about one-third of its ultimate strength, it is not considered safe to stress ordinary cast iron in tension to more than 2 tons per sq. inch. Even with the higher qualities, some authorities believe, and with sound reason, that the stress should never exceed 3 tons per sq. inch for a statical load. As to compressive strength, it appears from Mr. Hodgkinson's experiments, that it varies from about 25 to 52'5 tons per sq. inch ; averaging 38 - 5. And that the average ratio of tensile to compressive strength is 1 to 5 641. More recent experiments give somewhat higher values. 272. Wrought Iron. Wrought or malleable iron, which is very nearly pure iron, is obtained from cast iron by eliminating the greater part of the carbon in a reverberatory furnace. The pig iron sometimes undergoes two processes one called refining, the other puddling. These are chemically the same ; briefly, the former is usually done in a hearth termed a refinery. The pig iron and scrap are placed in alternate layers with coke upon a bed of ignited fuel at the bottom of the hearth. A blast is supplied at a pressure of about 1 to 2 Ibs. per sq. inch, according to the quality of the coke. The charge is melted in about 2 to 2 hours, and in about another hour the blast has sufficiently oxidized the impurities in the iron (when basic iron slags and hammer-scale are added the refining is accelerated) and a plate about 3" in thickness is formed ; the refined metal, being very brittle, is easily broken into pieces suitable for puddling. The fracture is a silvery-white ; the top part being dull and cellular, and the lower part compact. This iron is ready for puddling. About 4 cwt. of it forms a charge for the reverberatory furnace, and in about half an hour it is partially melted, forming a pasty mass, which is stirred with iron tools so as to bring all parts under the oxidizing influence of the air and fetling. 2 The iron becoming less and less fusible as the carbon and impurities are removed by oxidation, the C forming, with the of the air, C0 2 , requires the temperature to be gradually raised. The metal, which is now comparatively pure, is collected in balls or blooms weighing about 80 Ibs., and, being now in a soft spongy condition, it is subjected to a hammering or squeezing, called shingling, and whilst these shingled blooms are hot enough they are rolled into rough puddled bars, which are of very inferior quality, having a tensile strength of about 9 tons per sq. inch only ; they are not used by engineers, as they require to be further improved. This is done by cutting up the bars into short lengths, which are piled crossways into a faggot or pile, reheated, and hammered or rolled again, usually into bars which are commercially known as merchant's bars. This iron is still of low tenacity, and not very uniform in quality or structure ; it is used for common girder work, gratings, ladders, fire bars, bearers, etc. The process of cutting, piling, reheating, and rerolling, may be repeated several times to give the iron a fibrous structure, according to the quality of the iron required. Thus best bar is made from faggots of merchant bars. Its strength is now much improved, and it is more uniform in quality ; in fact, it is suitable for general smithing purposes, having a strength, if of good material, of 23 or 24 tons per sq. inch. The best best, or double best, is made from faggots of selected best iron, and best best best, or treble best, from faggots of best best iron. (Bars and plates of these qualities are commonly marked B ; BB ; and BBB respectively.) It has a very silky uniform fibre, and good qualities have a tensile strength of 25 to 27 tons, an elongation of 25 per cent., and a contraction at fracture of about 50 per cent., and it will bend double cold. 1 Refer to Table 13. 1 The action is assisted by the covering or fetling of the bottom of the f nrnace, formed of scales of oxide of iron. PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES 235 Slabs from faggots of selected scrap iron are used to make up heavy forgings, new iron being seldom now used for this purpose. Among the best known qualities of wrought iron \ve have Swedish iron, and Yorkshire iron from Lowmoor, Farnley, Leeds Forge, and Bowling, used for the most difficult forgings for boiler plates which require flanging, for furnace plates exposed to furnace flames, etc. ; and treble lest Staffordshire is largely used for chains, boiler plates and general forgings, domes, and such parts of furnaces and chambers as are not exposed to the direct action of the flame ; although slightly inferior to best York- shire, it is recognized as being of high quality. Whilst in charcoal iron we have the purest, and therefore the most soft and ductile quality. 273. Cold shortness in wrought iron, or brittleness when cold, is produced by the presence of a small proportion of phosphorus : and red shortness, or brittleness when hot, by the presence of sulphur. Although wrought iron has in recent years been largely supplanted by mild steel for many purposes, it is still extensively used, particularly on account of its weldable property, for although it cannot be cast in moulds, it assumes, when heated, a sticky or viscous condition, so that when two or more pieces are brought together at the proper temperature they may be united by blows of a hammer or by pressure, or, in other words, welded. 274. Strength of Wrought Iron. It is found that when iron bars or plates are rolled, the molecules of the iron are elongated or spread into a fibrous condition ; this gives the metal (more especially when thin, as in boiler plates) a tensile strength in the direction of the fibres somewhat greater (about 7 to 15 per cent.) than in a direction at right angles to them. 1 And the elongation is greater in the former than in the latter. The ultimate tensile strength of wrought iron ranges from about 18 to 27 or 28 tons per sq. inch ; those qualities with the greater strengths tending to be hard and steely. Indeed, strengths of 32 tons have been produced ; but such iron is hard, brittle, and almost unweldable. The contraction of the area of the transverse section where rupture occurs is usually taken as a measure of toughness or ductility of the metal. This contraction ranges from about 7 to 45 per cent, of the area. As a rule bars are stronger than plates, angles, tees, and like sections. Wrought iron in tension elongates about y ooo of its length for each ton per sq. inch of its section, up to the limit of elasticity. The elastic strength (the strength up to its limit of elasticity) is not often less than 50 per cent, of the ultimate strength, and may be taken at about 12 tons per sq. inch, in both tension and compression. The percentage of elongation (in terms of the length) before rupture occurs, is also important. Obviously, it will be greater for short specimens than for long ones, as most stretch occurs near the fracture, so it is necessary to state the length of the specimen in giving the elongation. Usually 8" is the length for tensile tests. Ductile iron, such as is required for flanged plates or difficult forgings, usually has an elongation of 15 to 20 per cent., and a tensile strength with the fibre of about 25 tons. Wire Drawing and Cold Rolling considerably increase the tenacity and hardness of wrought iron, but after annealing, it practically returns to its original strengtli and softness. 275. Steel. Preliminary Remarks. We have seen that wrought iron contains very little carbon, an amount not exceeding some 0'4 per cent. ; and that cast iron is rich in carbon, and may contain from about 3 to nearly 5 per cent. On the other hand, steel lies intermediate between cast iron and wrought iron, being pure iron combined with carbon and other elements, such as manganese, silicon, phosphorus, etc., each of which influences the physical properties of the metal, and some special qualities are alloyed with 1 Fairbairn was apparently the first to discover by actual testa this difference; but, strangely enough, in his communication to the Eoyal Society, credited the strength across the fibres with the higher value, doubtless owing to some mistake in marking the plates. 236 MACHINE DRAWING AND DESIGN FOR BEGINNERS such elements as nickel, chromium, vanadium, etc., to give them certain required properties. The hardest steels contain about 1'2 to 1'6 per cent, of carbon, and the mildest from about 016 to O4 per cent. The latter, called low carbon steel, much resembles wrought iron, which it has for many purposes supplanted, as we have before remarked. It is weldable and does not harden when suddenly cooled. With a little carbon, the steel is stronger and harder, and is used for rails, wheel tyres, etc. ; but when the percentage of carbon reaches - 5, the steel has the remarkable property of hardening. Steel is obtained either by the abstraction of carbon from cast iron, or by the addition of carbon to wrought iron, as we shall see. The former represents the cheaper qualities, and the latter the more expensive ones. We will now give some attention to the various kinds of steel in use, commencing with the former. 276. Bessemer Steel is made from grey pig iron, free from phosphorus and comparatively free from sulphur, containing a small quantity of manganese and silicon and a large proportion of free carbon. In the Bessemer process, there are essentially two opera- tions, the conversion of molten cast iron into pure iron, and by the addition of a small and definite quantity of carbon, the turning of pure iron into steel. The pig iron is melted in a cupola, and run into a converter lined with firebrick, and mounted in hollow trunnions, through which air is blown through the metal for about twenty minutes, removing all the carbon : the oxygen of the air combining with the carbon of the iron forming C0 2 , and in so doing burning out the carbon. From 5 to 10 per cent, of spiegeleisen, 1 an iron containing a known proportion of carbon and manganese, is then added, and the blowing resumed long enough to incorporate the mixture. The steel is then run into a ladle, and from the ladle to iron moulds to form ingots. These being more or less porous, are reheated, 2 and run through the five grooves of a clogging mill, or worked under the steam hammer, and finally rolled or forged into the required shape. This steel, which is named after Bessemer, the inventor of the process, 3 is largely used for structural purposes, tyres, rails, etc. Fairly good steel can be made from iron containing phosphorus, by the Thomas- Gilchrist process. The phosphorus is absorbed by the converter lining, which is prepared from magnesium limestone, the product is known as basic steel, the original metal being called acid steel. 277. Siemens-Martin or Open Hearth Steel. This steel is produced by melting (heated by gas to an intense violet heat) a certain quantity of pig iron in the hearth of a Siemens reverberatory furnace, and adding wrought iron till the bath attains the desired degree of carbonization, or by mixing cast iron and certain kinds of iron ores. The oxides and free oxygen are removed, and carbon and manganese added by the introduction of a small quantity of ferro-manganese (a somewhat similar substance to spiegeleisen), which is rich in carbon and manganese. The amount of carbon left in the metal is ascertained by testing a small quantity, which is removed by a ladle, quenched, broken up and tested by the chemist on the works. If found satisfactory, the charge is tapped and the metal run into ingot moulds. The operation is slower but more completely under control than that of Bessemer's. The regularity and ease with which any grade of steel required can be produced by it has led to its being freely adopted ; in fact, it is now the most general method of producing on a large scale steel of good and uniform quality at such a comparatively low cost that it can compete in price with Bessemer steel. This is largely due to the modern practice of using a basic lining for the Siemens furnace for the 1 White pig iron containing 5 to 10 per cent, of manganese is known as Spiegeleisen. This gives to the metal the small proportion of carbon required, and the still smaller quantity of manganese which seems to be so essential for the production of good steel. * The ingots are usually taken from the moulds when their skin has solidified (their interior being still more or less liquid), and placed in an oven to soak and allow the temperature to become more equalized. They then have a bright cherry-red heat. ' See Engineering, Nov. 22, 1901. PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES 237 dephosphorization of pig iron. A grade of this steel with a tensile strength of 26 to 32 tons per sq. inch, and not less than 20 per cent, elongation in 8", is largely used for the crank and tunnel shafts of merchant ships and war vessels, etc. ; and steel plates, bars, and forgings are made almost exclusively from ingots run from Siemens furnaces or from Bessemer converters. 278. Mild Steel. Usually in speaking of mild steel we refer to such steels as are worked up in bars, plates, angles, etc., from Siemens open hearth or Bessemer ingots. The ingots are reheated and hammered into slabs, which are again reheated and rolled into plates or bars. Such steels do not harden perceptibly when heated and quenched in cold water. Owing to the low percentage of carbon they contain (015 to 0'5 per cent.) they resemble wrought iron, and can be easily welded, 1 with the additional advantage that plates of much greater area and weight, and bars of much greater length 2 can be obtained without extra cost per unit of weight. Mild steel has now superseded wrought iron for many purposes, particularly for boiler plates and stays, bolts and shafting, engine details, etc. The lower the ultimate strength of mild steel the higher is its elasticity, but it is a necessary condition that boiler plates must be ductile. The best Yorkshire iron plates stretch about 18 per cent, before rupture, and it is found that steel plates with about 20 per cent, of elongation have not a tensile strength greater than 30 tons per sq. inch. But this steel is largely used for boilers, as it lias nearly double the elasticity of ordinary iron boiler plates, and nearly 50 per cent, greater strength. For parts of a boiler that are flanged a somewhat softer metal is used, generally one with an ultimate elongation of 25 per cent., and a tensile strength of 26 to 28 tons per sq. inch. Such engine parts as piston and connecting rods, shafts, valve rods, are often now made of mild steel forged from Siemens or Bessemer ingots. And ordinary mild steel bars having an ultimate tensile strength of 30 to 32 tons per sq. inch, and an elongation of at least 25 per cent., are used for boiler stays, studs, bolts, etc. A harder steel of 35 to 40 tons tensile strength, and 15 per cent, elongation, being used for pins and such like pieces. 279. Steel Castings, or cast in steel, means that the object is cast in form by mild melted steel being poured into a mould. When bar blister steel is melted in crucibles and poured from them into the mould, we get crucible steel castings. But large steel castings, such as beams for stationary engines, stern posts, propellers, large shafts, pistons, cross heads, standards for steam hammers, large stop valves, etc., etc., are now made by more direct methods and of less cost, the furnace being charged with pig iron, scrap steel, and broken ingot moulds. 3 Steel castings have the disadvantage of not being perfectly sound, owing to the pores or blow-holes in the metal, which may be below the surface and therefore out of sight, but more often they are on or near the surface, and can often be cut away in machining. In this respect they are also superior to iron castings, as blow-holes in the latter may be in the body of the casting. Apparently, any want of density in steel castings, owing to the presence of pores, can only be dealt with by subjecting the fluid metal to great pressure, on the Whitworth principle ; but, of course, the cost of this treatment is prohibitive for most jobs. Notwithstanding this disadvantage, castings in steel are now produced without rolling, hammering, or other mechanical treatment, which are superior in ductility and strength to castings in any other metals in ordinary use, particularly cast iron, and we may safely look forward to further improvements in quality, and to a great extension in their use. In the opinion of some engineers, where hardness and resistance to wear are concerned, the castings made by English manufacturers are unsurpassed, but tougher and more ductile castings can be got from the Continent at an extra cost of about 50 per cent. 1 In welding steel, oare should be taken that the pieces to be united contain -the same proportion of carbon or the welding temperature will be different. ! Steel bars are rolled up to 150' in length, and plates with an area of 70 sq. feet and more. 3 A full charge for an open hearth furnace may consist of hematite pig 8 tons 8 cwt., Weardale pig 1-5 tons, scrap steel 2-5 tons, broken ingot moulds 1 ton, broken skulls and scrap 2'5 tons, Elba ore 2-75 tons, manganese (80 per cent.) 2'21. 238 MACHINE DRAWING AND DESIGN FOR BEGINNERS It would be impracticable or too expensive to forge certain parts of motor-cars, 1 such as trailing wheels of heavy cars, and motor- buses, brake discs, chain wheels, etc., but these can with advantage be steel castings. Such castings are, as a rule, made of a medium hard quality, the tensile strength of which is about 78,000 to 85,000 Ibs. per sq. inch, and the elongation 18 per cent, for 2" length and 1" diameter. 280. Motor-Car Steels. One of the most remarkable features of the development of the motor-car, is the wonderful improve- ments in the qualities of steel which have been made by steel makers, in meeting the demands of motor-car constructors for materials of the highest excellence, both as regards tensile and elastic strength. These qualities are usually measured by static and by dynamic tests to determine the resistance to shock and the endurance of fatigue, the great importance of which is now well under- stood. We have already given some particulars of high-class steels, but the new steels manufactured for motor-car work demand special attention. Probably no English firms have done more, if as much, in this movement than the famous one of Vickers Sons and Maxim, and, more recently, Messrs. Willans and Robinson, so, therefore, some particulars of the special steels they manufacture for this work should be referred to. Messrs. Vickers and Co. truly remark that : " In the construction of all modern machinery, the most suitable material for use is that which will combine with a sufficiently high factor of safety the least possible weight in any given part." For a steel to have high tensile strength is not enough. To be suitable and safe in machinery undergoing severe shocks, a steel must have three main qualifications. It must, in the first place, have a high limit of elasticity, so that it will be able to endure high stresses without deformation. It must also be tough and ductible, so that it can receive excessive and suddenly applied shocks without undergoing breakage. And, finally, it must be, as far as possible, unaffected by long-continued vibration. The introduction of new steels possessing these qualifications makes possible a very appreciable reduction of weight in many parts of a motor-car. 281. Copper. The most important and useful metal used by the engineer next to iron is copper. Its ores are very widely distributed, being found in almost every part of the world. It is a metal which is both ductile and malleable when hot and cold, but as it possesses the latter quality in a higher degree than the former, it is used to greater advantage when rolled, hammered, or worked into sheets, cylindrical pipes, 2 hemispherical pans and such like forms, than when drawn through a drawplate into fine wire. It is possessed of considerable elasticity and strength when wrought, its tensile strength being about 15 tons per sq. inch. But in the ingot or cast condition, it contains much oxide and many cavities, therefore it is not so strong, often breaking easily with less than half the above tension. When pure it may be worked up by hammering or drawing to a state of great strength and toughness. When hammered or worked cold copper becomes brittle, but it is restored to its proper degree of toughness by heating to about 500 F., or in other words, by annealing. When heated to redness it can be drawn down, upset and forged, but if overheated the surface, by exposure to the air, becomes converted into black scales of peroxide. Although copper loses strength as its temperature is increased, being at its best when cold, and is affected by the use of sulphurous coal, it is still used to some extent for locomotive furnace boxes. The ultimate strength of copper may be taken as follows : 1 An abstract of an article, " Locomotive PartB of Cast Steel," by Mons. du Bousquet, which appeared in the Revue Generate des Chemins defer, is given in the Proc. Intl. C.E., vol. clxviii. p. 375, in which the author, in referring to some experiments on the use of cast-steel piston heads, guide bars and their supports, coupling rods, and brake gear, etc., in actual practice, concludes that " the experiments prove that caet-tttel parts may be tafely uieii in many caeesfor which forgings have always been considered necessary." 2 Copper pipes of 6" diameter and upward are made from sheets rolled or hammered into the required form and brazed at the seams, the joints being practically as strong as the original sheet. Smaller pipes are usually made by drawing, but these cannot be relied upon being of uniform thickness. PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES 239 STRENGTH OF COPPER. When carefully drawn into wire 38,000 to 60,000 Ibs. per sq. inch. . Pure Wrought, Copper bolts 36,000 Ordinary 33,000 Copper Castings 19,000 to 26,000 Copper when employed by itself is largely used for many purposes, 1 but when combined with other metals to form alloys, it is more extensively used for engineering purposes. Boron appears to affect copper much as carbon does iron ; wire has been made of such alloy with a tensile strength of 27 tons per sq. inch, and without loss of electrical conductivity. For some years now a process (Ebnore's) has been at work by means of which copper is deposited by electrolysis, the metal being pure and remarkably strong. Bars of copper are melted in an ordinary furnace and granulated by being run into cold water, being afterwards placed on a copper tray at the bottom of a tank, which serves as the anode, or positive terminal; revolving on its horizontal axis above this tray is a copper cylinder, constituting the cathode, or negative terminal ; a solution of sulphate of copper, or blue vitriol, is the electrolyte, and in this the revolving cylinder is completely immersed, contact being made with a copper brush. An agate burnisher, pressing upon the deposited surface, is automatically traversed from end to end, and it is claimed that this burnishing action gives to the metal its remarkable tensile properties. 282. Tin is seldom used alone by the engineer, as its tensile strength is too low (about 2 - l tons per sq. inch) and its cost too high, but as one of the chief constituents of gun-metal or bronze, it is of great value. Owing to its immunity from the corrosive action of salts and acids, it is used as a protective covering to other metals. The Admiralty, and some Mercantile Shipping Companies require all condenser tubes to be coated with tin, when fitted in iron condensers. Thin sheet iron coated with tin, known as sheet tin, is used for oil feeders, lamps, and for liners or distance pieces between brasses. 283. Lead is to a small extent used as a constituent of certain alloys, as we shall see, but for many purposes it is used alone. Its ductility, and therefore the ease with which it can be bent to any form, and its resistance to the corrosive action of sea and bilge water, fit it for use as bilge piping, and for emptying and filling the ballast tanks of ships. It is also used for jointing pipes when their flanges are rough or uneven. Sheet lead is used for covering the engine-room floors of ships when they are made of wood, and to protect the covering of boilers from wet. The tensile strength, of lead piping is 1 ton per sq. inch, and that of sheet lead 0'8. 284. Zinc is largely used to alloy with copper to form brass and other alloys. It is also employed as a covering for iron to protect it from the action of the atmosphere or of sea water, etc. ; being much cheaper than tin and easily applied to iron to galvanize it, 2 it is used on a much more extended scale than tin is. It has long been known that a galvanic couple will prevent corrosion in marine boilers and hot wells, so blocks of zinc, or the residuum from the galvanizing bath (called hard spelter), are placed in metallic contact with the iron of the boiler in such places as experience proves requires protection. Of course the purer the zinc the more perfect the action. 1 Refer to Arts. 186 and 145. The iron is cleaned by dilute acid and friction, it is then heated and plunged into a bath of melted zinc covered with sal-ammoniac, and is stirred about until the surfaces become alloyed with zino. Mallet recommends an amalgam of zinc 2202, mercury 202, and about 1 of sodium or potassium; this melts at 680. The cleansed iron is dipped in this, nnd removed as soon as it reaches the temperature of the alloy. 240 MACHINE DRAWING AND DESIGN FOR BEGINNERS 285. Gun-metal, or Bronze, is an alloy of copper and tin (and sometimes a small proportion of zinc) in varying proportions ; there being no particular mixture to which this name properly belongs. Strangely enough, when copper and tin are alloyed in good proportions harder metal than either of them is produced, with a density greater than the mean density of the constituent. The metal is also more fusible and less likely to corrode than copper. It is found that with castings rapidly cooled (chilled), the density, strength, and toughness are increased, due to the composition becoming more uniform. From experiments made at Woolwich, 1 upon alloys of the usual proportions, the following results were obtained : TENSILE STRENGTH OF GUN-METAL. 12 parts of copper and 1 of tin 29,000 Ibs. per sq. inch. 11 1 30,700 10 1 33,000 9 1 38,000 The last of these compositions is the best known ; it is fairly hard and very tough. Although much higher values have occasionally been registered for special mixtures, 2 33,000 Ibs. or between 14 and 15 tons per sq. inch, may be taken as a general average for good gun-metal. Compared with steel and iron, gun-metal offers a small resistance to compression. This resistance is found to vary very much with the perfection of the alloy, the rate of cooling employed to prevent the separation of the tin, and the amount of fluid pressure in the mould due to the height of the deadhead. The elastic Limit in compression is about 14,000 and the ultimate strength 27,000 Ibs. per sq. inch. The general effect of tin in the alloy is to increase its hardness. It also whitens the colours. Zinc alloyed with copper in small quantities increases fusibility without reducing the hardness. In larger quantities it prevents forging when hot, but increases malleability when cold. Although a small quantity of zinc added to common bronze makes it mix better, it is seldom used in gun-metal. For heavy bearings hardness is considered to be of more importance than strength, although of course a good strength is required. A suitable metal is formed of 79 per cent, copper, and 21 of tin ; its tensile strength is nearly 14 tons per sq. inch. The alloy specified for propellers and all bronze castings by the Admiralty (known as Admiralty bronze) is 87 per cent, copper, 8 per cent, tin, and 5 per cent, zinc, giving a tensile strength of over 14 tons per sq. inch. Copper and tin mix well in almost all proportions. The alloys, or proportions, given in the above Table are among the best known ones. 286. Phosphor Bronze is an alloy of copper and tin to which some lead and phosphorus have been added ; it is harder than ordinary gun-metal, of superior strength and very close-grained, the usual proportions of the above being 79, 10, 10, and 1, respectively. But its strength, hardness, and ductility can be varied by altering the proportions. Its strength, etc., appears to be as follows : soft quality elastic limit equals about 5 tons, and ultimate strength 22 tons per sq. inch ; with about 30 per cent, of elongation. Hard quality elastic limit equals about 25, and ultimate strength 33 tons per sq. inch, with of 3 or 4 per cent, of elongation. It bears remelting better than gun-metal, but depreciates after many repeated re-meltings. It is very red-short, and liable to 1 Anderson's " Strength of Materials," p. 85. 1 Dr. Thurston found that the alloy which gave the maximum strength of 70,000 Ibs. per sq. inch was one which consisted of copper 55, zinc 43, and tin 2 per cent., but this could hardly be called gun-metal. PRINCIPAL MATERIALS USED IN THE CONSTRUCTION OF MACHINES 241 crack. When drawn into wire it has the extraordinary strength of 100 to 150 tons per sq. inch unannealed. But when annealed its strength is reduced by about 50 per cent. As it is a good metal for resisting shocks it is used with advantage for bearings for rolling mills, railway axles and crank shafts (particularly motor-car ones), and for such pieces as propeller blades and pump rods. The strength of this metal is also somewhat less affected by heat than gun-metal is, and it can be rolled into extremely thin sheets, and is then useful for the valves of air pumps, etc. The following table gives particulars of the ultimate and elastic strength, etc., of the principal materials used by the engineer : TABLE 13. ULTIMATE AND ELASTIC STRENGTH or MATERIALS. Material. Ultimate tensile strength. Ultimate compress! ve strength. Elongation per cent, on 8" length. Elastic limit. Young's modulus of elasticity (E). Aluminium castings, about 98 per cent, pure . Common grey cast iron Tons per sq. Inch. 5 to 7 7 to 9 Tons per sq. inch. 44 to 47 2 to 3 Tons per sq. Inch. Tons per sq. inch. Special cast iron for cylinders, etc 10'5 to 13-5 47 to 50 Malleable castings 16 Wrought-iron plate 22 to 23 16 to 18 Good welding iron, small forgings ... 22 to 24 16 to 18 14 to 18 12 to 16 12,700 Siemens-Martin, mild forged steel 24 to 27 19 to 21 20 to 25 12 to 19 13600 Siemens-Martin, forged steel for shafts . . . Tool steel unhardened . . . 29 to 35 48 to 57 23 to 28 20 to 25 12 to 22 35 to 40 14,000 14000 Siemens-Martin, steel castings ... . . 25 to 32 20 to 28 18 to 20 12 to 19 13,600 24 to 28 1 9 to 24 20 to 25 16 13600 Best gun-metal, bronze for valves, etc. . . . Rolled brass 12 to 19 9-5 10 to 20 5,700 7000 Muntz metal 22 Manganese bronze (bolts) 25 to 32 20 to 45 " ,, ,, (propeller blades) .... Delta metal .... . 19 to 29 22 to 24 15 to 25 11*6 6350 Aluminium (cast) ... 8 (sheet) . 12 Copper (bolts) 17 (plates) 13 to 15 38 9 7000 Oak (with grain) . . 7 4-2 760 Teak (Indian) 6'7 5-4 1 070 Pine (with grain) . 7 2-8 760 Elm (British) 6'2 Ash (with grain) . 7-6 4-2 630 6-7 5.4 Lignum vitse 7-1 4 The strength in shear of most of the above metals varies from 0-7 to 0'9 of the strength in tension ; 0-8 may be assumed without serious error. 2: CHAPTER XXVI MISCELLANEOUS TABLE 14 Greatest working pressures, p, per sq. inch of projected area l (Lxd) on various bearing surfaces (Unwin and other authorities). Pressure per sq. Inch in Ibs. Crank pins of shearing machines, slow speed, intermittent load 3000 Cross head neck journals (intermittent load, oscillating motion), the higher pressures for locomotives and destroyers .... 800 to 2100 Gudgeon pins of petrol engines 800 to 1000 Crank pins, small land engines '. 150 to 200 marine engines 400 to 500 fast land engines 500 to 800 slow land engines 800 to 900 torpedo boats and destroyers 850 to 1000 locomotives 1200 to 1800 and crank shaft journal of petrol engines 350 to 400 Locomotive axle boxes Passenger 190 Goods 200 Shunting 220 Locomotive tender and carriages 300 to 380 Main crank shaft bearings, according to speed, fast to slow, as follows : ordinary freight steamers 200 to 225 quick running steamers 225 to 300 ironclads and large cruisers 250 to 350 small light cruisers 350 to 400 torpedo boats, steam tugs, etc 400 to 550 Ply-wheel shaft bearings (unvarying load) 150 to 250 Eccentric sheaves, stationary engines 60 marine practice . . ' 70 to 140 Line shafting on gun-metal steps 200 oast-iron steps . 50 Eccentric straps 70 to 140 Pivots, wrought-iron shaft on gun-metal step 200 to 700 cast-iron shaft on gun-metal step 200 to 450 wrought-iron shaft on lignum vitse bearing 1000 to 1400 Collar thrust bearings for propeller shafts (according to speed) 50 to 80 Slides, cast iron on Babbit metal 200 to 300 cast iron on cast iron (according to speed, fast to slow) 40 to 100 Steel or iron shaft on lignum vitse (water lubrication) 350 Faces of link blocks 220 to 350 Pins of 550 to 1000 Thurston's rule relating to pressure and velocity is very important as a guide. It is, the product of the rubbing tpeed in feet per minute and the pressure in Ibt. per q. inch, should not exceed 50,000. 1 Deducting area of oil grooves. QUESTIONS SUITABLE FOR EXAMINATIONS AND HOME WORK 243 287. Questions in Machine Construction and Drawing. The following questions have been selected (and more or less modified) from the Polytechnic Annual Examination Papers set during the past few years by the author : QUESTIONS SUITABLE FOR EXAMINATIONS AND HOME WORK STAGE 1 (or First Year's work) 1. Show two methods of connecting two wrought iron plates at right angles to each other. 2. Make a dimensioned sketch showing the proportions of cast iron wheel teeth, and name the various parts and curves used. Pitch 3". 3. Give sketches and a description of an adjustable pedestal with brasses. How would you lubricate it, and how adjust it when worn, say J" in a downward direction ? 4. Sketch and describe the action of a syphon lubricator, and state the kind of bearings it is used on. 5. Illustrate two methods of connecting together the ends of two circular bars. One method to be suitable for an alternate push and pull, the other for a twisting action. The bars require to be easily disconnected. 6. Describe two forms of lubricator. Explain the action of each and on what kind of bearing you would use it. 7. Show three methods of locking nuts. Under what conditions is it desirable to use them ? 8. Give sketches of the various forms of keys used. What are the proportions and tapers, and how are they used? Describe a " loose collar with set-screw," and say what it is used for. 9. Sketch two or three forms of cranks, and show how the pins are connected. 10. What is the object of the snug and the cotter, shown in the drawing example (Fig. 709), and why are they used ? 11. How would you adjust the connecting rod end when the brasses had worn, say J inch, in the direction of the length of the rod? What is the object of the circular projection at the back of each brass, and what is it called ? 12. Show two methods of jointing two circular rods, one joint to be suitable for a pulling action and capable of adjustment, the other to be formed so that one of the rods may have a straight line motion and the other a motion through an angle of 20. 13. Sketch and describe how you would make steam tight (a) the piston rod of a steam engine, pressure 80 Ibs., (6) the ram of an hydraulic press water-tight, pressure 700 Ibs. per sq. inch. 14. Sketch the different forms of key used, give the proportions of each, and explain what class of work each is specially adapted for. Also sketch a gib and cotter, and say of what material these details should be made. 15. The hole in a solid bearing has worn down j": how would you proceed to restore it to its original condition? What is a chipping piece, and a long hole? and where are they used ? Give sketches. 16. Referring to the drawing exercise (Fig. 427). How would you alter the height of the centre from 3j" to 3J"? and how would you adjust the brasses when worn down J" ? What is the bearing used for ? 17. Sketch a f" Whitworth bolt. a f" Snap head rivet. a Taper pin, split. a Snug. Say of what each would be made and where used, and figure each proportionally. 18. Eeferring to the drawing example (Fig. 682). (a) What are the various portions of the cross head" made of ? (6) Why are the bolts tnrned smaller in the central portion than at the ends ? (c) Describe the lock washer and how it is used, (d) What is the cross head used for ? 19. Sketch, in plan and section, a double riveted butt joint, diagonally riveted with double cover plates. Figure it proportionally. What is chain riveting? Compare the two arrangements. 20. Sketch a half crank, showing how the pin is fitted and the crank fixed to the shaft. What should each part be made of? 21. Sketch two teeth of about 2" pitch, suitable for ordinary cast iron wheels. Figure them proportionally, writing on names of parts and curves used. 22. Sketch (a) a gib head sunk key, give proportions and taper ; (6) a ij" gland stud, say how many threads per inch it has, and show the shape of them. 23. Sketch two different forms of stuffing box, one for high pressure steam, the other for low pressure. Describe how you would pack them and what with. 24. Referring to the drawing example (Figs. 424 to 426). (a) What are the various portions of the bearing made of? Why are the steps in four parts, how are they adjusted when worn, and why is the upper part of the bearing made of cast iron? 25. What conditions make it desirable to uso mortise wheels ? Give sketches illustrating their construction and proportions. What materials may be used for the cogs ? 244 MACHINE DRAWING AND DESIGN FOR BEGINNERS 26. Answer one of the following, but not both : (a) Sketch two different forms of stuffing box, oue for high pressure steam, the other for low pressure. Describe how you would pack them and what with. (6) How would you pack the ram of an hydraulic press, and the piston of a double-acting hydraulic cylinder ? 27. Sketch a lubricator suitable for (a) the slide bars of an engine, (6) a loose pulley, (e) a line shaft bearing, and describe carefully the action of each. 28. Sketch and describe a form of connecting rod end, cither (a) for horizontal engine, (6) locomotive engine, (e) marine engine. How would you adjust the steps when worn go ag not to alter the length of the rod ? 29. Referring to the drawing examples (Figs. 728 to 735). Why are the brackets cast separately from the bed plate, how are the brackets lubricated, and what is the object of the groove and oil holes in the brackets ? Of what material should each part be made ? 30. Sketch two teeth (about 2" pitch) suitable for a cast iron spur wheel, machine cut. Figure them proportionally, write on names of each part and the curves used. 31. Sketch proportionally (about half size) a single riveted butt joint with double cover plates for J" plates. Show plan (about 2 pitches) and sectional elevation, figure it proportionally, and say of what materials each part should be made. 32. Sketch (about full size) a J" bolt, 3" long, with a circular head, a bevelled washer and an hexagonal nut. Of what may it be made, and how many vee threads per inch should it haye ? Make an enlarged view showing proportions and shape of thread, and say how the bolt may be prevented from turning when the nut is put on. Figure the bolt, nut, and washer proportionally. 33. Sketch and describe an adjustable spanner, or a ratchet brace. How would each be used ? 34. Make a sketch of a valve suitable for admitting the explosive mixture to the cylinder of a petrol engine. 35. Sketch two teeth (about 2" pitch) suitable for a cast iron spur wheel, machine cut. Figure them proportionally, write on names of each part and the curves used. How do you measure the diameter at pitch of a toothed wheel ? 36. Sketch a form of stuffing box, either for high or low pressure. Describe how you would pack it. 37. Sketch and describe a form of coupling suitable for the main shafting of an engineer's workshop. Why do you recommend the particular one you show ? 38. Sketch (about full size) a j" stud, fitted with a capstan-nut and split pin. You may make it any length. 39. Make a hand sketch of a simple form of knuckle joint, and state what part of a steam engine is fitted with this joint. 40. Show by a hand sketch how leather is used to make fluid-tight a spindle for a hydraulic valve. 41. Make a hand sketch of a loose collar, and be careful to show the shape of the end of the set-screw. How should this end be treated to make it effective and durable ? 42. Sketch and dimension a cog, suitable for a mortise wheel, the pitch of whose teeth is 3". Of what wood should such cogs be made, and why ? 43. Referring to the drawing example (Fig. 738), of what materials should the piston, gudgeon pin, and set-screws be made ? Would you harden any portion of them? If so, how and why? How would you make the piston more pressure tight in the cylinder? 44. Sketch the rim portion of a C. I. spur-wheel showing the teeth about 2" pitch, give the proportions, names of parts and curves used (a) for ordinary cast gear. (6) for machine cut gear. 45. Sketch and describe either (a) a stuffing box, suitable for a steam pressure of about 50 Ibs. per sq. inch, describe how you would pack it and what with ; or (6) the packing yon would use for an hydraulic ram. 46. How would you joint two cast iron pipes : (a) by a socket joint, or (6) by a flanged joint for a pressure of about 30 Ibs, per square inch ? Sketch a section of either, describe it and the method of jointing, and materials used. 47. Sketch and describe a connecting rod end suitable for either (a) a stationary engine, (5) a locomotive, (e) a marine engine, or (d) a motor-car engine. How would you adjust it when worn so as not to alter the length of the rod? 48. Show by sketches the sectional shading or lining used to indicate the following materials : Cast iron, wrought iron, steel, and brass. 49. Show any form of centrifugal lubricator (suitable for an overhung crank pin) that you are acquainted with. 50. Show by sketches three different ways of keying wheels to a shaft, and explain under what conditions each would br used in practice. 51. A single riveted lap joint has J" plates, j" rivets, both steel, /, and /, (the ultimate strength in shear and tension) being 23 and 28 tons per sq. inch respectively . Find the most efficient pitch, also the efficiency of the joint. 52. Make neat sketches of the following : a tee-head bolt, an eye bolt, and a capstan nut. STAGE 2 (or Second Year's work). 53. Show by sketches and descriptions how you would lubricate any three of the following : (a) slide valve and steam cylinder, (6) overhung crank pin of horizontal engine, (e) crank pin of high speed engine, (d) a loose pulley, (e) an ordinary pedestal, (/) footstep for vertical shaft, (g) an eccentric, (A) the stem thrust bearing of a propeller shaft. State the kind of lubricant you would employ in each cage, and how you would ensure its distribution. Name/our conditions with which u good lubricant should comply. QUESTIONS SUITABLE FOR EXAMINATIONS AND HOME WORK 245 54. Make a sketch of a vertical section of the half of a mortise mitre wheel, 1J" pitch. Sketch profile of large end of teeth, showing how they are developed, and give proportions of teeth, method of fixing, and materials employed. 55. Sketch either a double bar guide, or a slipper guide for an engine, and say how you would readjust it when worn. What is the usual pressure allowed per sq. inch of surface on the guide ? When is it necessary to use a guide with two surfaces ? 56. Give sketches and description of any form of friction gear with which you are acquainted. Show a means of putting it in and out of gear. What are the advantages and disadvantages of this form of gear ? 57. Describe briefly the constituent parts and characteristics of cast inon, wrought iron, steel, and give an example of the use of each. 58. How would you join two 4" cast iron pipes (a) for a low pressure cold water main, (6) for a steam pressure of 60 Ibs. per sq. inch, (c) for an hydraulic main, 700 Ibs. per. sq. inch ? 59. Two wrought iron rods, one inch diameter, are to be connected by a cottcred joint suitable for alternate compression and tension. Sketch the joint and give the formulae you would use for calculating the various parts. Where would you prefer it to fail first, and why? 60. In how many ways can a riveted joint fail ? Calculate the strength of a double riveted lap joint of jj" wrought iron plates, 3f" lap, J" rivets pitched diagonally, If" centres. Ultimate strength of plates in tension and rivets in shear 45,000 and 40,000 Ibs. per sq. inch respectively. Bearing stress, 90,000 Iba. per sq. inch. Where would the joint fail first? 61. A steam cylinder of cast iron, 10" bore, pressure 70 Ibs. per sq. inch, has wrought iron fastenings to the covers, f" diameter. How many of them are required (taking/, = 3000 Ibs.)? How would you arrange them (a) where a port occurred, (b) upon the side opposite to a port ? 62. Explain how the valve shown in the drawing example (Figs. 354 and 355) acts, and how the various parts of it are made water-tight. How is it connected to the pipe main ? 63. Sketch and describe the forms of cranked shafts most suitable for (a) A horizontal stationary engine. (6) A locomotive engine, (o) A marine engine. Compare their respective good points. Of what metal should each be made ? 64. Sketch and describe a metallic packed stuffing box suitable for a piston rod 4" diameter. How are the whole of the gland studs of a large marine engine tightened by turning one nut ? 65. How would you line a large pair of bearing steps with anti-friction metal ? What metal would you use for the purpose, and how would you put it in ? 66. Sketch and describe joints suitable for a steam pipe, 6" diameter, 80 Ibs. pressure ; a horizontal pipe for cold water supply, 4" diameter, 30 Ibs. pressure ; a pipe for cold water, 5" diameter, 700 Ibs. pressure. How would you joint each length ? 67. Calculate the strength of a mild steel double riveted butt joint with double butt covers. Plates J" thick ; pitch straight 2J", diagonally Ij" ; lap 3J" ; rivets 5" diameter, pitched diagonally. Where would the joint probably fail, and what would be the percentage of strength compared with solid plate ? 68. Sketch and describe another method of fitting the steps in the drawing example (Fig. 424). Of what materials would they be composed? 69. Sketch and describe a removable coupling suitable for the shafting of an engineer's workshop. Of what melal would you make it? 70. Sketch and describe two methods of connecting lengths of cast iron piping for water supply together. What jointing materials would you use ? Does the position of the pipe in any way influence your selection of a suitable joint ? 71. In how many ways can a riveted joint fail? Write down the formulae you would use for calculating the tearing, crushing, and shearing of a double riveted lap joint. 72. Sketch and describe (a) a gusset stay, (5) a tie rod stay, (c) a screwed stay suitable for a boiler. In what positions would each be fixed, and what would they be made of? 73. Sketch and describe an end for the connecting rod, suitable for attaching to the cross head shown in the drawing example (Fig. 682). 74. Referring to the drawing example (Fig. 682). (a) What is the object of making the slipper loose, as shown ? (6) Of what materials should the various parts of the cross head be made? (c) What composition would you use for the metal strips, and why are they used? ((/) The hole in the brasses has worn horizontally J" larger on the right and left of the pin : liow would you adjust these? (e) What is the object of enlarging the bore of the brasses where they come together? 75. A steam cylinder of cast iron, 10 inches bore, pressure 100 Ibs. per sq. inch, has wrought iron fastenings, 1" diameter to the covers. How many of them are required (taking/, = 3000 Ibs.)? How would you arrange them (o) where a port occurred, and (6) upon the side opposite to a port? 76. Referring to the drawing example (Figs. 689 and 690). How would you adjust the brasses when worn J" out of truth on the side farthest from the cylinder, and also when worn g" in a downward direction ? Of what is each portion of the bearing made, and how is it lubricated ? What is the object of lipping the cap ? 77. Referring to the drawing example (Figp. 728 to 7i'5). Why are the brackets cast separately from the bed plate ? Describe how you would line off and machine the commutator bracket. 246 MACHINE DRAWING AND DESIGN FOR BEGINNERS 78. Sketch and describe a connecting rod little end, or a cross head suitable for one of the following : a horizontal engine, a marine engine, a locomotire engine, a motor-car engine. Describe how you would adjust it when worn, BO as not to shorten the rod. 79. Sketch (about half size) and figure proportionally a double riveted (diagonal) butt joint with double cover straps. 80. In how many ways can a riveted joint fail? Write down the formula you would use (a) in calculating the tearing, crushing, and shearing of a double riveted lap joint, (6) in determining the efficiency of the joint. 81. Sketch two teeth (about 2J" pitch) of a spur mortise wheel, give proportions, name of each part, and the curves used. Show how the fixing is accomplished (a) into the ordinary rim, (6) when occurring over an arm. What material would you recommend for the teeth ? Why are mortise wheels now practically obsolete ? 82. Sketch and describe a connecting rod big end, suitable for either (a) a horizontal engine, (6) a marine engine, (e) a locomotive, or (d) a motor or gas engine. How would you prevent the rod from shortening when adjusting for wear ? 83. In how many ways can a riveted joint fail ? Write down the formulae you would use in calculating the tearing, crushing, and shearing of a single riveted butt joint. 84. What limits the size of the rivet for a given thickness of plate ? 85. Sketch (about half .size) and figure proportionally a double riveted (zig-zag) butt joint with double cover plates. Where would such a joint be used in a cylindrical boiler ? 86 A steam cylinder of cast iron, 10" bore, pressure 100 Ibs. per sq. inch, has wrought iron studs, I" diameter to the covers. How many of them are required (taking/* = 3000 Ibs.)? How would you arrange them (a) where a port occurred, and (6) upon the side opposite to a port? 87. Sketch and describe a metallic packed stuffing box suitable for a large piston rod. How are the whole of the gland studs tightened by turning one nut ? 88. Make a sketch of a valve suitable for admitting the explosive mixture to the cylinder of a petrol engine. What is an automatic inlet valve ? 89. Sketch any engine or machine detail in which the adjustment is made by using a gib and cotter. What is the use of the former? When is it necessary to use a set-screw in connection with the cotter ? 90. Make a hand sketch of a double riveted zig-zag lap joint for j" mild sheet plates. Taking /, = 28 and/ = 23 tons per sq. inch, what should the pitch of the rivets bo ? What efficiency would this joint have ? If you have not time to calculate the latter, write down an expression which will represent it. 91. Make a hand sketch of any roller bearing you may be acquainted with. 92. Make a hand sketch of a piston suitable for the cylinder shown on Fig. 628, and give the principal dimensions. 93. If you assume that J" has been added to the thickness of the cylinder (Fig. 628) to allow for inequalities of thickness and reboring, what would you estimate the bursting pressure of the cylinder to be ? To what pressure would you say it would be safe to work it under steam ? 94. A boiler has f " plates which meet, forming a three-plate junction ; the joint is made by double butt straps, the circumferential seams being single, and the longitudinal seams double riveted. Make sketches in sectional elevation and plan of joint. Give reasons for your arrangement. 95. How are the tubes put into the tube plates (a) of the combustion chamber of a marine boiler, or (6) the firebox of a locomotive boiler ? Sketch and describe either, giving average sizes and materials used. What is a " Serve " tube and its object ? 96. Which do you consider the best method of fixing condenser tubes in place? Sketch it and give usual sizes, and describe its merits and the materials used. Would you put steam or condensing water through the tubes ? Give reasons for your preference. 97 In a certain hydraulic press the whole load of 100 tons is taken on two steel bolts, and the working stress at the root section of the threads has been fixed at 6000 Ibs. per sq. inch. What size should the bolts be? And what pitch of threads would you recommend? Bearing in mind that the material is steel, would you elect to use plus threads, if so, why ? 98. A single riveted lap joint, J" plates, jj" rivets, both steel,/, and f, the ultimate strength in shear and tension, being 23 and 28 tons per sq. inch respectively. Find the most efficient pitch, also find the efficiency of the joint. 99. The trunnions (or axle ends) of a mixing machine have an effective length of 10", and the weight which comes on each one is 1J tons. What should their diameter be if the skin stress is not to exceed 5500 Ibs. per sq. inch? Note. In this arrangement you are to assume that the trunnions are only subjected to lieuding. 100. What are the conditions which allow a wheel to be fixed to a shaft by cone keys ? Make a sketch of the arrangement. 101. Make a sketch of a quadruple riveted butt joint, the straps to have scalloped edges. What is the object of giving the edges this form? 102. What advantages have led engineers to use a finer pitch than the standard Whitworth ones for the bolts of cross heads and of connecting rod ends? 103. Calculate the pitch of the studs of a steam cylinder, the diameter of the stud circle being 30", and the number of studs 35. If the diameter of the cylinder at the cover be 25'5", and the steam pressure 80 Ibs. per sq. inch, what is the amount of tensional load upon each stnd due to steam pressure alone ? BOARD OF EDUCATION EXAMINATION PAPERS 247 Permission to publish the following papers in Machine Construction and Drawing has been kindly given by the Controller of H.M. Stationery Office. BOARD OF EDUCATION EXAMINATION SUBJECT II. MACHINE CONSTRUCTION AND DRAWING (1906) STAOE 1 Before commencing your work, yon must carefully read the following instructions: Put the number of the question before your answer. You are expected to prove your knowledge of machinery, as well as your capability of drawing neatly to scale. You are therefore to supply details omitted in the sketches, to fill in parts left incomplete, and to indicate, by diagonal lines, parts cut by planes of section. No credit will be given if the candidate shows that he is ignorant of projection. The centre lines should be clearly drawn. Your answers should be clearly and cleanly drawn in pencil, except the portion specified to be done in ink. The answers to the questions as well as the drawings should be made on the numbered paper supplied, comprising one sheet of drawing paper with tracing paper and squared foolscap attached. The tracing paper may be detached for the purpose of making the tracing, and must be carefully re-attached. The value attached to each question is shown in brackets after the question. You are to confine your answers striatly to the questions asked. The examination in this subject lasts for four hours. Trace the eye bolt shown on the accompanying Diagram X. Draw either Example 1 or Example 2, Diagram X, but not both. The example should be drawn on the side of the paper on which the candidate's number is printed. Also answer any two, but not more than two, of the questions numbered 11 to 15. Tracing, Diagram X Trace in ink on the tracing paper supplied the eye-bolt shown on Diagram X. Insert the dimensions and print the title as shown. The lines should be very black, of uniform and moderate width, and as continuous as possible. (14) Example 1, Diagram X 11-inch Bearing The diagram gives dimensioned hand sketches of details of a simple bearing. Draw full size, inserting dimensions : (a) An elevation corresponding with A, but in section, adding the cap and one of the J" studs. (6) An elevation, projected from (a), looking on the face indicated by the arrow. In this view the cap, cap screws, and the J" studs should be shown. (c) A plan. N.B. Do not draw the pictorial view, nor the parts separated as in the diagram. Dotted lines, representing hidden parts, are not required. (65) SUBJECT II. Stay* / /W6. NOTE. Dorwtdrtut /At now as shown 6ttt folleirt/u- instmrtunsai t/if atfanpanyvujxatnina4um pcyirr Alternative Example 2. Example 1. BRACKET BEARING. Example 2. CONNECTING LINK. BOARD OF EDUCATION EXAMINATION PAPERS 249 Alternative Example 2, Diagram X. End of a Connecting Link of an Air Compressor Make full size separate scale drawings of details, with dimensions, as follows : (a) A longitudinal and an end view of the rod end A. The screw thread may be drawn in the manner shown. (6) Three views of the nut B. (c) Three views of the wedge C. (d) Three views of the head D. N.B. No credit will be given for drawing the parts assembled, as in the diagram. Dotted lines, representing hidden parts, are not required. Questions, only two to be answered. The sketches in answer to these questions should be drawn freehand on the squared foolscap paper the lines on which may be taken as \-inoh apart. 11. Sketch full size, inserting dimensions, two views of a wheel boss, fixed to a shaft by means of a sunk gib key, as follows : Diameter of shaft 2" Diameter of boss *" Length of boss 3" Width of key I" Depth of key I" Taper of key, J" per foot. (8) 12. Name the materials of which the parts of Example 1, and the several parts A, B, C, D, E, and P of Example 2 would be constructed. (8) 13. Sketch full size, inserting dimensions, a 1" rag bolt or Lewis bolt, suitable for securing the frame of a machine to a stone foundation. Explain how the bolt is fixed in the stone. 14. Explain briefly, with sketches, how you would set out, drill, and tap the hole marked H, in Example 1, on the diagram. 15. Sketch in section the armature of a small drum wound motor, showing clearly how the stampings are secured. (8) STAGE 2 Before commencing your work, yon must carefully read the following instructions : A table of logarithms and functions of angles and useful constants is supplied for each candidate on whose behalf application has been made for a paper in Stage 3 or in Honours. Put the number of the question before your answer. You are expected to prove your knowledge of machinery, as well as your capability of drawing neatly to scale. You are therefore to supply details omitted in the sketches, to fill in parts left incomplete, and to indicate, by diagonal lines, parts cut by planes of section. No credit will be given if the candidate shows that he is ignorant of projection. The centre lines should be clearly drawn. Your answers should be clearly and cleanly drawn in pencil, except the portion specified to be done in ink. In Stage 2 the answers to the questions, as well as the drawings, should be made on the numbered paper supplied, comprising one sheet of drawing paper with tracing paper and squared foolscap attached. The tracing paper may be detached for the purpose of making the tracing, and must be carefully re-attached. The value attached to each question is shown in brackets after the question. You are to confine your answers strictly to the questions asked. The examination in this subject lastt for four Itours. Trace the Crank shown on the accompanying Diagram Z. Draw either Example 3 or Example 4, Diagram Y, but not both. The example should bo drawn on the side of the paper on which the candidate's number is printed. Also answer any two, but not more than two, of the questions numbered 21 to 25. 2 K 250 MACHINE DRAWING AND DESIGN FOR BEGINNERS Tracing, Diagram Z Trace in ink, on the tracing paper supplied, the drawing of a crank shown on diagram Z. The lines should be very black, of uniform and moderate width, and as continuous as possible. (28) DIAGRAM Z. BOARD OF EDUCATION EXAMINATION PAPERS 251 Example 3, Diagram T Adjustable Footstep Bearing Draw to scale and complete the two projections partly shown in Diagram Y, Example 3, and also draw a vertical section through line EF, correctly projected, looking in the direction of the arrow marked G. Scale half size. No dotted lines need be shown and figured dimensions need not be inserted. (10) Alternutive Example 4, Diagram Y Lift Valve Draw, full size, an outside view corresponding to the vertical section shown in Example 4, Diagram Y. Draw also a sectional plan through line CO, with the spindle K removed. Finally draw a sectional elevation taken through the centre line, looking in the direction of the arrow marked H. Also make a plan and the two end elevations of the spindle marked K, all the necessary dimensions being shown on it. Scale full size. No dotted lines need be shown and figured dimensions need not be inserted in the three first views. (140) Questions, only two to be answered The sketches in amwer to these questions should be drawn freehand on the squared foolteap paper 21. State of what material you would make the parts marked M, N, 0, P, in the footstep drawing, Diagram Y, Example 3. Also sketch an arrangement to prevent the rotation of the footstep bearing (N) in the casting 0. ' (16) 22. A wrought iron crank shaft is formed by bending a 2" round bar. How would you proceed to turn the crank pin? (16) 23. A plate girder is made up of a vertical web 2' deep connected to top and bottom flanges, 1' wide, by two angle irons 3" x 3" x J". The web and flange plates are J" thick. Sketch a section of the above girder, putting in the necessary dimensions. Show also a suitable stiffener. (16) 24. Sketch to scale, half size, inserting dimensions, a double riveted butt joint with two straps, as used in the longitudinal joint of a boiler. Rivets j" diameter, pitch 3", and thickness of plate J". What would be the efficiency of this joint ? (16) 25. .Show, by sketches, the method of holding and insulating the bars of a commutator of a continuous current dynamo. The shaft is 3" diameter, and the outside of the bars 8" diameter. (16) Stage l.-(1908) Trace the copy shown on the accompanying Diagram X. Draw either Example 1 or Alternative Example 2, Diagram X, but not both. The example should be drawn on the side of the paper on which the candidate's number is printed. Also answer any two, but not more than two, of the questions numbered 11 to 15. Tracing, Diagram X Trace in ink on the tracing paper supplied the two views of the eye bar shown on Diagram X. Insert the dimensions and print the title as shown. The lines should be very black, of uniform and moderate width and as continuous as possible. (14) DIAGRAM Y. SUBJECT ill, STAGE 2, 1906. NOTE. Do not draw the views as shown, but follow the instructions on the accompanying Examination Paper. ADJUSTABLE FOOTSTEP BEARING. LIFT VALVE. 2tf--- VERTICAL SECTION SLIDING BUSH FOR LIFTING VALVE PART OF SECTIONAL PLAN THROUGH C.D. DIAGRAM X. SUBJECT II, STAGE I. I9O8. NOTE. Do not draw Example 1 or 2 as shmen, but follow the instructions on the accompanying Examination Paper. JOINT IN GIRDER WORK. Copy /< I Alternative. Example Z. !-< /oi'i *)-- /ait" PISTON-ROD END AND CROSS HEAD. 254 MACHINE DRAWING AND DESIGN FOR BEGINNERS Example 1, Diagram X Joint in Girder Work A girder G, 21" deep, is built up of 16" X |" flange plates, J" web, 4j" x 4{" x f" angles, and 1" rivets of 4" pitch. A cross girder H, 10" deep, of rolled joist section, with 7J" X |" flanges and J" web, rests on the lower flange of G, and is riveted to G by means of two 3}" x 3J" x J" angle pieces, each 7{" long, and a bent 7J" X 85" X j" tee piece, as shown in the dimensioned pictorial sketch. Draw, to a scale of J, inserting dimensions, two elevations and a sectional plan of the joint, the horizontal section plane being taken through the axis of the cross girder H. N.B. Do not draw a pictorial view after the manner of the diagram. (70) Alternative Example 2, Diagram X Piston-Rod End and Cross Head Make separate scale drawings of details, inserting dimensions, as follows : (a) Two views of the piston-rod-end A. The screw thread may be represented conventionally as in the diagram. Scale \. (6) Three views of the nut B. Scale \. (c) Two views of the locking plate C. Scale J. (