K"c\ Division o f A g r i c u 1 t w r a I Sciences U N I V € R S \ T Y OF CALIFORNIA ''»rfa o o 100 90 80 70 60 50 40 30 20 10 23 2" stroke IK?" stroke '_ ^ 1" stroke 100 200 300 400 500 600 700 800 900 1,000 Frequency (cpm) Fig. 7. Effect of frequency and stroke on the removal of French prunes. The range in per cent removed for each stroke given was caused by the variation in bonding force between fruit and tree, and by tree structure. Ranges of removal for the different strokes overlap, causing the apparent variation in shading. High per cent removal of fruit was the result of low bonding force, a stiff tree with few long hangers, and few fruit in the lower-center portion of tree. ated; however, it was noted that the removal was not appreciably affected by clamp positions of one-fourth to one-half of the way from the main crotch to tree extremities. The values of p and /x given here are for this range of clamp positions. Results of limited tests on olives sug- gested that a similar relationship could be developed. The greater difficulty in removing olives signifies a lower value for k with olives than with prunes. The values of p and ft are also likely to be different for olives than for prunes. Force and power requirements. Study of the force and power required to shake prune tree limbs with fixed- amplitude shakers indicated that both factors varied with the frequency and stroke of the shaker, position of attach- ment on the limb, size of limbs, and the angle between the shaker and the limbs (figs. 8, 9). The power required was approximately proportional to the square of the stroke. The force was directly pro- portional to stroke. Power required de- pends on the damping, stroke, and fre- quency of every part of the limb, and complete analysis of the power would be extremely complicated, particularly as the stroke at points other than the point of attachment vary with frequency. When fruit-removal curves (fig. 7) are compared with the power curves (fig. 9) it is found that less power is usually 10 1,600 1,400 1,200 1,000 - 800 - 600 400 200 Lt /\ VA" stroke, — = H ±^1 \ u 7 v "" / \ / a ^ - */ / \ : it , Yl stroke, — = it - // // >w> Yi" stroke, — = H Lx ) Lt L" stroke, — = \i Lt 1 1 1 1 1 1 u 200 400 600 800 1,000 1,2001,400 Frequency (cpm) Fig. 8. Relationship of force, frequency, stroke, and position of attachment for shaking 5"-diameter prune tree limbs. The ratio of U (distance from crotch to shaker clamp) to L (distance from crotch to end of limb) gives the position of attachment. Decrease in force as frequency was increased above 900 cpm was apparently the result of approaching a natural frequency of the limb. needed to obtain a given per cent removal with long strokes and low frequencies. For example, to get 90 per cent removal of prunes the frequency, stroke, and pow- er are as follows: • 400 cpm, 2 inches and 1 horse- power • 600 cpm, IV2 inches and 1% horsepower • 1100 cpm, 1 inch and 3 horsepower Possible damage to trees must also be considered. Observations indicated that limb breakage increased more rapidly with an increase in stroke than with a comparable increase in frequency, where- as injury to the bark is associated with large shaking forces, and therefore is most likely at high frequencies. Lowering the clamp position from a position one-third of the way out the limb to a position one-sixth of the way out the limb increased the power by about 35 per cent and the maximum force by about 75 per cent. I 5 o O bC 3 a 120 r bX) 90 a o W 3 1 1 1 1 1 1 1 u ^ • Jx^T* '/ Actual total power ^^ //Calculated total power, //"including shaker friction / - /? r\ - *y / \ *" x ^% ~ s /^^. Calculated power required / for limb vibration ^^— ^ ^r *> S^ 1 *i l 1 l l l 1 - 12 16 20 24 28 32 Frequency ratio ( — J Fig. 22. Power needed for limb vibration with inertia shaker, and total power needed including shaker friction. Data is for same test as figures 20 and 21, with Vh" eccentric ty and I y~ V* o 2 3 o w 2- i r i i i r 2" Eccentricity -> ' X / S / / ' ^^ v 1.125" Eccentr icity ^ J I I L 2 4 6 8 10 12 14 16 Frequency (cps) Fig. 23. Power required to overcome friction of slider-crank shaker tested. was determined in the field from the aver- age pressure and flow rate in the hydrau- lic power system. Analysis of the curves shows that a high percentage of total power required at higher frequencies was used in over- coming shaker friction. A static test on this unit indicated that an average torque of about 60 inch-pounds was required to overcome static friction in the bearings. Additional losses occur during operation as a result of dynamic forces, and there is a reduction of hydraulic-motor efficiency because of pulsating loads. Torque. Maximum torque is equal to mroi 2 S (± 1 - sin oc ) /4. This equation (Appendix B) does not account for torque required to, overcome shaker fric- tion, or peak torques caused by the crank- shaft assembly not developing purely sinusoidal motion. These are canceling effects. Because of this, and because sin oc has a maximum and minimum of ± 1, it is reasonable to design for a maximum torque of mru) 2 S/2. When maximum torque is high at the higher frequencies due to the o> 2 factor, sin oc is small ; consequently, the quantity ± 1 - sin oc is approximately 1. Thus a safety factor of approximately 2 (which is self-compensating for internal shaker friction) is achieved. This calculated maximum torque is reliable for use in the design of shafting, but as this is the peak torque encountered the power source need not be selected to match. Because inertia of rotating parts helps overcome peak torque, torque requirements of the power source should be selected from average power consumption. Force. The design force is mru 2 [(S/2r) 2 + l+(S/r) cos oc] 1 ^ (Appendix B). It has been found that the ratio S/2r ap- pearing in this equation will usually be between 0.1 and 0.75 (depending on rela- tive masses) . Figure 24 gives the relation- ship [S/2r) 2 + l + (S/r) cos cc]K as a function of the phase angle oc and the S/2r ratio, and also shows that the value of the radical is less than 1 for the large phase angles found at high frequencies (fig. 21), where the maximum force is large due to the w 2 factor. Therefore, ex- perience indicates that it is practical to design for a maximum force mru 2 . DESIGN PROCEDURE First, estimate total shaker mass. For limb-shakers this mass should be as much, or more, than the effective mass of the larger limbs to maintain a fairly uni- form stroke over various limb sizes. The lighter the unit, the smaller will be the reactive loads and the easier the unit will be to maneuver. Therefore, compromises in the actual design are necessary to de- termine what combination of shaker mass and eccentricity is most desirable. Next, by adding the estimated shaker mass to the effective mass of the larger 1 1 02 o o 1.5 ^1 ^ + i—i 10 5 *>l o S ll 1961 1962 c? 40 30 20 O 10 o a* o ?:•:%•; •:•:•:•:« :?•:•:•:•: :':$# %•:% ':•:•:%- !••••••••• ••••••••'•: :*>:•> :•:•:•:•:•; ViYi'ilitfM'W'ftYiiYiWiYn'i 40 r- 30 20 10 •X*X*I l?W fiYrrWnWilTi iiiitiYi iiliV 1 1 i 1 1 1 faH 10 20 30 40 50 60 70 ° 10 20 30 40 50 60 70 Removal force at time of first pick (oz.) 40 30 20 - — '&•!%' 10 •IvX*!' 1 10 20 30 40 50 60 70 Removal force at time of last pick (oz.) Fig. 40. Comparison of removal force in "easy" and "hard" years, 1961 and 1962 respectively. The total area in each diagram represents total fruit on tree and each column represents the per cent of fruit within the removal force ranges indicated. In 1961, fruit was easier to remove than In 1962 since it loosened appreciably as it matured, particularly late in the season. lem of total removal with the blower particularly difficult. Figure 40 shows typical differences in distributions of the removal force early and late in the sea- son for "easy" and "hard" years. Blower tests during the hard year resulted in a total removal during the season of about 55 per cent (table 13), which is not practical. The blower method of harvest resulted in 6 to 7 per cent windfalls, while me- chanical shakers resulted in 8 to 10 per cent windfalls in one orchard and 14 to 21 per cent in the second orchard. The high number of windfalls in the second orchard harvested by mechanical shakers was caused by a strong wind removing loose fruit before the first pick. The pri- mary difference between the two methods of shaking seems to be the interval be- tween pickings and the natural drop before the first picking. With the blower, the first picking can be scheduled early and consequently few windfalls will have occurred before harvesting; also, the shorter interval between harvests yields fewer windfalls. The above results demonstrate that both pulsating-air blowers and mechan- ical shakers can selectively remove prunes in the coastal areas of California. But there are two inherent problems: the first 41 is that when fruit continues to loosen as it matures, windfalls associated with use of mechanical shakers become excessive for catching-frame harvest; secondly, when fruit does not continue to loosen as it matures throughout the season total removal with blowers is not practical. A solution might be to do early pickings with a blower and a cleanup with a me- chanical shaker, if harvest costs are not excessive. This combination might be satisfactory for use with catching frames. PICKUP MACHINE DEVELOPMENT Mechanical harvesting of figs and coastal area prunes has proved to be difficult because the fruits ripen over a long period and usually drop to the ground upon ma- turing, which necessitates more than one picking. Considering the potential prob- lems of considerable windfalls, the use of pickup machines has an advantage of minimum risk. Pickup machines used prior to 1956 were usually either mechanical or vacu- um-type devices. Mechanical devices were less complicated and required less power, and so the principles applied in construct- ing various mechanical pickup machines were analyzed. The analyses involved lab- oratory tests in which high-speed movies were taken of the pickup action of each principle (Fridley and Adrian, 1959) . The units, which were all basically reel- type devices similar to a leaf-sweeper reel, were tested by duplicating field con- ditions. High-speed movies of these units re- vealed presence of characteristics impos- sible to observe on a machine in the field. Small reels, rotating with the direction of travel and gauged close to the ground, exert downward force on the fruit be- cause the fingers are traveling downward when they first come into contact with it. But large reels, rotating against the di- rection of travel, roll the fruit which has windrowed in front of the reel. The wind- row is the result of two things: (1) if the fingers of the reel are radial, they are nearly vertical at the time of contact with the fruit, and consequently the force ap- plied to the fruit is essentially horizontal ; (2) if curved fingers are used to develop a force on the fruit at a more desirable angle, there is an appreciable interval during which the finger will contact only the top side of the fruit, rolling it ahead. Figure 41 shows the interval of contact between the finger and the fruit and the angle of the finger (®) when contacting the fruit. These two factors depend on the ratio of reel diameter to fruit diameter (-y , fig. 42), and results are improved by decreasing this ratio. NEW PRUNE PICKUP PRINCIPLE A reel (or roller) diameter about equal to the fruit diameter would be optimum. However, using a roller of this diameter results in an upward force being applied on one side of the fruit. To produce a resultant force which passes upward through the center of gravity, a second roller was placed above and in front of the first roller. Thus the new pickup prin- ciple (fig. 43) consisted of a small roller rotating against the direction of travel, and a second roller above and in front of the first and rotating in the opposite direction. (The second roller is flexible, to prevent damaging the fruit as it passes between rollers.) The first machine incorporating the pickup principle discussed above consist- ed basically of the pickup head which lifted fruit off the ground and threw it onto the flat section of an L-shaped con- 42] Fig. 41. Fruit pickup with a reel-type device rotating against the direction of travel. Contact between the fingers of the reel and the fruit is best during interval a. Travel of the finger tip from A to B results in rolling the fruit. Percentage of fruit rolled can be reduced by increasing the ratio of a to b. veyor. Satisfactory floatation of the pick- up head was achieved by gauge wheels and rubber augers used to clear a path for the wheels. An attempt was made to float the pickup head on runners, but on a 100 80 o 2 60 s 40 20 ^ Efficiency -Angle (•) 100 80 60 40 20 4 8 12 16 20 24 Ratio of reel diameter to fruit diameter (!) Fig. 42. Theoretical pickup performance as affected by the ratio of reel diameter to fruit diameter. (For details see page 42.) cloddy surface clods were crowded into the path of the pickup unit. Front pickup rollers from 2 to 4 inches diameter and rear roller from % to 1% inch diameter were tested; a 3-inch roller and a 1-inch roller combination were found to be most suitable. Several mate- rials were tried for the rear rollers, and fluted garden hose proved to be satis- factory; flutes were necessary to main- tain sufficient friction for positive fruit pickup. In general, best results were obtained with the rear roller about % to % inch above the ground, with the front roller just low enough to touch the smallest fruit on the ground (about % to 1 inch above ground). The best distance between the rollers was achieved when the front roller was compressed slightly as small fruit passed between the rollers. T43] Resilient forward roll Resilient rear pickup roll agaatfSaEi^ Zone of seizure + *1 Fig. 43. New pickup principle for picking up fruit from ground. Field tests of the principle revealed two problems: the absence of a positive transfer of fruit from the pickup mech- anism to the conveying system, and the poor wearing qualities of the resilient forward roller (a steel shaft covered with foam rubber and enclosed with a skin of gum rubber) . A second model was then designed which incorporated the pickup rollers into the elevating system (fig. 44) . Foam rubber was replaced with a rubber- fingered belt which served in both pickup and elevation capacities ; the fingers were l 1 /^ inch long, % 6 inch in diameter and % inch apart — a wider spacing would also be satisfactory. The pickup roller was constructed by slipping a 1-inch water hose over a %-inch shaft. Results. The average rate of harvesting prunes with the 3-foot-swath machine was 18 boxes per hour (about four times the average rate of hand pickup) . The new pickup principle caused no visible damage to harvested fruit, com- pared to no damage by hand pickup but 1 to 11 per cent damage for existing pickup machines. The picking up of dirt and missing fruit was found to be affected by soil preparation (as is the case with other harvest methods) . With good prep- aration, negligible fruit was missed by either the new machine or hand harvest. Fig. 44. Second pickup ma- chine field testing. Insert shows the pickup principle incorpo- rated with conveyor system. [44] Existing machines missed about 2 per cent of the fruit under similar conditions. About % to 3 per cent of the material picked up by the new machine was dirt. Hand harvest averaged % per cent, and existing pickup machines averaged 4 to 13 per cent. Proper ground preparation was essen- tial for best performance with this unit, although preparation was not as critical as with most other machines. Preparation consists of leveling surface ripples, filling holes, and rolling the ground in order to push clods into the surface. On a well- prepared surface, all fruit should be at substantially the same elevation. COMMERCIAL DEVELOPMENT In 1963 a study of commercial pickup machines using the new principle on prunes was conducted on two soil types. The first, a gravelly loam soil, was pre- pared by rolling four times with a smooth- roller after the growers conventional preparation for hand harvest. The second, a loam soil, was prepared by two passes with a ring-roller smooth-roller combina- tion, but this was not sufficient for good machine performance and the soil was rolled two more times. After rolling four times the machine did a fair job on both soils, despite pronounced undula- tions in the surface. However, a landplane would have improved results by reducing the number of prunes missed and the amount of dirt picked up. Time and travel studies were con- ducted for harvesting two-thirds of an acre with a 5-foot-swath machine which had been designed for bulk handling. The times required for various operations were : • picking — 35 seconds per tree • turning at end of row — 24 seconds • changing bins — 2 minutes. The average yield was one box per tree per picking. Rows were 18 trees long and 4 passes of the machine were required for each row; total time for all operations was 45 seconds per tree. Assuming a field efficiency of 75 per cent, the average harvest rate would be 60 trees per hour and 60 boxes per hour. Adding one man for shaking, the output of the two-man crew would be 30 boxes per man-hour. Improvement in harvest rate could be expected when harvesting larger blocks. With 18 trees per row and 4 passes of the machine per row as in this trial, an aver- age of approximately 12 per cent of the total time was required for turning. On properly prepared land, machines using the new principle had the following advantages: a positive pickup of fruit as the machine moved into it, a low impact force on fruit, and no soil disturbance by the pickup roller. Use on prunes and figs has demonstrated that the positive pickup and small impact force results in little or no fruit damage. The machines perform equally well on walnuts. CLOD SIZE REDUCTION A conical roller was built and tested to determine if it produced more reduction in clod size than did a comparable cylin- drical roller. Theoretical analysis indi- cated that a conical roller would develop a torsional stress when a clod was in con- tact with the roller at two points, due to the velocity differential along the length of the roller. The performance of each roller was determined by comparing clod size before rolling to clod size after two passes with the roller. Soil samples were taken at four locations in the path of the roller and contained the top 1 inch of soil. Comparisons were based on a sieve anal- ysis similar to that used for concrete ag- gregates (Henderson, 1955) and failed to indicate any advantage resulting from use of the conical roller. [45 CATCHING-FRAME DEVELOPMENT Progress in tree shaking led to the need for a high-capacity, efficient catching- frame for fruit collection, and in 1958 a program was initiated to determine what type of catching apparatus would best fit these needs. An ideal catching-frame should have sufficient capacity to handle the output of a shaker, it should require a low labor input, and it should not inter- fere with shaker operation. Frames in use up to 1958 were of three basic types: two-plane surfaces sloping toward the tree, two-plane surfaces slop- ing away from the tree, and an inverted umbrella wrapped around, and sloping toward, the tree trunk. Existing catching-frames that sloped toward the tree were high at the outside on two sides of the tree, and this inter- fered with boom-shaker operation. In addition, delay was caused by the neces- sity of removing the fruit before moving to the next tree. However, these frames had the advantage of being low at the trunk, thus permitting a good seal below the tree crotch. Sloping-out frames were low on their outer periphery, thus making tree limbs easily accessible to the shaker; however, their inside was high and a poor seal re- sulted due to interference of the limbs which branched out below the elevation of the seal. Good drainage of these frames was a problem. Inverted umbrella frames had two dis- advantages: their high outside periphery interfered with boom-shaker operation, and they had to be completely drained before moving. The primary disadvantages of all three types were the high portions of the frames, which were about 4% to 5 feet at their highest point. LOW-PROFILE CATCHING-FRAME The factors just discussed were con- sidered in determining the main com- ponents to be incorporated into a catch- ing apparatus. A low-profile machine had many advantages, such as ease of posi- tioning a boom-shaker on tree limbs, ease of maneuvering the catching-frame under interfering branches, and a low seal for eliminating fruit losses (flexibility foi different trunk sizes would be the only requirement) . A low-profile self-propelled frame was constructed and field tested in 1958 (Adrian and Fridley, 1959). The frame was designed to have individual units on each side of the tree. Each unit was self- propelled and moved straight down the tree row to minimize time loss in moving (there was less maneuvering, and no time was required to wrap frame around tree). The wide conveyor (fig. 16) was chosen because in addition to producing a low profile, it need not be drained be- fore moving, thereby increasing effi- ciency. Results of limited tests on prunes were favorable. Output was 30 boxes per man-hour, with a shaker speed of 30 trees per hour — twice the output of any opera- tion previously observed, and six times the average hand-harvest rate. Filling and handling of standard field boxes was a problem, however. More extensive tests were conducted in two prune orchards in 1959 (Adrian, et al., 1960). One was a typical prune orchard with many scaffolds and low branches. The second orchard was pruned for mechanical shaking — few primary limbs were left, (in order to minimize the number of hookups) and few low branches (in order not to inter- fere with operator visibility) . Field boxes were used in the first orchard and bulk [46] Fig. 45. Trees properly pruned for mechanical harvesting. bins in the second. A tractor-mounted boom shaker was used in both orchards. Field test results. Table 14 shows the times required for the various operations of the catching-frame and tree-shaker under the two orchard conditions. Tree structure in the specially pruned orchard reduced the time needed for several oper- ations — moving shaker from limb to limb, moving shaker into tree, moving frame — and resulted in a harvest rate of 60 trees per hour (compared to 23 trees per hour in the typical orchard) . For shaking limbs, the tree should have three or four scaffold limbs to minimize Fig. 46. Low-profile catching frame incorporating bulk handling. [47] Table 14 EFFECT OF HANDLING METHODS AND TREE STRUCTURE ON RATE OF HARVESTING FRENCH PRUNES WITH BOOM SHAKER AND LOW-PROFILE DRAPER CATCHING-FRAME Tree structure Item Typical orchardf Specially pruned orchard! Tree shaker operation: 12 6.8 22 4 100 17 20 3.8 154 23 1 4 3 6.5 140 28 12 4 150 19 8.6 4.6 7.3 2-3 21 Catching-frame operation: 12 13 4.8 Over-all operation : 59 60 Crew: 1 2 2 3.0 Harvest rates : Rate of shaker-frame operation (boxes per hour) * 170 57 8 4 180 37 * Lug box capacity averages 50 pounds. t Fruit handled in lug boxes. X Fruit handled in bulk. the number of shaker attachments. Scaf- fold limbs should originate no lower than 24 inches from the ground, to permit a good seal with the catching-frame and to permit sufficient room for shaker attach- ment if a trunk shaker is to be used. For easier shaker attachments, the first branching of primary scaffold limbs should not be less than 24 inches from the head. In a typical orchard, 5 men were needed for fruit handled in boxes, but a 3-man crew using bins handled more fruit in a pruned orchard. COMMERCIAL DEVELOPMENT Subsequent to the tests described above, several manufacturers developed various versions of the design ideas mentioned. One of the most mechanized systems is a two-unit catching-frame designed for prunes and incorporating a trunk shaker (fig. 47). The unit carrying the shaker has a sloping surface which deflects all fruit from half the tree onto the second unit ; it also covers the tree row and seals at the tree trunk. The second unit has the fruit-handling system and a pan the length of the frame, which is laid on the ground adjacent to the tree: the pan is tilted to dump fruit collected from the first unit onto the conveyor. Average harvest rates, assuming a field efficiency of 75 per cent, are 65 trees per hour and 260 boxes per hour using two men. Another popular machine for prunes has been a conveyor having canvas sheets attached to a powered roller so that fruit can be pulled in and dumped onto the [48] Fig. 47. Two-man harvesting frame with trunk shaker mounted under the deflecting surface on the right side. Unit on left conveys fruit to a bulk trailer in the rear. Pan in foreground is in catching position. conveyor. The advantage of these units is low initial investment, and their use is made possible by the fact that prunes are relatively resistant to injury. They require more labor than the more mech- anized units. CATCHING-FRAME DESIGN AND FRUIT INJURY The possible use of catching-frames for peaches, apricots, and other soft fruits led to the study of methods of minimizing injury to fruit caused by the catching operation (Claypool, L. L. 1962; Fridley et al., 1964) . Studies were made of pro- tection afforded by padding material placed over hard surfaces, and of decel- eration of fruit before impact with the catching surface. The first investigation sought to de- velop data relative to energy relationships in fruit bruising, and the ability of cer- tain materials to absorb a high per cent of the kinetic energy gained by the fruit while falling. It was found that damage to fruit caused by impact on hard sur- faces can be minimized by use of effective padding to absorb (or store) kinetic energy of the fruit at impact without ex- ceeding an allowable stress of the fruit. A material which absorbs the energy — one with a high hysteresis — is preferred over one which momentarily stores the energy, as this would result in fruit be- ing accelerated upward toward other fall- ing fruit. A thin layer of padding is more desirable than a thick layer from a design standpoint, and therefore the shape of the stress-strain curve for the material should also be considered, as the area under this curve gives an indication of the energy it can absorb (or store) . Injury caused by fruit hitting other fruit already on the catching surface is a serious problem, particularly where fruit is concentrated in or near convey- ors. Accordingly, strips of lightweight canvas webbing were suspended above [49] Fig. 48. Catching frame incorporating decelerator strips and expanded poly- ethylene padding. the catching surface to decelerate the fall- ing fruit (fig. 48). Tests on apricots, peaches, and olives indicated that the strips should be narrow (about 3 inches) to prevent forming pockets which will hold fruit. Spacing between strips needs to be slightly less than the fruit diameter but sufficient to prevent fruit being sup- ported, and two or three offset layers are required. Table 15 gives results of drop tests and fruit-injury data resulting from impacts of different energy levels on dif- ferent materials and thicknesses. In one test the combined use of pad- ding and deceleration strips was studied on two varieties of clingstone peaches. The frames used were presumed to be one of several equally suitable commer- Table 15 COMPARISON OF FRUIT INJURY RESULTING FROM IMPACT ON DIFFERENT MATERIALS Blenheim apricots* Peak clingstone peaches* Treatment Drop height Fruit severely damaged Drop height Fruit severely damaged feet 15 15 15 10 15 10 15 10 15 15 per cent 6 66 4 12 7 22 10 9 4 feet l l A 10 7V 2 7V 2 10 per cent 2 Canvas decelerator strips (2 layers) Fruit onto fruit on taut canvas Sponge rubber %-in. thick 22 Sponge rubber %-in. thick 14 Polyurethane foam 13^-in. thick 32 Expanded polyethylene J^-in. thick 17 Expanded polyethylene 1-in. thick 10 8 6 • Average of 12 apricots or 3^ peaches per pound. [50] cial models. Both halves of the frame and to prevent strips from turning on were modified by covering the entire edge. Mountings for the strips, installed catching surface with a 1-inch layer of ex- on the ends of the catching frame, were panded polyethylene. As the base for the designed to permit individual tightening, padding on one unit %-inch plywood was as effectiveness of the strips is greatly re- used, and 2- x 4-inch welded wire, tightly duced if they are allowed to sag. Plastic stretched, was used on the other unit. La- strips did not sag appreciably due to tem- boratory studies had demonstrated that perature or humidity changes, but they bouncing of fruit was reduced with the did occasionally loosen, wire (which also provided added cush- The maximum drop for fruit falling ioning.) from the decelerator strips onto other Three layers of strips, made of woven fruit was 16 inches, and from the strips plastic lawn-chair webbing, were in- onto the conveyor was 6 inches. Evalua- stalled over lengthwise conveyors on both tion of fruit injury indicated a 3 to 7 per frames. These strips were 2% inches cent increase over that resulting from wide, spaced 1% inches between layers hand harvesting. Most of this injury was and 2% inches between strips in the same caused by fruit hitting limbs as it fell layer; layers were offset 1% inch. Each through the tree. Deceleration of fruit on layer of strips was cross-tied at 24-inch padded catching-surfaces resulted in intervals to help maintain proper spacing little or no injury. ACKNOWLEDGMENTS The authors wish to thank the many individuals and groups without whose help this work would not have been possible. Particularly, thanks are due to Roy Bainer, Coby Lorenzen, R. R. Parks, M. O'Brien, A. A. McKillop, J. B. Powers, C. E. Schertz and other members of the Agricultural Engineering Department at Davis for generously giving their time for consultation, guidance, and drafting and construction of equip- ment; to G. K. Brown, H. L. Brewer, S. L. Szluka, L. L. Claypool, M. W. Miller, J. E. DeVay and other University personnel for working cooperatively on various aspects of the reported work ; to Patrick Long, Robert Conklin, James Rumsey, and Clarence Wong for assistance in conducting tests and collecting data ; to growers for graciously cooperating in field tests; to manufacturers for the use of equipment; and to Farm Advisors and Extension Specialists for assistance in arranging and conducting field tests and demonstrations. LITERATURE CITED Adrian, P. A. and R. B. Fridley. 1965. Dynamics and Design Criteria of Inertia-type Tree Shakers. Transactions of the ASAE 8(1):12-15. Adrian, P. A. and R. B. Fridley. 1959. New Concept of Fruit Catching Apparatus. Transactions of the ASAE 2(1) :30-31. Adrian, P. A. and R. B. Fridley. 1961. New Tree Shaker on Fruit Catching Frame. California Agriculture 15(8) :12-13. Adrian, P. A., R. B. Fridley, and A. D. Rizzi. 1960. Pruning for Mechanical Harvest. Western Fruit Grower 14(6) : 17-18. Adrian, P. A. and R. B. Fridley. 1964. Shaker-clamp Design in Relation to Allowable Stresses of Tree Bark. Transactions of the ASAE 7(3) :232-34, 237. [51] Brewer, H. L., R. B. Fridley, and P. A. Adrian. 1961. Blower-shaker for Mechanical Harvesting of Prunes. California Agriculture 15(9) :5. Claypool, L. L. 1962. Mechanizing Harvest — the Horticultural Point of View. Western Fruit Grower 16(6): 13-15. Claypool, L. L., M. W. Miller, W. H. Dempsey, and Paul Esau. 1962. The Influence of Harvesting Procedures and Storage on the Quality of Dried French Prunes from Coastal Regions. Hilgardia 33(8) : 319-48. Claypool, L. L., W. H. Dempsey, Paul Esau, and M. W. Miller. 1962. Physical and Chemical Changes in French Prunes During Maturation in Coastal Valleys. Hilgardia 33(8) :311-18. DeVay, J. E., Harley English, F. L. Lukezic, and H. J. O'Reilly. 1960. Mallet Wound Canker of Almond Trees. California Agriculture 14(8) :8-9. DeVay, J. E., F. L. Lukezic, Harley English, K. Uriu, and C. J. Hansen. 1962. Ceratocystis Canker. California Agriculture 16 (1) :2-3. Fairbank, J. P. 1946. Mechanical Tree Shaker and Such. Diamond Walnut News 23(4) :4-6. Fridley, R. B. and P. A. Adrian. 1959. Development of a Fruit and Nut Harvester. Agricultural Engineering 40(7) :386-87, 391. Fridley, R. B., H. Goehlich, L. L. Claypool, and P. A. Adrian. 1964. Factors Affecting Impact Injury to Mechanically Harvested Fruit. Transactions of the ASAE7(4):409-11. Fridley, R. B. and R. R. Parks. 1957. Research Shows the Way. Western Fruit Grower 11(6) : 18-19 Fridley, R. B. and P. A. Adrian. 1960. Some Aspects of Vibratory Fruit Harvesting. Agricultural Engineering 41(1) :28-31. Henderson, S. M. and R. L. Perry 1955. Agricultural Process Engineering. New York: John Wiley, pp. 122-23. Jacobsen, L. S. and R. S. Ayre. 1958. Engineering Vibrations. New York: McGraw-Hill, pp. 282-94. Lamouria, Lloyd H. and H. T. Hartmann. 1955. Machine Harvesting of Olives. California Agriculture 9(12) :8, 13. Lamouria, L. H., H. T. Hartmann, R. W. 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[52] APPENDIX A STATISTICAL ANALYSIS OF FRUIT REMOVAL For the purpose of multiple regression analysis the equation Per cent removed = 100 - lOOe"* 5 ™", was changed into the form, or Per cent not removed 100 = g-fcS p JV A , ( , per cent not removed\ . 7 , , « , , In I -ln^ — J = ln/c+pln£ + /im A r or Y = C + pXi + X, The statistical results are shown in Appendix table A. The exponent p var- ied from 1.83 to 1.23, with an average value of 1.6. The value of fx ranged from 0.80 to 1.39, with an average value of 1.1. The significance of the relationship was checked by determining the cor- relation coefficient between the meas- ured removal and the calculated re- moval for p = 3/2 and n = 1 . The results were : XiX 2 = 10,227 x? = 9,710 X 2 2 = 10,878 r = 0.993 where, Appendix Table A RESULTS OF MULTIPLE REGRESSION ANALYSIS OF FRUIT REMOVAL STUDY CONDUCTED ON PRUNES 1957 1958 Item Grower orchard University orchard value 2 Xl2 2 X2* S XlXi S x\y 2 xiy n V 1.5515 1 . 2450 -0.7257 1.3294 0.0371 33 1.23 0.80 0.0084 3.4508 1.3872 -0.5071 5.4572 1.3272 14 1.83 1.39 0.000088 0.6807 0.6571 6 1.13 k 0.00112 Note: Xi — In (stroke) Xt = In (frequency) 'per cent not removed^ li /] In In f - 100 = deviation of X\ from mean = deviation of Xj from mean = deviation of Y from mean = number of runs xi = deviations of calculated values from mean x 2 = deviations of measured values from mean r = correlation coefficient. This is significant, as the grees of freedom. 1 per cent significance level is [53] 0.641 for 13 de- APPENDIX B ANALYTICAL ANALYSIS OF SHAKER DESIGN To describe many complex systems mathematically it is possible for most engineering purposes to make qualifying assumptions. In the case of vibration problems it is frequently sufficient to describe a system with few or possibly even one degree of freedom. This has been done for the following analysis. Assumptions made for analysis (Jacobsen and Ayre, 1958; Thomson, 1954): 1. The system has a single degree of freedom. 2. The exciting force varies sinusoidally. 3. The restoring force is proportional to displacement. 4. Damping is viscous (damping force is proportional to velocity). 5. Steady-state vibration occurs. 6. Energy is conserved by the shaker. The following differential equation then applies. Differential equation of motion: From Newtons second law of motion, F = ma, it can be seen that : Spring force + damping force + applied force = inertia force dx d^ d^x or — kx — c — — m — (x + r cos oot) = (M t — m) — [1J Where x = instantaneous displacement from equilibrium position — ft. k = spring stiffness — lb. /ft. c = coefficient of viscous damping — lb. /ft. — sec. r = eccentricity — ft. m = mass of unbalance — slugs M t = total mass of the system including m — slugs t = time — sec. co = exciting frequency — rad/sec. Differentiating the third term with respect to t, we obtain : -kx - c -j- - m — + mrco 2 cos oot = (M t - m) -—■ [2] And rearranging and simplifying, M t -Tfi + c — + kx = rarco 2 cos oot [3] The solution of equation [3] is of the form S X = — cos (oot — a) [4] where S = limb displacement, ft., and a = phase angle (amount the displace- ment lags impressed force). From which and dx dt co sin {wt d 2 x S 2 t , v — = --co 2 cos (co*- a). [5] [6] By substituting these values into equation [3] and analyzing the resulting expres- sion, it can be shown that for co> >co n (where oi n is the fundamental mode fre- quency) : 8 2mr [7] Force. The exciting force in the differential equation [3] which describes the sys- tem, does not actually exist internally in the vibrator unit, since the center of rotation oscillates. If the force resulting from this oscillation is subtracted, the actual physical force applied on the rest of the system by the unbalanced mass is : mr co 2 cos oit — m