Optimization of machining fixture layout for tolerance requirements under the influence of locating errors

Transcription

1 MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol. 2, No. 1, 2010, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY MultCraft Lmted. All rghts reserved Optmzaton of machnng fxture layout for tolerance requrements under the nfluence of locatng errors S. Vshnupryan 1*, M. C. Majumder 2, K. P. Ramachandran 1 1 Department of Mechancal and Industral Engneerng, Caledonan College of Engneerng, Muscat, OMAN 2 Department of Mechancal Engneerng, Natonal Insttute of Technology, Durgapur, INDIA * Correspondng Author: vshnu@caledonan.edu.om Abstract Dmensonal accuracy of workpart under machnng s strongly nfluenced by the layout of the fxturng elements lke locators and clamps. Setup or geometrcal errors n locators result n overall machnng error of the feature under consderaton. Therefore t s necessary to ensure that the layout s optmzed for the desred machnng tolerance for a gven devaton n the set up or geometry of the locator. Also, the locator layout should be capable of holdng the workpart n a unque poston durng machnng thus provdng determnstc locaton. Ths paper proposes a Genetc Algorthm (GA) based optmzaton method to arrve at a layout of error contanng locators for mnmum machnng error satsfyng the tolerance requrements and provdng determnstc locaton. A three dmensonal workpece under the locatng scheme s studed. Results ndcate that by optmally placng the error contanng locators the geometrc error component of the machnng error can be substantally reduced thus enablng complance to overall dmensonal requrements. Keywords: Machnng error, optmal layout, locator error, genetc algorthm 1. Introducton Fxtures form an ntegral part of the manufacturng process and are requred to hold the workpece n the desred poston. The fxture desgn should am at restranng unwanted movement of the workpece under the acton of cuttng forces throughout machnng. Dmensonal accuracy of the machned part thus depends on the desgn of the locators and the layout and can contrbute up to 20-60% of the overall machnng error of the workpece (Qn, 2008). The fxture should be capable of holdng the workpece n a unque poston for machnng. Ths condton s called determnstc locaton. Asada and Andry (1985) used the knematc model and concluded that a full rank Jacoban matrx s the necessary condton for determnstc postonng of the workpece. They also derved the condton for attachablty and detachablty of the workpece wthn a fxture. Ca et al. (1997) used a varatonal method for achevng robust fxture confguraton. A non lnear programmng method was used wth an objectve of mnmzng the postonal error of the workpece resultng from source errors at the locators. Ths work consdered the requrement for determnstc locaton but dd not present a model for the analyss of machnng error on a requred feature. Choudhur and De Meter (1999) presented a model to relate datum establshment errors to locator geometrc varablty. The work studed the effect of gven locator errors on the varaton of machnng feature under a partcular locatng scheme. Agan, determnstc locaton was not addressed and the effect of locator postons on the resultant machnng error was not dscussed. Rong et al. (2001) used three dfferent approaches of locatng and analyzed the postonal varaton of locatng ponts resultng from the error of the locators and the locatng features. The work however dd not address the ssue of determnstc locaton. Song and Rong (2005) dscussed the crtera for the locatng completeness. Some researchers optmzed the clampng force (L and Melkote,2001 a) or clampng sequence (Raghu and Melkote, 2004) to mnmze the workpece postonal error. (L and Melkote, 2001 b) optmzed the fxture layout to mnmze the workpece error. Snce the workpece s evaluated by ts complance to the specfed tolerance, nfluence of locator errors on the requred machnng tolerance receved much attenton n recent years. For example Wang (2002) studed the effect of fxel errors on the tolerance of crtcal dmensons. Ths work suggested employng a D optmalty model to obtan an optmal layout. Marn and

2 153 Ferrera (2003) dscussed the effect of determnstc locator errors on profle tolerance of machned parts. Qn et al. (2006) dscussed an optmzaton methodology to mnmze the workpece postonal varaton. However machnng error s not dscussed. The same authors (2007) presented a method for locatng desgn based on the degrees of freedom constraned by the layout. Cases of complete, partal over and under over locatons were dscussed. Wang et al. (2007) analyzed the dfferent error components of the workpece surface. However ths study dd not dscuss the effect of locator layout on machnng error. Evolutonary technques for solvng optmzaton problems have been found to have a hgher probablty n fndng the global optmum values compared to tradtonal technques. GA s one such technque that fnds ncreased use n solvng optmzaton of locator layout problems. The task s to arrve at a partcular layout of fxture elements that provdes the mnmum error on the workpece (Kaya, 2005; Krshnakumar and Melkote, 2000; Padmanaban and Prabaharan, 2008). Smple two dmensonal cases are studed n these three works. The way of correlatng the layout optmzaton procedure to the tolerance on crtcal machnng features on the workpece s not dscussed. Chen et al. (2007) optmzed the locator layout to control the deformaton of a workpece. But geometrc errors of locators were not consdered. Whle the above mentoned studes have provded mportant and extensve concepts of fxture desgn they have one or more lmtatons such as not addressng the effect of locator geometrc errors on overall machnng error, condton for determnstc locaton and correlaton of layout optmzaton wth the crtcal machnng feature. Most of the above works employed tradtonal optmzaton methods that may not yeld the global optmum results. Snce the fnal machnng accuracy of the workpece depends on the correctness of the locators t s essental that the locators are machned to the requred accuracy and set up wthout any errors. However t s possble that errors are present n the form of dmenson or set up of the locators whch wll be transferred to the workpece thus causng devaton from the requred dmenson. Effect of locator error s comparable to the workpece elastc deformaton n case of low elastcty work parts. In the case of a rgd, bulky workpece the locator error s much more predomnant. Hence the locator layout s to be desgned optmally so as to mnmze the effect of the locator errors on the fnal machnng accuracy of the workpece. In ths paper, a GA based optmzaton of locator layout s attempted consderng the geometrc errors of locators satsfyng the condtons of tolerance requrements on the crtcal machnng feature whle ensurng determnstc locaton. Rest of the paper s organzed as follows. The source errors are revewed n Secton 2. Secton 3 gves a bref account of determnstc locaton and ts requrements. Concepts of GA and ts applcaton to the present work are dscussed n Secton 4. Secton 5 presents the numercal llustraton of the case studed. Results are dscussed n Secton 6. Major conclusons drawn n the study are presented n Secton 7 of the paper. 2. Source errors and resultant errors 2.1 Workpece postonal error Fxture elements (locators and clamps) are requred to hold the workpece n the desred poston throughout the machnng process. It goes wthout sayng that any devaton n these elements wll translate nto a faulty postonng of workpece thus resultng n machnng error. Locators may devate from the deal condton n two ways. Frst s n the form of the dmenson or shape of the locator whch s known as geometrcal error. The second s due to the wrong set up. In ths case the locator s correct n shape or dmenson but ts placement s ncorrect wthn the layout. Apart from these, the workpece locatng surface can also have devatons. These errors are part of the source errors and are llustrated n Fgure 1. Consder a fxture workpece system as shown n Fgure 2. We defne three co ordnates systems. The global co ordnate (GCS) system s fxed to the machne table, the workpece coordnate system (WCS) s fxed to the workpece and LCS s the locator coordnate system. At each contact pont the normal vector s denoted as n (n x, n y, n z ) and the source error n all the locators s collectvely wrtten as a vector. Note that ths denotes change n vector r c. As a result of these source errors the workpece poston and orentaton change, denoted by ΔX and ΔΘ. Now the workpece postonal error n GCS s wrtten as δp =[ ΔX ΔΘ ]=[δx, δy, δγ] T for 2 D δp =[ ΔX ΔΘ ]=[δx, δy, δz, δα, δβ, δγ] T for 3 D (1) Now the Jacoban matrx s defned as (Qn, 2008) T T T [ J J J ] T J = (2) m = 1 m denote the number of locators wth J = [ nx, ny, ny x nx y ] for 2D = [ n, n, n, n y n x, n z n x, n x n y ] J for 3 D (3) x y z z y x z The normal vectors n..n m are collectvely wrtten n the form of a normal vector matrx as N=dag (n 1 n 2. n m ) Now the followng relaton can be wrtten between source error and workpece postonal error + T δp = J N δs y x (4)

3 154 where J + s a Moore Penrose nverse matrx of J. Ideal poston of locator Actual poston of locator Ideal poston of workpece Actual poston of workpece Ideal dmenson of locator Actual dmenson of locator Desred poston of workpece Actual poston of workpece (a) (b) Fgure 1. Source errors n locatng (a) Set up errors (b) Dmensonal errors {GCS} Workpece δrw δθw {WCS} rc w n rw rc rl Contact pont Locator '' {LCS} Fgure 2. Coordnate systems and postonal error {GCS} {WCS} Workpece rp rc w rw rc rl rp w {LCS} Fgure 3. Machnng error P Locator '' 2.2 Machnng error Effect of the source errors results n the workpece postonal error δp as dscussed earler. If the processng datum and the locatng datum do not concde, t s called datum error (δdt). Ths error, combned wth the workpece postonal error result n what s called the machnng error δm of the workpece. Machnng error denotes the relatve moton of the cuttng tool wth respect to the processng datum. In a workpece ths machnng error can be depcted as the change n r p as shown n Fgure 3. Note that r p denotes the locaton of the processng datum n GCS. If the WCS and GCS are dentcally orented and the datum related error s neglected the followng relatonshp can be wrtten. δm=b δp (5) where B s the poston matrx of the processng pont and s gven by z y B = z 0 x y x 0

4 155 wth x, y and z beng the coordnates of the pont consdered. 3. Determnstc locaton When postoned n a fxture the workpece surface s made to contact all the locators. Determnstc locaton s sad to be acheved f the workpece s held n a unque poston when all fxture elements are made to contact the workpece surface. In other words determnstc locaton means that the workpece cannot make an nfntesmal moton whle mantanng contact wth all the locators. Asada and Andry (1985) showed that for determnstc locaton the Jacoban matrx should have a full rank. In other words, for determnstc locaton, rank (J)= 3 for 2D rank (J)=6 for 3D (6) 4. GA based fxture layout optmzaton 4.1 Workng of GA Tradtonal optmzaton technques based on mathematcal prncples suffer from many lmtatons that nclude dependence of convergence on the chosen ntal soluton, gettng stuck to a sub optmal soluton, problem specfc nature of the algorthms and neffcent handlng of problems wth dscrete varables (Deb, 2005). New evolutonary technques are found to perform better n ths context compared to tradtonal methods. One such technque s the GA. GA s a computerzed search and optmzaton algorthm based on the mechancs of natural genetcs and selecton. GA operates on a populaton of potental solutons applyng the prncples of survval of the fttest to produce better approxmaton solutons. At each generaton, a new set of approxmaton s created by the process of selectng ndvduals accordng to ther level of ftness n the problem doman and breedng them together usng operators borrowed from the natural genetcs. Ths process leads to the evaluaton of populaton of ndvduals that they were created from just as n natural adaptaton. The workng of GA s as follows. a. Intalzaton and representaton A populaton of solutons s created randomly. Each entry n the populaton s called a chromosome. The populaton thus generated wll contan N P number of chromosomes where N P s the populaton sze specfed. N P =50 n ths work. The chromosome can be represented usng bnary or real codng. In the present problem, real varable codng s used. Length of a chromosome depends on the number of varables used n the problem. Varables n ths problem are the locator coordnates. Ths study consders the locatng scheme hence there are sx locators wth X,Y and Z coordnates to be determned. So the problem s of dmenson 18. b. Evaluaton of ftness Each chromosome s evaluated for ts ftness. The ftness functon F(x) s derved from the objectve functon f(x) of the problem. For maxmzaton problems, ftness functon s the same as the objectve functon. For mnmzaton problems the ftness functon s defned as 1 F( x) = 1+ f ( x) (7) c. Testng for termnaton crtera The algorthm can be termnated by specfyng dfferent condtons lke the number of generatons, specfc objectve value, mprovement of objectve functon n successve generatons etc. The GA keeps searchng the soluton space for the best soluton. After certan number of generatons, the chromosomes become smlar. Beyond a certan pont n tme, a condton wll be reached that no better soluton can be found. Hence to save tme, certan number of generatons be specfed so as to stop the search. Otherwse the algorthm wll keep runnng wthout fndng any better soluton. In the present work, the algorthm has been programmed to stop f the objectve functon value remans same for 50 consecutve generatons. Ths s called stall generatons Ns. If the condton s not satsfed a new generaton s formed and the process repeats tll the maxmum number of generatons (N G ) s reached. In ths work, N G =150. d. Creaton of new generaton GA essentally performs three operatons to create a new generaton. These are Reproducton, Cross over and Mutaton. Reproducton: At ths stage parent chromosomes are selected from the populaton based on ther ftness and a matng pool formed. The probablty of a chromosome for selecton depends on ts ftness F.The probablty for selectng the th chromosome

5 156 F p = (8) N P j=1 where N P denotes the populaton sze. In reproducton, good chromosomes n a populaton are assgned a larger number of copes to form the matng pool. In ths study the rank based Roulette wheel selecton method s adopted for selectng chromosomes for reproducton. Cross over: The crossover operaton nvolves n two chromosomes exchangng certan part of ther genetc nformaton to produce new chromosomes. To retan some goodness already present n the matng pool only a certan percentage of chromosomes are nvolved n cross over. Ths s gven by the value of cross over probablty p c. Cross over operaton for real and bnary codng are done dfferently. In bnary codng sngle pont crossover, multpont crossover and unform crossover are commonly used technques. In real value codng the methods of cross over nclude dscrete cross over, lne cross over and ntermedate cross over. Dscrete cross over s used n ths study. Mutaton: After cross over s performed, the chromosomes undergo mutaton. Ths operator makes local changes n a chromosome to hopefully create a better chromosome. Smlar to the cross over operaton a random number s generated and f the number s less than the mutaton probablty p m (p m = 0.02 n ths work) mutaton s performed. Otherwse the chromosome s unchanged. In ths work an Incremental operator s used for mutaton. The ncremental operator works as follows. An ncrement value δ s chosen dependng on the problem doman and bounds. A partcular varable n the chromosome s chosen randomly. Mutaton operator ether adds or subtracts ths value from the varable to form a new chromosome Let a b c be the strng before mutaton. The strng after mutaton can be a+ δ b c or a- δ b c Flowchart shown n Fgure 5 outlnes the GA process. Smple Genetc Algorthm ( ) { ntal Populaton; evaluate populaton; Whle termnaton crteron not reached { reproducton; perform crossover and mutaton; evaluate populaton; } } Fgure 4. Genetc algorthm 4.2 Applcaton of GA to layout optmzaton As stated earler ths work consders the source error present n the locators n form of geometry and set up. When a workpece s loaded nto ths fxture and machned t results n devaton of the actual dmensons from the desred ones. Wth the manufacturng tolerances (mtol) beng specfed t s mandatory that the devatons should le below the tolerance specfcatons. The nfluence of source error of a locator on the overall machnng error depends on ts poston n the layout. The objectve s to fnd the locaton of each error contanng locator so as to mnmze the resultant error. In ths context the problem statement can be made as follows. Arrve at a determnstc layout whch, for gven source errors results n the least dmensonal error of the crtcal machnng feature whle complyng wth the tolerance requrements.in other words, Determne L x,y,z () so as to mnmze δx z y δm j = δy = B j δp = z x { J N T δs} (9) δz y x 0 wth [ ] T j δ s = δs1... δs subject to (x,y,z) max (x,y,z) (x,y,z) mn

6 157 δx (or) δy (or) δz mtol where =1:6 j=a,b,c In executon, layouts are generated randomly (ntal populaton) wth the bounds specfed for each locator. Magntude of source error n each locator s specfed by the user. Each of these locators s frst checked for the condton of determnstc locaton dscussed n Secton 3. Wth these nputs the GA runs for the specfed number of generatons and arrves at the optmal layout the layout wth least machnng error of the feature consdered. Flow chart shown n Fgure 5 explans the method adopted. 5. Numercal llustraton To llustrate the above mentoned procedure, a rectangular block studed by Qn et al. (2008) s presented. A through slot s to be mlled on a workpece of dmensons 220 mm 122 mm 112 mm. The crtcal machnng feature n ths case s the dstance between the far edge of the workpece and the slot, shown as 25±0.006 n Fgure 7. Snce the workpece s located based on the locatng prncple there are sx locators n total. The normal vectors and the assumed errors n each locator are gven n Table 1. Usng equaton (9) the overall machnng error s computed at the three processng datum ponts A,B and C whose coordnates are (220,122,112), (110,122,112), (0,122,112) respectvely. For each layout the maxmum of errors among A, B and C are calculated and GA s used to arrve at the mnmum of ths maxmum error. Correspondng layout s the optmal layout. In the present case GA s run for 10 tmes and optmal layouts are obtaned. Table 2 shows the layouts and error values correspondng to each run. It can be seen that among the 10 runs, run 10 gves the least value of error ( mm). The convergence pattern of GA correspondng to ths run s shown n Fgure 8. Comparng the error values wth the requred tolerance on the crtcal dmenson (0.006 mm) t can be seen that all the layouts are vald for the present case (maxmum error beng mm n Run 1). Table 1 Normal vectors and errors n locators Locator Normal vector Source error (mm) Postonal constrants used n optmzaton 6. Results and dscusson L 1 (0,0,1) x 10, 101 y 62, z=0 L 2 (0,0,1) x 125.5, 101 y 62, z=0 L 3 (0,0,1) x 66, 59 y 10,z=0 L 4 (0,-1,0) x 20, y= 122, z=56 L 5 (0,-1,0) x 95, y= 122, z=56 L 6 (1,0,0) x=0, 102 y 30, z=56 The machnng error s of the form δx δm j = δy z δ j The vector conssts of machnng error n the X, Y and Z drectons. However n ths study the machnng error relates to the devaton of the dstance of the slot from the top edge of the workpece shown as 25± Hence the Y component of the machnng error, δy s of nterest. For each layout generated δm j s computed usng Equaton (5) and GA s nvoked to arrve at the mnmum machnng error. Many GA runs are performed and the results of 10 such runs are gven n Table 2. The least machnng error vares from a mnmum of mm (Run 10) to a maxmum of mm (Run 1). Other values of machnng error are near dentcal. Interestngly Run 2, Run 3 and Run 6 have exactly same value of machnng error ( mm). Ths proves that the fxture optmzaton problems are multmodal n nature. For the same or near the same objectve value (δy n ths case) the layouts are dfferent. Ths means that gven the locator error and bounds on locator postons, f dfferent layouts are possble for the same machnng error. Ths provdes the user wth the flexblty of choosng layouts wthout mposng too much restrcton.

7 158 The relatve mpact of each locator error on the resultant machnng error s worth consderng. For dong ths, the layout wth the least error, the one obtaned n Run 10 s taken. Frst, error of locator 1 s ncreased n steps of 10% tll the error value s doubled. Error values of all other locators reman the same as gven n Table1. Change of wth ncreasng error value of locator 1 s computed. The process s repeated for other locators whle keepng same the error of all but that locator. The results are plotted n Fgure 7. It can be seen that effect of locator 4 s more pronounced followed by locator 3 and locator 2. Locator 5 has lttle mpact on the change of the machnng error whle the nfluence of locator 6 s not seen to affect the machnng error. Ths means that locator 4 should be produced wth strcter tolerance or should be set up more precsely snce the mpact of t s seen to be more consderable than others. As the optmzaton process contnues, chromosomes tend to become smlar. Because of ths the objectve functon, n ths case the machnng error, tends to reman at a value wthout any further mprovement. The objectve functon s then sad to have converged. As dscussed n Secton 4 the optmzaton process s termnated based on ether the number of stall generatons or the maxmum number of generatons. Fgure 8 shows the convergence of GA. Fgure 8a corresponds to run 10 that returned the least error among the 10 runs. It can be seen that the machnng error value steadly falls for the frst 96 generatons and remans unchanged thereafter. Snce the stall generaton value has been specfed as 50, the process contnues for further 50 generatons and stops at generaton number 146. As mentoned earler, the least machnng error obtaned n the process s mm. To study the effect of ncrease n populaton sze, GA s run wth N P ncreased to 70 and the correspondng convergence pattern s shown n Fgure 8b. The least error obtaned here s mm after 148 teratons. Table 2 GA based optmal poston of locators and correspondng machnng error G.A Run Locator 1 Locator 2 Locator 3 Locator 4 Locator 5 Locator 6 x y z x y z X y z x y z x y z x y z Least error (mm) *

8 159 GA parameters Populaton of layouts Consder generaton, layout j Jacoban matrx J No Determnstc? j= j+1 Yes Fnd δm ya,δm yb, δm yc Errors of locators (δm y ) j = max( δm ya,δm yb, δm yc ) No j=n P? Yes (δm y ) = mn ( δm y ) j=1:np N S reached? Yes Termnate, store results = N G? =+1 No No Yes Termnate, store results Genetc operators Fgure 5. Flow chart of the analyss

9 160 A 25±0.006 B C Z L5 L4 L2 X Y L6 L1 L3 Fgure 6. Workpece fxture system under study Fgure 7. Effect of ncrease n locator error Fgure 8a.Convergence of GA (N P =50)

10 161 Fgure 8b.Convergence of GA (N P =70) 7. Conclusons Snce the locator error s an mportant factor contrbutng to the overall machnng error mnmzaton of the contrbuton of locator error reduces the machnng error. In ths work an attempt has been made for optmzng the fxture layout takng nto consderaton the effect locator errors. Determnstc locaton s ensured throughout the optmzaton process and mnmal machnng error s arrved at complyng wth the machnng tolerance specfcaton. Ths also provdes the user wth a flexblty n choosng the layout accordng to the requrements. Also, for a gven machnng tolerance on workpece, f the mnmum possble error can be found for a gven set of locator errors, workng backward, t s possble to determne the allowable tolerance on the locator. Ths may be advantageous n cases where a less strct tolerance on locator wll be acceptable thus reducng the cost of manufacture of locators. The model presented here s generc n the sense that the same can be appled to any crtcal feature of the workpece by choosng approprate datum ponts. Future work wll nclude the determnaton of the components of machnng error caused by machnng and clampng forces. The fxture layout would be optmzed so as to mnmze the overall machnng error. In ths work the locators are assumed to contan error n ther normal drecton. A quadratc model would help analyze the case of locators wth errors along the tangental drectons also. References Asada,H, Andre B Knematc analyss of workpart fxturng for flexble assembly wth automatcally reconfgurable fxtures, Journal of Robotc Automaton, Vol.2, pp Ca,W; Jack Hu, S ; Yuan, J.X.1997.A varatonal method of robust fxture confguraton desgn for 3D workpeces, Journal of Manufacturng Scence and Engneerng, Vol.119, pp Chen W., N L., Xue J Deformaton control through fxture layout desgn and clampng force optmzaton, Internatonal Journal of Advanced Manufacturng Technology, Vol.31, pp Choudhur, S.A ; De Meter, E.C Tolerance analyss of machnng fxture locators, Journal of Manufacturng Scence and Engneerng, Vol.121, pp Deb K Optmzaton for engneerng desgn-algorthms and examples, Prentce Hall of Inda, New Delh. Kaya, N Machnng fxture locatng and clampng poston optmzaton usng genetc algorthms, Internatonal Journal of Computers n Industry, Vol. 57, pp Krshnakumar K, Melkote S.N Machnng fxture layout optmzaton usng the genetc algorthm, Internatonal Journal of Machne Tools and Manufacture, Vol. 40,pp L,B, Melkote S.N. 2001a. Fxture clampng force optmzaton and ts mpact on workpece locaton accuracy, Journal of Advanced Manufacturng Technology, Vol.17, pp L,B, Melkote S.N Improved workpece locaton accuracy through fxture layout optmzaton, Internatonal Journal of Advanced Manufacturng Technology, Vol. 39, pp L,B, Melkote S.N. 2001b. Optmal fxture desgn accountng for the effect of workpece dynamcs, Internatonal Journal of Advanced Manufacturng Technology, Vol.18, pp Marn R.A., Ferrera P.M Analyss of the nfluence of fxture locator errors on the complance of work part features to geometrc tolerance specfcatons, Journal of Manufacturng Scence and Engneerng, Vol.125, pp

11 162 Padmanaban,K.P, Prabhaharan, G Dynamc analyss on optmal placement of fxturng elements usng evolutonary technques, Internatonal Journal of Producton Research, Vol. 46, pp Qn, G.H, Zhang, W.H, Wan, M A mathematcal approach to analyss and optmal desgn of a fxture locatng scheme, Internatonal Journal of Advanced Manufacturng Technology, Vol.29, pp Qn,G.H, Zhang W.; Wu Z.; Wan M Systematc modelng of workpece fxture geometrc default and complance for the predcton of workpece machnng error, Journal of Manufacturng Scence and Engneerng, Vol. 129, pp Qn,G.H, Zhang W., Wan M A machnng-dmenson based approach to locatng scheme desgn, Journal of Manufacturng Scence and Engneerng Vol.130, pp Raghu A., Melkote S.N Analyss of the effects of fxture clampng sequence on part locaton errors, Internatonal Journal of Machne Tools and Manufacture, Vol. 44, pp Rong, Y, Hu, W, Kang Y, Zhang,Y, Yen D.W Locatng error analyss and tolerance assgnment for computer aded fxture desgn, Internatonal Journal of Producton Research, Vol. 39, pp Song, H ; Rong, Y Locatng completeness evaluaton and revson n fxture plan, Robotcs and Computer Integrated Manufacturng, Vol.2, pp Wang, M Tolerance analyss for fxture layout desgn, Assembly Automaton, Vol. 22, pp Wang,Y; Chen, X ; Gndy, N Surface error decomposton for fxture development, Internatonal Journal of Advanced Manufacturng Technology, Vol.31, pp Bographcal notes S. Vshnupryan s currently servng as a Lecturer n the Department of Mechancal and Industral engneerng, Caledonan College of Engneerng, Muscat, Sultanate of Oman. An M. Tech n Machne Desgn from the Indan Insttute of Technology, Madras, he has around ffteen years of teachng experence and currently pursung Ph D n the Natonal Insttute of Technology, Durgapur, Inda. He has co authored text books on Desgn of machne elements and Desgn of Transmsson systems. Dr. M C Majumder s a Professor n the Department of Mechancal Engneerng and Member Secretary of the Senate, Natonal Insttute of Technology, Durgapur, Inda. He has a PhD from the Indan Insttute of Technology, Kharagpur, Inda. He has guded many Ph D scholars. Hs prme area of research s Trbology. Dr. K. P. Ramachandran s currently the Assocate Dean (Post Graduate Studes & Research), Caledonan College of Engneerng, Muscat, Sultanate of Oman. He has a experence of 25 years n engneerng nsttutons and as a consultant for many ndustres. He has research nterest n the vbraton nstrumentaton & measurement, analyss and control, condton montorng of rotatng machnery. He has been conferred Sr C.V. Raman award for the best techncal paper publshed n the journal of Vbraton & Acoustcs (1997). He s n the edtoral board and techncal revewer for nternatonal journals and conferences. He has guded PhD students n the area of condton montorng and mantenance management. Receved January 2010 Accepted February 2010 Fnal acceptance n revsed form March 2010