Parametric Deduction Optimization for Surface Roughness

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1 Amercan Journal of Appled Scences 7 (9): , 2010 ISSN Scence Publcatons Parametrc Deducton Optmzaton for Surface Roughness Tan-Syung Lan Department of Informaton Management, Yu Da Unversty Maol County, Tawan 361, ROC Abstract: Problem statement: Surface roughness s a major consderaton n modern Computer Numercal Control (CNC) turnng ndustry. Most exstng optmzaton researches for CNC fnsh turnng were ether accomplshed wthn certan manufacturng crcumstances, or acheved through numerous equpment operatons. Therefore, a general deducton optmzaton scheme s deemed to be necessary for the ndustry. Approach: In ths study, four parameters (cuttng depth, feed rate, speed, tool nose runoff) wth three levels (low, medum, hgh) were consdered to optmze the surface roughness for Computer Numercal Control (CNC) fnsh turnng. Addtonally, twenty-seven fuzzy control rules usng trapezod membershp functon wth respectve to seventeen lngustc grades for the surface roughness were constructed. Consderng thrty nput and eghty output ntervals, the defuzzfcaton usng center of gravty was moreover completed. Through the Taguch experment, the optmum general deducton parameters can then be receved. Results: The confrmaton experment for optmum deducton parameters was furthermore performed on an ECOCA-3807 CNC lathe. It was shown that the surface roughness from the fuzzy deducton optmzaton parameters are sgnfcantly advanced comparng to those from benchmark. Concluson: Ths study not only proposed a parametrc deducton optmzaton scheme usng orthogonal array, but also contrbuted the satsfactory fuzzy approach to the surface roughness for CNC turnng wth profound nsght. Key words: Computer numercal control, orthogonal array, fuzzy deducton, surface roughness INTRODUCTION Machnng operatons have been the core of the manufacturng ndustry snce the ndustral revoluton (Rao, 2006). The exstng optmzaton researches for Computer Numercal Controlled (CNC) turnng were ether smulated wthn partcular manufacturng crcumstances (Svarao et al., 2009; Ln et al., 2001; Ln, 1998; Meng et al., 2000), or acheved through numerous frequent equpment operatons (Kopac et al., 2002; Tosun and Ozler, 2004). Nevertheless, these are regarded as computng smulatons and the applcablty to real world ndustry s stll uncertan. Therefore, a general optmzaton scheme wthout equpment operatons s deemed to be necessarly developed. Surface roughness s commonly consdered as a major manufacturng goal (Tosun and Ozler, 2004) for turnng operatons n many of the exstng researches. The machnng process on a CNC lathe s programmed by speed, feed rate and cuttng depth, whch are frequently determned based on the job shop experences. However, the machne performance and the product characterstcs are not guaranteed to be acceptable. Therefore, the optmum turnng condtons have to be accomplshed. It s mentoned that the tool 1248 nose run-off wll affect the performance of the machnng process (Yeh and La, 1995). Therefore, the tool nose run-off s also selected as one of the control factors n ths study. Parameter optmzaton for surface roughness s a hard-solvng ssue because of the nteractons between parameters. Problems related to the enhancement of product qualty and producton effcency can always be related to the optmzaton procedures. Taguch method, an expermental desgn method, has been wdely appled to many ndustres. It can not only optmze qualty characterstcs through the settng of desgn parameters, but also reduce the senstvty of the system performance to sources of varaton (Huh et al., 2003; Suhal et al., 2010; Km et al., 2003; Benhamd and Othman, 2009). The Taguch method adopts a set of orthogonal arrays to nvestgate the effect of parameters on specfc qualty characterstcs to decde the optmum parameter combnaton. These knds of arrays use a small number of expermental runs to analyze the qualty effects of parameters as well as the optmum combnaton of parameters. To acheve the deducton optmzaton, t s necessary to frst descrbe the dynamc behavor of the system to be controlled. Because of the number,

2 complexty and unclear, vague nature of the varables of the dynamc systems that may nfluence the decson maker s decson, fuzzy set theory s the most sutable soluton (Zadeh, 1965; Zmmerman, 2001). Fuzzy lngustc models permt the translaton of verbal expressons nto numercal ones (Gungor and Arkan, 2007). Therefore, the nput output relatonshp of the process can be descrbed by the collecton of fuzzy control rules nvolvng lngustc varables rather than a complcated dynamc mathematcal model. Wth all the vewponts above, ths study consders four parameters (cuttng depth, feed rate, speed, tool nose runoff) wth three levels (low, medum, hgh) to optmze the surface roughness n CNC fnsh turnng. The fuzzy control rules usng trangle membershp functon wth respectve to seventeen lngustc grades for surface roughness are addtonally constructed. The defuzzfcaton s then quantfed usng center of gravty and ntroduced as the Sgnal-to-Nose (S/N) rato to Taguch experment and thus the optmum deducton parameters can then be receved. Ths study defntely proposes a fuzzy deducton general optmzaton approach and satsfactory fuzzy lngustc technque for mprovng surface roughness n CNC turnng wth profound nsght. MATERIALS AND METHODS In ths study, the varable quantfcaton and deducton optmzaton for CNC turnng operatons are proposed usng fuzzy set theory and Taguch method respectvely. They are descrbed as below. Fuzzy set theory: Let X be a unverse of dscourse, A s a fuzzy subset of X f for all x X, there s a number μ (x) [0,1] A assgned to represent the membershp of x to A and μ (x) A s called the membershp functon of A. A trapezod fuzzy number A can be defned by a trp-let (a, b, c, d) (Fg. 1) (Kaufmann et al., 1991). The membershp functon s defned as: μ ~ (x :a,b,c,d) = A x a a < x b b a 1 b< x c x d c< x d c d 0 otherwse (1) Fg. 1: Trapezod fuzzy numbers In ths study, the three most mportant parameters for the surface roughness are prmarly concluded through lterature revew. Addtonally, twenty-seven fuzzy control rules usng trapezod membershp functon wth respectve to seventeen lngustc grades wll be constructed followng IF-THEN rules. To elmnate the computaton, thrty nput and eghty output ntervals are consdered to prepare the defuzzfcaton. Through Cartesan product, the degree of membershp for both nput and output can thus be attaned as: R = Input Output (2) Here: Input = The parameter Output = The attrbute R = The fuzzy relaton between the parameter and attrbute The OR rules are then utlzed for combnng rules for maxmum degree of membershp as: μ R1+μ R2 = max{ μr1, μ R2} (3) where, R1 and R2 symbolze for the two rules. In ths study, the average value usng center of gravty s determned to represent the fuzzy set as: F(x ) = x μ (x ) μ A A (x ) where, F(x ) s the fnal ratng of actvty, descrbes the membershp functon of fuzzy set A. Taguch method: The Taguch method s a robust desgn method technque (Palankumar, 2008; Ross, 1249 (4) μ (x ) A

3 1995), whch provdes a smple way to desgn an effcent and cost effectve experment. In order to effcently reduce the numbers of conventonal expermental tasks, the orthogonal array (Senapat et al., 2007; We et al., 2002) by usng desgn parameters (control factors) n column and standard quanttes (levels) n row s proposed and further adopted. The performance measure, Sgnal-to-Nose rato (S/N) (Park et al., 2005) proposed by Taguch s used to obtan the optmal parameter combnatons. The larger S/N means the relaton to the qualty wll become better. The lower qualty characterstc wll be regarded as a better result when consderng the smaller-the-best qualty. The related S/N rato s defned as: n 2 y S/N = 10 log db = 1 n ( ) (5) Where: n = The number of experments for each expermental set y = The qualty characterstc at the -th experment On the contrary, the larger qualty characterstc wll have better result t when consderng the largerthe-best qualty, therefore, by takng the nverse of qualty characterstc nto Eq. 13, the related S/N rato can also be deduced and shown n Eq. 14: S/N = -10 log n 2 ( db) (6) =1 1 y n In ths study, the defuzfcaton result s ntroduced to the Taguch experment as the S/N rato. Therefore, t s judged as the qualty of smaller-the-best. In addton to the S/N rato, a statstcal Analyss of Varance (ANOVA) (Wu and Chyu, 2002) can be employed to ndcate the mpact of process parameters. In ths way, the optmal levels of process parameters can be estmated. Research desgn: Surface roughness s consdered the major goal n ths study. Four parameters wth three levels are selected to optmze the fnsh turnng based on the orthogonal array. Addtonally, twenty-seven fuzzy control rules wth respectve to seventeen lngustc grades for each attrbute are constructed. Consderng thrty nput and eghty output ntervals, the defuzzfcaton usng center of gravty s thus completed for the Taguch experment and the optmum deducton parameters can then be receved Constructon of orthogonal array: In ths study, the four turnng parameters (A-speed, B-cuttng depth, C- feed rate and D-tool nose runoff) (Lan and Wang, 2009) wth three dfferent levels (low, medum and hgh) (Table 1) are constructed for the deducton optmzaton of machnng operaton. In Table 1, the three levels of speed, cuttng depth and feed rate are consdered accordng to the machnng handbook suggested by the tool manufacturer. The tool nose runoff s postoned by usng dfferent shms located under the tool holder. The orthogonal array s then selected to perform the nne sets of deducton experments. Table 1: Orthogonal array Parameter A B (cuttng C D (tool nose Experment (speed) depth) (feed rate) runoff) 1 Low Low Low Low 2 Low Medum Medum Medum 3 Low Hgh Hgh Hgh 4 Medum Low Medum Hgh 5 Medum Medum Hgh Low 6 Medum Hgh Low Medum 7 Hgh Low Hgh Medum 8 Hgh Medum Low Hgh 9 Hgh Hgh Medum Low Table 2: Fuzzy rules for surface roughness Rules Speed Feed rate Deducton 1 Low Low medum 2 Low Medum large 3 Low Hgh largest 4 Low Low medum 5 Low Medum large 6 Low Hgh largest 7 Low Low medum 8 Low Medum large 9 Low Hgh largest 10 Medum Low small 11 Medum Medum medum 12 Medum Hgh large 13 Medum Low small 14 Medum Medum medum 15 Medum Hgh large 16 Medum Low small 17 Medum Medum medum 18 Medum Hgh large 19 Hgh Low smallest 20 Hgh Medum small 21 Hgh Hgh medum 22 Hgh Low smallest 23 Hgh Medum small 24 Hgh Hgh medum 25 Hgh Low smallest 26 Hgh Medum small 27 Hgh Hgh medum Table 3: Trapezod ranges of three lngustc levels for parameters Lngustc level Low Medum Hgh Range [0,12.5,15] [0,2.5,27.5,30] [15,17.5,30]

4 Table 4: Trapezod ranges of seventeen lngustc levels for attrbutes Lngustc level Smallest Extreme small Super small Small small Small Range [0,2.5,5] [0,2.5,7.5,10] [5, 7.5,12.5,15] [10,12.5,17.5,20] [15,17.5,22.5,25] Smaller Much smaller A lttle smaller Medum A lttle larger Much larger [20,22.5,27.5,30] [25,27.5,32.5,35] [30,32.5,37.5,40] [35,37.5,42.5,45] [40,42.5,47.5,50] [45,47.5,52.5,55] Larger Large Large large Super large Extreme large Largest [50,52.5,57.5,60] [55,57.5,62.5,65] [60,62.5,67.5,70] [65,67.5,72.5,75] [70,72.5,77.5,80] [75,77.5,80] Table 5: Quantfed results for lngustc results Lngustc level Smallest Extreme small Super small Small small Small Smaller Much smaller A lttle smaller Defuzzfcaton Medum A lttle larger Much larger Larger Large Large large Super large Extreme large Largest Fuzzy control rules: The twenty-seven fuzzy control rules wth respectve to seventeen grades for the surface roughness n ths study are determned. From the exstng lterature (Petropoulos et al., 2006), t s found that the surface roughness can be expressed as: m n R( = a,zd,t,p,q,3z) = CV f where the machnng speed (V) and feed rate (f) are concluded as prorty parameters to surface roughness. Therefore, the fuzzy rules can be descrbed as shown n Table 2. Defuzzfcaton: In ths study, the three parameter levels are selected based on the Taguch expermental method, therefore, each trangle membershp functon s related to the peak pont of ts fuzzy area. Consderng thrty nput and eghty output ntervals, the defuzzfcaton of seventeen lngustc grades usng center of gravty can then be completed. The degree of membershp for nput (parameter) and output (attrbute) can be descrbed as shown n Table 3 and 4 respectvely. Utlzng the average value of the fuzzy set to represent the entre set, we then have the quantfed result for the fuzzy tem of seventeen lngustc grades as shown n Table 5. RESULTS AND DISCUSSION By consderng the parameter combnatons of the 4 nne sets of experment based on the L(3) 9 orthogonal array, the quantfed results from fuzzy deducton for the surface roughness are determned and shown as Table 6. Introducng the deducton results as the Sgnal to Nose rato (S/N) for surface roughness under smaller-the-best expectaton, the results of factor responses are calculated and lsted n Table 7. The mean effects for S/N ratos are then drawn by MINITAB 14 and shown as Fg. 2. Therefore, the optmum fuzzy deducton multattrbute turnng parameters are found to be A (Low), B (Hgh), C (Hgh) and D (Low or Hgh). Table 6: Fuzzy deducton results Attrbutes experment Surface roughness Table 7: Result of factor responses Parameter Level A B C D Low Medum Hgh Delta Rank Table 8: Parameters and levels Level Low Medum Hgh Parameter (level 1) (level 2) (level 3) A: Speed (m/mn) B: Cuttng depth (mm) C: Feed rate (mm/rev) D: Tool nose runoff (mm) -0.1 ± The fnshng dameter turnng operaton of S45C (ϕ45 mm 250 mm) work pece on an ECOCA-3807 CNC lathe s arranged for the experment. The TOSHIBA WTJNR2020K16 tool holder wth MITSUBISHI NX2525 nsert s utlzed as the cuttng tool. The four turnng parameters (speed, cuttng depth, feed rate and tool nose runoff) wth three dfferent levels (low, medum and hgh) (Table 8) are expermentally dstngushed for the machnng 4 operaton on the bass of L9 (3 ) orthogonal array. In Table 8, the three levels of speed, cuttng depth and feed rate are dentfed from the machnng handbook suggested by the tool manufacturer. The tool nose 1251

runoff s postoned by usng dfferent shms located under the tool holder and determned by measurng the tp after face turned the work pece. When the tool nose s set approxmately 0.

5 runoff s postoned by usng dfferent shms located under the tool holder and determned by measurng the tp after face turned the work pece. When the tool nose s set approxmately 0.1 mm hgher (lower) than the center of the work pece, t s regard as Hgh (Low). When the tool nose s set wthn ±0.03 mm, t s consdered as Medum. The surface Roughness (R a ) of machned work peces are measured on the MITSUTOYO SURFTEST at three dfferent segments of 40mm, 80mm and 120 mm from the face, therefore, the average data are receved as the attrbute of surface roughness. To verfy the applcablty of the optmum result acheved by our proposed deducton optmzaton technque, the machnng operatons under both fuzzy lngustc optmzaton parameters and benchmark parameters; A (medum), B (medum), C (medum), D (medum), whch are often ntroduced nto the confrmaton experment n many of the studes (Tosun and Ozler, 2004; Ln and Ln, 2006) for comparson to the optmum parameters, are performed on the CNC lathe. The machned results are concluded and lsted n Table 9. From Table 9, t s observed that the surface roughness under fuzzy deducton parameters are sgnfcantly mproved by 14.4 and 23.1% respectvely and the average result s also mproved by 18.75% from the benchmark parameters. It s shown that our proposed general deducton optmzaton technque can really advance the surface roughness for CNC turnng. Fg. 2: Plot of man effects Table 9: Confrmaton results Surface roughness Fuzzy deducton optmzaton parameters µm (A1B3C3D1) Fuzzy deducton optmzaton parameters µm (A1B3C3D3) Benchmark parameters (A2B2C2D2) µm 1252 CONCLUSION In ths study, the parametrc deducton scheme was proposed and appled to acheve the optmum CNC fnsh turnng parameters under the consderatons of surface roughness. A confrmaton experment of the optmum deducton parameters was conducted to ndcate the effectveness of the proposed fuzzy optmzaton method. Through the confrmaton test, the expermental results valdate the potency that the surface roughness can be advanced from our parametrc deducton optmzaton technque. Parametrc optmzaton s a hard-solvng ssue because of the nteractons between parameters. Ths study not only proposes a deducton optmzaton approach usng orthogonal array, but also contrbutes the satsfactory fuzzy technque for mprovng the surface roughness n CNC turnng wth profound nsght. The competton of manufacturng ndustry wll then be economcally excted through the proposed development n ths study. ACKNOWLEDGEMENT Fnancal support for ths study was provded by the Natonal Scence Councl Tawan, R.O.C., under the contract of NSC E REFERENCES Benhamd, M. and M.B. Othman, Hardware mplementaton of a genetc algorthm based canoncal snged dgt multplerless fast Fourer transform processor for multband orthogonal frequency dvson multplexng ultra wdeband applcatons. J. Math. Stat., 5: Gungor, Z. and F. Arkan, Usng fuzzy decson makng system to mprove qualty-based nvestment. J. Intell. Manuf., 18: DOI: /s x Huh, H., J.H. Heo and H.W. Lee, Optmzaton of a roller levelng process for Al7001T9 ppes wth fnte element analyss and Taguch method. Int. J. Mach. Tool Manuf., 43: DOI: /S (02) Kaufmann, A., M.M. Gupta and B. Esposto, Introducton to Fuzzy Arthmetc Theory and Applcatons. 1st Edn., Van Nostrand Renhold Company, New York, ISBN: 10: , pp: 384. Km, S.J., K.S. Km and H. Jang, Optmzaton of manufacturng parameters for a brake lnng usng Taguch method. J. Mater. Process. Technol., 136: DOI: /S (03)

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Research Article Fuzzy Linguistic Optimization on Surface Roughness for CNC Turning

Mathematical Problems in Engineering Volume 20, Article ID 7206, pages doi:.11/20/7206 Research Article Fuzzy Linguistic Optimization on Surface Roughness for CNC Turning Tian-Syung Lan Department of Information