YRJ-2009-09.pdf

Automatic straightness measurement of a linear guideusing a real-time straightness self-compensatingscanning stageC H Liu Y-R Jeng W Y Jywe S-Y Deng and T-H Hsu

Department of Mechanical Engineering National Chung Cheng University Chia-Yi Taiwan Republic of China

The manuscript was received on 5 August 2008 and was accepted after revision for publication on 16 April 2009

DOI 10124309544054JEM1319

Abstract In this paper a method is developed for straightness measurement of a linear guideby using a straightness self-compensating stage with an optical straightness measuring systeman eddy current sensor and a cross-roller type compensation stage Both the compensationstage and the optical straightness system were set up on a scanning stage to measure thestraightness error of the scanning stage The measured straightness error was fed back to thecontrol system to compensate directly in real time Thus straightness of a linear guide withoutthe added straightness error of the scanning stage could be measured The Hewlett Packardlaser straightness calibration system was used to verify the real-time compensated resultsStraightness error of the scanning stage was compensated from the worst straightness error of20mm150mm to 09mm150mm The eddy current sensor measured straightness of the linearguide and the measured result matched the result obtained by the coordinate measuringmachine

Keywords straightness dimensional measurement laser technology quadrant detectorerror separation linear guide

1 INTRODUCTION

Linear guides are widely used in machine tools orlinear stages The automatic straightness measure-ment technique of a linear guide is an importantissue for the manufacturers of linear guides Themanual measuring method which uses a contactedprobe is widely utilized in the factory but is timeconsuming The technique of displacement probesmounted on a scanning stage is the main automaticmethod of measuring straightness for linear guidesThus the straightness error of the scanning stage isone of the main error sources It is essential to sep-arate straightness error from the compound errors ofthe measured linear guide and the scanning stage Inindustrial applications it is difficult to assemble thescanning stage which is composed of two linearguides Straightness error is less than 1mm especially

for a long-travel scanning stage The air bearing sys-tem may be used with the good flatness of thegranite as the guiding system In order to reducestraightness error the XndashY stage with air bearing twoorthogonal high-accuracy plane mirrors and twolaser interferometers is mostly used in industry Thisarrangement can compensate such that straightnesserror is less than 20nm but is very expensive Thusthe XndashY stage is mostly employed in the litho-graphy process used by semiconductor manu-facturers and liquid crystal display manufacturersbut is not suitable to be used as the scanning stagewith a displacement probe to measure straightness ofa linear guide The coordinate measuring machine(CMM) is a representative measurement apparatususing a displacement probe to measure the profile ofthe workpiece For compensating straightness errorthe Hewlett Packard (HP) straightness calibrationsystem and the Renishaw laser straightness calib-ration system [1 2] are the most representativeinstruments for off-line calibration of a linear stageIntegrating the laser interferometer with severalposition-sensitive detectors [3ndash5] is also an effective

Corresponding author Department of Mechanical Engineer-

ing National Chung Cheng University 160 San-Hsing Ming-

Hsiung Chia-Yi 621 Taiwan Republic of China

email imeyrjccuedutw

JEM1319 IMechE 2009 Proc IMechE Vol 223 Part B J Engineering Manufacture

1171

method to measure simultaneously the multi-degrees-of-freedom motion errors The measuredgeometric errors are mapped to the spatial errors byway of an homogeneous transformation matrix Inthese methods straightness errors are often com-pensated via a series of discrete compensation dataThe scanning stage must have good repeatability andlow uncertainty Other research studies havedeveloped error separation methods to separate theprofile of the workpiece from the straightness error ofthe scanning stage [6] Giacomo et al presented asingle-probe measurement method with the reversaltechnique [6] Each workpiece is measured twice inopposite measurement directions and then thestraightness error of the workpiece is obtained byfitting the measurement results Thus the perform-ance of this method is directly affected by the prop-erties of the scanning stage Other multi-probemethods such as two-probe methods [7ndash11] three-probe methods or combined methods [12ndash18] havealso been developed effectively to separate straight-ness error from the scanning stage These methodsusing multiple sensors (displacement sensors orangle sensors) can eliminate the influences of bothtranslation motion error and tilt motion error Theintegration operation (two-probe method) or doubleintegration operation (three-probe method) of thedifferential outputs of the multiple probes are used toevaluate the surface profile The two-probe methodsuffers from the influence of tilt motion error Araiet al presented a straightness measurement systemwith two probes an autocollimator and a scanningstage [11] The surface profile of the workpiece andstraightness error of the scanning stage can beobtained respectively via the error separationmethod The zero-adjustment error will introduce an

offset in the differential output of the three-probemethod and thus yield a parabolic error term in theprofile evaluation result [15] Multiple-probe meth-ods are suitable for measuring a long workpiece witha fixed form such as a cylinder or a sphere owing totheir fixed interval between the probes

The current paper describes a straightness self-compensating stage with an optical straightnessmeasuring system by using a position-sensitivedetector and a compensation stage to measure on-line the straightness error of the scanning stage andto compensate it simultaneously This method issimple and directly compensates the error thus theextra straightness error induced from the scanningstage can be separated In the first part of the paperthe straightness measuring system and the com-pensation technique are described In the secondpart the straightness-compensated result of thescanning stage and the measured straightness resultof a linear guide for the proposed system and a CMMare described and compared

2 SYSTEM SET-UP AND WORKING PRINCIPLE

Figure 1 shows the overall system set-up with astraightness self-compensating scanning stagea straightness measuring system an eddy currentsensor the measured workpiece (a linear guide) andthe HP straightness calibration system The straight-ness self-compensating scanning stage included ascanning stage which is used as the measurementreference and a compensation stage In order toreduce friction the scanning stage is of normal typewith a ball screw and two linear guides and thecompensation stage is the cross-roller type with a ball

Measured workpiece

HP laser straightness calibration system

Collimated laser

Fiber optic cable

Eddy current sensor

Compensation stageScanning stage

Quadrant detector

X

Z

Y

O

Fig 1 The system set-up of the linear guide straightness system

Proc IMechE Vol 223 Part B J Engineering Manufacture JEM1319 IMechE 2009

1172 C H Liu Y-R Jeng W Y Jywe S-Y Deng and T-H Hsu

screw and two cross roller guides The compensationstage was set up on the scanning stage for com-pensating the horizontal straightness error of thescanning stage The straightness measuring systemwas composed of a collimated laser and a quadrantdetector (QD) The QD was set up on the com-pensation stage and the collimated laser was pro-jected on to the centre of the detector The directionsof the Y axis of the QD and the moving axis of thecompensation stage were parallel This method ofstraightness measurement is often used for off-linecalibration of computer numerically controlled(CNC) machine tools or for a linear stage [3ndash5] In thepresent paper the straightness system could be usedfor real-time measurement and the measuring resultcould be fed back into the compensation stage tomodify the horizontal straightness error of the scan-ning stage The HP calibration system was used toverify the measurement result and the compensatedresult The eddy current sensor was used to measurestraightness of the workpiece During the measuringprocess the compensation stage moved back andforth to ensure that the laser always projected on tothe centre of the QD the effect of straightness error ofthe scanning stage could thereby be reduced

21 Working principle of the straightnessmeasuring system

The real-time straightness measuring system is sim-ple and easy to implement in this self-compensatedscanning stage The QD can detect the position of thelaser spot and provide two-dimensional coordinateswhich can be calculated as follows

Dx frac14 Kx middotethVA thorn VDTHORN ethVB thorn VCTHORNVA thorn VB thorn VC thorn VD

eth1THORN

Dy frac14 Ky middotethVA thorn VBTHORN ethVC thorn VDTHORNVA thorn VB thorn VC thorn VD

eth2THORN

where VA VB VC and VD are the amplified voltagesignals of the four quadrants and Kx and Ky are theproportion parameters

The QD with a five-axis manual adjustment holderwas fixed on the compensation stage and the colli-mated laser with a three-axis holder was set up on afixed part

22 The control system of the straightnessself-compensating scanning stage

The control system of the straightness self-compensating scanning stage included the con-trollers of the scanning stage and the compensationstage The actuator of the scanning stage was a brushmotor (Sanyo P5) The working range and the res-olution of the scanning stage were 300mm and

025mm respectively The actuator of the compensa-tion stage was a brushless motor (Metronix) Theworking range and the resolution of the compensa-tion stage were 200mm and 01mm respectively Thecontrol system included the software (MatlabSimulink) a dSPACE processor (DS1104) and twodigital drivers (Elmo CEL-151660I) The sample fre-quency was 10kHz The proportionalndashintegralndashderivative (PID) controllers for two stages were usedin this paper The straightness measuring systemmeasured the horizontal straightness error of thescanning stage and the result was sent to the controlsystem to initiate the compensation stage During thescanning process the compensation stage main-tained the laser spot position on the centre of the QDThe block diagrams are shown in Fig 2

The signal connection between the QD and thecompensation stage can be expressed by

eethnTHORN frac14 VC Dy eth3THORNThe actuated signal input to the motor at the com-pensation stage can be expressed as follows

uethnTHORN frac14 KpeethnTHORN thorn KI

ZeethnTHORNdt thorn KD eethnTHORN

eth4THORN

where VC is the reference voltage and Kp KI and KD

are the controller gainsFigure 3 shows the frequency response of the con-

trol system The bandwidth of the control system wasabout 95Hz The bandwidth of the control systemwas sufficient to implement the compensation forthe straightness error

3 VERIFICATION

31 Verification of the QD

The HP-5529A laser-interferometer was utilized toverify the QD and eddy current sensor The QD andcorner cube reflector were both fixed on the com-pensation stage A laser source shot a light on to theQD as shown in Fig 4 When the compensation stagemoved the QD and corner cube were also movedThe verification result showed that the error of theQD was under ndash 025mm and the standard deviationwas about 03mm as shown in Fig 5 The propor-tional gain of the QD was 579mmV The measuringrange of the QD was ndash 25mm After calibration theQD was used to measure straightness error of thescanning stage and the result was compared with theHP laser straightness calibration system Figure 6shows the horizontal straightness error of the scan-ning stage measured by both these methods Themeasured straightness result was almost the sameand the worst value for horizontal straightness of thescanning stage was about 20mm


Automatic straightness measurement of a linear guide 1173

32 Verification of the eddy current sensor

The verification method of the eddy current sensor isshown in Fig 7 When the compensation stagemoved the eddy current sensor and corner cubewere also moved The laser interferometer was used

as the reference for the eddy current sensor The ve-rification range of the eddy current sensor wasndash 24mm The proportional gain of the eddy currentsensor was 7655mmV The standard deviation wasabout 016mm as shown in Fig 8

Fig 3 The frequency response of the compensation stage

InputPID in

Elmo controllerThe scanning stage

The motor encoder of the scanning stage

Signal processor in

Elmo controller

Output

Elmo controller

dSPACE

(a) Scanning stage

PID in

Elmo controllerThe compensation stage

Straightness measuring system

Signal processor in

Elmo controller

Output

Elmo controller

Input dSPACE

(b) Compensation satge

Fig 2 The block diagram of the real-time straightness error compensation system



33 Uncertainty of the system

Considering the structure of this system the set-uperror of its four components influences the uncer-tainty of the system These components include thecollimated laser the QD the compensation stageand the eddy current sensor The details are descri-bed below

1 Collimated laser The collimated laser revolvesaround the y axis causing the uncertainty Thusthis error can be written as

eCL frac14 l middot sin uCL eth5THORN

where eCL is the error l is the movement rangeand uCL is the angle revolved around the y axis

2 QD The QD revolves around its own centre andthe z axis thereby causing uncertainty asdescribed below(a) Revolved around its own centre When the

QD revolved around its own centre themeasurement results of its two axes inter-fered with each other This error can beeliminated by operators

(b) Revolved around the z axis The error and theangle uQD resulted from the QD revolvingaround the z axis The displacement Dd isobtained by the QD Thus this error can bewritten as

eQD frac14 Dd 1 cos uQD

eth6THORN

3 Compensation stage At this stage the resolutionof the compensation stage influences the uncer-tainty

4 Eddy current sensor At this stage the accuracy ofthe eddy current sensor is the major factorcausing the uncertainty

HP5529AInterferometer

Beam-splitterCorner CubeQD

Stage

Laser Source

Controller

Fig 4 Illustration of the QD verification

-30

-20

-10

0

10

20

30

-06 -04 -02 0 02 04 06Voltage (V)

Dis

plac

emen

t (micro

m)

(b) The error of the QD

(a) The displacement ndash voltage curve

-03

-02

-01

0

01

02

03

04

-25 -20 -15 -10 -5 0 5 10 15 20 25Displacement (microm)

Err

or (

microm)

Error Standard deviation

Fig 5 Verification result of the QD

-5

0

5

10

15

20

0 15 30 45 60 75 90 105 120 135 150X-stage moving distance (mm)

Unc

ompe

nsat

ed s

trai

ghtn

ess

erro

r (micro

m)

QD HP laser calibration system

Fig 6 Straightness error measurement result comparingHP laser calibration system and QD



Through the serious set-up process uCL l uQDzand the maximum Dd are under 066 arcsec 150mm5 and 50mm 5 respectively and the resolution ofcompensation stage and the accuracy of the eddycurrent sensor are 01mm and 09mm respectivelyThen

eCL frac14 l middot sin uCL frac14 150000sin066

3600

frac14 0480 mmeth THORN


frac14 50 1 cos5eth THORN frac14 0190 mmeth THORN

The uncertainty can be described by

Uncertainty frac14 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi04802 thorn 01902 thorn 092 thorn 012

pfrac14 1042

The uncertainty of this system is ndash 1042mm

4 EXPERIMENTAL RESULTS

41 The real-time straightness compensatedresult of the scanning stage

Before compensating the straightness error of thescanning stage the laser beam must be adjusted tobe parallel to the moving axis of the scanning stageFigure 9 shows the additional errors measured by theQD owing to the misalignment between the laserbeam and the moving axis This error resulted inincorrect straightness compensation and also affec-ted the straightness measurement of the workpieceFigure 10 is a photograph of this system in theexperiment Figure 11 shows the straightness errorcompensation result of the scanning stage The mis-alignment between the laser beam and moving axisresulted in a straightness error of about 5mm Themisalignment in the experiment was adjusted andmodified and the result is shown in Fig 12 After theadjustment three experimental tests were performedby using the real-time straightness compensated forthe scanning stage as shown in Fig 12 The averagecompensated result showed that the straightness

Fig 7 Illustration of the eddy current sensor verification

y = 7655x+04

-30

-20

-10

0

10

20

30

-0020 -0006 0006 0020Voltage (V)

Dis

plac

emen

t(microm

)

0

008

016

024

032

04

Stan

dard

dev

iato

in (

microm)

Voltage Standard deviation Slope


-1-08-06-04-02

002040608

1

-25 -20 -15 -10 -5 0 5 10 15 20 25

Calibrated position (microm)

Err

or (

microm)

(b) The error of the eddy current

Fig 8 Verification result of the eddy current sensor



error of 20mm was reduced to 085mm and thestandard deviation was about 02mm as shown inFig 13

42 Verification of the real-time compensatingscanning stage and CMM

In this experiment straightness of a linear guide wasmeasured Nine sample points on the linear guidewere measured and the experimental conditionsare shown in Table 1 The measured results werecompared with the CMM (model Discovery II D-8Sheffield Measurement Inc probe head modelMH20i Renishaw plc probe holder model TP20Renishaw plc and probe part number A-5000ndash3626Renishaw plc details are provided in Tables 2 to 5) Inorder to show the improved performance by usingthe self-compensation function the experiment wasconducted under two different conditions with thereal-time self-compensating function and withoutthe real-time self-compensating function Thestraightness error of the linear guide was 40mmwithout using the self-compensating function butthis was reduced to 16mm when using the self-

compensating function as shown in Fig 14 TheCMMwas utilized to verify the experiment The resultshowed that straightness of the linear guide was also16mm as shown in Fig 14 With the real-time self-compensating stage the measured result matchedthe result obtained by the CMM

Fig 10 Photograph of the system at the experimentalstage

0

1

2

3

4

5

0 15 30 45 60 75 90 105 120 135 150Distance moved (mm)

Stra

ight

ness

(μm

)

Fig 11 Compensated straightness error with misalign-ment

y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)

Fig 12 Straightness error measurement with better align-ment

y = 00408x

-8-6-4-202468

1012

0 15 30 45 60 75 90 105 120 135150Distance moved (mm)

Stra

ight

ness

(μm

)

Fig 9 Error induced by the misalignment

-06

-05

-04

-03

-02-01

0

01

02

03

04

0 15 30 45 60 75 90 105 120 135 150Moving distance(mm)

Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV

Fig 13 Compensated straightness error with better align-ment



5 CONCLUSION

A real-time straightness error compensation systemfor straightness measurement of a linear stage hasbeen successfully developed and described in thispaper Using a straightness self-compensation scan-ning stage with a submicron straightness com-pensation system and the eddy current sensor tomeasure straightness of the linear guide this methodseparated straightness error of the scanning stagedirectly and obtained the exact straightness of a lin-ear guide Straightness error of the scanning stagecan be reduced to less than 1mm in the system Thismethod is characterized as simple direct and real-time compensation so the profile of fixed-formworkpieces is accurately measured Furthermorestraightness error of the scanning stage is instanta-neously eliminated thus the profile of free-formworkpieces can be effectively measured within theworking range of the detector In future research thetravelling of the scanning stage will be increased to4m for linear guides of 4m length

Table 1 Experimental conditions

Temperature 20 Cthorn 1 CHumidity 50thorn 5Noise lt 45dbParticle lt 104m3

Table 2 Parameters of Discovery II D-8 (Sheffield Meas-urement Inc) [19]

Specification

X travel 508mm (20 in)Y travel 609mm (24 in)Z travel 406mm (16 in)Resolution 01mmRepeatability 25mmLinear accuracy (rangeof full travel) perB8941 section 543

X 4mm (000016 in)Y 45mm (0000 18 in)Z 35mm (000014 in)

Volumetric accuracy MPEE ndash 575mm MPEP 45mmMax velocity 254mmsSoftware Measure max

MPEE (mm)frac14 5thornL(mm)200 where measured length L is150mmMPEE Maximum permissible error of indication of a CMM for sizemeasurement according to ISO 10360-2MPEP Maximum permissible probing error according to ISO10360-2

Table 3 Parameters of MH20i (Renishaw plc) [20]

Specification

Length 61mmDiameter 48mmWeight 210 gProbe mounting TP20 kinematic mountHead mounting MS range of shanksCable connection 5 pin DIN 180 socketA-axis indexing 0 to 90 in 15 repeatable stepsB-axis indexing 180 in 15 repeatable stepsRepeatability ofposition

15mm (TP20 and 10mm stylus fitted)25mm (EM2 extended module and10mm stylus)

Table 4 Parameters of TP20 (Renishaw plc) [21]

Sense directions All modules except 6W ndashX ndashY thornZ6W ndashX ndashY ndashZ

Suitable interface PI4-2 PI7-2PI200 UCC

Pre-travel variation LF ndash060mmSF EM1 EM2 ndash080mmMF ndash100mmEF ndash200mm6W ndash150mm

Unidirectionalrepeatability

LF SF EM1 EM2 ndash035mmMF ndash050mmEF ndash065mm6W ndash080mm

Repeatability ofstylus changing

MCR20 ndash050mmManual ndash100mm

Stylus range M2

Mounting method M8 thread

Table 5 Parameters of A-5000-3626 (Renishaw plc) [22]

Part no A-5000-3626PS no RS7RDescription M2 STR D2 5BALL L192 S30Section no 34Thread M2Component starBalltip size (mm) 20Balltip material RudyLength (mm) 192Stem material Stainless steelEffective working length (mm) 120Mass (g) 18

-24-20

-16-12-8-4

04

812

1620

24

1 2 3 4 5 6 7 8 9Measuring point

Stra

ight

ness

mea

sure

men

t (μm

)

Compensated CMMUncompensated

Fig 14 Comparison between compensated resultuncompensated result and CMM



ACKNOWLEDGEMENTS

The work was supported by the National ScienceCouncil Taiwan Republic of China (number NSC 95-2622-E-150-032-CC3)

REFERENCES

1 Hewlett Packard Company Limited Optics and laserheads for laser interferometer positioning systems prod-uct overview 2000

2 Renishaw Company Limited Performance measure-ment and calibration systems performance measure-ment brochure no 10-35 2007

3 Ni J Huang P S and Wu S M A multi-degree-of-freedom measuring system for CMM geometric errorTrans ASME J Engng Ind 1992 114 362ndash369

4 Fang K C and Chen M J A 6-degree-of-freedommeasuring system for the accuracy of X-Y stage Preci-sion Engng 2000 24 15ndash23

5 Liu C H Jywe W Y Hsu C C and Hsu T HDevelopment of a laser-based high-precision six-degrees-of-freedom motion errors measuring systemfor a linear stage Rev Scient Instrum 2005 7655110-1ndash55110-6

6 Giacomo B D de Magalhaes R C A andPaziani F T Reversal technique applied to the meas-urement of straightness errors In ABCM symposiumseries in mechatronics 2004 Vol 1 pp 479ndash487

7 Tanaka H Tazawa K O-Hori M and Sekiguchi HApplication of new straightness measurement methodto large machine tool Ann CIRP 1981 30 455ndash459

8 Tazawa K Sato H and O-Hori M A new method forthe measurement of straightness of machine tools andmachined work Trans ASME J Mech Des 1982 104587ndash592

9 Kiyono S and Gao W Profile measurement ofmachined surface with a new differential method Pre-cision Engng 1994 16 212ndash218

10 Gao W and Kiyono S High accuracy profile meas-urement of a machined surface by the combinedmethod Measurement 1996 19 55ndash64

11 Arai Y Gao W Kiyono S and Kuriyagawa TMeasurement of straightness of a leadscrew-driven

precision stage Key Engng Mater 2005 295ndash296 259ndash

26412 Whitehouse D J Measuring Instrument Patent

4084324 US 197813 Tanaka H and Sato H Extensive analysis and devel-

opment of straightness measurement by sequential

two-point method Trans ASME J Engng Ind 1986

108 176ndash18214 Gao W and Kiyono S On-machine profile measure-

ment of machined surface using the combined three-

probe method JSME Int J 1997 40 253ndash25915 Gao W Yokoyamab J Kojima H and Kiyono S

Precision measurement of cylinder straightness using a

scanning multi-probe system Precision Engng 2002 26

279ndash28816 Kume T Enami K Higashi Y and Ueno K Evalu-

ation of error propagation in profilometry using stitch-

ing In Proceedings of the 9th International Workshop

on Accelerator alignment SLAC California 26ndash29

September 2006 pp TH002 1ndashTH002 817 Paziani F T Giacomo B D and Tsunaki R H

Development of an automated and dedicated measur-

ing system for straightness evaluation J Brazilian Soc

Mech Sci Engng 2007 XXIX(3) 290ndash29818 Kiyono S and Gao W On-machine measurement of

large mirror profile by mixed method JSME Int J Ser

C 1994 37 300ndash30619 Product information on coordinate measuring machine

Discovery Endeavor see httpwwwtarkkuustuontifi

EsitteetSheffieldSheffield20Europe20Brochure

pdf (Sheffield Measurement Incorporated)20 Product information on MH20i probe head see http

wwwrenishawcomen7384aspx (Renishaw plc)21 Product information on TP20 compact module touch-

trigger probe see httpwwwrenishawcomen6670

aspxtocTarget3 (Renishaw plc)22 For information on styli and accessories see http

resourcesrenishawcomdownload(13ef957aa9c04fd4

9353f92ef328486F)Lang=enampinline=true pp 90



method to measure simultaneously the multi-degrees-of-freedom motion errors The measuredgeometric errors are mapped to the spatial errors byway of an homogeneous transformation matrix Inthese methods straightness errors are often com-pensated via a series of discrete compensation dataThe scanning stage must have good repeatability andlow uncertainty Other research studies havedeveloped error separation methods to separate theprofile of the workpiece from the straightness error ofthe scanning stage [6] Giacomo et al presented asingle-probe measurement method with the reversaltechnique [6] Each workpiece is measured twice inopposite measurement directions and then thestraightness error of the workpiece is obtained byfitting the measurement results Thus the perform-ance of this method is directly affected by the prop-erties of the scanning stage Other multi-probemethods such as two-probe methods [7ndash11] three-probe methods or combined methods [12ndash18] havealso been developed effectively to separate straight-ness error from the scanning stage These methodsusing multiple sensors (displacement sensors orangle sensors) can eliminate the influences of bothtranslation motion error and tilt motion error Theintegration operation (two-probe method) or doubleintegration operation (three-probe method) of thedifferential outputs of the multiple probes are used toevaluate the surface profile The two-probe methodsuffers from the influence of tilt motion error Araiet al presented a straightness measurement systemwith two probes an autocollimator and a scanningstage [11] The surface profile of the workpiece andstraightness error of the scanning stage can beobtained respectively via the error separationmethod The zero-adjustment error will introduce an

offset in the differential output of the three-probemethod and thus yield a parabolic error term in theprofile evaluation result [15] Multiple-probe meth-ods are suitable for measuring a long workpiece witha fixed form such as a cylinder or a sphere owing totheir fixed interval between the probes

The current paper describes a straightness self-compensating stage with an optical straightnessmeasuring system by using a position-sensitivedetector and a compensation stage to measure on-line the straightness error of the scanning stage andto compensate it simultaneously This method issimple and directly compensates the error thus theextra straightness error induced from the scanningstage can be separated In the first part of the paperthe straightness measuring system and the com-pensation technique are described In the secondpart the straightness-compensated result of thescanning stage and the measured straightness resultof a linear guide for the proposed system and a CMMare described and compared

2 SYSTEM SET-UP AND WORKING PRINCIPLE

Figure 1 shows the overall system set-up with astraightness self-compensating scanning stagea straightness measuring system an eddy currentsensor the measured workpiece (a linear guide) andthe HP straightness calibration system The straight-ness self-compensating scanning stage included ascanning stage which is used as the measurementreference and a compensation stage In order toreduce friction the scanning stage is of normal typewith a ball screw and two linear guides and thecompensation stage is the cross-roller type with a ball

Measured workpiece

HP laser straightness calibration system

Collimated laser

Fiber optic cable

Eddy current sensor

Compensation stageScanning stage

Quadrant detector

X

Z

Y

O

Fig 1 The system set-up of the linear guide straightness system







eth1THORN


eth2THORN










eth4THORN




3 VERIFICATION









InputPID in



Signal processor in

Elmo controller

Output

Elmo controller

dSPACE

(a) Scanning stage

PID in



Signal processor in

Elmo controller

Output

Elmo controller

Input dSPACE














eth6THORN





Stage

Laser Source

Controller


-30

-20

-10

0

10

20

30

-06 -04 -02 0 02 04 06Voltage (V)

Dis

plac

emen

t (micro

m)



-03

-02

-01

0

01

02

03

04


Err

or (

microm)



-5

0

5

10

15

20


Unc

ompe

nsat

ed s

trai

ghtn

ess

erro

r (micro

m)







3600






pfrac14 1042






y = 7655x+04

-30

-20

-10

0

10

20

30

-0020 -0006 0006 0020Voltage (V)

Dis

plac

emen

t(microm

)

0

008

016

024

032

04

Stan

dard

dev

iato

in (

microm)



-1-08-06-04-02

002040608

1

-25 -20 -15 -10 -5 0 5 10 15 20 25


Err

or (

microm)










0

1

2

3

4

5


Stra

ight

ness

(μm

)


y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)


y = 00408x

-8-6-4-202468

1012


Stra

ight

ness

(μm

)


-06

-05

-04

-03

-02-01

0

01

02

03

04


Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV




5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES














































eth1THORN


eth2THORN










eth4THORN




3 VERIFICATION









InputPID in



Signal processor in

Elmo controller

Output

Elmo controller

dSPACE

(a) Scanning stage

PID in



Signal processor in

Elmo controller

Output

Elmo controller

Input dSPACE














eth6THORN





Stage

Laser Source

Controller


-30

-20

-10

0

10

20

30

-06 -04 -02 0 02 04 06Voltage (V)

Dis

plac

emen

t (micro

m)



-03

-02

-01

0

01

02

03

04


Err

or (

microm)



-5

0

5

10

15

20


Unc

ompe

nsat

ed s

trai

ghtn

ess

erro

r (micro

m)







3600






pfrac14 1042






y = 7655x+04

-30

-20

-10

0

10

20

30

-0020 -0006 0006 0020Voltage (V)

Dis

plac

emen

t(microm

)

0

008

016

024

032

04

Stan

dard

dev

iato

in (

microm)



-1-08-06-04-02

002040608

1

-25 -20 -15 -10 -5 0 5 10 15 20 25


Err

or (

microm)










0

1

2

3

4

5


Stra

ight

ness

(μm

)


y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)


y = 00408x

-8-6-4-202468

1012


Stra

ight

ness

(μm

)


-06

-05

-04

-03

-02-01

0

01

02

03

04


Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV




5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES














































InputPID in



Signal processor in

Elmo controller

Output

Elmo controller

dSPACE

(a) Scanning stage

PID in



Signal processor in

Elmo controller

Output

Elmo controller

Input dSPACE














eth6THORN





Stage

Laser Source

Controller


-30

-20

-10

0

10

20

30

-06 -04 -02 0 02 04 06Voltage (V)

Dis

plac

emen

t (micro

m)



-03

-02

-01

0

01

02

03

04


Err

or (

microm)



-5

0

5

10

15

20


Unc

ompe

nsat

ed s

trai

ghtn

ess

erro

r (micro

m)







3600






pfrac14 1042






y = 7655x+04

-30

-20

-10

0

10

20

30

-0020 -0006 0006 0020Voltage (V)

Dis

plac

emen

t(microm

)

0

008

016

024

032

04

Stan

dard

dev

iato

in (

microm)



-1-08-06-04-02

002040608

1

-25 -20 -15 -10 -5 0 5 10 15 20 25


Err

or (

microm)










0

1

2

3

4

5


Stra

ight

ness

(μm

)


y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)


y = 00408x

-8-6-4-202468

1012


Stra

ight

ness

(μm

)


-06

-05

-04

-03

-02-01

0

01

02

03

04


Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV




5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES



















































eth6THORN





Stage

Laser Source

Controller


-30

-20

-10

0

10

20

30

-06 -04 -02 0 02 04 06Voltage (V)

Dis

plac

emen

t (micro

m)



-03

-02

-01

0

01

02

03

04


Err

or (

microm)



-5

0

5

10

15

20


Unc

ompe

nsat

ed s

trai

ghtn

ess

erro

r (micro

m)







3600






pfrac14 1042






y = 7655x+04

-30

-20

-10

0

10

20

30

-0020 -0006 0006 0020Voltage (V)

Dis

plac

emen

t(microm

)

0

008

016

024

032

04

Stan

dard

dev

iato

in (

microm)



-1-08-06-04-02

002040608

1

-25 -20 -15 -10 -5 0 5 10 15 20 25


Err

or (

microm)










0

1

2

3

4

5


Stra

ight

ness

(μm

)


y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)


y = 00408x

-8-6-4-202468

1012


Stra

ight

ness

(μm

)


-06

-05

-04

-03

-02-01

0

01

02

03

04


Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV




5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES












































3600






pfrac14 1042






y = 7655x+04

-30

-20

-10

0

10

20

30

-0020 -0006 0006 0020Voltage (V)

Dis

plac

emen

t(microm

)

0

008

016

024

032

04

Stan

dard

dev

iato

in (

microm)



-1-08-06-04-02

002040608

1

-25 -20 -15 -10 -5 0 5 10 15 20 25


Err

or (

microm)










0

1

2

3

4

5


Stra

ight

ness

(μm

)


y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)


y = 00408x

-8-6-4-202468

1012


Stra

ight

ness

(μm

)


-06

-05

-04

-03

-02-01

0

01

02

03

04


Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV




5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES















































0

1

2

3

4

5


Stra

ight

ness

(μm

)


y = -00032x

-6-4-202468

10121416


Stra

ight

ness

(μm

)


y = 00408x

-8-6-4-202468

1012


Stra

ight

ness

(μm

)


-06

-05

-04

-03

-02-01

0

01

02

03

04


Com

pens

ated

str

aigh

tnes

s er

ror

(μm

)

AVG STDEV




5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES










































5 CONCLUSION





Specification






Specification











Stylus range M2




-24-20

-16-12-8-4

04

812

1620

24


Stra

ight

ness

mea

sure

men

t (μm

)





ACKNOWLEDGEMENTS


REFERENCES










































ACKNOWLEDGEMENTS


REFERENCES










































YRJ-2009-09.pdf

Documents

Transcript of YRJ-2009-09.pdf