Assessment of the impact of calculation methodologies on defect determinations in manufacturing

Transcription

1 iginal Aticle HME Poceedings of IDMME - Vitual Concept 2010 Bodeaux, Fance, ctobe 20 22, 2010 Assessment of the impact of calculation ologies on defect deteminations in manufactuing Bui-Minh H. 1, Segent A. 1, Villeneuve F. 2, Duet D. 1, (1) : SMME Laboatoy, Univesity of Savoie 5 chemin de Bellevue, Annecy le Vieux, Fance Phone: Fax: { hien.bui-minh, alain.segent, daniel.duet}@univ-savoie.f (2) : G-SCP Laboatoy 46 avenue Félix Viallet Genoble, Fance Phone: Fax: fancois.villeneuve@g-scop.inpg.f Abstact: Many eseach woks on s to detemine manufactuing have been developed. btained esults fom these studies can be used fo impoving poduct qualities. If manufactuing ae classified accoding to causes of eos, it might include: machining (machine tool, cutting tool, tool-path, machining pogam), positioning (wok-holde eos, datum eos (suface deviations fom a pevious setup), eos of contacts between wok-piece and wok-holde) [KV], themal eos, and skill opeation pocedue of technicians, o it could be eos of calculation s, which ae used to detemine the fom measued data. In this aticle, impact of calculation ologies on manufactuing is assessed. Fistly, the basic concept of calculation s is pesented. Secondly, diffeent calculation s used fo detemining manufactuing in an expeimental application ae poposed. Finally, influences of the diffeent calculation s on esults ae estimated. Key wods: machining defect, positioning, impact, calculation ology, Small Displacement Toso (SDT). 1- Intoduction and liteatue eview In ecent yeas, many eseach woks on s to detemine manufactuing have been developed. Among the s, thei esults can be used to pedict souces of in ode to impove poduct quality in fabications. If the manufactuing ae chaacteized accoding to causes of eos, it might be illustated in figue 1. Model of Manufactued Pat (MMP) [VV1, VV2, and VV3] that is poposed by Villeneuve and Vignat is used to simulate the manufactuing pocess in tems of deviation. This model can be used in toleance analysis and synthesis. Manufactuing ae consideed using two independent components: machining and positioning deviation. In ode to sepaate the machining and positioning dispesions, Tichadou et al. [TL] poposed a double measuement of the wok-piece. Eos of detemination s Machining Manufactuing Machine tool eos Cutting tool eos Tool-path eos Cutting paametes,... Positioning Wok-holde eos Wok-piece datum eos Contact eos Figue 1 : Manufactuing the Themal eos Skill opeations... Consideing eos of cutting tools, Laue et al. [LA] obseved of cutting tool duing flank milling, and calibation ae then used to minimize uncetainties of manufactuing. Besides, cutting paamete is also a facto affecting poducts, some expeimental esults ae available, such as Sun et al. [SW] pesented stategies and algoithm on how to select width of cut, feed ate and spindle speed; Beauchamp et al. [RM1] investigated effects of six independent vaiables (cutting speed, feed ate, depth of cut, tool nose adius, tool length and type of boing ba) on suface oughness in a lathe dy boing opeation. In addition, Ramesh et al. [RM2, BC] focused on effects of geometic, cutting-foce induced, fixtue-dependent and themal eos on accuacy of a machine tool. Geometic, kinematic ae consideed as a basic inaccuacy of a machine tool; o changes in tempeatue of the vaious machine elements ae causes of inceasing inaccuacy of machine tools; wok-piece displacements on a fixtue ae also taken into account and could be educed using tool-path compensation. In geneal, manufactuing ae detemined using diffeent calculation s fom measued data. Diffeent calculation s can give diffeent esults; consequently, poposed s should be assessed to be able to choosing Pape Numbe IDMME_P106-1-

2 a suitable. Howeve, thee ae few studies on influences of calculation s on obtained esults in manufactuing. This aticle consides impacts of diffeent s that ae used to detemine manufactuing. Concetely, sensitivity of the calculation s is shown in an expeimental application. 2- Basis concept of calculation s The s used fo detemining the manufactuing ae based on the Small Displacement Toso (SDT) concept, which has been developed since the seventies by Boudet and Clément [BM, EB]. This concept is based on an assumption of small displacements of a igid body. It allows solving a geneal poblem of the fit of a geometical suface model to a set of points. A SDT is epesented using two vectos: vecto R includes thee small otations,, x y zand vecto L includes thee small tanslations t,t,t x y z. Thank to the SDT concept, Villeneuve et al. [VV4] have extended to manufactuing pocess whee machining deviations wee obtained using measuement of elationships between a nominal pat (pefect sufaces) and a eal pat. A SDT can be used to show diffeent sufaces, fo instance: two otations and one tanslation (along a nomal vecto of a plane) in a SDT ae used fo plane, o two otations and two tanslations (along two axes, which ae pependicula with cylinde axis) ae used fo a cylinde SDT, etc. Let () be the oigin system of a plane, which has a nomal vecto along. A SDT of this plane is expessed using thee components, which ae diffeences between an associated plane and a nominal plane (figue 2). The plane SDT is shown as in equation (1). x 0 (1) T Plane R L 0 (,,, ) y 0 tz Associated suface (,,, ) The fist measuements ae caied out inside a machine tool duing machining. The second measuements ae caied out on a. The dawing of a wok-piece and a machined pat ae illustated in figue 3. Two planes of a pat, which is fixed on a fixtue on the machine, ae machined using an endmill (20). 48 Ø30 Wok-piece Machined plane 1 Figue 3 : A machined pat Machined plane 2 Plane 0 As peviously mentioned, a double measue is caied out in ode to detemine the manufactuing. The fist measuement (figue 4a) is caied out inside the machine afte machining without disassembly the machined pat out of the fixtue. A (Mah-Vision MS222) (figue 4b) is then used to measue 50 machined pats, which ae maked in execution ode fom 1 to 50. Real suface tz y Vi x Nominal suface a) b) Figue 4 : Measuements on the machine (a) and the (b) Figue 2 : A SDT of a plane [KV] Accoding to this concept, SDTs of two machined planes and a SDT elation of two planes ae obtained in the following expeimental application. 3- Expeimental application A batch of 50 pats is machined using machine (DMG- Deckel Maho DMU 50). Diffeent can occu duing a manufactuing pocess. In paticula, the two following pincipal ae consideed in this study. A positioning vaiability of wok-pieces on a fixtue, A machining vaiability of machined pats, Vaiability of positioning and machining ae detemined using the two following independent measuements. A coodinate system of the machined pats is used fo compaing two diffeent esults that ae obtained using the two machines. The coodinate system is defined using a cylinde and a bottom plane of each machined pat. Hee, the bottom plane of a machined pat is called a locating plane. Figue 5 : A coodinate system of a machining/measuing pogam Pape Numbe IDMME_P106-2-

3 It is impotant to notice that a locating plane cannot be measued in the fist measuement (). Consequently, a plane (a pefect plane) of a coodinate system of a machining/measuing pogamme (figue 5) is used to define a pat s coodinate system in this case. Convesely, a locating plane of a machined pat can be measued using the. Measued points of a cylinde and machined planes of each pat ae obtained fo analysing positioning and machining. 4- Calculation ologies Hee, thee components in a SDT of each plane (two otations aound and ; one tanslation along ) ae obtained. The best-fit least-squae pesented by Alistai [A] is used to econstuct machined planes and a cylinde of a pat fom measued points, namely associated planes and associated cylindes. Centoid of a machined plane (figue 6) is used as an oigine of a efeence fame fo expessing a plane SDT. Theefoe, centoids of machined planes ae needed to identify. G 1 SDTs of machined plane 1 and 2 ae expessed in fames R G 1 and R G2 as in equation (1) TPL1 1 0 and TPL t 1 0 t (G 1,R) 2 (G 2,R) (1) The two SDTs can be expessed in a fame R as in equations (4) and (7), whee is a centoid of a locating plane. 1 D DG1 S/R G1 (2) 3R d D d 01.1 t z1 0 d 01 3.R. 1 t 1 4 (3) 1 d TPL1 1 d R.1 t 1 4 (4) D D G 2 G2 S/R 2 G 2 (,R) G=3R/4π R Figue 6 : Centoids of machined planes (5) 3R d D d 02.2 t 2 0 d 02 3.R. 2 t 2 4 d TPL2 2 d R.2 t 2 4 (,R) whee d 01, d 02 ae distances between machined planes 1, 2 and a locating plane. Futhemoe, elationships of machined plane 1 and 2 can be expessed using the following SDT (8). 1 2 d 01.1 d TPL d 01.1 d 02.2 (8) R.1 t 1.R.2 t (,R) It is impotant to emphasize that components of a SDT ae vaiations of of 50 pats. Thus, tanslation and otation of 50 machined pats ae detemined, and thei vaiations ae then obtained. 4.1 Detemination of otation components Two diffeent coodinate systems defined fo analysis ae a coodinate system of machine (MCS) and a coodinate system of pat (PCS) as in figue 7. MCS is defined using thee axes of a machine () and its oigin is: o o M (6) (7) An intesection point of a cylinde and locating plane of the fixtue (on the machine), A point that is moved along machine 15mm (adius of pats) fom an intesection point of locating plane and an end-plane, which is pependicula with pat s cylinde axis, of a V-block (on the ), M P P P P M M n n cyl pl1 Figue 7 : Coodinate systems PCS is defined as follows: o -axis is a wok-piece s associated cylinde axis. o, ae the same diection with and machine. M n pl 2 Pape Numbe IDMME_P106-3-

4 o n the machine, its oigin is an intesection point of an associated cylinde axis and a locating plane of the fixtue. o n the, its oigin is an intesection point of an associated cylinde axis and a locating plane of a machined pat. The otation components ae calculated in the PCS as follows. M P Pojection points M P Pojection points n M 1 n P 2 points Associated plane M n cyl cyl pl M n pl M M n cyl n pl cyl pl M Figue 8 : Rotation components Fom figue 8, angles between a cylinde axis and a nomal vecto of machined planes is defined as in equation (9). (pl/cyl) (pl/) (/cyl) (pl/cyl) (pl/) (cyl/) o (pl/cyl) (pl/) (/cyl) (pl/cyl) (pl/) (cyl/) (9) Thus, the otations of the machined planes aound x, y axes ae: n ypl n ycyl actan actan n zpl n zcyl (10) n xpl n xcyl actan actan n zpl n zcyl whee n pl, n pl : pojections of a nomal vecto npl n xpl,n ypl,nzpl of a machined plane on the plane () and (). n cyl, n cyl : pojections of the diection vecto ncyl n xcyl,n ycyl,nzcyl of the associated cylinde axis on the plane () and (). 4.2 Detemination of tanslation components Thee diffeent s ae poposed in ode to detemine tanslation components of SDTs using the two coodinate systems (MCS and PCS) In this, centoid of each associated plane is pojected on the axis of the MCS ( M ) (figue 9.a). Vaiations of the pojected points of plane 1 and 2 then ae obtained. These ae tanslation components of the SDTs of the two machined planes Hee, centoids of associated planes ae pojected on an associated cylinde axis in the PCS ( P ) (figue 9.b). The tanslation components of SDTs of the machined planes ae vaiations of the pojected points of plane 1 and 2. - M A point intesection of an associated plane and an associated cylinde axis is consideed in the PCS (figue 9.c). Vaiations of these points ae obtained as tanslation components of SDTs. Some emaks ae deived as follows: Results obtained on the machine ae machining. d 01 and d 02 ae notations of tanslation of machined planes and plane 0 (locating plane). In this case, of locating a) b) c) Figue 9 : Calculation s plane equal zeo. Results obtained on the might include: machining of machined planes, contact between wok-pieces and the fixtue on the machine, and of wok-piece s locating planes. Hence, thee ae diffeences of the two above esults (d 01, d 02 ), which ae obtained using two diffeent machines. Relationships of two machined planes ae estimated using a deviation d Pesentation of esults The following esults show components of SDTs, which its otation ae detemined using only one, while tanslation ae detemined using thee diffeent s Rotation components Rotation components of SDTs in table 1 ae obtained using measuements on the machine and the. Rotation components in the PCS Name s (ad) * s (ad) * s 2 (ad 2 ) ** s 2 (ad 2 ) ** Table 1 : Rotation components (in the PCS) * : Standad deviation; ** : Vaiance, --: undetemined values As it can be seen, diffeences of vaiances ( 1, 1 ; 2, 2 ) fom the two diffeent machines ae insignificant. Howeve, vaiances of otation ( 0, 0 ) obtained on the ae geate than machining ( 1, 1 ; 2, 2 ). In othe Pape Numbe IDMME_P106-4-

5 wods, the positioning ae significant; consequently these ae taken into account in calculations of tanslation components Tanslation components As it is mentioned, influences of calculation s as well as positioning ae assessed using the following esults. In this pesent study, influence of measuing machines is not taken into account. Howeve, noise measuements ae veified and these ae insignificant. 1- Rough esults of measuements on the machine and esults of measuements on the Figue 10 epesents the esults obtained on the machine. The esults show tanslation vaiations of the two machined planes ( s 2 2 d01,s d02 ) and the wok-piece s locating planes (planes 0). As it is mentioned in the section 3, vaiations of the wokpiece s locating planes equal zeo ( s 2 0 0). (Note: 0 in d 01 and d 02C epesents the pefect plane.) Figue 10 : Tanslation components by measuements on the machine ( ) (Note: 0 in d 01 and d 02 epesents a locating plane of a wok-piece.) Figue 11 : Tanslation components by measuements on the ( ) Figue 11 shows tanslation components of the two machined planes, which ae obtained using the. As it is afoementioned, these tanslation might include: machining of machined planes, contact between wok-pieces and the fixtue on the machine, and of wok-piece s locating planes. s (mm) s 2 (mm 2 ) Tanslation Name d01 d02 d Table 2 : Tanslation Table 2 shows vaiances of tanslations of 50 pats. These vaiances ae obtained using the thee diffeent s on the two diffeent machines. Two planes of a pat ae machined using two diffeent machining pocesses and diffeent tool paths. In othe wods, the two pocesses ae independent. Consequently, machining obtained ae independent. These ae veified by the following step. a) Veification of elations: Accoding to popeties of vaiance and covaiance in pobability theoy and statistics, two andom vaiables whose covaiance is zeo ae called uncoelated. These apply to the esults of measuements on the machine in ode to veify elations of two vaiables ( s 2 2 d01,s d02 ). If the two vaiables ae independent, then thei elations can be shown as in equation (11) sd12 sd01 sd02 (11) The esults obtained on the machine ae veified using equation (11), but they ae not satisfied. Moeove, figue 10 shows that the tanslation of the two machined planes incease togethe duing machining times (fom the 1 st pat to the 50 th pat). It means that these ae dependent. It could be due to tempeatue vaiations, which ae not taken into account in the pesent study. In addition, the spindle of the machine has not a themal compensation device. Consequently, these dift should be coected. In a pevious study [SD], esults show that evolution of tempeatue depends on measuing times. In geneal, a measuement eo has two components: andom and systematic. The andom component causes a spead in the esults of measuement, wheeas the systematic Pape Numbe IDMME_P106-5-

6 component causes a bias in the esults. The difts of d 01 and d 02 in figue 10 ae systematic eos. Consequently, these should be coected. b) Diffeences of the esults on the two diffeent machines: It can be seen that diffeences between vaiances of the machined planes on the and the machine ae significant (figues 10, 11 and table 2). These can be explained by the two following souces: Positioning of wok-pieces on the fixtue in the machine, Defects of locating planes of wok-pieces (plane 0), These two points will be detailed late. c) Diffeences of the esults on the same machine: Results obtained on the same machine with the thee s ae diffeences. Thus, influences of the s on the obtained esults ae significant. A sensitivity of these s will be consideed in the section late. 2- Coection of the ough esults on the machine As the pevious conclusions, the esults obtained on the machine ae coected using systematic components. These components ae detemined using tendlines of measued data. k k k d0ico d0imeas i (12) k whee d 0imeas is a tanslation defect of the machined plane i of the k th pat. k d 0ico is a tanslation defect of the machined plane i of the k th pat afte coection. k i is a dift of the machined plane i of the k th pat. This is calculated using a powe equation as follows: k m i a.k (13) k is a pat numbe (1, 50). a) Veification of elation: In table 3, tanslation ae coected using the systematic components. s (mm) s 2 (mm 2 ) Coected tanslation Name d01 d02 d Table 3 : Coected tanslation Afte coection, the esults of two s (pojection M and intesection ) ae satisfied, theefoe the coections of a systematic component ae necessay. b) Diffeences of the esults on the same machines: Despite the systematic coection, thee ae still diffeences of the obtained esults by the s. It means that influences of the s ae significant. c) Diffeences of the esults on two diffeent machines: The systematic component coections ae not sufficient to obtain simila esults by two diffeent machines. Hence, the two facto effects (plane 0 and positioning of wokpieces) will be consideed in the next section. 3- Influence of positioning on the tanslation components In ode to quantify a sensitivity of the calculation s and positioning (on the machine), coelation coefficients of the tanslation and otation of the wok-pieces on the fixtue ae obtained as in table 4. Name RotCyl of Coelation coefficients RotCyl of RotCyl of d d d Table 4 : Coelation coefficients The esults show that all the coelation coefficients ae less than o equal to 0.5. It means that elationships between the tanslation and positioning ae weak. Thus, the influences of positioning on the calculations of tanslation components ae insignificant. 4- Influence of locating planes on the tanslation components The wokpiece s locating planes ae used to establish the LCSs, which ae used to obtain. Thus, these planes can influence the obtained esults. The following table (5) shows coelation coefficients of tanslation and the otation of these planes. Name Rot0 of Coelation coefficients Rot0 of Rot0 of d d d Table 5 : Coelation coefficients It can be seen that the coelation coefficients ae small. Theefoe, influence of the wokpiece s locating planes is insignificant on the tanslation. 5-Conclusions As examination of expeimental esults, the calculation ologies stongly influence on the measuement Pape Numbe IDMME_P106-6-

7 esults. Convesely, effects of the wok-piece s geometical eos and the positioning on the calculations of tanslation ae insignificant. This study pesents that choice of numeical analysis s fo identification can influence on quality of measuement esults. Theefoe, data analysis s ae impotant in contolling poduct quality. The esults also indicate that, in some expeiments, the measuement vaiability is a sum of a andom dispesion and a systematic dispesion. Then the systematic component should be coected in ode to etain only the andom component. This study deal with the poblem of elative position of two paallel planes. This seems tivial, but it has not been analysed. Manufactued Pats. In Digital Entepise Technology, Spinge US, , [VV2] Villeneuve F., Vignat F. Manufactuing pocess simulation fo toleance analysis and synthesis. In Advances in Integated Design and Manufactuing in Mechanical Engineeing, Spinge Nethelands, , [VV3] Villeneuve F., Vignat F. Simulation of the manufactuing pocess in a toleancing point of view: Geneic esolution of the positioning poblem.in Models fo Compute Aided Toleancing in Design and Manufactuing, Spinge Nethelands, , [VV4] Villeneuve F., Vignat F., Landon. Toleancing fo manufactuing: a thee-dimensional model. Intenational Jounal of Poduction Reseach, 39: , Refeences [A] Alistai B-F., Least squaes Best-fit geometic elements, In NPL epot, [BC] Boudet P., Clément A. A study of optimal-citeia identification based on the small displacement scew model. Annals of the CIRP, 40: , [BM] Boudet P., Mathieu L., Latigue C. and Ballu A. The concept of the small displacement toso in metology. In Advance Mathematical Tool in Metology II, Edited by Wok Scientific Publishing Company, Seies Advances in Mathematics fo Applied Sciences, 40: , [EB] El Maaghy W., Boudet P., ElMaaghy H. Small displacement toso theoy and vaious compensation schemes foe complex fom ealization. CPI, Casablanca, Moocco, [KV] Kamalinejad M., Vignat F. and Villeneuve F. Simulation of the geometical of manufactuing. In the Intenational Jounal of Advanced Manufactuing Technology, 45(7-8): , [LA] Laue A., Anselmetti B. Deviation of a machined suface in flank milling. Intenational Jounal of Machine tool and Manufactue, 43: , [RM1] Ramesh R., Manan M. A., Poo A. N. Eo compensation in machine tool a eview. Pat I: geometic, cutting-foce induced and fixtue-dependent eos. Intenational Jounal of Machine tool and Manufactue, 40: , [RM2] Ramesh R., Manan M. A., Poo A. N. Eo compensation in machine tool a eview. Pat II: themal eos. Intenational Jounal of Machine tool and Manufactue, 40: , [SD] Segent A., Duet D., Nguyen D.S. and Villeneuve F. Pefomances d un moyen de mesue in situe su M..C.N.. In Contôles essais mesues, 35-39, [SW] Sun G., Wight P. Simulation-based cutting paamete selection fo ball end milling. Jounal of Manufactuing of Systems, 24(4): , [TL] Tichadou S., Legoff., Hascoet J-. 3D manufactuing dispesions: two expeimental applications. In CIRP, [VV1] Vignat F., Villeneuve F. Simulation of the Manufactuing Pocess, Geneation of a Model of the Pape Numbe IDMME_P106-7-