Thermal Stress Prediction within the Contact Surface during Creep Feed Deep Surface Grinding

Transcription

1 5 th Intrnational & 26 th All India Manufacturing Tchnology, Dsign and Rsarch Confrnc (AIMTDR 204) Dcmbr 2 th 4 th, 204, IIT Guwahati, Assam, India Thrmal Strss Prdiction within th Contact Surfac during Crp Fd Dp Surfac Grinding Audhsh Narayan *, Vinod Yadava 2 * Dpartmnt of Mchanical Enginring, Motilal Nhru National Institut of Tchnology Allahabad ,India, anarayan@mnnit.ac.in 2 Dpartmnt of Mchanical Enginring, Motilal Nhru National Institut of Tchnology Allahabad , India, vinody@mnnit.ac.in Abstract This papr prsnts th application of a hybrid approach comprising of Nural Ntwork (NN) and Gntic Algorithm (GA) for modling and optimization of Crp Fd Dp Surfac Grinding (CFDSG) procss. Finit Elmnt Mthod (FEM) has bn usd to gnrat data st for NN modl to prdict th quivalnt thrmal strss within th contact zon of th workpic. Subsquntly, NN modl has bn coupld with GA to find optimum input-output paramtrs of CFDSG. Th proposd hybrid approach is wll capabl to prdict thrmal strsss in th workpic quickly and also minimiz it with rasonabl accuracy during CFDSG procss. Kywords: Crp Fd Dp Surfac Grinding, Finit Elmnt Mthod (FEM), Nural Ntwork, Gntic Algorithm Introduction Crp Fd Dp Surfac Grinding is comparativly a rcnt dvlopmnt in grinding tchnology whr th opration is prformd with high dpth of cut, vry slow workpic spd and low whl spd. Du to high dpth of cut, CFDSG is bing usd in th industris to incras productivity and surfac quality simultanously with a singl machining opration rathr than using milling and thn fin surfac grinding. Undr such a high dpth of cut, much highr matrial rmoval rat can b achivd in comparison to shallow cut surfac grinding. Th major diffrncs btwn CFDSG and convntional (shallow cut) grinding ar th workpic spd and dpth of cut. Convntional grinding is charactrizd by high workpic spds (0.05 to 0.5 m/s), small dpths of cut (-25 µm) and small lngth of contact btwn th workpic and grinding whl, varying btwn to 3 mm, whras CFDSG utilizs low workpic spds (0. to 20 mm/s) and highr dpths of cut ( to 0 mm) which also lads to highr contact lngth (Parnt t al., 202). CFDSG is mainly usd for machining difficult to machin matrials such as nickl bas alloys, tungstn carbid, tool stl and di stls. CFDSG has major applications in th arospac industry and in particular for th manufactur of turbin blads for aircraft ngins mad from nickl bas alloys. It can also b usd to produc broachs, pump rotors, dis and automobil rockr arm tc. (Andrw, 985).Thrmal damag du to high tmpratur constituts th major problm whn using this procss. High contact tmpratur wakns th bond strngth of th whl, promoting abrasiv whl war rsulting to dcras in th procss prformanc. High hat gnratd during CFDSG, inducs thrmal strsss within th workpic. Thrfor, acomprhnsiv thrmal strsss analysis is rquird not only for bttr undrstanding of th procss but ar also vry much usful for simulation, optimization and control of th procss. To dtrmin th thrmal strsss, a suitabl mathmatical modl in th form of diffrntial quations is rquird to b dvlopd. Ths diffrntial quations can b solvd using any computational mthod. Finit lmnt mthod (FEM) is on of th most widly usd computational tool to solv ths diffrntial quations. Major problm in quantitativ prdiction of output using FEM is th larg computational tim and dpndncy of rsults on mshing rlatd paramtrs such as typ and ordr of lmnts, siz of lmnts and thir non-uniform distribution in th msh, connctivity pattrn of lmnts and othrs. Bcaus of ths rasons, th prdiction of output for varid oprating conditions bcoms cumbrsom with using FEM. In th prsnt study, an attmpt has bn mad to dvlop a NN-basd modl of CFDSG procss using th data gnratd through its thrmal FEM-basd modl to ovrcom th problm of mshing rlatd tim consuming procdur of FEM. Authors (Tsai and Hochng, 996; Gupta t al., 997; Mahdi and Zhang, 999a; Mahdi and Zhang, 999b; Moulik t al.,200; Xiao t al., 2002; Hamdi t al. 2004; Wang t al., 20) hav attmptd for thrmal strss modling of convntional (shallow cut) surfac grinding procsss but litratur rlatd to thrmal strss modling of CFDSG is not availabl so far. Most of th studis availabl in shallow cut surfac grinding ar rlatd to computational dtrmination of thrmal strsss considring diffrnt shap and quantity of hat flux to th workpic, nrgy partition, ffct of convction and ffct of tmpratur dpndnt proprtis of workpic matrial. Paramtric studis ar also availabl showing th ffct of whl spd, workpic 566-

2 Thrmal Strss Prdiction within th Contact Surfac during Crp Fd Dp Surfac Grinding spd, dpth of cut on thrmal strsss. But authors hav not found any analytical or computational modl dvlopd for th dtrmination of thrmal strsss gnratd in th workpic du to CFDSG. Fw authors (Sdighi and Afshari,200; Joshi and Pand, 20; Rddy and Pratihar 20) hav attmptd for modling and optimization of manufacturing procsss using NNGA coupld approach in th fild of CFDSG, lctric discharg machining and lctron bam wlding procsss. But most of thm ar using xprimntal data st for th training and tsting of NN-basd modl. Vafasfat (2009) dvlopd a NN modl to prdict th grinding forcs during crp fd grinding of nickl basd supr alloy with aluminium oxid grinding whl using xprimntally masurd grinding forcs for 9 sts of xprimnts. Thy also maximizd th matrial rmoval rat using nonlinar constraind optimization tchniqu. Sdighi and Afshari (200) dvlopd a nural ntwork modl to prdict th surfac roughnss in crp fd grinding of cobalt basd supr alloy with aluminium oxid grinding whl using xprimntally masurd surfac roughnss for 6 sts of xprimnts. Thy also optimizd th procss using GA. Joshi and Pand (20) dvlopd a NN-basd modl for prdiction of output paramtrs in trms of shap of cratr, MRR and TWR during di-sinking EDM procss and optimization was don using NSGA II to slct th optimum procss paramtrs for roughing and finishing oprations using computational datast gnratd by FEM. Rddy and Pratihar (20) dvlopd a NN-basd modl to prdict th tmpratur during lctron bam wlding procss using input-output data st gnratd by FEM basd tmpratur modl. In this papr, a back propagation nural ntwork (NN) modl has bn dvlopd to prdict th maximum quivalnt thrmal strss at th contact surfac during CFDSG. For training and tsting of th NN-basd modl, data sts wr gnratd using FEM-basd thrmal strss modl. 2 Modling of CFDSG In th prsnt work, first a tmpratur modl has bn dvlopd to find th tmpratur, and thn followd by th thrmal strss modl to calculat th thrmal strsss in th workpic. To mak th analysis of tmpratur and thrmal strsss tractabl, th following assumptions hav bn mad. Workpic matrial is homognous, isotropic and lastic-prfctly plastic. Thrmal proprtis of workpic matrial ar considrd to b indpndnt of tmpratur. Contact btwn th workpic and whl is considrd as an inclind flat plan surfac but in ral situation it is curvd with larg radius of curvatur. Hnc, hat flux is assumd to b right angld triangularly distributd inclind hat sourc. A plan strain conditions ar assumd (ε zz =0). Inrtia and body forc ffcts ar ngligibl during strss dvlopmnt. Following govrning quation (Cngl, 2005) and boundary conditions for isotropic and homognous matrial and without hat gnration can b usd to find th tmpratur variation in th workpic domain OABCDEO as shown in Fig.. T T T k + k = ρc in domain (OABCDEO) () x x y y t T=T 0 in th workpic domain whn t=0 (2) whr, T 0 is th ambint tmpratur of th workpic. T k = qw + h( T T0 ) n on th lin BC T k = h( T T0 ) y on th lin AB and CD T = 0 x on OA and DE T = T on OE s whn t>0 (3) Fig.. Discrtizd domain usd for th dtrmination of tmpratur and thrmal strss distribution Th transint tmpratur distribution in th workpic, obtaind by solving th hat conduction quation () along with th initial and boundary conditions, is usd as input for th calculation of th thrmal strsss. In cas of plan strain typ thrmal strss problm, govrning quations (Rddy, 2005) and boundary conditions can b usd as follows: xy + = 0 x y in th workpic domain OABCDEO (4) xy + = 0 x y whr, and ar th normal strsss and xy is th shar strss. Hr, th body and inrtia forcs ar nglctd. Th boundary conditions in trms of displacmnt and traction can b givn as follows. u y =0 on OE (5a) Bcaus th bottom surfac is fixd on th tabl. t x = t y = 0 on OA, AB, BC, CD and DE (5b) Bcaus thr is no tangntial load acting. Th strss-strain rlationship du to tmpratur ris T can b writtn as: = D ε T m (6) { } [ ]{ } { } whr, [D] is th lasticity matrix,{} is th strss vctor,{ε} is th strain vctor and{m} is th vctor rlatd to proprtis of th workpic matrial. Th xprssion for {}, {ε}, {m} and [D] ar as follows: 566-2

3 5 th Intrnational & 26 th All India Manufacturing Tchnology, Dsign and Rsarch Confrnc (AIMTDR 204) Dcmbr 2 th 4 th, 204, IIT Guwahati, Assam, India { } T { xy} { ε} T { ε ε ε xy} { m} xy = (7) = (8) Eα t = 2ν 0 ν ν 0 E [ D] ν ν 0 (0) = ( + ν )( 2 ν ) 0 0 2ν 2 Hr, E is Young s modulus,ν is Poisson s ratio and α t is th cofficint of thrmal xpansion. To find th plastic zon whr th quivalnt thrmal strss is mor than th yild strss of th workpic matrial, th following xprssions for th dviatoric strss componnts ar usd. S = ( zz ) (a) 3 S = ( zz ) (b) 3 S = (c) xy Szz zz ( zz ) 3 = + + (d) Th quivalnt (or ffctiv) strss, q is givn by th following quation. = 3J (2) q 2 whr, J2 = ( S + S + Szz ) + Sxy 2 A point in plastic zon is idntifid by th following inquality. q y (3) whr, y is th yild strss of th workpic matrial 3 Finit Elmnt Formulation Galrkin s FEM is applid to quations (4) and (5) to find th thrmal strss distribution. Aftr applying th Galrkin s mthod, th following lmntal quation is obtaind. [ SK ] { } { SF} (9) δ = (4) whr, [SK] is lmntal cofficint matrix for strsss,{δ} is th lmntal nodal displacmnt vctor and {SF} is th lmntal forc vctor for strsss. Ths matrics can b xprssd as follows: T [ SK ] [ B] [ D] [ B] dxdy (5) = Ω T { } = [ ] { } SF T B m dxdy Ω (6) T { δ} = u x u y u2x u2 y u8 x u 8 y (7) whr, [B] is th matrix consisting of drivativ of nodal shap functions and it rlats th displacmnt and strain and T is th lmntal ris in tmpratur du to grinding. Elmntal ris in tmpratur, T can b calculatd by th following quation. 8 T = Ni Ti T (8) 0 i= whr, N is th nodal shap function of th typical lmnt, T is th typical lmntal nodal tmpratur which is calculatd from th tmpratur modl. Whn lmntal quantitis of quation (4) ar assmbld using assmbly rul, th following global quations ar obtaind. SGK GU = SGF (9) [ ]{ } { } whr, [SGK] is th global cofficint matrix,{gu} is th global nodal displacmnt vctor and{sgf} is th global right sid vctor. Aftr dtrmination of th nodal displacmnts from th quation (9), strain is calculatd using th following quation. { ε} [ B] { δ} = (20) Now, thrmal strss is calculatd using quation (6). Th quivalnt strsss ar also calculatd at ach nod and compard with th yild strss to idntify whthr yilding occurs or not. Th primary variabl of abov FEM basd thrmal strss modl is validatd using th litratur (Kim t al., 2006). Validation rsults can b b sn in author s papr (Narayan and Yadava, 202). Aftr validation of FEM- basd thrmal strss modl, it is usd to gnrat th data for dvloping th NN-modl. Tabl shows th oprating conditions for gnrating th data. Tabl Proprtis of th workpic (AISI 5200) and grinding whl (CBN) matrial and grinding procss conditions for prdiction of quivalnt thrmal strss. Entity Valu Dnsity of th workpic, ρ 785 kg/m 3 Spcific hat of th workpic,c Thrmal conductivity of th workpic, k Young s modulus, E Poisson s ratio,ν 0.3 Cofficint of thrmal xpansion, α t Yild strss, y Dpth of cut, d Workpic spd, Whl spd, Thrmal conductivity of th CBN, k g Whl diamtr, d s Convction cofficint of grinding fluid 506 J/kgK 34.3 W/mK MPa / o K 300 MPa -3 mm mm/s m/s 240 W/mK mm 5000 W / m 2 K 4 Nural Ntwork Modling For th prsnt problm, Back Propagation Nural Ntwork (BPNN) modl has bn dvlopd to prdict th output. Th input paramtrs ar workpic spd, whl spd, dpth of cut and whl diamtr. Maximum quivalnt thrmal strss is considrd as th output paramtr. Thrfor, th BPNN modl consists of four input nods and on output nod. A total of 00 data st wr gnratd using FEM-basd thrmal strss modl. Out of 00 data st, 90 data st wr usd for NN training purpos and th rst ar usd for NN tsting. Division of th data st is don using th functions availabl in th nural ntwork tool box in Matlab. Th data division is normally prformd automatically whn th ntwork is traind

4 Thrmal Strss Prdiction within th Contact Surfac during Crp Fd Dp Surfac Grinding Bfor training th ntwork, input and output data st wr normalizd to mak th training mor fficint. Sigmoidal functions ar gnrally usd in multilayr fd forward ntwork lik back propagation ntwork, radial basis function ntwork tc. In th prsnt work, tan-sigmoidal function has bn usd for hiddn as wll as output nurons. Thrfor, input and output data st wr normalizd from 0. to 0.9 which ar within th rang of tan-sigmoidal valus. In this way, th ntwork output always falls into a normalizd rang. Th ntwork output was thn rvrs transformd back into th units of th original data whn th ntwork is put to us in th fild. Scal conjugat gradint algorithm was usd to train th ntwork. Various ntwork wr formd by varying th numbr of hiddn layrs, numbr of nurons in th hiddn layrs and numbr of pochs on th basis of numbr of input paramtrs and output paramtrs and training of ntworks wr prformd. Aftr training th ntworks, prdiction rror was calculatd for ach ntwork using computational data. Aftr xhaustiv hit and trial mthod, a ntwork of 4-7- is found suitabl on th basis of calculatd prdiction rror. Thrfor, NN modl basd on 4-7- NN architctur has bn finally chosn for th prdiction of th output. Figur 2 shows NN-architctur for th prsnt problm. Maximum prdiction rror is found as 3.4 % and avrag rror is.7% for th tsting datasts as shown in Fig.3. Th tsting data st gnratd by FEM-basd modl and its comparison with NNbasd modl is givn in Tabl 2. Fig. 2. Schmatic diagram of 4-7- BPNN ntwork architctur. Tabl 2 Comparison btwn FEM and NN modl using tsting data st. Run d d s FEM- Modl NN- Modl Error (mm) (m/s) (mm) (mm) q (MPa) q (MPa) (%) Aftr validation of th NN-modl, it has bn usd to prdict th quivalnt thrmal strss at th contact surfac of th whl-workpic. Effct of diffrnt input paramtrs such as workpic spd, whl spd, dpth of cut, whl diamtr on maximum quivalnt thrmal strss hav also bn studid. Prdiction rror (%) Tsting data sts Fig. 3. Prdiction accuracy of 4-7- BPNN ntwork. 5 Equivalnt Thrmal Strss Prdiction using Nural Ntwork Aftr training and tsting of NN modl, it is usd to prdict th maximum quivalnt thrmal strss in th contact zon of th whl-workpic. Effct of workpic spd Figur 4 shows th variation of maximum quivalnt strss within th contact zon for varying workpic spd at diffrnt whl spd. Pak valus of quivalnt strsss obtaind ar 527, 63 and 692 MPa at whl spds of 20, 25 and 30 m/s rspctivly. It is obsrvd that quivalnt strss is incrasing as th workpic spd incrass. Incras in th quivalnt strss may b du to high and non-uniform tmpratur gnratd within th contact surfac at highr workpic spd. High and non-uniform tmpratur gnratd within th contact zon may b du to high amount of hat appars at highr workpic spd. Equivalnt strss is also incrasing with incras in whl spd but ffct is nominal in comparison to workpic spd =20 m/s =25 m/s =30 m/s Workpic spd (mm/s) Fig. 4. Variation of quivalnt strss within th contact zon with workpic spd at diffrnt whl spd (d=2 mm, d s=300 mm)

5 5 th Intrnational & 26 th All India Manufacturing Tchnology, Dsign and Rsarch Confrnc (AIMTDR 204) Dcmbr 2 th 4 th, 204, IIT Guwahati, Assam, India Effct of whl spd Figur 5 shows th variations of th quivalnt strss within th contact zon for varying whl spd at diffrnt workpic spds. Pak valus of quivalnt strsss obtaind ar 608, 232 and 779 MPa at workpic spds of 0.5,.0 and.5 mm/s rspctivly. It is obsrvd that quivalnt strss incrass as th whl spd incrass from 20 to 35 m/s. But th ffct of whl spd on quivalnt strss is again nominal in comparison to th workpic spd. It is also obsrvd that workpic spd has th most dominant ffct on quivalnt strss in comparison to othr paramtr in cas of CFSG =0.5 mm/s =.0 mm/s =.5 mm/s Whl spd (m/s) Fig. 5. Variation of quivalnt strss within th contact zon with whl spd at diffrnt workpic spd (d=2 mm, d s=300 mm). Effct of dpth of cut Figur 6 shows th variation of quivalnt strss within th contact surfac for varying dpth of cut at diffrnt whl spds. Pak valus of quivalnt strsss obtaind ar 346, 387 and 47 MPa at whl spds of 20, 25 and 30 m/s rspctivly. It is obsrvd that quivalnt strss incrass as dpth of cut and whl spd incrass. It is also obsrvd that th dpth of cut has th largr ffct on quivalnt strss than th whl spd. Whn dpth of cut incrass, mor spindl powr is rquird to driv th grinding whl, consquntly, amount of cutting forc rquird in grinding incrass rsulting incras in th contact surfac tmpratur during CFSG. Du high amount hat gnratd within th contact zon, tmpratur and its gradint incrass rsulting incras in th quivalnt strss at highr dpth of cut. Effct of whl diamtr Figur 7 shows th variation of quivalnt strss within th contact surfac for varying whl diamtrs from 250 to 350 mm at diffrnt workpic spds. Pak valus of quivalnt strsss obtaind ar 63, 28 and 882 MPa at workpic spds of 0.5,.0 and.5 mm/s rspctivly. It is obsrvd that th quivalnt strss dcrass as whl diamtr incrass. But quivalnt strss is incrasing with incras in workpic spd. During grinding procss, whn diamtr of th grinding whl incrass, contact lngth and ara of th contact surfac incrass. Du to larg ara of contact surfac at highr whl diamtr, hat xtractd out of th contact surfac incrass. Consquntly, tmpratur and its gradint dcrass within th contact surfac at largr whl diamtr. Thrfor, lowr quivalnt strss is obsrvd at largr whl diamtr =20 m/s =25 m/s =30 m/s Dpth of cut (mm) Fig. 6. Variation of quivalnt strsss with dpth of cut at diffrnt whl spd (= mm/s, d s=300 mm) Whl diamtr (mm) =0.5 mm/s =.0 mm/s =.5 mm/s Fig.7. Variation of quivalnt strsss with whl diamtr at diffrnt workpic spd (=30 m/s, d=2 mm). 6 GA Basd Optimization Maximum quivalnt thrmal strss prdictd by th NN modl has bn optimizd using GA. For optimization, a function fil for objctiv function (quivalnt thrmal strss) was cratd in MATLAB 7.6.Objctiv function was usd for minimization of maximum quivalnt thrmal strss using Matlab optimization tool box. Numbr of variabls and thir rangs wr ntrd in spac providd. Numbr of input paramtrs and thir rang ar shown in Tabl 3. Tabl 3 Input paramtrs and thir rangs. Input Paramtrs Workpic spd Whl spd Dpth of cut Whl diamtr Tabl 4 GA paramtrs Paramtrs Rang mm/s m/s -3 mm mm Valus 566-5

6 Thrmal Strss Prdiction within th Contact Surfac during Crp Fd Dp Surfac Grinding Population siz 20 Crossovr probability 0.8 Numbr of gnrations 00 Stall gnration 00 An xtnsiv study was conductd to dtrmin th appropriat st of GA paramtrs which ar shown in Tabl 4. Aftr slction of GA paramtrs, optimization solvr was run and optimization trminatd aftr 00 gnrations. Bst fitnss valu of th function is obtaind as 502 MPa during convrgnc of th solution. Optimum valus of th input paramtrs, ar shown in Tabl 5. Tabl 5 (mm/s) Optimum conditions obtaind from GA-NN Input Paramtrs (m/s) d (mm) d s (mm) Output Paramtr q (MPa) Conclusions Basd on th dvlopd NN modl, maximum quivalnt thrmal strss in th contact zon of whl-workpic is prdictd by varying th input paramtrs such as dpth of cut, workpic spd, whl spd and whl diamtr. Furthr, maximum quivalnt thrmal strss prdictd by NN modl is optimizd using gntic algorithm (GA). Following conclusions can b drawn from th prsnt invstigation. (i) Th NN-GA hybrid approach has bn found capabl to optimiz procss paramtr of CFDSG ffctivly. (ii) NN-basd modl is found to show.7 % of avrag prdiction accuracy for tsting data st during prdiction of output prformanc paramtr in vry short priod of tim. (iii) Rsult of GA optimization to minimiz maximum quivalnt thrmal strss is found to b 502 MPa. (iv) Equivalnt thrmal strss is found incrasing with incras in dpth of cut, workpic spd and whl spd but th workpic spd has th most dominant ffct on quivalnt thrmal strss. Equivalnt thrmal strss is found dcrasing with incras in whl diamtr. (v) This hybrid approach can b usd for prdiction and optimization of procss paramtr for any cumbrsom procss basd on th datast gnratd by FEM. Rfrncs [] Parnt, M.P.L., Jorg, R.M.N., Viira, A.A. and Baptista, A.M.(202), Exprimntal and numrical study of th tmpratur fild during crp fd grinding, Intrnational Journal of Advancd Manufacturing Tchnology, Vol.6, pp [2] Andrw, C., Hows, T.D. and Parc, T.R.A., 985, Crp Fd Grinding, Industrial Prss Inc., Nw York. [3] Tsai, H.H., and Hochng, H. (996), Numrical invstigation of transint thrmal strsss of workpic in surfac grinding, Journal of Thrmal Strsss, Vol.9, pp [4] Gupta, R., Skhon, G.S. and Shishodia K.S. (997), Strss du to moving band sourc of hat and mchanical load on th work surfac during grinding, Journal of Matrials Procssing Tchnology, Vol.70, pp [5] Mahdi, M. and Zhang, L.C. (999), Rsidual strsss in ground componnts causd by coupld thrmal and mchanical plastic dformation, Journal of Matrials Procssing Tchnology, Vol. 95, pp [6] Mahdi, M. and Zhang, L. (999), Applid mchanics in grinding. Part 7: rsidual strsss inducd by th full coupling of mchanical dformation, thrmal dformation and phas transformation, Intrnational Journal of Machin Tools and Manufactur, Vol.39, pp [7] Moulik, P.N., Yang, H.T.Y. and Chandraskhar, S. (200), Simulation of thrmal strsss du to grinding, Intrnational Journal of Mchanical Scincs, Vol.43, pp [8] Xiao, G., Stvnson, R., Hanna, I.M. and Huckr, S.A. (2002), Modling of Rsidual Strsss in Grinding of Nodular Cast Iron, Journal of Manufacturing Scinc and Enginring, Vol.24, pp [9] Hamdi, H., Zahouani, H. and Brghau, J.M. (2004), Rsidual strss computation in a grinding procss, Journal of Matrials Procssing Tchnology, Vol. 47, pp [0] Wang, G.C., Hua, C.L., Liu, J.D., Pi, H.J. and Liu, G. (20), Study of Rsidual Strss Distribution in Surfac Grinding, Ky Enginring Matrials, Vol.487, pp [] Sdighi, M. and Afshari, D. (200), Crp fd grinding optimization by an intgratd GA-NN systm, Journal of Intllignt Manufacturing, Vol.2, pp [2] Joshi, S.N. and Pand, S.S. (20), Intllignt procss modlling and optimization of di-sinking lctric discharg machining, Applid Soft Computing, Vol., pp [3] Rddy, D.Y.A. and Pratihar, D.K. (20), Nural ntwork-basd xprt systms for prdictions of tmpratur distributions in lctron bam wlding procss, Intrnational Journal of Advancd Manufacturing Tchnology, Vol.55, pp [4] Vafasfat, A. (2009), Optimum Crp Fd Grinding Procss Conditions for Rn 80 Suppr Alloy Using Nural Ntwork, Intrnational Journal of Prcision Enginring and Manufactur, Vol.0, No. 3, pp. 5-. [5] Kim H.J., Kim N.K. and Kwak J.S. (2006), Hat flux distribution modl by squntial algorithm of invrs hat transfr for dtrmining workpic tmpratur in crp fd grinding, Intrnational Journal of Machin Tools and Manufactur, Vol.46, pp [6] Narayan, A., and Yadava, V. (202), Thrmal Strss Distribution in th Workpic during Crp-Fd Surfac Grinding, Intrnational Journal of Abrasiv Tchnology, Vol.5, No.2, pp [7] Y.A. Cngl (2005), Hat Transfr: A Practical Approach, scond d., Tata McGraw Hill, Nw Dlhi, India. [8] J.N. Rddy (2005), An Introduction to Finit Elmnt Mthod, third d., Tata McGraw-Hill, Nw Dlhi, India