COMPARISON OF A MACHINE OF MEASUREMENT WITHOUT CONTACT AND A CMM (1) : OPTIMIZATION OF THE PROCESS OF METROLOGY.

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1 TEHNOMUS - New Technologes and Products n Machne Manufacturng Technologes COMPARISON OF A MACHINE OF MEASUREMENT WITHOUT CONTACT AND A CMM (1) : OPTIMIZATION OF THE PROCESS OF METROLOGY. WOLFF Valery 1, TRAN DINH Tn 2 1 IUT Lyon 1, Unversty of Lyon, valery.wolff@unv-lyon1.fr 2 Unversty of Lyon 1, tdtnbd@yahoo.com Abstract: In the feld of the control of manufactured products, the process of measurement usually proceeds on a type of machne (for example CMM) and the totalty of measurement s then carred out. We propose here to study the capactes of 2 types of measurng machnes n order to gude the operator towards an optmzed choce of the process of measurement. The takng nto account of the capablty of the machne assocated wth the feasblty (faclty of use) of measurement wll be also supplemented by the takng nto account the tme necessary to realze measurement. A better knowledge of the lmts of each machne wll allow an optmzaton of the process of control. Keywords: metrology, control, CMM, no-contact measurng system, ndustral vson 1 Introducton The three-dmensonal metrology s one of the man problem for many ndustres for achevng dmensonal and geometrc product control. The control of techncal parts for the plastc ndustry, automotve or electroncs s more and more usng the optcal measurng systems wthout contact. The other way s to use a CMM (coordnate measurng machne) for a more classcal control. We have chosen to work wth these two types of machne to develop our study. We try to defne a methodology to optmze the use of these dfferent types of measurng machnes. 2 Problematc There are three man steps durng the realzaton of manufactured products: the stages of desgn, manufacture and control. The desgner defnes the functonal dmensonng of the parts by usng the GPS standards. The tradtonal method, for the control of the parts n metrology, conssts n defnng a measurement plan n adequacy wth the measurng nstruments avalable (We have to separate, for example, the measurement of the roughness of a surface, and the 3D control of geometrcal specfcatons). We can note that an operator usually prefers to use only one machne when t s possble. For example, n the case of the use of a CMM, the entrety of measurement wll be carred out on the machne (dmenson, form, and poston specfcatons). The dea we want to develop here, relates to the possblty of a dstrbuted control: usng dfferent measurng nstruments for dfferent specfcaton. Is t preferable, n term of cost, to carry out the totalty of a control on the same machne? Or s t better to carry out measurements on varous machnes? Ths queston s the base of the process plannng n manufacturng actvty. But, t s a non studed pont for the control of the parts. 3 Study The context of the study s the ndustral vson systems [2] and we are usng the optcal methods for dmensons measurng. In our study, the system s equpped wth an optcal devce (camera) gvng to the operator an mage of the measured part. The optcal machne s a TESA V300 (Fgure 1). It s a manual machne wth trple lghtng: dascopc, epscopc and LED. Each axs (X/Y/Z) has a resoluton of 0.05 m. 9

2 TEHNOMUS - New Technologes and Products n Machne Manufacturng Technologes tol Tolerance Fgure 1 : Tesa Vso Measurement method For ths study, we use a reference standard rng. So, we can compare the results of the measurement to the theoretcal value. Ths s a standard datum rng wth dameter accuracy less than 10-3 mm. The TESA Vso provdes 3 possbltes: manual selecton of each pont, automatc acquston for each pont, global acquston of a profle (automatc sector detecton). The frst step of the study was to measure dameter dsperson by usng dfferent ways to capture a geometrcal element on a standard rng. The obtaned results [8] show that the mnmum dameter dsperson s gven by the manual method (Fgure 2). Theoretcal value 3 Automatc 2 1 Global profle Manual acquston 15 15,005 15,01 15,015 15,02 15,025 15,03 15,035 15,04 Fgure 2 : accuracy of measurement methods In ths artcle, we have chosen the manual mode. It s the best way to get accurate results for our experments. By measurng the reference standard rng, we can obtan several values: the dameter, the XY poston of the center and the crcularty default (form). The fgure 3 shows the defnton of the crcularty. Fgure 3 : crcularty default The real lne (we can call t: real crcle ) must be ncluded nto an area: the Tolerance Zone. In the case of the crcularty, the tolerance zone s defned by two crcles wth the same center, and wth a radus dfference lower than the value of the specfcaton. If we are usng the Tesa Vso machne n a classcal way, we can obtan each crcle we measure wth only three data: dameter, form and poston. But, for the form nformaton, we have only a global result wthout any possblty to have a detaled measure. For example, we choose to acqure 20 ponts for a crcle. We could expect to have 20 pars of XY coordnates. In the Tesa Vso 300, the machne calculates a theoretcal best ft crcle assocated to the 20 ponts and gves only the fnal result: the default of form (crcularty). Because we want to have a detaled study of the results of each measurement, we have chosen to measure all ponts ndependently. After that, we use an Excel Sheet to calculate the same nformaton we could have obtaned wth the Tesa Vso. The method of calculaton s presented nto the next paragraph. 3.2 The calculaton method In the mechancal engneerng feld, the metrology often needs to calculate mathematcal elements assocated wth real elements. In the GPS (geometrcal product specfcaton) concept, the term of skn model represents the real surfaces (fgure 4). The most common method used to assocate a theoretcal element to a skn model s the method of least squares [1]. Ths method allows estmatng the numercal values of the form. 10

3 TEHNOMUS - New Technologes and Products n Machne Manufacturng Technologes Nomnal element Assocated model $ Fgure 4 : skn model and mathematcal assocaton Skn model It exsts wth several varatons: t s smpler verson s called ordnary least squares (OLS), a more sophstcated verson s called weghted least squares (WLS), whch often performs better than OLS because t can modulate the mportance of each pont n the fnal soluton. Recent varatons of the least square method are alternatng least squares (ALS) and partal least squares (PLS). [1] The oldest (and stll most frequent) use of OLS s lnear regresson, whch corresponds to the problem of fndng a lne (or curve) that best fts a set of ponts. In the standard formulaton, a set of N pars of coordnates {x, y } s used to fnd a par of parameters, and (fgure 5) Solvng these 2 equatons gves the least square estmates of, and. The OLS method can be extended to more than one ndependent varable (usng matrx algebra) and to non-lnear functons. In ths artcle, we are calculatng the default of form of the datum rng. The result of the experment (coordnates of ponts) to determne the crcle requres to use the polar coordnates. e y x Fgure 6 : least square method for a crcle The fgure 6 shows the parameters we use to determne a theoretcal crcle assocated to a real set of ponts. Fgure 5 : least square method for a lne The least square method defnes the parameters and as the values whch mnmze the sum of the dstances e ² (hence the name least squares) between the measurements and the model. What leads to mnmze the functon: 2 ( e ) (1) Ths s acheved usng standard technques from calculus, namely the property that a quadratc (.e., wth a square) formula reaches ts mnmum value when ts dervatves s equal to zero. Ths gves the followng set of equatons (called the normal equatons): 0 and = 0 (2) Z : dstance s measured from the nomnal crcle e : error after calculaton R: radus varaton of the expermental crcle compare wth the nomnal crcle u, v: dstance between the two centers (small dsplacement) Based on the fgure 6, e s calculated as follows: e z u cos v sn R (3) After calculaton, we replace u, v and R nto the equaton (3). The values (e max - e mn ), determne the default of form of the crcle. 3.3 The desgn of experment In the am to compare the two machnes we have, the expermentaton was carred out n a 11

4 TEHNOMUS - New Technologes and Products n Machne Manufacturng Technologes smlar way on the Tesa Vso 300 and the trmesure CMM. We used the manual mode for TESA Vso 300 wth the setup parameters as follows: down lght, zoom at 50%, and manual acquston of the ponts. The CMM allows to measure crcles and to export all ponts after the measurement operaton. We measured the datum rng several tmes. For each machne, we get the ponts from fve measures. Each measure, s composed of twenty ponts wth X, Y coordnates. The fgure 7, shows the poston of the centre of a measured crcle obtaned by the calculaton of the two parameters u and v. If we want to compare (wth a graph) our results on the crcularty default, we need to have all of the ponts x,y expressed nto the same datum coordnate system. X Y u 0,00 8,504-0,038 v 0,00 8,128 2,512 dr 0,002 0,010 CMM emn - 0,005 8,066-2,678 emax 0,005 X Y u 0,001 8,504 0,137 v 0,001 8,126 2,503 dr 0,002 Vso 300 0,010 emn - 0,005 8,068-2,685 emax 0,005 Table 1 : CMM and Vso300 datum system least square method gves u = v = 0 (table 1). The only one parameter s R. For TESA V300 machne, we measured 8 ponts on the crcle to determne the center of the crcle. Ths center s then defned as the orgn of the system. Ths s necessary before to obtan 20 ponts by second measurement operaton. In ths case we can have small dsplacement: u and v have small values (Table 1). Ths s one of the assumptons of the least square method. After performng the experments, we calculate wth an excel sheet the parameters of each crcle composed of 20 ponts. 3.4 The statstcal approach We made fve measurements for each type of machne. For more accurate results durng the analyss, we took the average value wth two methods (Fgure 8). The frst approach: Each set of 20 ponts measurement determne a crcle by usng the least squares method. Each measurement allows obtanng a crcularty default. We wll then calculate the average value of the crcularty parameter. The second approach: After performng the experment, we calculate the average (x, y ) coordnate for each pont of each measurement. The least square method s used only after ths step. We determne the parameters of a crcle calculated wth the average set of ponts. Fgure 8 : statstcal method The am of these two approaches was to determne the best methodology (n term of tme of measurement and calculaton). Fgure 7 : nomnal (dot) and optmzed (red lne) crcles On the CMM machne, t s easy to obtan all coordnates wth a defned orgn. The software allows defnng an orgn before to save all the coordnates (x, y ). In ths case, each crcle s used as the orgn of the system. The calculaton of the 4 Results and analyss The qualty of the measured crcle (crcularty default) has the same average value for the two machnes we used (0,007 mm on the CMM and 0,010 mm on the Vso300). 12

5 TEHNOMUS - New Technologes and Products n Machne Manufacturng Technologes The repeatablty of the measure between each set of 5 measurements allows us to say that the result can be studed (fgure 9). Vso300 0, 90, 180 or , 135, 225 or 315 CMM Fgure 9 : graphcal results The most mportant result we have notced relates to the graphcs on fgure 10 (case of the Vso300). The graphcal observaton shows that the area where we can obtan the outer and the nner pont of each measure s at a dfferent place. For the CMM machne, the results are good at the postons: 0, 90, 180, 270 and for the TESA Vso300 machne, the best results are at ponts 45, 135, 225, and 315. Ths can be explaned by the way we acqure the ponts. On the CMM machne, the move of the sensor s controlled by a numercal system wth two X and Y axs. The drecton of the move gves more relablty f we use only one movement at the same tme: X only or Y only. Fgure 11 : vso300 acquston The combnaton of the two axs for a smultaneous move nvolve a dfferent dsperson due to the detecton of the measured surface by the sensor. In the case of the Vso300 machne, t s more dffcult for the operator to be precse when he try to measure a pont wth the tangent poston than wth a clear ntersecton of the cursor and the crcle (Fgure 11). 5 Concluson Ths artcle s a frst step for a more global study. It shows that the choce of the machne we want to use s maybe lnked to the capablty of the measurement machne (average value of the crcularty n our case), but also lnked to the tme we want to spend for the measurement operaton. The choce of the ponts (number and poston), and the way to acqure each pont s a subject that wll be expermented n a next study. We wll also extend the study by takng nto account the velocty of the machne (n partcular for the CMM machne). small dsperson large dsperson Fgure 10 : best result area for the Vso300 References [1] Herve Abd, Least Squares, The Unversty of Texas at Dallas, Rchardson, TX , USA. [2] P. Bourdet, C. Lartgue, A. Contr. Les capteurs 3D état de l art, problématque lée à la précson des systèmes de numérsaton 3D." 3ème congrès Numérsaton 3D/Human Modelng, Pars, ma [3] J.-L. Charron. Mesure sans contact Méthodes optques (parte 1). Technque de l Ingéneur, [4] J.-L. Charron. Mesure sans contact Méthodes optques (parte 2). Technque de l Ingéneur,

6 TEHNOMUS - New Technologes and Products n Machne Manufacturng Technologes [5] R. Chrstoph, H. Neumann. Multsensor coordnate Metrology: Measurement of form, sze, and locaton n producton and qualty control. Verlag modern ndustre, [6] D. Gava. Vson conoscopque 3D : calbraton et reconstructon. Thèse de doctorat, Unversté René Descartes Pars V, [7] C. Mehd-Souzan. Numérsaton 3D ntellgente d objets de formes nconnues basée sur des crtères de qualté. Thèse de doctorat, Ecole Normale Supéreure de Cachan, [8] Valery Wolff, Arnaud Lefebvre, Dmtr Pachel, Jasper Thjs, Capablty of measurng machne: Case of an optcal measurng machne wthout contact, Proceedngs of IDMME Vrtual Concept 2010 Bordeaux, France, October 20 22, [9] H. Zhao. Multsensor ntegraton and dscrete geometry processng for coordnate metrology. Thèse de doctorat, Ecole Normale Supéreure de Cachan,