GRINDING PARAMETERS SELECTION USING TLBO METHOD

Transcription

1 INTERNATIONAL JOURNAL OF MANUFACTURING TECHNOLOGY AND INDUSTRIAL ENGINEERING (IJMTIE) Vol. 2, No. 2, July-Dmbr 2011, pp GRINDING PARAMETERS SELECTION USING TLBO METHOD R. V. Rao 1 * & V. D. Kalyankar 1 ABSTRACT: In this rsarh ork a n advand algorithm is applid for th pross paramtr optimization of grinding pross. This algorithm is inspird by th tahing-larning pross and it orks on th fft of influn of a tahr on th output of larnrs in a lass. Th grinding pross involvs a numbr of paramtrs hih may afft th prodution rat, ost and quality of omponnts. Sltion of optimum grinding paramtrs is vry important to satisfy all th onfliting objtivs of th pross. An appliation xampl is onsidrd in this ork that inludd various onfliting objtivs subjtd to th larg numbr of onstraints of th grinding pross. This xampl as attmptd prviously by various rsarhrs using traditional and advand optimization algorithms. Hovr, th rsults obtaind by th proposd n algorithm hav outprformd th prvious rsults. Th dtaild algorithm is xplaind in this papr follod by th dtails of appliation xampl and rsults. Kyords: Grinding, paramtrs, optimization, tahing-larning basd optimization. 1. INTRODUCTION Grinding is a matrial rmoval and surfa gnration pross usd to shap and finish omponnts mad of mtals and othr matrials. Th prision and surfa finish obtaind through grinding is also vry high. Various input pross variabls for grinding pross ar hl spd, orkpi spd, dpth of ut, orkpi hardnss, hl diamtr, lad of drssing, t., and th output pross variabls ar surfa roughnss, grinding fors, tmpratur, thrmal damag, mahin stiffnss, spifi grinding nrgy, dimnsional auray, t. [1]. Du to th highly omplx natur, th paramtr optimization of grinding pross oftn boms a mixd-intgr non-linar optimization problm ith onstraints and multimodal haratristis, hih at prsnt is rgardd as on of th most hallnging problms in optimization. Svral thniqus of modling and optimization in grinding pross paramtr optimization problms ar usd by many rsarhrs in th past. Wn t al. [1], L and Shin [2], Saravanan t al. [3], Asokan t al. [4], Krishna [5], Stpin [6], Mani and Patvardhan [7], Paar t al. [8], Rao and Paar [9]. It is obsrvd from th litratur that som traditional and advand optimization algorithms had bn applid for th pross paramtr optimization of grinding pross. Hovr, to hk hthr any furthr improvmnt is possibl, th proposd TLBO algorithm [10] is trid for pross paramtr optimization of grinding pross. 2. TEACHING-LEARNING BASED OPTIMIZATION TLBO is a tahing-larning pross inspird algorithm proposd rntly by Rao t al. [10] basd on th fft of influn of a tahr on th output of larnrs in a lass. Th algorithm mimis tahing-larning ability of tahr and larnrs in a lass room. Tahr and larnrs ar th to vital omponnts of th algorithm and dsribs to basi mods of th larning, through tahr (knon as tahr phas) and intrating ith th othr larnrs (knon as larnr phas). Th output in TLBO algorithm is onsidrd in trms of rsults or grads of th larnrs hih dpnd on th quality of tahr. So, tahr is usually onsidrd as a highly larnd prson ho trains larnrs so that thy an hav bttr rsults in trms of thir marks or grads. Morovr, larnrs also larn from th intration among thmslvs hih also hlps in improving thir rsults. 1 S. V. National Institut of Thnology, Surat, Gujarat, India, ( * Corrsponding author: ravipudirao@gmail.om)

2 i n r a s t h m a n r s u l t o f t h l a s s r o o m f r o m a n y v a l u M A t a n y i t r a t i o n i, 92 Intrnational Journal of Manufaturing Thnology and Industrial Enginring (IJMTIE) TLBO is population basd mthod. In this optimization algorithm a group of larnrs is onsidrd as population and diffrnt dsign variabls ar onsidrd as diffrnt subjts offrd to th larnrs and larnrs rsult is analogous to th fitnss valu of th optimization problm. In th ntir population th bst solution is onsidrd as th tahr. Th orking of TLBO is dividd into to parts, Tahr phas and Larnr phas. Working of both th phas is xplaind blo Tahr Phas It is first part of th algorithm hr larnrs larn through th tahr. During this phas a tahr tris to 1 to his or hr lvl (i.. T A ). But pratially it is not possibl and a tahr an mov th man of th lass room M 1 to any othr valu M 2 hih is bttr than M 1 dpnding on his or hr apability. Considrd M j b th man and T i b th tahr at any itration i. No T i ill try to improv xisting man M j toards it so th n man ill b T i dsignatd as M n and th diffrn btn th xisting man and n man is givn by [10], Diffrns _ Man i = r i (M n T F M J ) (1) Whr T F is th tahing fator hih dids th valu of man to b hangd, and r i is th random numbr in th rang [0, 1]. Valu of T F an b ithr 1 or 2 hih is a huristi stp and it is didd randomly ith qual probability as, F [ (,){ } ] T = round 1+ rand (2) Basd on this Diffrn_Man, th xisting solution is updatd aording to th folloing xprssion 2.2. Larnr Phas X = X + Diffrn Man (3) n, i old, i _ It is sond part of th algorithm hr larnrs inras thir knoldg by intration among thmslvs. A larnr intrats randomly ith othr larnrs for nhaning his or hr knoldg. A larnr larns n things if th othr larnr has mor knoldg than him or hr. Mathmatially th larning phnomnon of this phas is xprssd blo. onsidring to diffrnt larnrs X i and X j hr i j ( ) n, i old, i i i j i X = X + r X X If f (X i ) < f (X j ) (4) ( ) X = X + r X X If f (X j ) < f (X i ) (5) n, i old, i i j i Apt X n if it givs bttr funtion valu. Implmntation stps of th TLBO ar summarizd blo: Stp 1: Initializd th population (i.. larnrs ) and dsign variabls of th optimization problm (i. numbr of subjts offrd to th larnr) ith random gnration and valuat thm. Stp 2: Slt th bst larnr of ah subjt as a tahr for that subjt and alulat man rsult of larnrs in ah subjt. Stp 3: Evaluat th diffrn btn urrnt man rsult and bst man rsult aording to quation (1) by utilizing th tahing fator (TF). Stp 4: Updat larnrs knoldg ith th hlp of tahr s knoldg aording to quation (3) Stp 5: Updat th larnrs knoldg by utilizing th knoldg of som othr larnr aording to quations (4) and (5). Stp 6: Rpat th produr from stp 2 to 5 till th trmination ritrion is mt. 3. APPLICATION EXAMPLE Th multiobjtiv grinding pross problm rntly usd by Paar t al. [8], Rao and Paar [9] is onsidrd in this xampl. Th sam modl as arlir attmptd by Wn t al. [1] using quadrati programming, Saravanan t al. [3] using gnti algorithm and Krishna [5] using diffrntial volution algorithm. Th dision variabls onsidrd in this modl ar, hl spd V s (m/min), orkpi spd V (m/min),

3 Grinding Paramtrs Sltion Using TLBO Mthod 93 dpth of drssing do (mm), and lad of drssing L (mm/rv). Th thr objtivs onsidrd in this rsarh ork ar: (a) Minimization of prodution ost. (b) Maximization of prodution rat in trms of orkpi rmoval paramtr. () Minimization of surfa roughnss. Hovr, ths thr objtiv funtions ar dividd into to groups kping in vi th spifi rquirmnt of rough grinding and finish grinding opration Cas 1: Rough Grinding For rough grinding opration th folloing to objtiv funtions ar onsidrd ith th ondition that th surfa roughnss valu should not xd 1.8 µm. (a) Minimization of prodution ost C T ($/p); (b) Maximization of prodution rat in trms of orkpi rmoval paramtr WRP (mm 3 /minn) Cas 2: Finish Grinding For th finish grinding opration th folloing to objtiv funtions ar onsidrd ith th ondition that orkpi rmoval paramtr should not b lss than 20 mm 3 /minn (a) Minimization of prodution ost C T ($/p); (b) Minimization of surfa roughnss R a (µm) Objtiv Funtions Th various objtiv funtions for this modl ar givn by quations (6)-(8). [1, 3, 5, 8 and 9] Prodution Cost M L + L b + b a abl M S d Mth MπbsD abl π() do bsd Cd CT = + Sp t Cs p V 1000 fb ap DbsapG π 60p Vr 60Nt 60pN dlvs1000 pg pn d pn (6) td Whr M is ost pr hour of labour and administration, L is lngth of orkpi, L is mpty lngth of grinding, b is idth of orkpi, b is mpty idth of grinding, f b is ross fd rat, a is total thiknss of ut, a p is don fd of grinding, S p is numbr of spark out grinding, D is diamtr of hl, b s is idth of hl, G is grinding ratio, S d is distan of hl idling, p is numbr of orkpis loadd on th tabl, V r is spd of hl idling, t 1 is tim of loading and unloading orkpis, t h is tim of adjusting mahin tool, N t is bath siz of th orkpis, N d is total numbr of orkpis to b ground btn to drssing, N td is total numbr of orkpis to b ground during lif of drssing, and C d is ost of drssing Workpi Rmoval Paramtr 11/ ( 1 + ( 2 / 3 )) ( / ) / do L L V Vs Vs WRP = (7) D VOL d R 43/ / / g Whr, VOL is hl bond prntag, d g is grind siz and R is orkpi hardnss Surfa Roughnss R a av 3 = T if T av is in btn Whr, R a = T if T av is in btn (8) av T av 16/ 27 16/ 27 / 27 dg a 3 p do 16/ 27 V = L / (9) D L Vs

4 94 Intrnational Journal of Manufaturing Thnology and Industrial Enginring (IJMTIE) 3.4. Constraints Thrmal Damag Constraint Th grinding pross rquirs vry high nrgy pr unit volum of matrial rmovd. Th high thrmal nrgy auss damag to th orkpi and it lads to th rdud prodution rat. Th spifi nrgy U is alulatd by quation (10). Whr, K u is th ar onstant. 4 /. Vs. V KuVs La VsD U = A0 + / / / apv DV s VD a 1 2 (10) p Vap Th ritial spifi nrgy U* at hih burning starts is xprssd in trms of th oprating paramtrs as, U * 1/ 4 D = / 4 1/ 2 (11) ap V Th thrmal damag onstraint is thn spifid as: U* U 0 (12) Whl War Paramtr Constraint For singl-point diamond drssing, th hl ar paramtr (WWP) is givn by quation (13). 27/ ( 1 ( / )) ( / ) 1 ( 2 / 3 ) 3/ 5/ 38 27/ kaapdg R + do L L V V V WWP =. / VOL / D VOL ( + do L ) Th hl ar paramtr onstraint is givn by quation (14). s (13) Mahin Tool Stiffnss Constraint WRP G WWP 0 (14) Th rlationship btn grinding stiffnss K (N/mm), hl ar stiffnss K s (N/mm), and oprating paramtrs during grinding is givn by quations (15)-(16) Whr, K K V f b = 1000 (15) WRP V f s b s = 1000 (16) WWP To avoid hattr during mahining, folloing onstraint has to b fulfilld MSC MSC R m 0 (17) K m 1 V 1 2K VsG Ks = Whr R m is dynami mahin haratristis and K m is Stati mahin stiffnss. This multiobjtiv optimization modl ith th givn pross paramtrs, objtiv funtions, and th onstraints for th rough grinding as is no solvd by using th proposd TLBO algorithm. Th sam onstant valus ar usd as that usd by prvious rsarhrs Paramtrs Optimization for Rough Grinding Th ombind objtiv funtion (to b minimizd) formulatd for rough grinding opration ( Z R ) is rittn as. (18)

5 Grinding Paramtrs Sltion Using TLBO Mthod 95 Whr, C T *= 10 ($/p); WRP*= 20 mm 3 /minn. Min Z R = W 1 (C T /C T *) W 2 (WRP/WRP*) () W 1 and W 2 ar th ighing fators for C T and WRP rsptivly. Th valus of W 1 and W 2 may b didd by th pross plannr. In this xampl sam valu of 0.5 is onsidrd for ah of W 1 and W 2 as onsidrd by prvious rsarhrs. Paramtr bounds for th four pross variabls ar givn by th quations (20)-(23) V s 2023 m/min (20) 10 V m/min (21) 0.01 do mm (22) 0.01 L mm/rv (23) Tabl 1 Comparison of Rsults of Various Algorithms for Rough Grinding Opration Mthod V s V Do L C T WRP R a Z R QP [1] GA [3] DE [5] * DE # PSO [8] SA [9] HS [9] ABC [9] TLBO * Valus rongly alulatd by Krishna [5] # orrtd valus. Tabl 2 Improvmnt in th Combind Objtiv Funtion Using Various Algorithms Ovr QP Mthod Combind obj funtion % improvmnt ovr QP QP [1] GA [3] PSO [8] SA [9] HS [9] ABC [9] TLBO Population siz of 700 is onsidrd for th TLBO algorithm in this xampl and th rsults ar obtaind in 50 gnrations. Th proposd TLBO algorithm has solvd this multiobjtiv modl sussfully and givs signifiant rsults. Tabl 1 shos th optimum pross paramtr rsults obtaind by TLBO for th abov xampl along ith th prviously publishd rsults obtaind by th prvious rsarhrs using othr mthods. Tabl 2 shos th improvmnt in th ombind objtiv funtion for rough grinding using various algorithms ovr that of quadrati programming. For rough grinding opration to objtiv funtions i.. minimization of prodution ost and maximization of prodution rat ar onsidrd to obtain th ombind objtiv funtion (Z R ), ith th ondition that th surfa roughnss valu should not xd 1.8 µm. Th ombind objtiv funtion obtaind by Wn t al. [1] is , Saravanan t al. [5] is , Paar t al. [8] is and that obtaind by Rao and Paar [9] is , and for SA, HS and ABC rsptivly. Th proposd TLBO algorithm has givn th ombind objtiv funtion valu of hih is muh bttr than that of SA, HS and ABC. Th prodution ost (C T ) and surfa roughnss (R a ) inrass along ith th ombind objtiv funtion in othr ass hras th sam is onsidrably rdud in as of TLBO algorithm. This indiats that th algorithm handls th ombind objtiv funtion as ll as individual funtions vry ffiintly. Also th numbr of gnrations takn by SA, HS and ABC ar about 80, hras th TLBO givs th optimum rsults in about 50 gnrations

6 96 Intrnational Journal of Manufaturing Thnology and Industrial Enginring (IJMTIE) only. TLBO givs ovr 90% of improvmnt ovr th traditional optimization thniqu lik quadrati programming and approximatly 10% of improvmnt ovr th advand optimization thniqus lik SA, HS and ABC. 4. CONCLUSION Th fftiv optimization of th grinding pross paramtrs affts dramatially th ost and prodution tim of th omponnts as ll as th quality of th final produts. A n advand optimization thniqu, TLBO, is prsntd hih is basd on th fft of influn of a tahr on th output of larnrs in a lass. Multiobjtiv appliation xampl is onsidrd for grinding pross ith larg numbrs of onstraints. Th proposd TLBO algorithm is sussfully applid to this multiobjtiv problm and th rsults ar ompard ith th prvious rsults. Th rsults shod th bttr prforman of TLBO algorithm ovr othr naturinspird optimization algorithms onsidrd. Comparison btn th rsults provd th supriority of th n algorithm in trms of bttr rsults and omputational tim. Th onvrgn rat of this algorithm is vry high and it rquirs vry f numbrs of itrations for onvrgn to th optimal solution ompard to th othr advand optimization algorithms. REFERENCES [1] Wn, X. M., Tay, A. A. O., N, A. Y. C., Miro-omputr-basd Optimization of th Surfa Grinding Pross. Journal of Matrials Prossing Thnology, 29, (92), [2] L, C. W., Shin, Y. C., Evolutionary Modling and Optimization of Grinding Pross. Intrnational Journal of Prodution Rsarh, 38/12, (2000), [3] Saravanan, R., Asokan, P., Sahidanandam, M., A Multi-objtiv Gnti Algorithm (GA) Approah for Optimization of Surfa Grinding Oprations. Intrnational Journal of Mahin Tools and Manufatur, 42/12, (2002), [4] Asokan, P., Baskar, N., Babu, K., Optimization of Surfa Grinding Oprations Using Partil Sarm Optimization Thniqu. J. of Manufaturing Sin and Engg., 127/4, (2005), [5] Krishna, A. G., Optimization of Surfa Grinding Oprations Using a Diffrntial Evolution Approah. Journal of Matrials Prossing Thnology, 183, (2007), [6] Stpin, P., A Probabilisti Modl of th Grinding Pross. Applid Mathmatial Modlling, 33/10, (2009), [7] Mani, A., Patvardhan, C., Solving Crami Grinding Optimization Problm by Adaptiv Quantum Evolutionary Algorithm. IEEE Intrnational Confrn on Intllignt Systms, Modlling and Simulation, 2010, DOI / ISMS.2010., [8] Paar, P. J., Rao, R. V., Davim, J. P., Multiobjtiv Optimization of Grinding Pross Paramtrs Using Partil Sarm Optimization Algorithm. Matrials and Manufaturing Prosss, 25/6, (2010), [9] Rao, R. V., Paar, P. J., Grinding Pross Paramtr Optimization Using Non-traditional Optimization Algorithms. Prodings of Institution of Mhanial Enginring Part B: Journal of Enginring Manufatur, 224/6, (2010), [10] Rao, R. V., Savsani, V. J., Vakharia, D. P., Tahing larning-basd Optimization: A Novl Mthod for Constraind Mhanial Dsign Optimization Problms. Computr-Aidd Dsign, 43, (2011),