The Effect of Input Shaping on Coordinate Measuring Machine Repeatability

Transcription

1 The Effect of Input Shaping on Coordinate Measuring Machine Repeatabilit (Proceedings of the 199 IFToMM World Congress on the Theor of Machines and Mechanisms) William E. Singhose and Warren P. Seering Department of Mechanical Engineering Massachusetts Institute of Technolog Cambridge, MA Neil C. Singer Convolve, Inc. Armonk, NY Kewords: Vibration, Input Shaping, Measurement Abstract Coordinate Measuring Machines (CMMs) are a strategic element in the manufacture of high-precision parts because their measurements of part geometries are used for qualit control and feedback on the manufacturing process. Proper CMM operation requires accurate knowledge of the position of the CMM's part sensor. The performance of a CMM is limited b background vibration levels, environmental conditions (temperature changes, cleanliness of the environment, etc.), accurac in the measurement equipment (encoders and part sensor), and structural deflections between the encoders and the part sensor. The most important limitation depends on the tpe of CMM and the operating conditions; however, structural deflection is alwas an important limitation because it introduces an error in the indicated position of the part sensor. The effect of input shaping, a method of reducing residual vibration, on the qualit of CMM measurements has been investigated. Tests were performed that verified the reduction of structural deflections when input shaping is used. Standard diagnostic tests were used to evaluate the repeatabilit of the CMM. Non-standard tests aimed at evaluating the CMM under adverse conditions were also performed. Input shaping improved measurement repeatabilit over a large range of operating parameters. Introduction Coordinate Measuring Machines (CMMs) measure manufactured parts to determine if tolerance specifications have been achieved. A CMM consists of a workspace in which parts are fixtured, a sensor for detecting the part surfaces, a mechanical assembl for moving the part sensor around the workspace, and a computer for calculating the part dimensions based on the sensor measurements. A sketch of a tpical CMM is shown in Figure 1. The CMM sketched in Figure 1 is shown with a touchtrigger probe part sensor This sensor uses a rub-tipped stlus to sense the part. When the stlus is brought into contact with a part surface, the deflection of the stlus triggers the computer to record the position indicated b the x,, and encoders. B probing the part on critical surfaces and recording their locations, the critical dimensions of the part can be calculated. A single ccle of a CMM measurement consists of four phases. First, the CMM performs a gross motion to move the part sensor to the vicinit of the part geometr that is to be measured. Second, the probe is allowed to come to rest. Third, the probe is reaccelerated to a small constant velocit in the direction of the part. This constant velocit portion of the measurement is called the pre-hit region because it immediatel precedes the contact between the probe and the part. Finall, the stlus contacts the part and the computer records the location of the contact. The position of a touch-trigger probe during a measurement with a mm pre-hit distance is shown in Figure. Encoder Touch- Trigger Probe Encoder Figure 1: Sketch of a Tpical CMM. x x Encoder The constant velocit in the pre-hit region is necessar so that the time dela between actual sensor contact and the computer's recognition of the contact can be subtracted from the measurements. If a constant velocit approach is not used, it is difficult to determine how far the probe travels during the signal propagation dela. If a CMM is to provide valuable qualit control, then its accurac and repeatabilit must be greater than the tolerance specifications for the part. Man CMM designs strive for accuracies of -1 µm and repeatabilities of - µm. The measurement qualit of a CMM is limited b background vibration levels, environmental conditions (temperature changes, cleanliness of the environment, etc.), accurac in the measurement equipment (encoders and part sensor), and structural deflections between the encoders and the part sensor. The difficult of obtaining micron level performance can be appreciated b examining the probe vibration when the CMM is subject to standard environmental disturbances. In order to detect the micron level probe vibration that is important in CMM measurements, a laser interferometer with a resolution of nanometers was used to measure x-direction motions of the probe. The interferometer retro-reflector was mounted on the -axis structural member in close proximit with the probe. Figure shows the measured vibration when a 1 lb. person with a normal gait walks past the CMM. Virtuall ever foot strike causes a vibration with an initial amplitude of - µm even though the machine weighs several thousand pounds and is stationed on a concrete floor. The most important limitation on CMM performance depends on the design of the CMM and the operating conditions, however, structural deflection between the encoders and touch-trigger probe is alwas an important limitation because it introduces an error in the measurement.

2 Position (mm) Position (µm) Pre-Hit Distance Pre-Hit Phase (Constant Velocit) Stop Before Pre-Hit 1 Approach Phase Probe Touches Part and then Retracts Time (sec) Figure : Probe Position During a Measurement. - X-Axis Encoder Measurement Laser Measurement of Probe - 1 Time (sec) Figure : Probe Vibration Caused b a Person Walking Past the CMM. Figure graphicall demonstrates how deflection in a CMM structure can adversel effect measurement accurac. In Figure a the part width is determined from two measurements. First, the probe is moved into contact with the left side of the part. At the moment the contact is made, the position indicated b the encoders is recorded. Next, the probe is moved to the opposite side of the part and brought into contact with the right face. The two encoder positions are then subtracted to obtain the part dimension. In Figure a the part is measured accuratel because the encoders indicate the true position of the probe. In Figure b the measurement is inaccurate because the structural deflections make the encoder readings differ from the true location of the contact points. If the structure is vibrating with an amplitude of during the pre-hit region, then the calculated dimension can have an error of ±. Several methods exist for limiting the structural deflection of a CMM. First, the acceleration and velocit of the machine can be limited. This solution is effective at reducing deflections, but it causes a decrease in throughput which makes it an unattractive solution. Second, the mechanical structure can be modified with additional stiffening members, damping materials, or configuration changes. This solution involves man of the classic design tradeoffs such as cost versus performance and solutions ma not appl across a product line containing CMMs of man sies and accurac levels. Alternativel, the hardware can be left unaltered and the command signals sent to the motors can be shaped so that deflections during the measurement phase are decreased[7, 11, 1]. Input shaping is a procedure that eliminates residual vibration b convolving a sequence of impulses with the desired command signal. The result of the convolution is then used to command the sstem. The impulse sequence used to shape the input is derived b solving a set of constraint equations which limit the residual vibration of the sstem. Input shaping requires that the residual vibration remain at a low level even in the presence of Encoder Gives Position of Left Face CMM Structure Touch-Trigger Probe L Encoder Part Measured Part Width = L (a) L+ Part Encoder Gives Position of Right Face Measured Part Width = L+ (b) Figure : Deflections Cause Measurement Errors. modeling errors. Several papers give detailed explanations of input shaping[,, 7-, 1, 1, 1, 19]. Methods for increasing the robustness of input shaping to modeling errors have been developed[1, 1]. Input shaping reduced residual vibration and maximum deflections during the slewing of a large nonlinear spacebased antenna[1, ]. Two-mode input shapers were used to increase the throughput of a silicon wafer handling robot[]. Input shaping was shown to be beneficial for long-reach manipulators[, ] and trajector following applications[, 1, 1]. This paper will investigate the effect of input shaping on the accurac and repeatabilit of CMM measurements. The operation of a CMM is not the tpical point-to-point application for which input shaping was designed. Rather, the important phase of the operation (the part detection) occurs while the machine is in motion and its timing occurs with some uncertaint because there is no wa to know a priori where the part is located or how much the structure will be deflected at the time of contact. The remainder of this paper is organied as follows. First, important parameters of a CMM measurement ccle are discussed. Experimental results showing the effect of input shaping on the structural deflections during the measurement will then be presented. The effect of input shaping on the measurement qualit will be demonstrated with the use of repeatabilit studies. Finall, conclusions will be drawn from the experimental results. Important Parameters of the Measurement Ccle There are several important parameters that determine the vibration during the critical pre-hit region. During the approach to pre-hit, the acceleration and approach distance are significant parameters. As the acceleration is increased,

3 the deflections during the approach phase become larger and the residual vibrations from these deflections in the pre-hit region increases. For short approaches, the deflection during the approach is smaller than for long approaches and, therefore, contributes less to the vibration during the pre-hit region. Certain approach distances lead to a natural cancellation of the approach phase vibration, i.e., the vibration induced b the acceleration is canceled b the vibration from the deceleration of the approach. This cancellation can be thought of as a naturall occurring posicast control[17]. It is difficult to utilie this natural cancellation on a consistent basis because its effectiveness is a strong function of approach distance, maximum acceleration, maximum velocit, probe location, and knowledge of the sstem dnamics. The period of time that is spent waiting between the approach phase and the pre-hit phase is also an important parameter because it allows the vibrations induced b the gross motion to settle out. As the waiting period increases, the residual structural vibration decreases, however, the throughput also decreases. The two important parameters effecting the vibration caused b the pre-hit phase are the pre-hit velocit and prehit distance. The pre-hit velocit is usuall a small percentage of the maximum velocit used during the approach phase. (The pre-hit velocities used in our experiments was 1% of the maximum velocit.) Increasing the pre-hit velocit would be desirable for throughput, but would lead to larger deflections because the acceleration to pre-hit velocit would last longer. On the other hand, a larger pre-hit distance ields better repeatabilit because vibrations from both the approach phase and the acceleration to pre-hit velocit have a longer period of time to damp out before contact is made with the part. While increasing the pre-hit distance will improve repeatabilit, it will also degrade throughput considerabl because the CMM is moving at a ver low velocit during the pre-hit. Reducing Structural Deflections In order to measure the structural deflections of the CMM, the laser interferometer was used to measure the position of the touch-trigger probe. Then, the position measured b the encoders was subtracted from the laser measurements to obtain the deflection between the encoders and the touch-trigger probe. Figure compares the deflections with the standard CMM controller to the deflections when input shaping is used. The two curves are both from a measurement ccle with a mm approach distance. The curves have been shifted in time so that their pre-hit regions align. The large deflections during the first part of the move are caused b the accelerations during the approach to prehit. The amplitudes of these deflections during the approach are relativel unimportant, however, the amplitudes become important during the pre-hit phase, when the probe contacts the part. If the deflection is not ero when the part is encountered, then the deflection leads to an inaccurac in the measurement, as was demonstrated in Figure. The deflection amplitude in the pre-hit region is decreased b a factor of about when input shaping is used. Repeatabilit Tests Laser interferometers are not practical for evaluating the performance of ever CMM, so the performance of a CMM is generall measured with a repeatabilit test. A Deflection (Laser-Encoder) ( µm). - - Shaped Deflection Unshaped Deflection Pre-Hit Region Time(sec) Figure : Comparison of Deflections During Shaped and Unshaped Measurement Ccles. repeatabilit test is conducted b repeatedl measuring the same part. A standard diagnostic repeatabilit test consists of - measurements of a fixtured part. After each measurement ccle, the probe returns to its starting position. For each of the measurements, the approach distance, pre-hit distance, and pre-hit velocit are kept constant. The minimum measured value is subtracted from the maximum measurement to obtain the repeatabilit of the CMM. Most CMMs have a repeatabilit of just a few microns. The repeatabilit of a CMM depends on several parameters, including the parameters listed above for the measurement ccle. Figure shows the individual measurements of a repeatabilit test using a 1 mm pre-hit distance and a mm approach distance. The repeatabilit for the unshaped measurements is:.7 mm -.7 mm which equals. µm. For the shaped measurements:. mm -. mm gives a repeat of. µm. For this set of measurement parameters input shaping improves repeatabilit b 1. µm. To ensure that the benefit of input shaping is not limited to this particular set of parameters, repeatabilit tests were conducted with several pre-hit and approach distances. Figure 7 shows the repeatabilit as a function of pre-hit distance for measurements with a mm approach distance. Each data point in Figure 7 represents the range of measurements obtained from a point repeatabilit test with the given pre-hit distance and a mm approach distance. In general, repeatabilit improves with increasing pre-hit distance. Figure 7 also demonstrates that input shaping improves repeatabilit over a wide range of pre-hit distances. Figure shows that input shaping also improves repeatabilit when a or 1 mm approach distance is used. Note that as the pre-hit distance increases, the benefit of input shaping over the standard controller decreases. Variable Pre-Hit Distance Repeatabilit Tests In the repeatabilit tests shown in Figures 7 and, the pre-hit distance and approach distance were held constant throughout the measurements. The standard repeatabilit tests are ver valuable for evaluating CMM performance when parts are fixtured in the workspace consistentl and when part geometries do not ver greatl. However, if consistent part fixturing is not used, then prehit distances could var significantl from part to part. To evaluate the CMM performance under adverse fixturing conditions, tests were performed with a pre-hit distance that changed for each measurement in the repeatabilit test. For the first measurement of the repeatabilit test the pre-hit distance was set at 1 mm. During each subsequent measure, the pre-hit distance was increased b.1 mm until the pre-hit distance reached 1.

4 Measured Part Location (mm) Shaped, 1mm Pre-Hit, mm Approach Unshaped, 1mm Pre-Hit, mm Approach Measurement Number. µm. µm Figure : Measurements During a Standard Point Repeatabilit Test. 7 1 Shaped mm Approach Unshaped mm Approach Figure Figure 7: Comparison of Shaped and Unshaped Repeatabilit for Several Pre-Hit Distances. 9 7 Shaped, mm Approach Shaped, 1 mm Approach Shaped, mm Approach Unshaped, mm Approach Unshaped, 1 mm Approach Unshaped, mm Approach Figure : Shaped and Unshaped Repeatabilit with, 1, and mm Approach Distances. mm. Each of the measurements composing this 1 point repeatabilit test are shown in Figure 9 for an approach distance of 1 mm. B subtracting the minimum measurement value from the maximum value we obtain a variable pre-hit distance repeatabilit of. µm with shaping and. µm without shaping. This improvement with input shaping is much larger than the improvement revealed b the standard repeatabilit tests shown in Figures 7 and. The large improvement with shaping is not restricted to an approach distance on 1 mm; Figure shows significant improvement for approach distances ranging from to mm. Furthermore, Figure 11 shows that shaping improves repeatabilit when the variable pre-hit test covers the range of pre-hit distances of 1.-. mm and.-. mm. Figure 11 also shows a clear trend in repeatabilit with input shaping; as approach distance increases, repeatabilit slowl degrades. The repeatabilit without shaping is not onl larger, it is more unpredictable. Variable Approach Distance Repeatabilit Tests In another variation on the standard repeatabilit test, the measurement approach distance can be varied instead of Measured Part Location (mm) Shaped 1 mm Approach Unshaped 1 mm Approach µm. µm Figure 9: Measurements During a Variable Pre-Hit Distance Repeatabilit Test (1 mm Approach). 1 Shaped (1-1. mm Pre-Hit) Unshaped (1-1. mm Pre-Hit) Figure 9 1 Figure : Shaped and Unshaped Variable Pre-Hit Distance Repeatabilit (1-1. mm Pre-Hit Distance). 1 Shaped(1-1.PH) Shaped(1.-PH) Shaped(-.PH) Unshaped(1-1.PH) Unshaped(1.-PH) Unshaped(-.PH) 1 Figure 11: Variable Pre-Hit Distance Repeatabilit for Several Ranges of Pre-Hit Distances. the pre-hit distance. Figure 1 shows the 1 measurements of a repeatabilit test when the approach distance was varied from -1 mm at a step of. mm and the pre-hit distance was held constant at mm. For this variable approach distance repeatabilit test the input shaping improved the repeat from 7. µm to. µm. Figure 1 shows that shaping improves the -1 mm variable approach distance repeatabilit over a range of prehit distances. Figure 1 demonstrates the improvement in repeatabilit also occurs for approach distances varing from -7 mm and from 1-17 mm. Once again, the repeatabilit with input shaping is consistent over a wide range of parameters, while the unshaped measurement repeatabilit is considerabl larger and unpredictable. Conclusions Deflections in the structural components of a coordinate measuring machine introduce error into the measurements because the CMM encoders do not indicate the true position of the part sensor. Input shaping decreases the deflections in a CMM structure during the critical phase when the sensor is brought into contact with the part. The decrease in deflection translates directl into improved

5 Measured Part Location (mm) Shaped mm Pre-Hit Unshaped mm Pre-Hit µm 7. µm Figure 1: Measurements During a Variable Approach Distance Repeatabilit Test ( mm Pre-hit Distance). 1 Shaped, -1 mm Approach Unshaped, -1 mm Approach Figure Figure 1: Comparison of Shaped and Unshaped Variable Approach Distance Repeatabilit (-1 mm Approach Distance). 1 1 Shaped(-7) Shaped(-1) Shaped(1-17) Unshaped(-7) Unshaped(-1) Unshaped(1-17) Figure 1: Variable Approach Distance Repeatabilit for Several Ranges of Approach Distances. measurement repeatabilit as measured b standard diagnostic tests. Non-standard tests designed to evaluate the CMM performance under adverse conditions that might be found in some industrial settings indicate that input shaping improves measurement qualit over a wide range of measurement parameters. Acknowledgments Support for this work was provided b Convolve, Inc. under NSF contract ISI-911 and the Office of Naval Research Fellowship Program. We would like to thank the Management and Engineering staff of Brown & Sharpe whose assistance was invaluable in this project. References [1] Banerjee, A. and W. Singhose, "Slewing and Vibration Control of a Nonlinearl Elastic Shuttle Antenna," AIAA Guidance, Navigation, and Control Conference, Scottsdale, AZ, 199. [] Banerjee, A.K., "Dnamics and Control of the WISP Shuttle-Antennae Sstem," The Journal of Astronautical Sciences, 1(1): p. 7-9, 199. [] Bhat, S.P. and D.K. Miu, "Precise Point-to-Point Positioning Control of Flexible Structures," ASME Journal of Dnamic Sstems, Measurement, and Control, 11(): p. 7-7, 199. [] Drapeau, V. and D. Wang, "Verification of a Closedloop Shaped-input Controller for a Five-bar-linkage Manipulator," IEEE International Conference on Robotics and Automation, Atlanta, GA, Vol., pp. 1-1, 199. [] Hde, J.M. and W.P. Seering, "Inhibiting Multiple Mode Vibration in Controlled Flexible Sstems," Proceedings of the American Control Conference, Boston, MA, [] Jansen, J.F., Control and Analsis of a Single-Link Flexible Beam with Experimental Verification, ORNL/TM-119, Oak Ridge National Laborator, 199. [7] Jones, S.D., Quantification and Reduction of Dnamicall Induced Errors in Coordinate Measuring Machines, Ph.D. Thesis, Universit of Michigan, Ann Arbor, MI, 199. [] Magee, D.P. and W.J. Book, "Filtering Schilling Manipulator Commands to Prevent Flexible Structure Vibration," American Control Conference, Baltimore, MD, 199. [9] Murph, B.R. and I. Watanabe, "Digital Shaping Filters for Reducing Machine Vibration," IEEE Transactions on Robotics and Automation, (April): p. - 9, 199. [] Rappole, B.W., N.C. Singer, and W.P. Seering, "Multiple-Mode Impulse Shaping Sequences for Reducing Residual Vibrations," ASME Mechanisms Conference, Minneapolis, MN, 199. [11] Seth, N., K.S. Rattan, and R.W. Brandstetter, "Vibration Control of a Coordinate Measuring Machine," IEEE Conference on Control Applications, Daton, OH, 199. [1] Singer, N.C. and W.P. Seering, "Preshaping Command Inputs to Reduce Sstem Vibration," ASME Journal of Dnamic Sstems, Measurement, and Control, 11(March): p. 7-, 199. [1] Singhose, W., T. Chuang, and N. Singer, "Reducing Deviations From Trajector Components with Input Shaping," American Control Conference, Seattle, WA, 199. [1] Singhose, W., L. Porter, and N. Singer, "Vibration Reduction Using Multi-Hump Extra-Insensitive Input Shapers," American Control Conference, Seattle, WA, 199. [1] Singhose, W., W. Seering, and N. Singer, "Residual Vibration Reduction Using Vector Diagrams to Generate Shaped Inputs," ASME Journal of Mechanical Design, 11(June): p. -9, 199. [1] Singhose, W. and N. Singer, "Initial Investigations into the Effects of Input Shaping on Trajector Following," American Control Conference, Baltimore, MD, 199. [17] Smith, O.J.M., Feedback Control Sstems. 19, New York: McGraw-Hill Book Compan, Inc. pp. 1-. [1] Tuttle, T.D. and W.P. Seering, "A Zero-Placement Technique for Designing Shaped Inputs to Suppress Multiple-Mode Vibration," American Controls Conference, Baltimore, MD, 199. [19] Zuo, K. and D. Wang, "Closed Loop Shaped-Input Control of a Class of Manipulators with a Single Flexible Link," Proceedings of the IEEE International Conference on Robotics and Automation, Nice, France, Vol. 1, pp. 7-77, 199.