Analysis of Material Removal Rate using Genetic Algorithm Approach

Transcription

1 Internatonal Journal of Scentfc & Engneerng Research Volume 3, Issue 5, May Analyss of Materal Removal Rate usng Genetc Algorthm Approach Ishwer Shvakot, Sunny Dyaley, Golam Kbra, B.B. Pradhan Abstract In the present scenaro of manufacturng ndustres partcularly n all of the machnng processes, the applcaton of varous optmzaton technques s playng vtal role whch seeks dentfcaton of the best process parametrc condton for that partcular manufacturng or metal removal process. Manufacturng process nvolves a number of process parameters (controllable and uncontrollable). Snce selecton of wrong cuttng parameter n any machnng process may lead to several negatve effects. For example, hgh mantenance cost of the lathe machne, poor surface fnsh of the work pece, short tool lfe, low producton rate, materal wastage and ncreased producton cost. In ths research paper, Genetc Algorthm (GA) has been appled for optmzng of machnng parameters durng turnng operaton of mld steel usng conventonal lathe machnes. The purpose of ths paper s to fnd the optmum parameters values for turnng operatons for maxmzng the materal removal rate. The machnng parameters that been consder n ths paper are cuttng speed, feed rate and spndle speed. The Turbo C compler s used to develop the GA smulaton. GA can be used n optmzaton problems such as schedulng, materals engneerng, optmal control, and so forth. Index Terms Genetc Algorthm, Optmzaton, Turnng operaton, turbo c, mld steel, GA optmzaton technque, materal removal rate, machnng, process parameters, feed rate, cuttng speed, machnng tme. 1 INTRODUCTION M ETAL cuttng s one of the mportant and commonly used manufacturng processes n any metal processng or busness ndustres. By machnng processes or manufacturng operatons, attempts are made to make a partcular product n several steps as of requred dmensons and shapes to ensure the qualty of machnng products for the ntended applcatons made for. The step-by-step machnng s done on the materal to reduce the machnng costs thereby ncreasng the machnng effectveness. Every manufacturng Industry ams at producng a large number of products wthn relatvely lesser tme. It has long been recognzed that condtons durng cuttng, such as feed rate, cuttng speed and depth of cut, should be selected to optmze the economcs of machnng operatons, as assessed by productvty, total manufacturng cost per component or some other sutable crteron. The optmzaton of cuttng parameters durng machnng s a dffcult task as t nvolves a number of aspects such as knowledge of machnng, emprcal equatons of tool lfe, cuttng forces, power consumed, machnng surface fnsh etc. All these aspects should be consdered durng machnng optmzaton to develop an effectve optmzaton crteron [1]. Manufacturng ndustres have long depended on the skll and experence of shop-floor machne-tool operators for optmal selecton of cuttng condtons and cuttng tools. Many authors have shown the optmzaton objectve as specfc cost from the begnnng of the researches n ths branch [2] to some of the most recent Ishwer Shvakot s currently pursung B. Tech. Degree program n Mechancal engneerng n Skkm Manpal Unversty, Inda, PH E-mal: shwar.swa@gmal.com Sunny Dyaley s Assstant Professor n Mechancal Engneerng Department n Skkm Manpal Unversty, Inda Golam Kbra s Assstant Professor n Mechancal Engneerng Department n Skkm Manpal Unversty, Inda B.B. Pradhan s Professor n n Mechancal Engneerng Department n Skkm Manpal Unversty, Inda works [3], [4], [5], [6], and [7]. A revew of artfcal ntellgence technques for CNC machnng parameter optmzaton n manufacturng ndustry was presented by [8] for provdng a better understandng of these technques n machnng control. Recently a study on manufacturng of freeform surfaces or sculptured surfaces usng CNC machnes has been performed n [9], whch prmarly focuses on three aspects n freeform surface machnng: tool path generaton, tool orentaton dentfcaton, and tool geometry selecton. A standard optmzaton technque usng genetc algorthm was developed by [10] to solve dfferent machnng optmzaton problems such as turnng, face mllng and grndng [11]. For a machnng process such as turnng, the cuttng condtons play an mportant role n the effcent use of the machne tool. There s an economc need to operate these machnes as effcently as possble. Snce the cost of turnng on these machnes s senstve to the cuttng condton, so the optmum value have to be determned before a work pece s put for processng. The present study s manly focused on optmzaton of process parameters of CNC turnng operaton consderng maxmzaton of materal removal rate (MRR) as the objectve functon. Feed rate, spndle speed and cuttng speed are consdered as process parameters wth specfed ranges. 2 EXPERIMENTAL METHODOLOGY AND CONDITIONS The experments are performed on a hgh precson conventonal lathe machne. Fg.1 shows the photographc vew of expermental set-up used for the present set of turnng operaton of mld steel workpece. A sngle pont hgh speed steel tool has been used as the cuttng tool. The round bar of mld steel materal of dmensons 30.4 mm n dameter and 140 mm n length s used as the workpece. The chemcal composton of the mld steel taken for expermentaton s shown n Table

2 Internatonal Journal of Scentfc & Engneerng Research Volume 3, Issue 5, May The nput parameters were consdered as spndle speed, cuttng speed and feed rate. The consdered ranges of these nput process parameters are shown n Table 2. The materal removal rate (MRR) n turnng operatons s the volume of materal or metal that s removed per unt tme n mm3/sec. For each revoluton of the workpece, a rng shaped layer of materal s removed. Materal removal rate has been calculated as per followng equaton. 2 2 (D 1 D 2 ) MRR = f N (1) 4 Here, D 1 s the ntal and D 2 s the fnal dameter of workpece, f s the feed rate and N s the spndle speed. The varous adjustable cuttng parameters durng turnng operaton s dscussed hereunder. from the workpece or the dstance from the uncut surface of the work to the cut surface, expressed n mm. It s mportant to note that the dameter of the work pece s reduced by two tmes the depth of cut because ths layer s beng removed from both sdes of the work. It s expressed n mm. Depth of cut can be calculated as per followng equaton, where D 1 s the ntal and D 2 s the fnal dameter of workpece. D1-D 2 DOC = Spndle Speed The rotatonal speed of the spndle and the workpece s n revolutons per mnute (rpm). The spndle speed s equal to the cuttng speed dvded by the crcumference of the workpece where the cut s beng made. In order to mantan a constant cuttng speed, the spndle speed must vary based on the dameter of the cut. If the spndle speed s held constant, then the cuttng speed wll vary. (2) 2.3 Feed Rate Feed always refers to the cuttng tool, and t s the rate at whch the tool advances along ts cuttng path. On most power-fed lathes, the feed rate s drectly related to the spndle speed and s expressed n mm (of tool advance) per revoluton (of the spndle), or mm/rev. The feed rate s calculated by usng the relaton of machnng tme. Fg.1 The expermental setup used for lathe turnng operaton TABLE 1 CHEMICAL COMPOSITION OF MILD STEEL Carbon Manganese Slcon Elements Others (C) (Mn) (S) Percentage Balance TABLE 2 PROCESS PARAMETERS AND THEIR RANGES Parameters Unt Range Feed rate mm/rev. 0.62, 0.73, 0.77, 0.82, 0.86, 0.89, 0.98 Spndle speed rpm 40, 90, 200, 400, 600 Cuttng speed m/mn Depth of cut mm 1 Cuttng flud --- tap water = (π D N)/1000, where, D s the dameter of workpece and N s the spndle speed 2.1 Depth of cut It s the thckness of the layer beng removed (n a sngle pass) Cuttng Speed Speed always refers to the spndle and the workpece. When t s stated n revolutons per mnute (rpm), t tells ther rotatng speed. But the mportant feature for a partcular turnng operaton s the surface speed, or the speed at whch the workpece materal s movng past the cuttng tool. It s smply the product of the rotatng speed tmes the crcumference of the workpece before the cut s started. It s expressed n meter per mnute (m/mn), and t refers only to the workpece. Every dfferent dameter on a workpece wll have a dfferent cuttng speed, even though the rotatng speed remans the same. The equaton of evaluatng of cuttng speed s already gven n Table 2. 3 RESULT AND DISCUSSION Lathe turnng experments on mld steel workpece have been conducted by varyng the spndle speed and cuttng speed at dfferent feed rate values. Fg. 2 shows the varaton of materal removal rate (MRR) at varous spndle speed whle varyng the feed rate parameters n the consdered range. From ths fgure, t s evdent that at low spndle speed of rotaton.e. at lower value of rotaton of workpece, the materal removal rate slghtly ncreases wth the ncrease of feed rate. As the feed rate ncreases, the amount of materal sheared off by the cuttng tool s hgh, resultng n hgher materal removal rate. However, at hgher settng of rotaton of the workpece,.e. at spndle speed rotatons of 600 rpm, the materal removal rate ncreases rapdly. It s due to the fact that, at hgher speed of rotaton, the materal s sheared off from the workpece sur-

3 Internatonal Journal of Scentfc & Engneerng Research Volume 3, Issue 5, May face very quckly due to hgher cuttng force. The nfluence of feed rate on machnng rate s shown n Fg. 3 at dfferent spndle speed values. From ths fgure, t s revealed that at low spndle speed of rotaton, the cuttng duraton or the machnng tme s very hgh for a partcular length of turnng operaton. However, at hgh spndle speed.e. hgh cuttng speed, the machnng tme s less due to more amount of removal of materal from the workpece. The fgure also depcts that wth ncreasng value of feed rate, the machnng tme s decreasng rapdly. 4 DEVELOPMENT OF REGRESSION EQUATION FOR MRR 4.1 Constrants and ther Ranges For developng the regresson model of materal removal rate and further optmzaton of MRR, a separate set of experments have been conducted usng the same set-up and tool-workpece confguratons. Durng machnng, some constrants are mposed on machnng processes and parameters, whch effect the optmal selecton of machnng condtons and therefore need to be handled carefully whle optmzng the machnng model. In the constructed optmzaton problem, three decson varables are consdered as cuttng speed, feed rate and spndle speed. The parameters spndle speed, feed rate and cuttng speed are bounded by upper and lower lmts, specfed by machnst or tool maker. These bounds are enlsted n Table 3. Table 4 shows the machnng parametrc combnatons and the correspondng values of materal removal rate and machnng tme. TABLE 4 MACHINING PARAMETRIC COMBINATIONS AND RESULTS OF RES- PONSES Fg. 2 Influence of feed rate and spndle speed on materal removal rate (MRR) Exp t.no Feed Rate Dept h of cut Spndle speed Cuttng speed MRR Machnng tme mm/r mm3/se mm rpm m/mn ev. c Mn Sl. No. Fg. 3 Influence of feed rate and spndle speed on machnng tme Ranges TABLE 3 RANGES OF CONSTRAINTS (VARIABLE BOUNDS) Spndle speed (rpm) Cuttng speed (m/mn) 1. Maxmum Mnmum Feed rate (mm/rev.) Regresson Analyss The frst necessary step for process parameter optmzaton n any metal cuttng process s to understand the prncples governng the cuttng processes by developng an explct mathematcal model. Here, statstcal regresson technque has been used to model the equaton usng Analyss of Varance (ANOVA). The objectve conssts of adjustng the parameters of a model functon to best ft a data set. A smple data set conssts of n ponts (data pars) (x, y) = 1,..., n, where x s an ndependent varable and y s a dependent varable whose value s found by observaton. The model functon has the form f(x, β), where the m adjustable parameters are held n the vector β. The goal s to fnd the parameter values for the model whch "best" fts the data. The least squares method fnds ts optmum when the sum, S, of squared resduals

4 Internatonal Journal of Scentfc & Engneerng Research Volume 3, Issue 5, May n 2 =1 S = r (3) s a mnmum. A resdual s defned as the dfference between the actual value of the dependent varable and the value predcted by the model. r = y - f (x, β) (4) An example of a model s that of the straght lne. Denotng the ntercept as β0 and the slope as β1, the model functon s gven by f(x, β) = β + β x (5) 0 1 A data pont may consst of more than one ndependent varable. For an example, when fttng a plane to a set of heght measurements, the plane s a functon of two ndependent varables, x and z, say. In the most general case there may be one or more ndependent varables and one or more dependent varables at each data pont. The mnmum of the sum of squares s found by settng the gradent to zero. Snce the model contans m parameters there are m gradent equatons. S j r = 2 r = 0, j = 1,..., m (6) j From equatons (4) and (6), the gradent equaton can be wrtten as f(x, ) 2 r = 0, j = 1,..., m (7) j The gradent equatons apply to all least squares problems. Each partcular problem requres partcular expressons for the model and ts partal dervatves. A regresson model s a lnear one when the model comprses a lnear combnaton of the parameters, m.e. f(x, ) = β (x ) (8) j j j=1 Here the coeffcents, ϕj, are functons of x. Lettng f(x, ) X = = (x ) (9) j j j In case the least square estmate (or estmator, n the context of a random sample),β s gven by ˆ X) T 1 T β = (X X y (10) The followng regresson equaton has been developed based on the expermental results shown n Table 4. Ths regresson equaton s acheved by feedng the expermental data to the statstcal Mntab software. In Fg. 4, the snapshot vew of the results of regresson analyss from Mntab software s shown. The regresson equaton developed for materal removal rate s as follow. MRR (Y) = X X X X 1X X 1X X 2X 3 (11) Here, X 1, X 2 and X 3 correspond to the process parameters feed rate, spndle speed and cuttng speed n uncoded values. Fg. 4 The snapshot vew of output results of regresson analyss from Mntab software TABLE 5 COMPARATIVE RESULTS OF MRR BASED ON EXPERIMENTAL AND REGRESSION BASED EQUATION Observaton Expermental Results Predcted Results from Regresson equaton 5 OPTIMIZATION BASED ON GENETIC ALGORITHM (GA) In 1975, Holland developed ths dea n hs book Adaptaton n natural and artfcal systems. He descrbed how to apply the prncples of natural evoluton to optmzaton problems and bult the frst Genetc Algorthms. Holland s theory has been further developed and now Genetc Algorthms (GAs) stand up as a powerful tool for solvng search and optmzaton problems. Genetc algorthms are based on the prncple of genetcs and evoluton [12]. Goldberg, 1989 gves an excellent ntroductory dscusson on GA, as well as some more advanced topcs. Genetc algorthms are a probablstc search approach whch s founded on the deas of evolutonary processes. The GA procedure s based on the Darwnan prncple of survval of the fttest. An ntal populaton s created contanng a predefned number of ndvduals (or solutons), each represented by a genetc strng (ncorporatng the vara-

5 Internatonal Journal of Scentfc & Engneerng Research Volume 3, Issue 5, May ble nformaton). Each ndvdual has an assocated ftness measure, typcally representng an objectve value. The concept that fttest (or best) ndvduals n a populaton wll produce ftter offsprng s then mplemented n order to reproduce the next populaton. Selected ndvduals are chosen for reproducton (or crossover) at each generaton, wth an approprate mutaton factor to randomly modfy the genes of an ndvdual, n order to develop the new populaton. The result s another set of ndvduals based on the orgnal subjects leadng to subsequent populatons wth better (mn. or max.) ndvdual ftness. Therefore, the algorthm dentfes the ndvduals wth the optmzng ftness values, and those wth lower ftness wll naturally get dscarded from the populaton. Ultmately ths search procedure fnds a set of varables that optmzes the ftness of an ndvdual and/or of the whole populaton. As a result, the GA technque has advantages over tradtonal non-lnear soluton technques that cannot always acheve an optmal soluton. For the genetc algorthm, the populaton encompasses a range of possble outcomes. Solutons are dentfed purely on a ftness level, and therefore local optma are not dstngushed from other equally ft ndvduals. Those solutons closer to the global optmum wll thus have hgher ftness values. Successve generatons mprove the ftness of ndvduals n the populaton untl the optmzaton convergence crteron s met. Due to ths probablstc nature GA tends to the global optmum, however for the same reasons GA models cannot guarantee fndng the optmal soluton. The GA conssts of four man stages: evaluaton, selecton, crossover and mutaton. These are brefly dscussed below. 5.1 Evaluaton The evaluaton procedure measures the ftness of each ndvdual soluton n the populaton and assgns t a relatve value based on the defnng optmzaton (or search) crtera. Typcally n a non-lnear programmng scenaro, ths measure wll reflect the objectve value of the gven model. The selecton procedure randomly selects ndvduals of the current populaton for development of the next generaton. Varous alternatve methods have been proposed but all follow the dea that the fttest have a greater chance of survval. 5.3 Mutaton The mutaton procedure randomly modfes the genes of an ndvdual subject to a small mutaton factor, ntroducng further randomness nto the populaton. Ths teratve process contnues untl one of the possble termnaton crtera s met: f a known optmal or acceptable soluton level s attaned; or f a maxmum number of generatons have been performed; or f a gven number of generatons wthout ftness mprovement occur. Generally, the last of these crtera apples as convergence slows to the optmal soluton. Populaton sze selecton s probably the most mportant parameter, reflectng the sze and complexty of the problem. However, the trade-off between extra computatonal `efforts wth respect to ncreased populaton sze s a problem specfc decson to be ascertaned by the modeler, as doublng the populaton sze wll approxmately double the soluton tme for the same number of generatons. Other parameters nclude the maxmum number of generatons to be performed, a crossover probablty, a mutaton probablty, a selecton method and possbly an eltst strategy, where the best s retaned n the next generaton s populaton. Fg5 Flow chart of Genetc Algorthms 5.2 Crossover The crossover procedure takes two selected ndvduals and combnes them about a crossover pont thereby creatng two new ndvduals. Smple (asexual) reproducton can also occur whch replcates a sngle ndvdual nto the new populaton. Fg. 6 Plot of Number of Generaton Vs Materal Removal Rate Unlke tradtonal optmzaton methods, GA s better at handlng nteger varables than contnuous varables. Ths s due to the nherent granularty of varable gene strngs wthn the GA model structure. Typcally, a varable s mplemented wth a range of possble values wth a bnary strng ndcatng the number of such values;.e. f x1 [0,15] and the gene strng s 4

6 Internatonal Journal of Scentfc & Engneerng Research Volume 3, Issue 5, May characters (e.g ) then there are 16 possbltes for the search to consder. To model ths as a contnuous varable ncreases the number of possble values sgnfcantly. Smlarly, other varable nformaton whch ads the search consderably are upper and lower bound values. These factors can affect convergence of the model solutons greatly. 5.4 Results of Optmzaton Fg. 6 shows the plot of materal removal rate (MRR) for varaton of number of generaton durng GA optmzaton. From ths plot, t s clear that the materal removal rate ncreases wth number of generaton. However, t s observed that after a certan number of generaton (90 generaton), materal removal rate remans constant. The optmal parametrc settng of feed rate, cuttng speed and spndle speed for whch the materal removal rate (MRR) s maxmum s shown n table 6. Spndle Speed, rpm TABLE 6 OPTIMIZATION RESULTS OF MRR ACHIEVED IN GA 6 CONCLUSIONS Cuttng Speed, m/mn Feed Rate, mm/rev Best Ftness of MRR, mm3/sec Ths paper presents a genetc algorthm optmzaton approach for fndng the optmal parameter settng durng turnng operaton n conventonal Lathe machne. In ths work the expermentaton s carred out n mld steel consderng three machnng parameter, vz., feed rate, spndle speed and cuttng speed. It has been found that materal removal rate ncreases wth the ncrease of feed rate. However, at low spndle speed of rotaton, the materal removal rate s hgh compared to hgh spndle speed of rotaton. Based on the results of experments, the regresson equaton for materal removal rate (MRR) has been developed usng statstcal Mntab software. The regresson equaton has been valdated through comparatve results of MRR acheved durng expermentaton. Genetc Algorthm (GA) has been used to acheve the optmum machnng parametrc combnaton n order to obtan the value of optmal result of materal removal rate. The results obtaned n ths paper can be effectvely utlzed for machnng, partcularly turnng operaton of mld steel materal n shop floor manufacturng.. Journal of Machne Tools & Manufacturng 39, [2] 2. Taylor, F.W., On the art of cuttng metals, Transactons of the ASME 28, [3] 3. Lang, M., Mgwatu, M., Zuo, M., Integraton of cuttng parameter selecton and tool adjustment decsons for multpass turnng, Internatonal Journal of Advanced Manufacturng Technology 17, [4] 4. Wang, J., Kuryagawa, T., We, X.P., Gou, G.M., Optmzaton of cuttng condtons usng a determnstc approach, Internatonal Journal of Machne Tools & Manufacture 42, [5] 5. Saravanan, R., Asokan, P., Vjayakumar, K., Machnng parameters optmzaton for turnng cylndrcal stock nto a contnuous fnshed profle usng genetc algorthm (GA) and smulated annealng (SA), Internatonal Journal of Advanced Manufacturng Technology 21, 1 9. [6] 6. Cus, F., Balc, J., Optmzaton of cuttng process by GA approach, Robotcs and Computer Integrated Manufacturng 19, [7] 7. Amolemhen, E., Ibhadode, A.O.A., Applcaton of genetc algorthms determnaton of the optmal machnng parameters n the converson of a cylndrcal bar stock nto a contnuous fnshed profle, Internatonal Journal of Machne Tools and Manufacture 44 (12 13), [8] 8. K.S. Park and S. H. Km, Artfcal ntellgence approaches to determnaton of CNC machnng parameters n manufacturng: A Revew, Artfcal Intellgence n Engneerng, 12, (1998). [9] 9. A. Lasem, D. Xue, P. Gu, Recent development n CNC machnng of freeform surfaces: A state-of-the-art revew, Computer-Aded Desgn, 42, (2010). [10] 10. R. Saravanan, G. Sekar,, M. Sachthanandam, Optmzaton of CNC machnng operatons subject to constrants usng genetc algorthm (GA), In: Internatonal Conference on Intellgent Flexble Autonomous Manufacturng Systems, Combatore, Inda, (2000). [11] 11. R. Saravanan, M. Sachthanandam, Genetc algorthm (GA) for multvarable surface grndng process optmzaton usng a multobjectve functon model, Int J Adv Manuf Technol. 17, (2001). [12] 12. S.N.Svanandam S.N.Deepa, Introducton to Genetc Algorthm, ISBN Sprnger Berln Hedelberg New York. [13] 13. Thomas Wese, Global Optmzaton Algorthms Theory and Applcaton, Verson: Smon Mardle and Sean Pascoe, An overvew of genetc algorthms for the soluton of optmsaton problems. Volume 13, Issue 1, ACKNOWLEDGMENT The authors wsh to thank Mr.Lopzong Lepcha and Mr.Sddharth Sandalya for ther supports n ths work. REFERENCES [1] 1. Sönmez, A.I., Baykasoglu, A., Derel, T., Flz, I.H., Dynamc optmzaton of multpass mllng operaton va geometrc programmng. Internatonal