Characterisation of 3-d Cartesian co-ordinate laser ... · laser interferometer tracking system W....

Characterisation of 3-d Cartesian co-ordinate

laser interferometer tracking system

W. Nerdnoi, X. Liu, S. Harb*Manufacturing Division, School of Engineering, Coventry University,

Email: wner•[email protected], [email protected]

Abstract

Calibration is an important process to assess and maintain the accuracy ofmachine tools. Most acceptance tests are based on static measurement cycleswhich are time consuming and laborious. With the development of laser trackingsystems (LTS) it is possible to calibrate a machine tool both statically anddynamically. This paper presents a simple approach to construct a 3-D lasertracking system based on Cartesian co-ordinates. This system employs a laserinterferometer for displacement measurement as well as a reference datum toperform the automatic tracking of a moving object, a Co-ordinate MeasuringMachine (CMM) as the tracking mechanism and an analogue PID controller tocontrol the tracking system. The prototype system has been constructed,assembled and tested. Results presented here are on the characterisation of thewhole system, including the static and dynamic tests of the tracking mechanism,the CMM. System models have been obtained by using identification techniqueand the simulated results are verified by the experiments.

1. Introduction

The accuracy of a machine tool determines the quality of products produced andalso the ability for economic productivity. A machine can be operated to meetthe designed accuracy only under the specified working conditions. However, inthe real world it is often difficult to achieve the desired accuracy due to thecomplexity and interactions of various factors involved. Error sources in themachining process are greatly influenced by the mechanical and thermal loadinggenerated from the cutting process and the operation conditions. These errorsources may be divided into two categories as:

• Quasistatic errors, which are defined as the 'errors of relative positionbetween a tool and a work-piece and these errors are varying slowly intime and are related to the structure of machine tool itself. These errorsources include the geometric/kinematics errors of the machine, the errorsdue to static and slowly varying forces such as the dead weight of the

' Now working at KLA Tencor, European Headquarters, Rosa, 19 Mulberry Business Park,Fishponds Rd, Wokingham, Berkshire RG41 2GY, UK

Transactions on Engineering Sciences vol 23, © 1999 WIT Press, www.witpress.com, ISSN 1743-3533

24 Laser Metrology and Machine Performance

machine's components and over-constrained slides and those due tothermally induced strains in the machine tool structure.

• Dynamic errors are caused by sources such as the spindle error motion,self-induced and forced vibrations of the machine structure, controllererrors and deflections under inertial forces.

The quasistatic errors, which are related to the geometric and kinematicsvariations of the machine tool, vary slowly with time and dominate nearly 70%of total errors of numerically controlled machine tools*. Among the machineerror sources, stationary geometric errors and thermally induced errors ofmachine linkages are known to be key contributors.

The calibration techniques guided by the standards [BS3800, Part2 (1991): ISO230-2, Part 2 (1988)] use static measurement cycles. In general, a machine axisis moved to the target position and measurements are recorded. Errors areestimated by a generalised geometric error model. For a 3-axis machine tool,there are 21 error components from the geometric error model, consisting of sixerror components along each axis and three squareness errors. The model ofmovement errors (translation errors and rotation errors) of each axis, andsquareness errors between each two axes are derived by using the homogeneoustransformation metrics based on the assumption of small angle approximation.Most of the error components can be measured using a laser interferometersystem except for ROLL errors.

The static measurement technique offers good results for compensation but it isobviously very time-consuming and labour intensive. For the last few decades,many efforts have been made to improve the calibration efficiency by errormodelling techniques to identify error parameters with a minimum number ofmeasurements. The positions of a standard artefact are measured to comparewith the nominal positions of machine tool and then error parameters aredetermined from a set of model equations. Ferreira et al/' •* introduced thequadratic model for the geometric error of machine tools. They further extendedthe model, generalised the concepts to Nth order of quasistatic error model andverified the first order model on a three-axis CNC machining centre, seereferences of Kiridena et al/' *• *. Recent advances in the laser interferometertechnology used for machine calibration allow data to be captured dynamically.Dynamic calibration overcomes the inherent problems of static calibration, beingquick to perform and providing detailed information on the machineperformance. Dynamic machine calibration on one axis movement has beenreported by Postlethwaite et al/

Laser tracking technology has been developed in recent years and has alreadyhad an impact on robot calibrations. There are three types of laser trackingsystems which are based upon three metrological principles, triangulation, multi-lateration and spherical co-ordinate. All systems in common have a trackingmechanism to lock a laser beam onto a moving retro-reflective target. Then theposition of the robot is calibrated by either known linear scales or a laser


Laser Metrology and Machine Performance 25

interferometer or the combination of the two. Gilby and Parker in 1982described the principle of a laser tracking triangulation system in which twoidentical tracking heads follow a common target attached to a robot. Each headhas two distinct mirrors mounted on two orthogonal rotation axes. The positionsof the mirrors are servo-controlled to maintain the retro-reflected laser beamaimed at the centre of the target. The knowledge of the mirror angles andtracking offsets allows the determination of one line of sight. Combining twolines of sight, one from each head, with the knowledge of the relative locationbetween the heads provides a means to calculate the position of the target bytriangulation. With this method there is no laser interferometer involved andMayer and Parker* reported an application of such a system. The multi-lateration method, on the other hand, defines a 3-D position of a robot by theintersection of three or more surfaces such as spheres. It usually requires morethan one interferometer system to measure the position. Greenleaf used foursingle mirror laser tracking interferometers and a common cat's eye target toprovide pm accuracy. Lau et al. reported a LITS where a laser interferometer isaccurately pointed, by means of a two-angle servo-system, to a reflector attachedto the robot's wrist. The measurement of the length of the laser beam and the twoangles of the positioning device gives the position of the retro-reflector inspherical co-ordinates. Shirinzadeh recently reported a laser-interferometer-based tracking system to follow a retro-reflector target in spherical co-ordinate.In this system, a CCD camera is employed to capture the return-beam fordynamic measurements.

All laser tracking systems offer a continuous measurement in a large volume.Systems based on interferometer techniques are sensitive to the loss of tracking.With the spherical co-ordinate systems, the measuring process has to be reset ifthe tracking beam is interrupted/blocked accidentally. This involved that thetarget has to be moved back to the pre-calibration position to repeatmeasurements. And the accuracy of this pre-calibration will affect greatly theaccuracy of later measurements. This is not the case with the triangulationmethod where absolute readings can be taken as soon as tracking is restored. Butthose systems generally require more than one laser stations which are moredifficult to manipulate and control. Both the triangulation and spherical approachhave the ultimate precision based on their angular measurement systems.

In an attempt to overcome the necessity for the pre-calibration process, a laserinterferometer tracking system based on Cartesian co-ordinates has beendeveloped. The origin of the co-ordinate system can be set anywhere convenientfor the working volume of the measuring system. The linear axes of the trackingmechanism provide a good datum to align the laser beam and thus facilitate theease of integration/removing. Moreover, the tracking mechanism offset and thebeam misalignment are static errors which can be compensated via calibration.These benefits however, are at the expense of the measuring volume andpossibly the dynamic performance. Tracking in Cartesian co-ordinates has thelowest ratio of measuring volume to size in comparison with other systems. The



measuring envelope is limited by the active size of the X-Y stage, which has tobe optimised among the accuracy, dynamic response and portability of thesystem. However, these factors tend to favour small and compact size systems,which are more attractive to the machine tool calibration in shop-floor situations.

2. Cartesian Co-ordinate 3-D Laser Tracking System

As shown in Fig.l, the system consists of a laser interferometer (HP5528A) fordimension measurement, a co-ordinate-measuring machine (CMM) as a trackingmechanism for X-Z movement, a servo-controller and a host computer. Detailsof the system configuration are given in Fig.2. The LIS measures theaccumulated distance of a target and the movement of the tracking system. Atwo-axis position sensor, the four-quadrant-detector (4QD), monitors themovement of target. And an analogue PID controller controls the trackingmechanism, the CMM (KemcoSOO), to follow the target. The target movementwill cause the laser beam to move, as shown in Fig.2 by arrows at the returnbeam. If the target moves in positive direction of X-axis, the laser spot on the4QD will be shifted to negative direction of x-axis and the servo-loop controlwill move the CMM in positive direction of X-axis to follow the target. Thedirection of the laser spot movement due to the target movement is summarisedin Table 1. The host computer controls the system operation and reads theposition of tracking mechanism and accumulated distance from LIS. The targetposition is measured in space by using two 45°-mirrors (Ml and M2) which areused to reflect the measuring laser beam along the three axes (X, Y and Z) ofCartesian co-ordinate system. Each mirror can be moved along one linear axis,the co-ordinate of target is determined from the position of these two mirrors andthe accumulated distance. The X and Z positions of the target are the X and Zpositions of mirrors and the Y position of the target is determined by theaccumulated distance minus X and Z positions. Because the measuring beamtravels along X, Y and Z-axes, the dead-path of LIS is the accumulated dead-paths of the 45°-mirror movement in X and Z-axes, which are 150 mm and50mm respectively. The LTS monitors the return beam by using a four-quadrant-detector (4QD). When the target moves, two movement signals from 4QD areused to control two 45°-mirrors to follow the target. Since the tracking system isa part of LIS, which is in Cartesians co-ordinate configuration, this system iscalled 'Cartesian 3D Laser Interferometer Tacking System' (Cartesian 3D-LITS).With this configuration, there is no need for the pre-calibration process and anypoint in the measuring space can be reset to act as the reference point, which isthe same as three-axis CNC machines.

3. Characterisation of tracking system

A moving bridge type of CMM is used as the tracking mechanism in thisproposed 3-D LITS. It has a base table of 450x560 mm and three movingcarriages supported by air bearings. Each axis is driven by a DC motor with atime belt mechanism and a tachometer. The Y-axis of CMM is disabled byclamping the outer-leg of the bridge. The performance of the CMM affects



directly the tractability of the system. The static behaviour of a CMM can befound by calibration and are generally given in its specifications. However, thedynamic characteristic of CMM is usually not known. Here we report anapproach to test the dynamic behaviour of the CMM used for this 3-D LITS.

3.1. Frequency response

The frequency response of the CMM is obtained by applying a driving signal toeach arm and measuring the corresponding movement. In the experiments, arandom signal was selected with a frequency range from 2 to 200 Hz. Theresponse of the CMM was monitored by a piezoelectric accelerometer (type4370). A spectrum analyser (AD3225) was used to analyse frequency responseand results are shown in Figs. 3.1 and 3.2. The results show that the naturalfrequency of X-axis is some where between 8 and 9 Hz. For Z-axis, the phaseresponse graph shows a high damping effect, as the slope of this curve is small.From the magnitude plot it is difficult to tell the resonant frequency. Looking atthe phase plot, the approximate frequency at a phase shift from +90° to -90° isabout 40 Hz.

3.2. System modelling

System identification technique based on experiments has been applied to modelthe tracking and control units. As shown in Fig. 4, a stimulating signal is fed intothe input of a system and the response signal of the system is observed. Bothsignals are recorded at the same time. By establishing a transfer function to eachunit, the relationship between input and output of the system can be formed. Thetesting results from the system were then modelled by an ARX-model in MatlabSystem-Identification-Toolbox. The driving mechanism consists of a poweramplifier and a moving carriage. The transfer function is modelled by two parts:one from the power amplifier to the tachometer of the driving motor, and anotherfrom the tachometer to the carriage position. The position of the carriage ismeasured by a long range linear variable differential transformer (LVDT). Figs.5.1 and 5.2 show the detailed transfer functions of the X-axis and Z-axis controlloops. The modelled system was then constructed in Matlab/Simulink and asinusoidal signal with a frequency of 0.5, 1, 2 and 5 Hz was applied,respectively. The same signal was applied to the real system and the responsefrom the 4QD was monitored. The simulated output was then compared with theexperiment result. Figs. 6 and 7 show the comparison results between thesimulations and experiments for X and Z axes at the frequency of 0.5, 1, 2, and 5Hz. The input driving signal is the small amplitude sinusoidal signal, theexperiment response is in solid line and the simulation response is in dashed line.Both axes can follow the input at a lower frequency up to 1 Hz and then show aphase delay at higher frequencies. At the lowest frequency, 0.5 Hz, thesimulation result is close to the experiment in amplitude but there is a slightphase shift. The experiment curve is not very smooth, which might be caused bythe inertia in the sliding system because both carriages are quite heavy. At ahigher frequency, the phase shift between experiment and simulation is small,



but there is a large difference in amplitude, especially in Z-axis. The reason forthis is possibly due to the fact that the Z-carriage has a pneumatic cylinder. Theforce for moving this cylinder has a non-linear characteristic, which iscomplicated to model. Therefore, it causes a larger difference betweenexperiment and simulation in Z-axis. The structures of moving carriages arecomplex, some higher frequencies may activate the vibration of sub-structure inthe carriage and this will affect the response of the system. Thus the experimentdata were pre-treated by a low-pass filter with a cut-off frequency of 10 Hzbefore the modelling. Thus the transfer function obtained is only close to the realsystem in a certain bandwidth. In general, the Z-axis has a wider dynamic rangethan the X-axis because of different resonance (9 Hz for X-axis and 40 Hz for Z-axis). However, due to the complexity in Z-axis, it is not recommended to drivethe both axes at a frequency higher than 5 Hz.

3.3. Tuning PID ControllerThe method of Quarter-Decay-Response (QDR) is used to tune the PIDcontroller. The system control loops for X and Z axes as shown in Fig. 5 weresimulated in Matlab/Simulink. The response output at 4QD was monitored whilethe PID parameter was adjusted until the amplitude of the response signal wasequal to a quarter of the previous cycle. By doing this, the optimum parametersof PID were obtained. As mentioned early, the system transfer function is onlysimplified version of the real system, hence the PID parameters obtained need tobe tuned in real time. The parameters were then set into the real system and astep response was carried out to test the system. In this particular trackingsystem, the step input was given by a disturbance by moving the X or Z carriageto a certain position. The was done by moving the target to a position where theoutput of 4QD is about 3 V which is equivalent to 0.3 mm, then switching on thePID control and monitoring the variation of the 4QD signal. The results of suchstep responses of X and Z-axes are shown in Fig. 7. The step was given from twodirections; positive step and negative step. The horizontal axis is shown insample number, which can be converted into time by multiplying the samplingtime interval of 7.8 ms.

3.4. Stability of Tracking System

Long term stability of the system is important for applications in calibratingmachine tools and robots. To minimise the effect of vibration on the trackingsystem, the target retro-reflector is fixed on the CMM table. When the controlleris switched on, the positions of X-axis, Z-axis, the accumulated distance of LISand the output of 4QD are measured. The stability test was run for six hours.Over this period, 1000 data-points were collected by the host computer whereeach data point was an average of 80 readings sampled in 21 seconds. The resultsof position stability show that during the first hour there is a high drift in theposition control, seen in Fig. 8. Generally it is higher in Z-axis than X-axis. Thismay be due to the fact that more parts attached to the Z-axis, which requires alonger time to reach the thermal equilibrium. The drift on the LIS is probably



caused by the housing of the 4QD. This warm-up period sometimes can be lessthan one hour There are nine stability tests carried out over a month and eachone was under slight different parameters of the PID-controller. It is noted thatthe position control is depended on the variation of 4QD signal, which directlyaffected by the characteristic of the tracking mechanism and the performance ofPID controller. In general, an average of standard deviation in position controlbetter than 10 um can be obtained with the existing system.

All the experiments have been performed in a temperature and humiditycontrolled metrology laboratory, normally at 20 ± 1°C and 40 ± 5% RH.

4. Conclusions

A 3-D Cartesian co-ordinate laser interferometer tracking system has beendesigned and built. It consists of a laser interferometer for displacementmeasurement as well as a reference datum to perform the automatic tracking of amoving object, a Co-ordinate Measuring Machine as a tracking mechanism andan analogue PID controller to control the tracking system. The performance ofthe prototype system has been tested and characterised. System identificationtechniques have been used to model the system transfer function. The model thusobtained can be used to predict the response of tracking system and tune the PIDparameters. The system can track a target in space with ease of measurement andset-up of the origin of co-ordinates. No pre-calibration is needed. Potentially itcan be use to calibrate a machine tool or a robot both statically and dynamically.The use of CMM as the tracking mechanism gives linear scales and a largeworking volume but the tracking speed is limited due to the low resonance in themoving parts of CMM. This problem causes an oscillation in the tracking systemand generates noise in measuring system. The tracking system can be improvedby using a compact two-axis stage for dynamic performance but at the cost ofworking volume. The stability of the system has been tested over a long timeperiod, and the repeatability is better than 10 jam. To reduce the drift effect, awarming up period of one hour is recommended before any measurement istaken and the environment temperature should be controlled.

References

[1] J. Kaczmarex. 'Principle of Machining by Cutting, Abrasion andErosion', Peregrinus, Hitchin, Herts, 1976.

[2] P.M. Ferreira and C.R. Liu, 'An Analytical Quadratic Model for theGeometric Error of a Machine Tool', J. Manuf. Systems, Vol. 5, No. 1,1986, pp. 51-62.

[3] P.M. Ferreira and C.R. Liu, A Contribution to the Analysis andCompensation of the Geometric Error of a Machining Centre', Annalsof the CIRP, Vol. 35/1, 1986, pp. 259-262.



[4] V.S.B. Kiridena and P.M. Ferreira, 'Kinematic Modelling of QuasistaticErrors of Three-axis Machining Centres', Int. J. Mach. Tools Manuf,Vol. 34, No. 1, 1994, pp. 85-100.

[5] V.S.B. Kiridena and P.M. Ferreira, 'Parameter Estimation andModelling Verification of first Order Quasistatic Errors Model forThree-axis Machining Centres', Int. J. Mach. Tools Manuf., Vol. 34,No. 1,1994, pp. 101-125.

[6] V.S.B. Kiridena and P.M. Ferreira, 'Computational Approaches toCompensating Quasistatic Errors of Three-axis Machining Centres', Int.J. Mach. Tools Manuf., Vol. 34, No. 1, 1994, pp. 127-145.

[7] S.R. Postlethwaite, D.G. Ford and D. Morton, 'Dynamic Calibration ofCNC Machine Tools', Int. J. Mach. Tools Manufact, Vol. 37, No. 3,1997, pp. 287-294.

[8] J.H. Gilby and G.A. Parker, 'Laser Tracking System to Measure RobotArm Performance', Sensor Rev., Oct. 1982, pp. 180-184.

[9] R. Mayer and G.A. Parker, 'A Portable instrument for 3-D DynamicRobot measurements Using Triangulation and Laser tracking', IEEETransactions on Robots and Automation, Vol. 10, No. 4, Aug. 1994, pp.504-516.

[10] H. Greenleaf, 'Self-calibrating Surface Measuring Machine', Adv.Technology Telescopes: SPIE, Vol. 332, 1982, pp. 327-334.

[11] K. Lau, R. Hocken and W. Haight, 'Automatic Laser TrackingInterferometer System for Robot Metrology', Precision Eng., Vol.8,No. 1, Jan. 1986, pp. 3-8.

[12] B. Shirinzadeh, 'Laser-interferometry-based Tracking for Dynamicmeasurements', Industrial Robot, Vol. 25, No. 1, 1998, pp. 35-41.

Table 1. Summary of laser spot movement direction

TargetMovement

+X-X+z-z+Y-Y

Laser SpotMovement on 4QD

-X+x+Y-YNoNo

CMMMovement

+X-X+z-zNoNo



Fig. 1 Configuration of 3D-LITS

Fig. 2 Optical layout of 3D-LITS



Power Spectrum0

Fig. 3.1 Frequency response of X-axis

Power Spectrum0-!

—A#Cl-30f

-7Cr\1

Phase Response

=K$

100 200Hz

Fig. 3.2 Frequency response of Z-axis


Laser Metrology and Machine Performance

OutputInput

33

FtcTCoritrol

Fig. 4 Set-up experiment for System Identification

Driving Syritm

Power Amp «> Tachometer. Tachometer =>LVDT

Fig. 5.1 Closed-loop diagram for X-axis system

Fig. 5.2 Closed-loop diagram for Z-axis system



1O 4QD voltage (V)

-5

-10 Data No2OO 4OO 6OO 8OO 1OOO

(a) 0.5 Hz

4QD voltage (V)

Data No2OO 4OO GOO 8OO 1OOO 12OO

(b) 1 Hz

4QD voltage (V)

Data No

(c) 2 Hz4OO 500

-10

4QD voltage (V)

Data No50 100 150 200 250 3OO

(d) 5 HzFig 6.1 Comparison results of simulation and experiment in X-axis.



-10

voltage (V)

2OO 4OO 6OO(a) 0.5 Hz

Data NoSOO 1 0OO

1O -4QP voltage (V)

-5

4OO(b) 1 Hz

8OO 1OOO

voltage (V)

Data No1OO 2OO SOO

(c) 2 Hz

-10

voltage (V)

Data NoSO 1OO 15O 2OO 2SO SOO

(d) 5 Hz

Fig 6.2 Comparison results of simulation and experiment in Z-axis.



5 4QO voltage (V)

-5 Data No2OO 4OO GOO 8OO 1OOO

4QD voltage (V)- ' • '

-5Data No

I 2OO 4OO GOO 8OO 1OOO

Fig. 7.1 Step response of tracking in X-axis.

4QD voltage (V)

Data No2OO 4OO GOO GOO 1OOO

-4QD voltage (V)

-5Data No

200 4OO GOO 800 1OOO

Fig. 7.2 Step response of tracking in Z-axis.


Laser Metrology and Machine Performance

Position (mm)0.5

-0.5

M<*WWUff*>

Time (hr)O 1 2 3 4 5 6

X position

0.5Position (mm)

-O.5Time (hr)

O 1 2 3 4

Z position

5 6

O.5Position (mm)

-0.5Time (hr)

O 1 2 3 4 5 6

LIS system

Fig. 8 Stability tests on position and measurement systems.

37


Characterisation of 3-d Cartesian co-ordinate laser ... · laser interferometer tracking system W....

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Transcript of Characterisation of 3-d Cartesian co-ordinate laser ... · laser interferometer tracking system W....