IFToMM95CMM

8/22/2019 IFToMM95CMM

1/5

The Effect of Input Shaping on Coordinate Measuring Machine Repeatability

(Proceedings of the 1995 IFToMM World Congress on the Theory of Machines and Mechanisms)

William E. Singhose and Warren P. SeeringDepartment of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, MA

Neil C. SingerConvolve, Inc.Armonk, NY

Keywords: Vibration, Input Shaping, Measurement

AbstractCoordinate Measuring Machines (CMMs) are a

strategic element in the manufacture of high-precision partsbecause their measurements of part geometries are used forquality control and feedback on the manufacturing process.Proper CMM operation requires accurate knowledge of theposition of the CMM's part sensor. The performance of aCMM is limited by background vibration levels,environmental conditions (temperature changes, cleanlinessof the environment, etc.), accuracy in the measurementequipment (encoders and part sensor), and structuraldeflections between the encoders and the part sensor. Themost important limitation depends on the type of CMM and

the operating conditions; however, structural deflection isalways an important limitation because it introduces anerror in the indicated position of the part sensor.

The effect of input shaping, a method of reducingresidual vibration, on the quality of CMM measurementshas been investigated. Tests were performed that verifiedthe reduction of structural deflections when input shaping isused. Standard diagnostic tests were used to evaluate therepeatability of the CMM. Non-standard tests aimed atevaluating the CMM under adverse conditions were alsoperformed. Input shaping improved measurementrepeatability over a large range of operating parameters.

IntroductionCoordinate Measuring Machines (CMMs) measure

manufactured parts to determine if tolerance specificationshave been achieved. A CMM consists of a workspace inwhich parts are fixtured, a sensor for detecting the partsurfaces, a mechanical assembly for moving the part sensoraround the workspace, and a computer for calculating thepart dimensions based on the sensor measurements. Asketch of a typical CMM is shown in Figure 1.

The CMM sketched in Figure 1 is shown with a touch-trigger probe part sensor This sensor uses a ruby-tippedstylus to sense the part. When the stylus is brought intocontact with a part surface, the deflection of the stylustriggers the computer to record the position indicated by thex, y, and z encoders. By probing the part on critical

surfaces and recording their locations, the criticaldimensions of the part can be calculated.A single cycle of a CMM measurement consists of four

phases. First, the CMM performs a gross motion to movethe part sensor to the vicinity of the part geometry that is tobe measured. Second, the probe is allowed to come to rest.Third, the probe is reaccelerated to a small constantvelocity in the direction of the part. This constant velocityportion of the measurement is called the pre-hit regionbecause it immediately precedes the contact between theprobe and the part. Finally, the stylus contacts the part andthe computer records the location of the contact. Theposition of a touch-trigger probe during a measurementwith a 2 mm pre-hit distance is shown in Figure 2.

xy

z

Touch-TriggerProbe

y Encoder

z Encoder

x Encoder

Figure 1: Sketch of a Typical CMM.

The constant velocity in the pre-hit region is necessaryso that the time delay between actual sensor contact and thecomputer's recognition of the contact can be subtractedfrom the measurements. If a constant velocity approach isnot used, it is difficult to determine how far the probetravels during the signal propagation delay.

If a CMM is to provide valuable quality control, thenits accuracy and repeatability must be greater than the

tolerance specifications for the part. Many CMM designsstrive for accuracies of 8-12 m and repeatabilities of 3-5m. The measurement quality of a CMM is limited bybackground vibration levels, environmental conditions(temperature changes, cleanliness of the environment, etc.),accuracy in the measurement equipment (encoders and partsensor), and structural deflections between the encoders andthe part sensor.

The difficulty of obtaining micron level performancecan be appreciated by examining the probe vibration whenthe CMM is subject to standard environmentaldisturbances. In order to detect the micron level probevibration that is important in CMM measurements, a laserinterferometer with a resolution of 3 nanometers was used

to measure x-direction motions of the probe. Theinterferometer retro-reflector was mounted on the z-axisstructural member in close proximity with the probe.Figure 3 shows the measured vibration when a 180 lb.person with a normal gait walks past the CMM. Virtuallyevery foot strike causes a vibration with an initial amplitudeof 3-4 m even though the machine weighs severalthousand pounds and is stationed on a concrete floor.

The most important limitation on CMM performancedepends on the design of the CMM and the operatingconditions, however, structural deflection between theencoders and touch-trigger probe is always an importantlimitation because it introduces an error in themeasurement.


2/5

1 Approach Phase

2

3Pre-Hit Phase

(Constant Velocity)Stop Before

Pre-Hit

Probe TouchesPart and then

Retracts

Pre-Hit Distance4

0

2

4

6

8

10

1.0 1.2 1.4 1.6 1.8 2.0

Position(mm)

Time (sec)Figure 2: Probe Position During a Measurement.

-4

-2

0

2

4

6

0 2 4 6 8 10 12

X-Axis Encoder Measurement

Laser Measurement of Probe

Position(m)

Time (sec)Figure 3: Probe Vibration Caused by a Person Walking

Past the CMM.

Touch-TriggerProbe

Part

Measured Part Width = L

Encoder GivesPosition ofLeft Face

yEncoder

Encoder GivesPosition ofRight Face

L

CMMStructure

y

z

4(a)

Part

Measured Part Width = L+2

L+2

y

z

4(b)Figure 4: Deflections Cause Measurement Errors.

Figure 4 graphically demonstrates how deflection in aCMM structure can adversely effect measurementaccuracy. In Figure 4a the part width is determined fromtwo measurements. First, the probe is moved into contactwith the left side of the part. At the moment the contact ismade, the position indicated by the encoders is recorded.Next, the probe is moved to the opposite side of the partand brought into contact with the right face. The twoencoder positions are then subtracted to obtain the partdimension. In Figure 4a the part is measured accuratelybecause the encoders indicate the true position of the probe.

In Figure 4b the measurement is inaccurate because thestructural deflections make the encoder readings differ fromthe true location of the contact points. If the structure isvibrating with an amplitude of during the pre-hit region,then the calculated dimension can have an error of2.

Several methods exist for limiting the structuraldeflection of a CMM. First, the acceleration and velocityof the machine can be limited. This solution is effective atreducing deflections, but it causes a decrease in throughputwhich makes it an unattractive solution. Second, themechanical structure can be modified with additionalstiffening members, damping materials, or configurationchanges. This solution involves many of the classic designtradeoffs such as cost versus performance and solutionsmay not apply across a product line containing CMMs ofmany sizes and accuracy levels. Alternatively, thehardware can be left unaltered and the command signalssent to the motors can be shaped so that deflections duringthe measurement phase are decreased[7, 11, 12].

Input shaping is a procedure that eliminates residualvibration by convolving a sequence of impulses with thedesired command signal. The result of the convolution isthen used to command the system. The impulse sequenceused to shape the input is derived by solving a set ofconstraint equations which limit the residual vibration ofthe system. Input shaping requires that the residualvibration remain at a low level even in the presence of

modeling errors. Several papers give detailed explanationsof input shaping[3, 5, 7-10, 12, 15, 18, 19].

Methods for increasing the robustness of input shapingto modeling errors have been developed[14, 15]. Inputshaping reduced residual vibration and maximumdeflections during the slewing of a large nonlinear space-

based antenna[1, 2]. Two-mode input shapers were used toincrease the throughput of a silicon wafer handlingrobot[10]. Input shaping was shown to be beneficial forlong-reach manipulators[6, 8] and trajectory followingapplications[4, 13, 16].

This paper will investigate the effect of input shapingon the accuracy and repeatability of CMM measurements.The operation of a CMM is not the typical point-to-pointapplication 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 occurswith some uncertainty because there is no way to know apriori where the part is located or how much the structurewill be deflected at the time of contact.

The remainder of this paper is organized as follows.First, important parameters of a CMM measurement cycleare discussed. Experimental results showing the effect ofinput shaping on the structural deflections during themeasurement will then be presented. The effect of inputshaping on the measurement quality will be demonstratedwith the use of repeatability studies. Finally, conclusionswill be drawn from the experimental results.

Important Parameters of the Measurement CycleThere are several important parameters that determine

the vibration during the critical pre-hit region. During theapproach to pre-hit, the acceleration and approach distanceare significant parameters. As the acceleration is increased,


3/5

-60

-40

-20

0.0

20

40

60

0.40 0.60 0.80 1.00 1.20

Shaped Deflection

Unshaped Deflection

Deflection(Laser-Encoder)(m)

Time(sec)

Pre-Hit Region

Figure 5: Comparison of Deflections During Shapedand Unshaped Measurement Cycles.

the deflections during the approach phase become largerand the residual vibrations from these deflections in thepre-hit region increases. For short approaches, thedeflection during the approach is smaller than for longapproaches and, therefore, contributes less to the vibrationduring the pre-hit region. Certain approach distances leadto a natural cancellation of the approach phase vibration,i.e., the vibration induced by the acceleration is canceled bythe vibration from the deceleration of the approach. Thiscancellation can be thought of as a naturally occurringposicast control[17]. It is difficult to utilize this naturalcancellation on a consistent basis because its effectivenessis a strong function of approach distance, maximumacceleration, maximum velocity, probe location, andknowledge of the system dynamics.

The period of time that is spent waiting between theapproach phase and the pre-hit phase is also an importantparameter because it allows the vibrations induced by thegross motion to settle out. As the waiting period increases,the residual structural vibration decreases, however, thethroughput also decreases.

The two important parameters effecting the vibrationcaused by the pre-hit phase are the pre-hit velocity and pre-hit distance. The pre-hit velocity is usually a smallpercentage of the maximum velocity used during theapproach phase. (The pre-hit velocities used in ourexperiments was 1% of the maximum velocity.) Increasingthe pre-hit velocity would be desirable for throughput, butwould lead to larger deflections because the acceleration topre-hit velocity would last longer. On the other hand, alarger pre-hit distance yields better repeatability becausevibrations from both the approach phase and theacceleration to pre-hit velocity have a longer period of timeto damp out before contact is made with the part. Whileincreasing the pre-hit distance will improve repeatability, itwill also degrade throughput considerably because theCMM is moving at a very low velocity during the pre-hit.

Reducing Structural DeflectionsIn order to measure the structural deflections of theCMM, the laser interferometer was used to measure theposition of the touch-trigger probe. Then, the positionmeasured by the encoders was subtracted from the lasermeasurements to obtain the deflection between theencoders and the touch-trigger probe.

Figure 5 compares the deflections with the standardCMM controller to the deflections when input shaping isused. The two curves are both from a measurement cyclewith a 25 mm approach distance. The curves have beenshifted in time so that their pre-hit regions align.

The large deflections during the first part of the moveare caused by the accelerations during the approach to pre-

hit. The amplitudes of these deflections during theapproach are relatively unimportant, however, theamplitudes become important during the pre-hit phase,when the probe contacts the part. If the deflection is notzero when the part is encountered, then the deflection leadsto an inaccuracy in the measurement, as was demonstratedin Figure 4. The deflection amplitude in the pre-hit regionis decreased by a factor of about 3 when input shaping isused.

Repeatability TestsLaser interferometers are not practical for evaluating

the performance of every CMM, so the performance of aCMM is generally measured with a repeatability test. A

repeatability test is conducted by repeatedly measuring thesame part. A standard diagnostic repeatability test consistsof 10-50 measurements of a fixtured part. After eachmeasurement cycle, the probe returns to its startingposition. For each of the measurements, the approachdistance, pre-hit distance, and pre-hit velocity are keptconstant. The minimum measured value is subtracted fromthe maximum measurement to obtain the repeatability ofthe CMM. Most CMMs have a repeatability of just a fewmicrons.

The repeatability of a CMM depends on severalparameters, including the parameters listed above for themeasurement cycle. Figure 6 shows the 50 individualmeasurements of a repeatability test using a 1 mm pre-hitdistance and a 20 mm approach distance. The repeatabilityfor the unshaped measurements is: 625.2735 mm -625.2687 mm which equals 4.8 m. For the shapedmeasurements: 625.2683 mm - 625.2650 mm gives a repeatof 3.3 m. For this set of measurement parameters inputshaping improves repeatability by 1.5 m.

To ensure that the benefit of input shaping is notlimited to this particular set of parameters, repeatabilitytests were conducted with several pre-hit and approachdistances. Figure 7 shows the repeatability as a function of

pre-hit distance for measurements with a 20 mm approachdistance. Each data point in Figure 7 represents the rangeof measurements obtained from a 50 point repeatability testwith the given pre-hit distance and a 20 mm approachdistance. In general, repeatability improves with increasingpre-hit distance. Figure 7 also demonstrates that inputshaping improves repeatability over a wide range of pre-hitdistances. Figure 8 shows that input shaping also improvesrepeatability when a 10 or 15 mm approach distance isused. Note that as the pre-hit distance increases, the benefitof input shaping over the standard controller decreases.

Variable Pre-Hit Distance Repeatability TestsIn the repeatability tests shown in Figures 7 and 8, the

pre-hit distance and approach distance were held constantthroughout the 50 measurements. The standardrepeatability tests are very valuable for evaluating CMMperformance when parts are fixtured in the workspaceconsistently and when part geometries do not very greatly.However, if consistent part fixturing is not used, then pre-hit distances could vary significantly from part to part.

To evaluate the CMM performance under adversefixturing conditions, tests were performed with a pre-hitdistance that changed for each measurement in therepeatability test. For the first measurement of therepeatability test the pre-hit distance was set at 1 mm.During each subsequent measure, the pre-hit distance wasincreased by 0.01 mm until the pre-hit distance reached 1.5


4/5

625.264

625.266

625.268

625.270

625.272

625.274

625.276

0.00 10.0 20.0 30.0 40.0 50.0

Shaped, 1mm Pre-Hit, 20 mm Approach

Unshaped, 1mm Pre-Hit, 20 mm Approach

MeasuredPartLocation(mm)

Measurement Number

4.8 m

3.3 m

Figure 6: Measurements During a Standard 50 PointRepeatability Test.

0

1

2

3

4

5

6

7

8

1 1.5 2 2.5 3

Shaped 20mm Approach

Unshaped 20mm Approach

Repeatability

(m)

Pre-Hit Distance (mm)

Data fromFigure 6

Figure 7: Comparison of Shaped and UnshapedRepeatability for Several Pre-Hit Distances.

2

3

4

5

6

7

8

9

10

1.0 1.5 2.0 2.5 3.0

Shaped, 10 mm ApproachShaped, 15 mm ApproachShaped, 20 mm ApproachUnshaped, 10 mm ApproachUnshaped, 15 mm ApproachUnshaped, 20 mm Approach

Repeatability(m)


Figure 8: Shaped and Unshaped Repeatability with 10,15, and 20 mm Approach Distances.

625.255

625.260

625.265

625.270

625.275

625.280

625.285

1.00 1.10 1.20 1.30 1.40 1.50

Shaped 15 mm Approach

Unshaped 15 mm Approach



10.4 m

4.2 m

Figure 9: Measurements During a Variable Pre-HitDistance Repeatability Test (15 mm Approach).

0

5

10

15

20

25

5 10 15 20

Shaped (1-1.5 mm Pre-Hit)

Unshaped (1-1.5 mm Pre-Hit)

Repeatability(m)

Approach Distance (mm)

Data fromFigure 9

Figure 10: Shaped and Unshaped Variable Pre-HitDistance Repeatability (1-1.5 mm Pre-Hit Distance).

0

5

10

15

20

25

5 10 15 20

Shaped(1-1.5PH)

Shaped(1.5-2PH)

Shaped(2-2.5PH)

Unshaped(1-1.5PH)

Unshaped(1.5-2PH)

Unshaped(2-2.5PH)

Repeatability(m)


Figure 11: Variable Pre-Hit Distance Repeatability forSeveral Ranges of Pre-Hit Distances.

mm. Each of the measurements composing this 51 pointrepeatability test are shown in Figure 9 for an approachdistance of 15 mm. By subtracting the minimummeasurement value from the maximum value we obtain avariable pre-hit distance repeatability of 4.2 m withshaping and 10.4 m without shaping. This improvementwith input shaping is much larger than the improvementrevealed by the standard repeatability tests shown inFigures 7 and 8.

The large improvement with shaping is not restricted toan approach distance on 15 mm; Figure 10 showssignificant improvement for approach distances rangingfrom 5 to 20 mm. Furthermore, Figure 11 shows thatshaping improves repeatability when the variable pre-hittest covers the range of pre-hit distances of 1.5-2.0 mm and2.0-2.5 mm. Figure 11 also shows a clear trend inrepeatability with input shaping; as approach distanceincreases, repeatability slowly degrades. The repeatabilitywithout shaping is not only larger, it is more unpredictable.

Variable Approach Distance Repeatability TestsIn another variation on the standard repeatability test,

the measurement approach distance can be varied instead of

the pre-hit distance. Figure 12 shows the 51 measurementsof a repeatability test when the approach distance wasvaried from 10-12 mm at a step of 0.04 mm and the pre-hitdistance was held constant at 2 mm. For this variableapproach distance repeatability test the input shapingimproved the repeat from 7.2 m to 3.5 m.

Figure 13 shows that shaping improves the 10-12 mmvariable approach distance repeatability over a range of pre-hit distances. Figure 14 demonstrates the improvement in

repeatability also occurs for approach distances varyingfrom 5-7 mm and from 15-17 mm. Once again, therepeatability with input shaping is consistent over a widerange of parameters, while the unshaped measurementrepeatability is considerably larger and unpredictable.

ConclusionsDeflections in the structural components of a

coordinate measuring machine introduce error into themeasurements because the CMM encoders do not indicatethe true position of the part sensor. Input shaping decreasesthe deflections in a CMM structure during the critical phasewhen the sensor is brought into contact with the part. Thedecrease in deflection translates directly into improved


5/5

625.272

625.277

625.282

625.287

625.292

10.0 10.5 11.0 11.5 12.0

Shaped 2 mm Pre-Hit

Unshaped 2 mm Pre-Hit



3.5 m

7.2 m

Figure 12: Measurements During a Variable ApproachDistance Repeatability Test (2 mm Pre-hit Distance).

0

5

10

15

1.0 1.2 1.4 1.6 1.8 2.0

Shaped, 10-12 mm Approach

Unshaped, 10-12 mm Approach

Repeatability(m)


Data fromFigure 12

Figure 13: Comparison of Shaped and UnshapedVariable Approach Distance Repeatability (10-12 mm

Approach Distance).

2

4

6

8

10

12

14

1.0 1.2 1.4 1.6 1.8 2.0

Shaped(5-7)Shaped(10-12)Shaped(15-17)

Unshaped(5-7)Unshaped(10-12)Unshaped(15-17)

Repeatability(m)


Figure 14: Variable Approach Distance Repeatabilityfor Several Ranges of Approach Distances.

measurement repeatability as measured by standarddiagnostic tests. Non-standard tests designed to evaluatethe CMM performance under adverse conditions that mightbe found in some industrial settings indicate that inputshaping improves measurement quality over a wide rangeof measurement parameters.

AcknowledgmentsSupport for this work was provided by Convolve, Inc.

under NSF contract ISI-9101441 and the Office of Naval

Research Fellowship Program.We would like to thank the Management and

Engineering staff of Brown & Sharpe whose assistance wasinvaluable in this project.

References[1] Banerjee, A. and W. Singhose, "Slewing andVibration Control of a Nonlinearly Elastic ShuttleAntenna," AIAA Guidance, Navigation, and ControlConference, Scottsdale, AZ, 1994.[2] Banerjee, A.K., "Dynamics and Control of the WISPShuttle-Antennae System," The Journal of AstronauticalSciences, 41(1): p. 73-90, 1993.

[3] Bhat, S.P. and D.K. Miu, "Precise Point-to-PointPositioning Control of Flexible Structures," ASME Journalof Dynamic Systems, Measurement, and Control, 112(4): p.667-674, 1990.[4] Drapeau, V. and D. Wang, "Verification of a Closed-loop Shaped-input Controller for a Five-bar-linkageManipulator," IEEE International Conference on Roboticsand Automation, Atlanta, GA, Vol. 3, pp. 216-221, 1993.[5] Hyde, J.M. and W.P. Seering, "Inhibiting MultipleMode Vibration in Controlled Flexible Systems,"Proceedings of the American Control Conference, Boston,MA, 1991.[6] Jansen, J.F., Control and Analysis of a Single-LinkFlexible Beam with Experimental Verification,ORNL/TM-12198, Oak Ridge National Laboratory, 1992.[7] Jones, S.D., Quantification and Reduction ofDynamically Induced Errors in Coordinate MeasuringMachines, Ph.D. Thesis, University of Michigan, AnnArbor, MI, 1993.[8] Magee, D.P. and W.J. Book, "Filtering SchillingManipulator Commands to Prevent Flexible StructureVibration,"American Control Conference, Baltimore, MD,1994.[9] Murphy, B.R. and I. Watanabe, "Digital ShapingFilters for Reducing Machine Vibration," IEEETransactions on Robotics and Automation, 8(April): p. 285-289, 1992.[10] Rappole, B.W., N.C. Singer, and W.P. Seering,"Multiple-Mode Impulse Shaping Sequences for ReducingResidual Vibrations," ASME Mechanisms Conference,Minneapolis, MN, 1994.[11] Seth, N., K.S. Rattan, and R.W. Brandstetter,"Vibration Control of a Coordinate Measuring Machine,"IEEE Conference on Control Applications, Dayton, OH,1993.[12] Singer, N.C. and W.P. Seering, "PreshapingCommand Inputs to Reduce System Vibration," ASMEJournal of Dynamic Systems, Measurement, and Control,

112(March): p. 76-82, 1990.[13] Singhose, W., T. Chuang, and N. Singer, "ReducingDeviations From Trajectory Components with InputShaping," American Control Conference, Seattle, WA,1995.[14] Singhose, W., L. Porter, and N. Singer, "VibrationReduction Using Multi-Hump Extra-Insensitive InputShapers," American Control Conference, Seattle, WA,1995.[15] Singhose, W., W. Seering, and N. Singer, "ResidualVibration Reduction Using Vector Diagrams to GenerateShaped Inputs," ASME Journal of Mechanical Design,116(June): p. 654-659, 1994.[16] Singhose, W. and N. Singer, "Initial Investigations

into the Effects of Input Shaping on Trajectory Following,"American Control Conference, Baltimore, MD, 1994.[17] Smith, O.J.M., Feedback Control Systems. 1958, NewYork: McGraw-Hill Book Company, Inc. pp. 331-345.[18] Tuttle, T.D. and W.P. Seering, "A Zero-PlacementTechnique for Designing Shaped Inputs to SuppressMultiple-Mode Vibration,"American Controls Conference,Baltimore, MD, 1994.[19] Zuo, K. and D. Wang, "Closed Loop Shaped-InputControl of a Class of Manipulators with a Single FlexibleLink," Proceedings of the IEEE International Conferenceon Robotics and Automation, Nice, France, Vol. 1, pp. 782-787, 1992.

Documents

IFToMM95CMM