key: cord-0317213-mjpo0k2y
authors: Nguyen, Vinh; Melkote, Shreyes N.
title: Identification of industrial robot frequency response function for robotic milling using operational modal analysis
date: 2020-12-31
journal: Procedia Manufacturing
DOI: 10.1016/j.promfg.2020.05.032
sha: 061a2092ab6637cef165bbe8fafbc36cdb7f3521
doc_id: 317213
cord_uid: mjpo0k2y

Abstract Impact hammer experiments are typically used for identifying the Frequency Response Function (FRF) of six-degree-of-freedom (6-dof) industrial robots for machining applications. However, the modal properties of 6-dof industrial robots change as a function of robot arm configuration. Hence, describing the robot’s modal parameters within its workspace requires off-line impact hammer experiments performed at discrete robot end effector positions, which are costly and time consuming. Instead, it is more efficient to calculate the robot FRF using Operational Modal Analysis (OMA), a method that utilizes data acquired during the actual machining process. This paper presents an OMA approach to identify the robot FRF from measured milling forces and robot tool tip vibrations. Analysis of the milling process data reveal that periodic forces produced in the milling process are accompanied by background white noise that induce broadband excitation across the robot structure’s frequency spectrum. Hence, the tool tip vibration signal contains the signature of the structure’s free response that enables the use of OMA to estimate the robot’s FRF. The FRF calculated using OMA is shown to be in good agreement with results obtained from impact hammer experiments.

There is growing interest in using six-degree-of-freedom (6dof) industrial robots for aerospace machining operations due to their flexibility of use and larger work volume [1] . In milling operations that are characterized by large periodic forces, the tool tip vibrations, and the resulting surface profile accuracy of the machined feature, are influenced by the modal vibration properties of the robot arm. Therefore, determining the appropriate machining conditions to achieve the required part accuracy and surface finish requires knowledge of the robot's modal properties. However, the modal parameters of a 6-dof industrial robot are known to vary within the workspace [2, 3] .

There is growing interest in using six-degree-of-freedom (6dof) industrial robots for aerospace machining operations due to their flexibility of use and larger work volume [1] . In milling operations that are characterized by large periodic forces, the tool tip vibrations, and the resulting surface profile accuracy of the machined feature, are influenced by the modal vibration properties of the robot arm. Therefore, determining the appropriate machining conditions to achieve the required part accuracy and surface finish requires knowledge of the robot's modal properties. However, the modal parameters of a 6-dof industrial robot are known to vary within the workspace [2, 3] .

Consequently, to describe the robot's modal parameters throughout its workspace, the modal properties must be sampled at multiple discrete arm configurations in the workspace. Measurements of the robot's dynamic behavior for a given arm configuration are usually performed using off-line impact hammer tests that apply an impulse excitation to the robot end effector using an instrumented modal impact hammer and the corresponding acceleration response is measured. A force impulse serves as a broadband excitation, and therefore excites structural modes across all frequencies. A system Frequency Response Function (FRF) can be computed from the displacement (twice integrated from acceleration) and the impulse force measurements [4] . However, conducting off-line 

There is growing interest in using six-degree-of-freedom (6dof) industrial robots for aerospace machining operations due to their flexibility of use and larger work volume [1] . In milling operations that are characterized by large periodic forces, the tool tip vibrations, and the resulting surface profile accuracy of the machined feature, are influenced by the modal vibration properties of the robot arm. Therefore, determining the appropriate machining conditions to achieve the required part accuracy and surface finish requires knowledge of the robot's modal properties. However, the modal parameters of a 6-dof industrial robot are known to vary within the workspace [2, 3] .

Consequently, to describe the robot's modal parameters throughout its workspace, the modal properties must be sampled at multiple discrete arm configurations in the workspace. Measurements of the robot's dynamic behavior for a given arm configuration are usually performed using off-line impact hammer tests that apply an impulse excitation to the robot end effector using an instrumented modal impact hammer and the corresponding acceleration response is measured. A force impulse serves as a broadband excitation, and therefore excites structural modes across all frequencies. A system Frequency Response Function (FRF) can be computed from the displacement (twice integrated from acceleration) and the impulse force measurements [4] . However, conducting off-line 

Impact hammer experiments are typically used for identifying the Frequency Response Function (FRF) of six-degree-of-freedom (6-dof) industrial robots for machining applications. However, the modal properties of 6-dof industrial robots change as a function of robot arm configuration. Hence, describing the robot's modal parameters within its workspace requires off-line impact hammer experiments performed at discrete robot end effector positions, which are costly and time consuming. Instead, it is more efficient to calculate the robot FRF using Operational Modal Analysis (OMA), a method that utilizes data acquired during the actual machining process. This paper presents an OMA approach to identify the robot FRF from measured milling forces and robot tool tip vibrations. Analysis of the milling process data reveal that periodic forces produced in the milling process are accompanied by background white noise that induce broadband excitation across the robot structure's frequency spectrum. Hence, the tool tip vibration signal contains the signature of the structure's free response that enables the use of OMA to estimate the robot's FRF. The FRF calculated using OMA is shown to be in good agreement with results obtained from impact hammer experiments.

There is growing interest in using six-degree-of-freedom (6dof) industrial robots for aerospace machining operations due to their flexibility of use and larger work volume [1] . In milling operations that are characterized by large periodic forces, the tool tip vibrations, and the resulting surface profile accuracy of the machined feature, are influenced by the modal vibration properties of the robot arm. Therefore, determining the appropriate machining conditions to achieve the required part accuracy and surface finish requires knowledge of the robot's modal properties. However, the modal parameters of a 6-dof industrial robot are known to vary within the workspace [2, 3] . * Corresponding author. Tel.: +1-757-952-5221.

E-mail address: vnguyen43@gatech.edu Consequently, to describe the robot's modal parameters throughout its workspace, the modal properties must be sampled at multiple discrete arm configurations in the workspace. Measurements of the robot's dynamic behavior for a given arm configuration are usually performed using off-line impact hammer tests that apply an impulse excitation to the robot end effector using an instrumented modal impact hammer and the corresponding acceleration response is measured. A force impulse serves as a broadband excitation, and therefore excites structural modes across all frequencies. A system Frequency Response Function (FRF) can be computed from the displacement (twice integrated from acceleration) and the impulse force measurements [4] . However, conducting off-line

There is growing interest in using six-degree-of-freedom (6dof) industrial robots for aerospace machining operations due to their flexibility of use and larger work volume [1] . In milling operations that are characterized by large periodic forces, the tool tip vibrations, and the resulting surface profile accuracy of the machined feature, are influenced by the modal vibration properties of the robot arm. Therefore, determining the appropriate machining conditions to achieve the required part accuracy and surface finish requires knowledge of the robot's modal properties. However, the modal parameters of a 6-dof industrial robot are known to vary within the workspace [2, 3] .

Consequently, to describe the robot's modal parameters throughout its workspace, the modal properties must be sampled at multiple discrete arm configurations in the workspace. Measurements of the robot's dynamic behavior for a given arm configuration are usually performed using off-line impact hammer tests that apply an impulse excitation to the robot end effector using an instrumented modal impact hammer and the corresponding acceleration response is measured. A force impulse serves as a broadband excitation, and therefore excites structural modes across all frequencies. A system Frequency Response Function (FRF) can be computed from the displacement (twice integrated from acceleration) and the impulse force measurements [4] . However, conducting off-line 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to impact hammer tests over the entire workspace of the robot can be tedious and time-consuming. Hence, identifying the FRF from process data gathered from the milling operation can aid in reducing robot downtime and associated costs.

Operational Modal Analysis (OMA) involves identifying a structure's modal properties using vibration data obtained under operating conditions e.g., the milling process. For instance, Suzuki et al. [5] calculated the transfer function of a CNC machine tool structure by inverse analysis of self-excited regenerative chatter. In addition, Wan et al. [6] used OMA to identify the process damping coefficients used in regenerative chatter models. However, performing OMA under chatter conditions is limited to cutting conditions that can induce chatter. Note that stable milling is characterized by periodic forces, which theoretically only excite the structure at harmonics of the spindle speed (as opposed to the entire frequency spectrum). Therefore, researchers have utilized random forced excitation for OMA. Similar to impulses, random forcing functions permit broadband excitation [7] . Poddar et al. [8] demonstrated a workpiece design that resulted in random force excitation in face milling operations. In addition, Li et al. [9] programmed the feed drives to induce random excitation in the machining process. Another method to introduce random excitation is to randomly change cutting parameters during the cutting operation [10, 11] . However, modifying the milling process to produce random excitation undermines the purpose of using OMA under normal operating conditions. Alternatively, OMA under stable milling operations without random excitation have been demonstrated to only identify the natural frequency of the structure [12, 13] , which is insufficient for optimal control and for predicting stable vibrations because identification of the natural frequency does not specify the amplitude of vibrations. Hence, OMA methods that have been demonstrated in CNC milling operations are inadequate for robotic milling applications.

Stable milling operations consist of both periodic content and random background noise [14, 15] . In addition, application of OMA in fields outside manufacturing, such as in vibrating civil structures [16] , in-flight helicopters [17] , and wind turbines [18] , have shown that forces containing both types of signals can generate broadband excitation of the structures, which enables estimation of FRFs. Because 6-dof industrial robots are significantly more compliant than their CNC machine tool counterparts, the background random noise can excite the robot's natural modes of vibration to measureable levels suitable for OMA. Note that implementing OMA under stable milling conditions to identify the complete FRF has not been demonstrated in prior literature for both CNC and robotic milling operations. Thus, in this paper, we propose using OMA to identify the modal parameters of a 6-dof industrial robot performing a stable milling operation. First, milling experiments used to collect vibration and force data are described. Subsequently, OMA is used to determine the FRF of the robot. The OMA-based FRF is then compared to the FRF determined from impact hammer tests. A discussion of the level of stochastic background noise in the measured force signal is presented. The paper concludes with a discussion of the major findings and future work.

This section describes the robotic milling experiments performed on a KUKA KR500-3 6-dof industrial robot. Figure 1 shows the measurement systems used to acquire milling process data. A 6-dof laser tracker (Leica AT960 with T-MAC) and a robot flange-mounted strain gauge based force/torque sensor (ATI Omega 160) were used to measure the instantaneous robot vibrations and the milling forces, respectively, in the X, Y, and Z directions. The resolutions of the laser tracker and force sensor are 15 μm [19] and 0.75 N [20] , respectively. It is assumed that the compliance of the robot dominates the system vibrations. Therefore, a constant matrix transformation was applied to the vibrations measured by the laser tracker at the location of the T-MAC, which was mounted to the side of the spindle as seen in Fig. 1 , to calculate the tool tip vibrations. In addition, the tool-spindle structure was assumed to be completely rigid, and therefore the forces measured by the force sensor are assumed to be those experienced by the tool tip. In addition, the milling forces measured by the force/torque sensor were inverse filtered using the approach presented in prior work to recover the undistorted milling forces [21] . A Beckhoff TwinCAT real-time programming environment was used to record the vibration and force time series signals at a sampling frequency of 1 kHz. Figure 2 shows the robot arm configuration used in the milling experiment used to gather the milling forces and tool tip vibrations utilized in OMA. Dry peripheral milling experiments were performed on an Acetal Resin workpiece using a two flute, 25.4 mm diameter, 30° helix angle, cobalt end mill. The feed per tooth, radial depth of cut, and axial depth of cut, were 0.5 mm, 6 mm, and 6 mm, respectively. The tool feed direction was aligned with the Y direction indicated in Fig.  2 . The spindle speed was 2700 RPM. Note that this speed corresponds to spindle and tooth passing frequencies of 45 Hz and 90 Hz, respectively. Hence, the excitation frequencies present in the milling force signal are located far from the dominant natural frequencies (~10 Hz in the X and Z directions and ~25 Hz in the Y direction) of the KUKA KR500-3 industrial robot used in this work. The robot joint values [ 1 … 6 ] corresponding to the arm configuration shown in Fig.  2 were [88.44, -13.62, 72.42, 180.90, 59.55, -0 .67] degrees.

Note that the FRF was assumed to be constant throughout the length of cut (50 mm). Figure 3 shows the time series and spectral decomposition of the measured milling forces. As expected, Fig. 3a shows that the force components exhibit a strong periodic behavior, which is consistent with the spectral decomposition shown in Fig. 3b . Specifically, the spectral decomposition of the milling forces shows that the milling force consists primarily of the spindle (45 Hz) and tooth passing (90 Hz) frequencies and their harmonics. However, Fig. 3a also shows the presence of a noise component superposed onto the periodic time series signal. Because white noise is uniform in magnitude across the frequency domain, the stochastic signal can induce broadband excitation of the robot structure. Figure 4 shows the corresponding time series and frequency decomposition of the robot tool tip vibrations. Fig. 4a shows forced vibrations that primarily correspond to the spindle and tooth passing frequency of 45 Hz and 90 Hz in the X, Y, and Z directions. Interestingly, the time series data also show vibrations at a lower frequency superposed onto the vibrations corresponding to the tooth passing frequency. These lower frequency vibrations, which are close to the robot's natural frequency of ~10 Hz in the X and Z directions and ~25 Hz in the Y direction, are also apparent in the frequency decomposition of the vibrations shown in Fig. 4b . These lower frequencies correspond to the robot's free vibration response characteristics even though the tooth passing frequency is the most dominant excitation frequency in the milling force signal. Consequently, OMA can be used to determine the robot FRF. 

This section describes the OMA method used to calculate the robot FRF from milling force and tool tip vibration data. The results of the OMA are presented along with determination of the minimum white noise variance required to calculate the robot FRF for a given sensor configuration.

Consider the power spectral density of the robot tool tip vibrations ( ) for a random white noise (or an impulse) force input to be

where ( ), ( ), and ( ) are the power spectral densities of the cutting force, robot structure, and noise of the vibration sensor, respectively [7] . Note that Equation (1) assumes that the measurement noise of the force sensor is small compared to the random white noise force. Thus, we can multiply Equation (1) by * ( ) , which is the complex conjugate of ( ) , resulting in * ( ) ( ) = * ( ) ( ) ( ) + * ( ) ( )

Each term in Equation (2) can be transformed into auto and cross spectral densities using Welch's Method that results in

where ( ) , ( ) , and ( ) are the force-vibration cross spectral density, the force auto spectral density, and the force-sensor noise cross spectral density. By assuming the vibration measurement sensor noise and input signal are not correlated, the cross spectral density ( ) approaches 0 after averaging. Hence, the following equation can be used to calculate the robot FRF

Thus, the FRF of the robot structure can be determined from Equation (4) after calculating the auto spectral density of the cutting force signal and the cross-spectral density of the force and vibration signals.

Modal impact hammer experiments were used to calculate the reference FRF to validate the proposed OMA method. Specifically, an impact hammer (PCB 086D05) was used to apply an impulse excitation collinear with a uniaxial piezoelectric accelerometer (PCB 352A21) mounted to the tool tip, as shown in Fig. 5 . The accelerometer was initially placed on the tool collinear with the X axis, and an impulse was applied in the accelerometer's measurement axis. The accelerometer was then placed on the tool collinear with the Y axis and the measurement was retaken. Finally, the accelerometer was attached to the bottom of the tool slightly off the tool axis and the impulse loadings were applied at a different location on the bottom of the tool to obtain the Z direction FRF. The time series force excitations and acceleration responses were recorded at 17 kHz using the MetalMax software. Similar to OMA, the FRF was calculated from the twice-integrated acceleration and the impact hammer force data using Equation (4). Fig. 6 shows that OMA using milling process data is a feasible approach to determine the robot FRF. However, the OMA method is only feasible due to the existence of background white noise in the milling force data that excites the robot structure. Hence, it is useful to estimate the minimum threshold of white noise required to excite the structure at a level measurable by the laser tracker. 

A simulation was performed to determine the minimum white noise threshold required for OMA to be effective for the experimental setup used in this work. A zero mean Gaussian white noise with variance 2 was simulated and used as input to the Y direction FRF shown in Fig. 6 . The Y direction FRF was used in the simulation since it is the least compliant FRF in the system and would therefore produce the smallest vibrations. Since no harmonic forces were used in the simulation, the simulated output is the corresponding robot vibration resulting from a force consisting of only Gaussian white noise. The peak-to-valley vibration amplitude was calculated for each input with variance 2 . If the peak-to-valley vibration amplitude is below the laser tracker resolution (15 μm), the sensor would be unable to measure the vibration corresponding to the white noise excitation. Figure 7 shows the simulation results. As expected, the peak-to-valley vibration amplitude increases with the noise variance. In addition, Fig. 7 shows that to satisfy the minimum threshold, the Gaussian white noise variance must be above 75 N 2 for this particular robot arm configuration. Fig. 7 . Gaussian white noise simulation results of peak-to-valley vibration vs.

input noise variance.

The following equation was used to verify that the noise variance in the milling forces shown Fig. 3 is sufficient to produce a measurable structural excitation

where P(f) is the power spectral density of the measured cutting force signal and T is the total time window. Note that the spindle rotation frequency and tooth passing harmonics of milling are present in the power spectral density, which distorts the calculation of 2 . Hence, the milling process harmonics were filtered from the power spectral density. The values of 2 for the measured X, Y, and Z forces were 232 N 2 , 278 N 2 , and 251 N 2 , respectively, which are all above the minimum threshold shown in Fig. 7 . In addition, the variance of the force sensor measurement noise (0.56 N 2 ) is significantly smaller than 2 for the measured X, Y, and Z forces, thus validating the assumption invoked in Equation (1). Hence, the noise in the milling experiments in this work is adequate to excite the robot structural modes sufficiently for the laser tracker to measure. However, note that a stiffer system would require larger 2 to excite its modes to a measurable level. Because 6-dof industrial robots are more compliant than their CNC counterparts, the free response is easier to measure in robotic milling applications. This explains why prior research in CNC milling were unable to calculate the FRF using OMA under stable and non-random milling conditions [8] [9] [10] [11] [12] [13] .

This paper presented a methodology for determining the FRF of industrial robots using OMA. The cutting forces and tool tip vibrations measured in robotic milling experiments were used to calculate the FRF of the robot structure. Even though the milling harmonics were far from the robot's natural frequencies, the vibration results showed that the robot's natural modes were still being excited by background white noise present in the time series force signal. The calculated FRF was shown to be in good agreement with the FRF determined from modal impact hammer tests for the same robot configuration. In addition, the minimum threshold for the input noise variance was calculated to validate the claim that sufficient white noise exists in the milling force signal to produce measurable excitation of the robot's natural frequencies. Future work includes using the FRF obtained from OMA to calibrate and augment models that predict the robot's modal properties as a function of arm configuration.

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This work was supported by Boeing Research & Technology and the Boeing Manufacturing Development Center at Georgia Tech through the Strategic Universities Program.

Author name / Procedia Manufacturing 00 (2019) 000-000