Application of Displacement Method for on-the-machine Measurement of a Work Profile

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1 Iteratioal Joural of Cotrol, Automatio ad ystems Vol.3 No.4 October 2014 Applicatio of Displacemet Method for o-the-machie Measuremet of a Work Profile Tsuyoshi himizu *, Takaaki Ishii ad Yuzairi Abdul Rahim Abstract This paper describes built-i applicatio of a improved displacemet method for a machie tool. A work piece is displaced logitudially i the displacemet method, but a referece piece is displaced i this study. The referece piece is set up beside the table of a prototype machie tool stage to measure a motio error. This referece piece is measured by eddy curret displacemet sesor ad the work piece is measured by laser displacemet sesor respectively. The referece piece ad the work piece are measured i the first series of measuremets. The the referece piece ad the work piece are measured i the secod series of measuremets after displacemet of the referece piece. Radom errors are give as measurig error i simulatios ad the error model is ormal distributio model. To execute a high accuracy measuremet of the full-coverage of the work piece profile, micro-meter order, the error of sesors must be approximately less tha 0.5m. Variatio of sesors is measured before experimet. The stadard deviatio of the eddy curret displacemet sesor was 0.11m, ad the laser displacemet sesor was 0.07m. Experimetal results usig the prototype machie tool stage are approximately same as Coordiate Measurig Machie. Keywords traightess profile, Displacemet method, Accumulated error, Differece formula, Motio error separatio O I. INTRODUCTION -machie measuremet is ecessary techiques because it is able to measure a work piece profile without uclamp the work piece off from the machie tool. O-machie measuremet such as the roudess measuremet 1, 2 ad the straightess measuremet 3 have bee studied. However, it has a problem that motio error of the machie tool ad the work piece profile are measured simultaeously 4-8. The the separatio of the motio error ad the profile is still research issue. ubmitted o July 10, Tsuyoshi himizu is with the Departmet of Mechatroics, Uiversity of Yamaashi, Japa Takeda, Kofu, Yamaashi, Japa. Takaaki Ishii is with the Departmet of Mechatroics, Uiversity of Yamaashi, Japa. Yuzairi Abdul Rahim is with the Iformatio ad Mechaical ystems Egi eerig, Uiversity of Yamaashi, Japa. *Correspodece to Tsuyoshi himizu ( tsuyoshi-s@yamaashi.ac.jp. Geerally, multi-probe method is used for the separatio of motio error from sesor outputs. The sesor outputs cotaied the profile of the work piece ad the motio error. The motio error ca be removed by the sequetial-two poit method ad the sequetial-three poit method Hwag et al. 9 set up two probes agaist oe probe ad they measured the roudess withi 0.05m stadard deviatio. Okuyama et al. 10 cosidered about the two poit method that iclude measurig errors. Kiyoo et al. 11 developed the sequetial-two poit method to apply o-machie measuremet. However, there are some problems i the multi probe measurig, which are the probe settig error or the probe motio error toward the practical use. I the displacemet method that Thwaite 12 proposed ca elimiate the motio error. The procedure is that a referece profile ad a work piece profile are measured simultaeously i the first measuremet, ad the moved work piece profile is measured i the secod measuremet. This method is easy-to-use approach ad high precisio measuremet 1 techique. Thwaite 12 proposed oly priciple idea of the displacemet method, ad Xiaoyog at el. 13, 14 developed the displacemet method for o-machie profile measuremet to apply to machie tool. We discuss improvemet of the displacemet method to built-i machie tool. I geeral, the motio error of ormal machie tools is more tha 10m. By buildig ito the machie tool, such as machiig ceters, it is possible to measure ad machie the work piece, ad it is possible to create a profile of a product by removig the motio error of the machie tool. Whe measurig the profile of the work piece by usig the stage that has a motio error, it is also able to perform the measuremet that ca remove motio error of the stage by built-i displacemet method. The displacemet method is possible to separate the profile of the work piece profile ad the motio error of the stage. I other method, it is possible to separate the motio error by a techique such as Fourier-Eight-esor (F8 method. 15 However, F8 method eeds 8 sesors. I that respect, by buildig the displacemet method ito the movig stage, it is possible to separate the motio error easily, ad eables accurate measuremet. I this paper we experimet some simulatios ad measuremets for built-i machie tool.

2 II. METHOD A. Displacemet method Displacemet method that was proposed by Thwaite 12 is a very simple ad high-precisio. Fig. 1 shows the priciple of displacemet method. After the first series of measuremets has bee take, the referece surface is displaced logitudially ad the secod series of measuremets is take at the origial locatios. The alterative method ca lead to a calculatio of straightess relative to a error free referece. A first positio y 1 is followig, y f xi q xi 1 i. (1 where f( is a ukow curve, q( is a referece curve, ad x is measured from a fixed positio i each case. Ad a secod positio y 2 with the displaced distace delta is followig, y f xi qxi 2 i. (2 y 2i - y 1i givig f yi i1 x f 1 0. (3 The q(x i is removed from sesor output i measuremets. Fig.1 Displacemet method 1 B. Applicatio of Displacemet Method for Machie Tool We discuss improvig displacemet method to apply the table of machie tool. Fig. 2 shows a model of developed displacemet method applied to the machie tool. A referece piece ad a work piece are attached to the machie tool's table, ad sesor 2 ad sesor 1 measures the referece piece ad the object to be measured. 1 ( ad 2 ( are the outputs of sesor 1 ad sesor 2 respectively. r( is a profile of the referece piece ad w( is a profile of the work piece. Whe motio error of the machie tool is m(, the sesor output is followig: ( w( (4 11 x ( (5 21 x where 11 ( is the measuremet result of the sesor 1 output, ad 21 ( is the measuremet result of the sesor 2 output i the first measuremet respectively. I the case of the measuremet model that illustrated i Fig. 2, the output of sesors 2 is iverted. The secod measuremet which is by shiftig the referece piece distace d i the x -directio, we ca obtai the outputs from the sesors as followig: ( w( (6 12 x ( x d (7 22 x where 12 ( is the measuremet results of the sesor 1 output, ad 22 ( is the measuremet result of the sesor 2 output i the secod measuremet respectively. The differece betwee (5 ad (7 gives 22( x d (8 If we are assumig that d is measurig iterval, (8 becomes a first-order differece equatio as followig: 22( x2 x2 x2 x1 22( x3 x3 x3 x2 22( x x x x 1 where Fig. 2 Developed displacemet method model for machie tool applicatio x k =x k-1 +d (k=1,2,,. Thus r(x is described cumulative sum of (9 as followig: 22( x r( x 1 k 2 (9 (10 Therefore, r(x 1 =0 gives a shape of the referece piece profile by (10. Fially, the motio error m( of the machie tool ca be calculated from (5, or (4, ad the profile of the work piece w( is foud from (6. 2

3 C. Error Effect of Displacemet Method The error is always cotaied i the output of the sesor. The ideal model with o error is showed i the previous sectio. The error model of our displacemet method is related i this sectio. It is assumed that the measurig error is i the sesor 2 that measures the referece piece. esor 2 performs twice measuremets. Error also occurs i the first ad the secod measuremets, ad the result of each measuremet cotais the error as followig: r ( ( 21( 21 x. (11 w( work profile m( motio error r( referece profile 500m 20m 120mm 20m r ( x d ( 22( 22 x. (12 Fig.3 Iput sigals where 21 is the error of the first measuremet ad 22 is the error of the secod measuremet. The r(x is defied by r( x 22 ( r( x1 k. (13 k 2 k 1 where k 21( 22(. The third term i (13 is the error term. I the case of ε is radom error, there is a possibility that the third term cacel each other. But it shows that the error is basically accumulated. The motio error m( ca be obtaied by r( substituted ito (11 after determiatio of referece piece from (13. However, some errors that have to be observed i sesor 2 are i m(. After determiatio of the motio error m(, the error that observed i sesor 1 assumed 1k (, the 11( w( 11(. (14 Fig.4 imulatio result of a referece profile Hece the error model of the work piece profile ca be obtaied by (14. III. IMULATION Accumulated error that was show i the third term of (13 was simulated to fid out the effect of the measuremet of the work piece profile. Fig. 3 shows the shape of iput wave. w( that meas the profile of the work piece is a square wave of 500m i height, m( that meas the motio error of the stage is a siusoidal wave with a amplitude of 20m, while r( that meas the profile of the referece piece is the liear shape. Ad variatios that were added i the simulatio are ormal distributio whose stadard deviatio is 2m. I additio, measuremet legth is 120mm. Fig. 4 shows the shape of r( which derived from (13. olid lie meas the shape of iput referece profile r( ad dashed lie meas the calculatio result of referece profile r(. The shape of referece profile is recostructed i whole. I this case, the error was observed approximately 4m at the maximum. This error is differet for each measuremet so that the mea ad the stadard deviatio were examied for each positio as the umber of 1000 repetitio times. Fig. 5 shows the simulatio result of a referece profile ad Fig.5 imulatio result of a referece profile ad TD. the stadard deviatio of each positio. Dashed lie meas the shape of iput referece profile r( ad solid lie meas the mea of calculatio result of each positio. I additio, the stadard deviatio is represeted by the error bars at each positio. From this figure, the accumulated error terms of 3

4 Fig.6 imulatio result of a motio error Fig.7 imulatio result of a work profile (13 that have a effect o the stadard deviatio are cofirmed. Mea values for each positio is approximately equal to the iput. It is possible to reduce the effect of radom error by averagig. The calculatio results of motio error ad work piece profile are show i Fig. 6 ad Fig. 7 respectively. Error bars represet the stadard deviatio for each positio as show i Fig. 6 ad Fig. 7. We fid out that the stadard deviatio is affected by the error of the referece piece profile calculatio. Because the accumulatio of error occurs, loger measuremet legth becomes more stadard deviatio icrease. The actual measuremet results have the potetial to be occurred i the rage of these error bars. o, high accuracy profile measuremet is possible with short measurig rage. I order to cofirm the relatioship betwee the error ad the measuremet legth, the simulatio was performed with varyig the error of stadard deviatios. Fig. 8 shows the result of these simulatios. The horizotal axis meas the measured positio, ad the vertical axis meas obtaied stadard deviatio. Ad 0.1 ~ 6m error stadard deviatio are give i the simulatio. If we wat that the profile calculatio error of the referece piece is uder a few micro m (μm, it is ecessary that the measuremet error of the referece piece should become less tha 0.5μm whe measuremet legth is at the 120mm. I the case of the measured legth is 60mm, whe the error cotaied i the referece profile r( becomes i about 5μm, the profile of the referece piece is able to be measured i 1μm measurig error from (13. Fig.8 imulatio result of TD of a referece profile Laser sesor Table IV. EXPERIMENT Referece piece Maual liear stage A. Experimetal setup Our prototype experimetal equipmet is show i Fig. 9. A table which is used i a machie tool is set up. The referece piece is attached to the table o which a precisio maual liear stage is set. Referece piece is measured by eddy curret sesor (ML-06, Applied Electroics Corp.. The work piece profile Fig.9 Experimetal setup Eddy curret sesor is measured by a laser displacemet sesor (LK-010, Keyece. The material of the work piece ad the referece piece is 50C. 4

5 Fig.10 Drift of eddy curret sesor output Fig.12 Result of sesors output Fig.11 Drift of laser displacemet sesor output Fig.13 Calculatio result of the referece profile The work piece is fiished by millig, ad the referece piece is fiished by gridig after millig. B. esor drift Fig. 10 shows the drift of the eddy curret sesor. Rage of the sesor output was 0.7m ad the stadard deviatio was 0.11m at the 500sec cotiuous measurig. Cosiderig Fig. 8 ad the stadard deviatio of the eddy curret sesor, profile of the referece piece ca be measured with a error of about 1m whe the measuremet rage is 100mm. Therefore, the motio error that derived from (11 ca be measured withi about 1m precisio error at this measuremet legth. Fig. 11 shows the drift of the laser displacemet sesor. Rage of the sesor output was 0.46m ad the stadard deviatio was 0.07m. We ca fid the shape of the work piece profile from (4' after the motio error m( obtaied, ad eve if the error cotaied i the referece piece measuremet is added, the work piece profile ca be measured about 2m at 100mm measuremet legth. C. Profile measuremet Fig. 12 shows the sesors output whe the referece piece Fig.14 Calculatio result of the work profile profile ad the work piece profile was measured. 'esor 1' meas the measuremet result of the work piece profile, ad 'esor 2' meas the measuremet result of the referece piece profile. I additio, the displacemet legth of the referece 5

6 piece was 5 mm. The measuremet result before the referece piece displaced is 21 (, ad the measuremet result after the referece piece displaced is 22 (. Because of the error icluded, the differece occurs i each shape. Mea values i 12 ( ad 11 ( is applied because the work piece profile is also measured twice. Fig. 13 shows calculatio results about the referece piece profile ad the motio error which are derived from 21 ( ad 22 (. The calculated motio error was 10m or less. I additio, the referece piece that is calculated is iclied. Therefore, we ca figure out that attachmet agle is affected. The calculatio result about the work piece profile is show i Fig. 14. The average value of 12 ( ad 11 ( is show as 'Work profile (raw data', ad measuremet results of the three-dimesioal coordiate measurig machie (CMM is show as 'CMM' for compariso. It is close to the result of the coordiate measurig machie after the data processig. I additio, the work piece profile has approximately equaled to measured result of the coordiate measurig machie. V. CONCLUION I this paper, we discussed the applicatio of improved displacemet method for machie tool to employ o-machie measuremet, ad the displacemet method was improved to build ito the stage for applicatio of machie tool. For applyig to machie tool, the simulatio was performed, ad it is foud that the accumulated error of the measuremet of the referece profile has a effect o the measuremet of the profile of the work piece. it is ecessary that the measuremet accuracy of the referece piece or the size of the work piece must be selected for the work piece profile measuremet. We have developed a prototype ito cosideratio about itegratio to machie tools, ad it was almost equal to the measuremet results ad three-dimesioal measurig device. I the future work, we add oe axis to the prototype ad exted to allow the measuremet of the flatess profile. REFERENCE [1] Wei Gao, atoshi Kiyoo, "O-machie roudess measuremet of cylidrical workpieces by the combied three-poit method", Measuremet, Volume 21, Issue 4, August 1997, Pages [2] Wei Gao, atoshi Kiyoo, Tadatoshi Nomura, "A ew multiprobe method of roudess measuremets", Precisio Egieerig, Volume 19, Issue 1, July 1996, Pages [3] Zi-qiag Yi, heg-yi Li, "Exact straightess recostructio for o-machie measurig precisio workpiece", Precisio Egieerig, Volume 29, Issue 4, October 2005, Pages [4] Eric H.K Fug,.M Yag, "A approach to o-machie motio error measuremet of a liear slide", Measuremet, Volume 29, Issue 1, Jauary 2001, Pages [5] Daisuke Koo, Atsushi Matsubara, Iwao Yamaji, Tomoya Fujita, "High-precisio machiig by measuremet ad compesatio of motio error", Iteratioal Joural of Machie Tools ad Maufacture, Volume 48, Issue 10, August 2008, Pages [6] D.L. Leete, "Automatic compesatio of aligmet errors i machie tools", Iteratioal Joural of Machie Tool Desig ad Research, Volume 1, Issue 4, December 1961, Pages [7] C.James Li, hegyi Li, Jiamig Yu, "High-resolutio error separatio techique for i-situ straightess measuremet of machie tools ad workpieces", Mechatroics, Volume 6, Issue 3, April 1996, Pages [8] Zi-qiag Yi, heg-yi Li, "High accuracy error separatio techique for o-machie measurig straightess", Precisio Egieerig, Volume 30, Issue 2, April 2006, Pages [9] Jooho Hwag, Chu-Hog Park, Wei Gao, eug-woo Kim, "A three-probe system for measurig the parallelism ad straightess of a pair of rails for ultra-precisio guideways", Iteratioal Joural of Machie Tools ad Maufacture, Volume 47, 2007, Pages [10] Eiki Okuyama, Hirotake Akata, Hiromi Ishikawa, "Multi-probe method for straightess profile measuremet based o least ucertaity propagatio (2d report/two-poit method cosiderig cross-axis traslatioal motio, pitch motio ad sesor's radom error", Precisio Egieerig, Volume 34, Issue 4, October 2010, Pages [11] atoshi Kiyoo, Wei Gao, "Profile measuremet of machied surface with a ew differetial method", Precisio Egieerig, Volume 16, Issue 3, July 1994, p [12] Thwaite E. G., 1973, "A method of obtaiig a error free referece lie for the measuremet of straightess", Messtechik, 10, p , [13] Xiaoyog Ai Et Al: "ome methods for profile measuremet ad a applicatio for o-machie measuremet", ystems, Ma, ad Cyberetics, IEEE MC '99 Coferece Proceedigs IEEE Iteratioal Coferece o Tokyo, JAPAN OCT. 1999, Piscataway, NJ, UA,IEEE, U, vol. 4, p ,1999. [14] Xiaoyog AI, Tsuyoshi HIMIZU, Makoto OBI, "traightess Measuremet Based O Usig Improved Displacemet Method", The Japa ociety of Mechaical Egieers (C, Vol.66, No.646, p , [15] Eric H.K. Fug, M. Zhu, X.Z. Zhag, W.O. Wog, "A ovel Fourier-Eight-esor (F8 method for separatig straightess, yawig ad rollig motio errors of a liear slide", Measuremet 47, p Tsuyoshi himizu received the B.Eg. degree i 1994 ad M.Eg. degree i 1996 both i mechaical systems egieerig from Uiversity of Yamaashi, Yamaashi, Japa. He received the Ph.D. degree i mechaical egieerig from Tokyo Uiversity of Agriculture ad Techology, Tokyo, Japa, i From 1996 to 1997, he worked i Mitsui eiki Kogyo Co., Ltd., aitama, Japa. From 1997 to 2006, he was a Research Associate at the Productio Egieerig Laboratory i Uiversity of Yamaashi. ice 2006, he has bee a Associate Professor with the Mechaical ystems Egieerig Departmet, Uiversity of Yamaashi. His research iterest icludes the developmet of machiig processig, the developmet of measuremet the work piece profile ad the developmet of measuremet three dimesioal shape. 6

7 Takaaki Ishii received the B.c. degree i 1987, the M.c. degree i 1990 both i physics from ophia Uiversity, Tokyo, ad the Ph.D. degree i 2000 from the Tokyo Istitute of Techology. I 1988, he was a Visitig Research Assistat of the Materials Research Laboratory at The Pesylvaia tate Uiversity, UA, doig research o ultrasoic motors. From 1990 to 1993, he was a egieer for ALP Electric Co., Ltd., i Niigata, Japa, egaged i research ito piezoelectric ceramics ad ultrasoic motors. He was a Research Associate of the Precisio ad Itelligece Laboratory at the Tokyo Istitute of Techology from 1994 to 2002, workig o ultrasoic motors, wear evaluatio of frictio materials, piezoelectric actuators ad other ultrasoic devices. He was a Research Associate of the Iterdiscipliary Graduate chool of Medicie ad Egieerig, Uiversity of Yamaashi from 2002 to He has bee a Associate Professor of the Iterdiscipliary Graduate chool of Medicie ad Egieerig, Uiversity of Yamaashi sice He curretly coducts research i high power ultrasoics. Dr. Ishii is a member of the Acoustical ociety of Japa ad the Japaese ociety of Tribologists, the Istitute of Electroics, Iformatio ad Commuicatio Egieers, the Japa ociety of Applied Electromagetics ad Mechaics, the Japa ociety of Mechaical Egieers ad the Japa ociety for Welfare Egieerig. Yuzairi Abdul Rahim received the B.Eg. degree i 2006 ad M.Eg. degree i 2008 both i Mechaical ystems Egieerig from Uiversity of Yamaashi, Yamaashi, Japa. From 2008 to 2012, he worked as a desig egieer for howa Glove Co., Ltd., i Himeji, Japa, used to hadle the desigig of the productio lies, research o ew techologies, ad supportig for techical support locally ad abroad. After that, he was trasferred to oe of howa Glove s factory which is situated i Malaysia called horubber (M d. Bhd. ad worked as a maiteace egieer. Now, he is studyig i Ph.D. programs (Iformatio ad Mechaical ystems Egieerig i Uiversity of Yamaashi, Yamaashi, Japa sice April 2014 uder Malaysia Educatio Miistry scholarship, which holds agreemet as fellow i chool of Maufacturig, Uiversity Malaysia Perlis (UiMAP, Malaysia. He curretly coducts some research i machiig ad gridig mechaism. 7