International Journal of Industrial Engineering Computations

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1 Internatonal Journal of Industral Engneerng Computatons 6 (205) Contents lsts avalable at GrowngScence Internatonal Journal of Industral Engneerng Computatons homepage: On the applcaton of response surface methodology for predctng and optmzng surface roughness and cuttng forces n hard turnng by PVD coated nsert Hessana Zaha a, Yallese Mohamed Athmane a, Bouzd Lakhdar a* and Mabrouk Tarek b a Mechancs and Structures Research Laboratory (LMS), 8 May 945 Unversty of Guelma, P.O. Box 40, 24000, Algera b Unversté de Tuns El Manar, Ecole Natonale d'ingéneurs de Tuns (ENIT), 2, Tuns, Tunse C H R O N I C L E A B S T R A C T Artcle hstory: Receved August Receved n Revsed Format October Accepted October Avalable onlne October Keywords: Hardened steel Surface roughness Cuttng forces PVD coated ceramc tools RSM ANOVA Ths paper focuses on the explotaton of the response surface methodology (RSM) to determne optmum cuttng condtons leadng to mnmum surface roughness and cuttng force components. The technque of RSM helps to create an effcent statstcal model for studyng the evoluton of surface roughness and cuttng forces accordng to cuttng parameters: cuttng speed, feed rate and depth of cut. For ths purpose, turnng tests of hardened steel alloy (AISI 440) (56 HRC) were carred out usng PVD coated ceramc nsert under dfferent cuttng condtons. The equatons of surface roughness and cuttng forces were acheved by usng the expermental data and the technque of the analyss of varance (ANOVA). The obtaned results are presented n terms of mean values and confdence levels. It s shown that feed rate and depth of cut are the most nfluental factors on surface roughness and cuttng forces, respectvely. In addton, t s underlned that the surface roughness s manly related to the cuttng speed, whereas depth of cut has the greatest effect on the evoluton of cuttng forces. The optmal machnng parameters obtaned n ths study represent reductons about 6.88%, 3.65%, 9.05% n cuttng force components (Fa, Fr, Ft), respectvely. The latters are compared wth the results of ntal cuttng parameters for machnng AISI 440 steel n the hard turnng process. 205 Growng Scence Ltd. All rghts reserved Nomenclature f ap Ra Fa Fr Ft X a aj aj : Cuttng speed (m/mn) : Feed rate (mm/rev) : Depth of cut (mm) : Arthmetc average of absolute roughness (µm) : Feed force (N) : Thrust force (N) : Tangental cuttng force (N) : Coded machnng parameters : Quadratc term : Coeffcents of lnear terms : Cross-product terms * Correspondng author. Tel: E-mal: ssam.bouzd@yahoo.com (B. Lakhdar) 204 Growng Scence Ltd. All rghts reserved. do: /j.jec

2 268 ANOVA : Analyss of varance RSM : Response surface methodology DF : Degrees of freedom Seq SS : Sequental sum of squares Adj MS : Adjusted mean squares PC% : Percentage contrbuton rato (%) R 2 : Correlaton coeffcent α : Clearance angle, degree γ : Rake angle, degree λ : Inclnaton angle, degree χr : Major cuttng edge angle, degree. Introducton The use of modern ceramc nsert materals n machnng s very attractve from ndustral pont of vew because they retan hgh strength up to a temperature of C. Nevertheless, cuttng nserts have poor relablty because they are brttle (Casto et al. 0). To overcome the mentoned shortcomng, TC, or TN to alumnum oxde are added as a coat on the nsert leadng to an ncrease both n ts thermal conductvty and thermal resstance. Therefore, coated tools have been used for machnng varous steel alloys and cast ron successfully. Physcal Vapour Deposton (PVD) s one among used technques for coatng tools. Its use s growng although ts usage relatvely low compared to the Chemcal Vapour Deposton (CVD) technque. Durng cuttng process, coated tools ensure hgher wear resstance, lower heat generaton and lower cuttng forces, thus enablng them to perform behavour at hgher cuttng condtons than ther uncoated counterparts (Koelsch, 992; Sahn, 3). Hard turnng s generally performed by superor hard tools lke CBN and ceramc. The benefts of hard turnng are the cost reducton per product, the mprovement of surface fnsh closer to grndng, the hgh productvty, the ablty to cut complex parts by sngle setup, the less costly equpment and the envronment frendly dry cuttng. Due to the development of PCBN cuttng tools (commercally avalable n the md-970s) and advanced ceramc grades, the turnng of steels wth hardness values exceedng HRC has been replaced extensvely and successvely the costly grndng operatons Lalwan et al. (8). The evoluton of cuttng force s consdered, among others as an mportant technologcal output helpng to control the machnng process. It s the essental crteron for the evaluaton of the necessary power machnng (choce of the electrc motor). It s also used for dmensonng of machne tool components and tool body. Moreover, ths output nfluences machnng system stablty. In hard turnng, cuttng forces have been found to be affected by a number of factors such as depth of cut, feed rate, cuttng speed, cuttng tme, workpece hardness, etc. The response surface methodology (RSM) s a collecton of mathematcal and statstcal procedures that are useful for modelng and analysng problems n whch response optmzaton s affected by several varables Montgomery (20). Varous nvestgatons have been carred out to study the performance of coated carbde nsert, ceramc and cubc boron ntrde (CBN) tools durng machnng of hard materals. Hessana al. (203) appled RSM to nvestgate the effect of cuttng parameters and tool vbratons on surface roughness n hard turnng of AISI 440 wth CC6 tool. Results show how much the surface roughness s hghly nfluenced by feed rate varaton. Suresh et al. (2) focused ther study on machnng mld steel and TN-coated tungsten carbde (CNMG) cuttng tools for developng a surface roughness predcton model usng RSM. Genetc algorthms (GAs) were also used to optmze the objectve functon and compared wth RSM results. It was observed that GA program provded mnmum and maxmum values of surface roughness and ther corresponded optmal machnng condtons. Asltürk and Akkus (20) carred out hard turnng experment on hardened AISI 440 steel (5 HRC) wth coated carbde nsert usng Taguch orthogonal array for surface roughness. Results of ths study ndcate that the feed rate has the most sgnfcant effect on the roughness Ra and Rz. In addton, the effects of two factor nteractons of the feed rate cuttng speed and depth of cut, cuttng speed appear to be sgnfcant. However, other machnablty characterstcs lke tool wear and tool lfe,

3 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 269 cuttng force, chp morphology and cuttng temperature have not been consdered for study and whch are essental for hard turnng study. Luo et al. (999) have nvestgated the relatonshp between hardness and cuttng forces durng turnng AISI 4340 steel hardened from 29 to 57 HRC usng mxed alumna tools. The results suggest that an ncrease of 48% n hardness leads to an ncrease n cuttng forces from 30% to 80%. It s reported that for work materal hardness values between 30 and HRC, contnuous chps were formed and the cuttng force components were reduced. However, when the work pece hardness ncreased above HRC, segmented chps were observed and the cuttng force showed a sudden ncrease. Davm and Fguera (7) nvestgated the machnablty of AISI D2 tool steel usng expermental and statstcal technques. Hard turnng operaton was performed on materal havng hardness of 60 HRC. The tests were conducted by usng cuttng speed, feed rate and tme as man parameters. The nfluence of cuttng parameters on the flank wear evoluton, specfc cuttng force and surface roughness varatons on machnablty evaluaton n turnng wth ceramc tools usng ANOVA was presented. Yallese et al. (9) have expermentally nvestgated the behavor of CBN tools durng hard turnng of AISI 52 tempered steel. The surface qualty obtaned wth the CBN tool was found to be sgnfcantly mproved than grndng. A relatonshp between flank wear and surface roughness was also establshed based on an extensve expermental data. Nesel et al. (20) exploted RSM to optmze the effect of tool geometry parameters on surface roughness n the case of the hard turnng of AISI 040 wth P25 tool. Park (2) observed that the radal force s the largest force component regardless the grade of the nsert used,.e. PCBN or ceramc durng turnng hardened steel n dry condtons. The specfc cuttng energy n the case of the hard turnng s found to be smaller than n grndng. Cuttng force and surface roughness were found to be smaller when cuttng wth PCBN tools compared to ceramc ones under smlar cuttng condtons. Ozel et al. (5) conducted a set of ANOVA and performed a detaled expermental nvestgaton on the surface roughness and cuttng forces n the fnsh hard turnng of AISI H3 steel. Ther results ndcated that the effects of workpece hardness, cuttng edge geometry, feed rate and cuttng speed on the surface roughness are statstcally sgnfcant. Davm and Fguera (7) performed expermental nvestgatons on AISI D2 cold work tool steel (60 HRC) usng ceramc tools composed approxmately of 70% AL2O3 and 30% TC n surface fnsh operatons. A combned technque usng an orthogonal array (OA) and analyss of varance (ANOVA) was employed n ther study. The test results showed the possblty that to acheve surface roughness levels as low as Ra < 0, 8 μm wth an approprate choce of cuttng parameters that elmnated cylndrcal grndng. Sahoo and Sahoo (20) conducted hard turnng of AISI 4340 steel (47 HRC) usng multlayer ZrCN coated carbde nsert and developed mathematcal model for surface roughness and flank wear. The optmzed process parameter for multple performance characterstcs has been obtaned usng grey based Taguch method. Mathematcal model output concluded that the RSM models proposed are statstcally sgnfcant and adequate because of ther R 2 value. Lma et al. (5) evaluated the machnablty of hardened AISI 4340 and D2 grade steels at dfferent levels of hardness by usng varous cuttng tool materals. The AISI 4340 steels were hardened to 42 and 48 HRC and then turned by usng coated carbde and CBN nserts. The hgher cuttng forces were recorded when AISI 4340 steel was turned usng low feed rates and depth of cut. Also, lower surface roughness values were observed for softer workpece materals when ncreasng cuttng speed and they are deterorated wth hgh feed rate values. The nfluence of cuttng speed, feed rate and machnng tme on machnablty aspects such as specfc cuttng force, surface roughness and tool wear n AISI D2 cold work tool steel hard turnng was studed by Gatonde et al. (9, 20) usng RSM and ANN based models. Vkram Kumar et al. (8) compared the performance of TCN and TAIN coated tools n machnng AISI 4340 hardened steel under dry, wet and mnmum flud applcaton condtons. Mnmum flud applcaton yelds better result compared to wet and dry machnng. However, hgh performance of the TAIN coated tool regardng wear resstance and surface fnsh. To nvestgate potentals of applcatons n hard turnng, (Lma et al. 7) have carred out turnng operatons usng coated carbde tools on AISI 4340 steel hardened from 2 to 525 HV. It was concluded that, the cuttng force ncreases wth the work materal hardness. However, t decreases slghtly as the work pece hardness ncreased from 2 to 345 HV. More et al. (6) have expermentally nvestgated the effects of cuttng speed and feed rate on tool wear, surface roughness and cuttng forces when turnng

4 270 of AISI 4340 hardened steel usng CBN-TN-coated carbde nserts. In addton, machnng cost analyss was also performed n economc condtons to compare CBN-TN-coated and PCBN nserts. Anero et al. (8) have studed the turnng of hardened steel usng TCN/Al2O3/TN coated carbde tool and PCBN tools durng turnng of hardened steel. They observed that hgh tool lfe could be acheved usng PCBN tool, but ther cost s twce the coated carbde one. Machnng medum hardened steels wth TCN/Al2O3/TN nserts tend to be more productve. The relatvely good performance of coated carbde tools n machnng hardened steel reled on the coatng combnaton of layers. Chou et al. (2), Thele et al. (0) and Ozel et al. (5) explaned the effects of varous factors affectng cuttng forces, surface roughness, tool wear and surface ntegrty n hard turnng of varous grades of steels usng CBN tools. Chou and song (4) concluded that better surface fnsh could be acheved usng a large tool nose radus on fnsh turnng of AISI 52 bearng steel usng alumna ttanumcarbde tools but generates deeper whte layers. Benga and Abrao (3) and Kumar et al. (3) observed superor surface qualty n turnng of hardened steel components usng alumna TC ceramc tools. In ths global framework, the am of the present study s to optmze and predcted surface roughness and cuttng force components n the case of the hard turnng by PVD coated ceramc nsert of AISI 440 steel alloy (56 HRC) based on statstcal method. Varous cuttng condtons (cuttng speed, feed rate, and depth of cut) were adopted for ths study and response surface methodology and 3 3 factoral desgn of experment, quadratc model have been developed wth 95% confdence level. 2. Expermental procedure 2. Equpment and materals The expermental work was carred out on a lathe (Tos TRENCIN; model SN 40C, spndle power 6.6 kw). The work materal used durng the turnng tests was hardened and tempered to 56 HRC steel alloy AISI 440 (70 mm dameter and 370 mm length). Its Chemcal composton s gven n Table. Coated ceramc nsert wth an ISO desgnaton of SNGA20408T0020 (sandvk, Grade CC60) was used n the expermental work wth clamp-type PSBN25 25K2 tool holder, yeldng to the followng prncpal angle: cuttng edge angle χr = 75, negatve nclnaton angle λ = -6, negatve rake angle γ = - 6, clearance angle α = 6 and tool nose radus R = 0.8 mm (Sandvk, 9). The tests were carred n dry cuttng condtons. Table Chemcal composton of AISI 440 steel. Composton C S Mn S P N Cu Cr V Mo Fe % Three levels were specfed for each process parameter as gven n Table 2. The factor levels were chosen wthn the ntervals recommended by the cuttng tool manufacturer (Kennametal, 0). Table 2 Attrbuton of the levels to the factors. Level Cuttng speed, (m/mn) Feed rate, f (mm/rev) Depth of cut, ap (mm) (low) (medum) (hgh) The cuttng forces whch are feed force (Fa), thrust force (Fr) and tangental force (Ft) were recorded usng a standard quartz dynamometer (Kstler 9257B) allowng measurements from -5 to 5 KN. The measurement chan also ncluded a charge amplfer (Kstler 9B30), data acquston hardware (A/D 2855A3) and graphcal programmng envronment (DYNOWARE 2825A-) for data analyss and vsualzaton. Each test for measurng the turnng forces lasted for 5 s and an acquston rate of 0

5 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 27 Hz was employed. The expermental setup s shown n Fg. ; the measurements of arthmetc surface roughness (Ra) for each cuttng condton were obtaned from a Surftest 20 Mtutoyo roughnessmeter wth a cut-off length of 0.8 mm and samplng length of 5 mm. The measurements were repeated at three equally spaced locatons around the crcumference of the workpece and the result s an average of these values for a gven machnng pass. (a) Workpece (b) Surftest 20 Dynamometer 2.2. Plan of experments Fg.. (a) Expermental setup wth measurement of the cuttng forces by pezoelectrc dynamometer and surface roughness, and (b) charge amplfers and PC based data acquston system. For the elaboraton of experments plan the method of Taguch for three factors at three levels was used by levels the values taken by the factors were averaged. Table 2 ndcates the factors to be studed and the assgnment of the correspondng levels. The array chosen was the L27 (3 3 ) whch have 27 rows correspondng to the number of tests (26 degrees of freedom) wth 3 columns at three levels as shown n Table 3 (Ross, 988). The factors and the nteractons are assgned to the columns. Table 3 Orthogonal arrayl27 (3 3 ) of Taguch (33). L27(3 3 ) The plan of experments s made of 27 tests (array rows) n whch the frst column was assgned to the cuttng speed (), the second column to the feed rate (f), the ffth column to the depth of cut (ap) and the remanng columns to the nteractons. A randomzed schedule of runs was created usng the desgn

6 272 of experment shown n Table 4. The response surface methodology (RSM) s a procedure for determnng the relatonshp between the ndependent process parameters wth the desred response and explorng the effect of these parameters on responses, ncludng sx steps (Ganed et al., 9). The latters, help to () defne the ndependent nput varables and the desred responses wth the desgn constants, (2) adopt an expermental desgn plan, (3) perform regresson analyss wth the quadratc model of RSM, (4) calculate the statstcal analyss of varance (ANOVA) for the ndependent nput varables n order to fnd whch parameter sgnfcantly affects the desred response, then, (5) determne the stuaton of the quadratc model of RSM and decde whether the model of RSM needs screenng varables or not and fnally, (6) optmze and conduct confrmaton experment and verfy the predcted performance characterstcs. Table 4 Desgn layout and expermental results. Run Coded factors Actual factors Response varables X X2 X3,(m/mn) f,(mm/rev) ap,(mm) [m Ra,(µm) Fa,(N) Fr,(N) Ft,(N) In the current study, the relatonshp between (cuttng speed (), feed rate (f) and depth of cut (ap)) and the outputs named Y, defnes machnablty of AISI 440 (56 HRC) n terms of cuttng forces and surface roughness. Ths relatonshp s gven by: Y + = F(, f, ap) e j () where Y s the desred machnablty aspect and F s a functon proposed by usng a non-lnear quadratc mathematcal model, whch s sutable for studyng the nteracton effects of process parameters on machnablty characterstcs. In the present work, the RMS based second order mathematcal model s gven by: Y = a o 3 + a X = 3 + a = X a j j X X j (2)

7 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 273 where ao s constant, a, a, and aj represent the coeffcents of lnear, quadratc and cross product terms, respectvely. X reveals the coded varables that correspond to the studed machnng parameters. The coded varables X,=,2,3 are obtaned from the followng transformaton equatons. o X = (3) Δ f fo X 2 (4) f ap apo X 3 (5) ap where X, X2 and X3 are the coded values of parameters, f and ap respectvely. o, fo and apo are factors at zero level. Δ, Δf and Δap are the ncrement values of, f, and ap, respectvely. 3. Analyss and the dscusson of expermental results The plan of tests was developed for assessng the nfluence of the cuttng speed (), feed rate (f) and depth of cut (ap) on both the surface roughness (Ra) and cuttng force components such as feed force (Fa), thrust force (Fr) and tangental cuttng force (Ft). The frst phase was concerned wth the ANOVA and the effect of the factors and of the nteractons. The second phase allowed to obtan correlatons between the process parameters (quadratc regresson). Afterwards, the results were through optmzed. Table 4 llustrates the expermental results for surface roughness (Ra) and feed force (Fa), thrust force (Fr) and tangental cuttng force (Ft). 3.. Analyss of varance ANOVA technque can be useful for determnng nfluence of any gven nput parameters form a seres of expermental results by desgn of experments for machnng process and t can be used to nterpret expermental data. The obtaned results are analyzed by statstcal analyss software (Mntab-6) whch s wdely used n many engneerng applcatons. The ANOVA table conssts of a sum of squares and degrees of freedom. The mean square s the rato of sum of squares to degrees of freedom and F rato s the mean square rato to the mean square of the expermental error. The results of the ANOVA wth the surface roughness and cuttng forces are shown n Tables 5 and 6 (a, b, and c), respectvely. Ths analyss was carred out for a sgnfcance level of α = 0.05,. e. for a confdence level of 95% (Ross, 988). Tables 5 and 6 (a, b, and c) show the P values, that s, the realzed sgnfcance levels, assocated wth the F- tests for each source of varaton. The sources wth the P value less than 0.05 are consdered to have a statstcally sgnfcant contrbuton to the performance measures (Ganed et al. 9). Also the last columns of the tables show the percent contrbuton of each source to the total varaton ndcatng the degree of nfluence on the results. The greater the percentage contrbuton, the hgher the factor nfluence on the performance measures. Table 5 Analyss of varance for (Ra). Sourse DF SeqSS AdjMS F.Value Prob > F Cont% f ap f ap f ap f ap Error Total

8 Effect of cuttng parameters on surface roughness Accordng to Table 5, the feed rate was found to be the major factor affectng the surface roughness (77.92%), ths results s n a concordance wth those publshed n (Hessana al. 203), (Aslan, 5) and (Yallese et al., 5). The cuttng speed and depth of cut factors affect the surface roughness by 5,47% and 2.35%, respectvely. It can be revealed that lower surface roughness values are obtaned at hgher cuttng speeds due to lower forces generated. At hgh cuttng speed, an mprovement n surface fnsh was obtaned snce less heat was dsspated to the workpece. It s known that the amount of heat generaton ncreases wth ncrease n feed rate, because the cuttng tool has to remove more volume of materal from the workpece (Davm, 20). The plastc deformaton of the work pece s proportonal to the amount of heat generaton n the work pece and promotes roughness on the work pece surface. Depth of cut parameter has a very less effect compared to that of the feed rate. Ths s due to the ncreased length of contact between the tool and the workpece. Ths mproves the condtons of heat flow from the cuttng zone. Smlar results were also observed by (Palankumar, 7). From nteracton plot Fg. 2a t can be observed on the one hand for a gven cuttng speed, the surface roughness sharply ncreases wth ncrease n feed rate. On the hand, surface roughness has a tendency to be reduced wth an ncrease n cuttng speed at constant feed rate. The mnmal surface roughness results wth the combnaton of low feed rate and hgh cuttng speed. Fg. 2b ndcates that the depth of cut s low; the surface roughness s hghly senstve to cuttng speed. An ncrease n the latter sharply reduces the surface roughness. Nevertheless, ths reducton becomes smallest wth hgher values of depth of cut whch usually does not much nfluence the surface roughness. Fg. 2c ndcates that for a gven depth of cut, the surface roughness ncreases wth the ncrease n feed rate, whereas depth of cut has less effect on surface roughness. It revealed that a combnaton of hgher cuttng speed along wth lower feed rate and depth of cut s necessary for mnmzng the surface roughness. An mprovement of surface fnsh Ra of 0.23 µm was recorded at hgher cuttng speed of 80 m/mn, feed rate of 0.08 mm/rev and depth of cut of 0.5 mm. (a) (b) (c) Ra 0,6 0,5 0, ,6 f 0,08 Ra 0, 5 0 0, ,3 ap Ra 0,5 04 0,3 0,08 f 0,6 0,3 ap Fg.2. (a) 3D surface plots for nteracton effects of feed rate and cuttng speed, (b) depth of cut and cuttng speed, and (c) depth of cut and feed rate on surface roughness Effect of cuttng parameters on cuttng force components Tables 6(a, b and c) shows the results of the ANOVA for feed force (Fa), thrust force (Fr) and tangental force (Ft). It can be found that depth of cut s the most sgnfcant cuttng parameter for affectng cuttng forces (Fa, Fr and Ft) (90.22%, 67.64% and %), respectvely. The cuttng speed affects the cuttng forces (Fa, Fr and Ft) by (3.66%, 5.0%, and 0.37%), respectvely. The feed rate affects the cuttng forces (Fa, Fr and Ft) by (2.6%, 7.36% and 4.60%), respectvely. In ths study, the factors and the nteractons present a statstcal sgnfcance Test F > Pα = 5% except for the nteracton ap and f ap for Ra, the nteracton 2 for Fr and effect of, f, and the nteracton f 2 for Ft. Notce that the error assocated to the Tables ANOVA for the Ra was approxmately.54%, for the Fa was approxmately 0.62%, for the Fr was approxmately 2.52% and for Ft was 2.02%. The nteracton [for Ra (f 2, ap 2, f, ap, f ap), for Fa ( 2, f 2, ap 2, f, f ap), for Fr ( 2, f 2, ap 2, f, ap) and for Ft ( 2, f 2, ap 2, f, ap, f ap )] do not present a physcal sgnfcance P

9 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 275 (percentage of contrbuton) < error assocated. As seen from the nteracton plots n Fg. 3, 4, 5, (a and b) for a gven cuttng speed, the feed force, thrust force and tangental force sharply ncreases wth the ncrease n feed rate or depth of cut. The component forces Fa, Fr and Ft are hghly senstve to depth of cut, as shown n Fg. 3, 4, 5, (c). From the above dscussons t can be manfest that the prected forces can be mnmzed by employng lower valuer of f and ap and wth hgher. Also t can be underlned Fr s usually the largest force among the other ones. The tangental cuttng force component Ft s the mddle force and Fa s the smallest one. Fa (a) ,6 f 0,08 (b) 25 Fa ,3 ap Fa (c) ,08 f 0,6 0,3 ap Fg.3. (a) 3D surface plots for nteracton effects of feed rate and cuttng speed, (b) depth of cut and cuttng speed, and (c) depth of cut and feed rate on feed force Fr (a) ,6 f 0,08 Fr (b) ,3 ap Fr (c) 2 0,08 f 0,6 0,3 ap Fg.4. (a) 3D surface plots for nteracton effects of feed rate and cuttng speed, (b) depth of cut and cuttng speed, and (c) depth of cut and feed rate on thrust force (a) (b) (c) Ft Ft 0,6 f 0, ,3 ap Ft 0,08 f 0,6 0,3 ap Fg.5. (a) 3D surface plots for nteracton effects of feed rate and cuttng speed, (b) depth of cut and cuttng speed, and (c) depth of cut and feed rate on tangental force Usng ANOVA to make ths comparson requres several assumptons to be satsfed. The assumptons underlyng the analyss of varance tell the resduals are determned by evaluatng the followng equaton (Zarepour et al., 6). ej = yj - ŷj (6)

10 276 where ej s the resdual, yj s the correspondng observaton of the runs, and ŷj s the ftted value. A check of the normalty assumpton may be made by constructng the normal probablty plot of the resduals. If the underlyng error dstrbuton s normal, ths plot wll resemble a straght lne Fg.6 (a, b, c and d). Snce the p-value s larger than 0.05, t s concluded that normalty assumpton s vald. The other two assumptons are shown vald by means of plot of resduals versus ftted values. Ths plot s llustrated n Fg.7 (a, b, c and d). The structure less dstrbuton of dots above and below the abscssa (ftted values) shows that the errors are ndependently dstrbuted and the varance s constant. For more nformaton the reader can refer to the reference refer to (Montgomery & Runger, 3). Table 6 Analyss of varance for cuttng force components: (a) Fa, (b) Fr and (c) Ft. Sourse DF SeqSS AdjMS F.Value Prob > F Cont% (a) Analyss of varance for (Fa) f ap f ap f ap f ap Error Total (b) Analyss of varance for (Fr) f ap f ap f ap f ap Error Total (c) Analyss of varance for (Ft) f ap f ap f ap f ap Error Total Regresson equatons Accordng to (Montgomery & Runger, 3), (Montgomery, 0), the correlaton between the factors and the performance measures were modeled by quadratc regressons. The models are reduced by elmnatng terms wth no sgnfcant effect on the responses. The estmated regresson coeffcents for surface roughness Ra and cuttng forces Fa, Fr and Ft usng data uncoded unts are shown n Tables 7 and 8 (a, b, c).

11 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 277 Percent (a) Percent (b) -0,04-0,03-0,02-0,0 0,00 0,0 Resdual 0,02 0,03 0, Resdual Percent (c) Percent (d) Resdual Resdual 0 20 Fg.6. Normal probablty plot of resduals for (a) Ra and for (b) Fa, (c) Fr and (d) Ft respectvely Resdual 0,03 0,02 0,0 0,00-0,0 (a) Resdual 5,0 2,5 0,0-2,5 (b) -0,02-5,0-0,03 0,3 0,5 Ftted Value 0,6-7, Ftted Value Resdual (c) Resdual (d) -20 Ftted Value Ftted Value 2 Fg.7. Plot of resduals vs. Ftted values for (a) Ra, and for (b) Fa, (c) Fr and (d) Ft, respectvely Table 7 Table of coeffcents for regresson analyss, Response Ra. Predctor Coeffcent SE coeffcent T Prob Constant f ap

12 278 The surface roughness (Ra) model s gven below n Eq. (7) wth a determnaton coeffcent R 2 = 98.5%; Adjusted R 2 was 97.5% Ra f ap.95 0 (7) The feed force model (Fa) s gven by Eq. (8) wth a determnaton coeffcent R 2 of 99.4%; Adjusted R 2 was 99. %. Table 8 Table of coeffcents for regresson analyss, Response (a) Fa, (b) Fr, and (c) Ft. Predctor Coeffcent SE coeffcent T Prob (a) Table of coeffcents for regresson analyss (Fa) Constant f ap ap ap F ap (b) Table of coeffcents for regresson analyss (Fr). Constant f ap f ap F ap (c) Table of coeffcents for regresson analyss (Ft). Constant f ap ap ap F ap Fa f 2.3ap 73.90ap -.3 ap f ap The thrust force model (Fr) s gven by Eq. (9) wth a determnaton coeffcent R 2 of 97.5%; Adjusted R 2 was 96. %. 2 Fr = f ap f + (9) 3.7 f ap f ap The tangental force model (Ft) s gven by Eq. (0) wth a determnaton coeffcent R 2 of 98%; Adjusted R 2 was 96.9 %. (8) 2 Ft = f ap ap (0) -.5 ap f ap The use of the Hessan matrx proved that the objectve functon s convex and admts a global mnmum. Example, for the surface roughness Ra we note that Ra s a convex functon and t s assumed a mnmum soluton ( = 9.5 m/mn, f = 0.2 mm/rev and ap = 0.4mm). Fg.8 ( a, b, c and d) also, show the predcted values of cuttng forces and surface roughness form response surface equatons (7 to 0) and the actual expermental values are reported n Table 4. The results of the comparson proves that predcted values of the surfaces roughness (Ra) and cuttng force components (Fa, Fr and Ft) are very close to those readngs recorded expermentally.

13 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 279 Surface roughness (µm) 0,8 0,6 0 (a) Ra measured Ra predcted Expermental Run Order Feed force (N) (b) Fa measured Fa predcted Expermental Run Order Thrust force (N) (c) Fr measured Fr predcted Expermental Run Order Fg.8. (a) The comparson between measured and predcted value of Ra and (b), (c), (d) comparson between measured and predcted value of Fa, Fr and Ft respectvely Table 9 ANOVA table for the ftted models (Ra). Source DF Seq SS Adj MS F-Value Prob > F Remarks Regresson < Sgnfcant Resdual error Total R % R 2 adjusted 97.5 % Table 0 ANOVA table for the ftted models for cuttng force components: (a) Fa, (b) Fr and (c) Ft. Source DF Seq SS Adj MS F-Value Prob > F Remarks (a) ANOVA table for the ftted models (Fa). Regresson < Sgnfcant Resdual error Total R % R 2 adjusted 99.% (b) ANOVA table for the ftted models (Fr). Regresson < Sgnfcant Resdual error Total R % R 2 adjusted 96. % (c) ANOVA table for the ftted models (Ft). Regresson < Sgnfcant Resdual error Total R % R 2 adjusted 96.9% Cuttng force (N) (d) Ft measured Ft predcted Expermental Run Order

14 280 Analyss of varance was derved to examne the null hypothess for regresson that s presented n Tables 9-0. The result ndcates that the estmated model by regresson procedure s sgnfcant at α- level of Optmzaton of response Accordng to Hessana et al. (3), Nesel et al. (20), one of the most mportant ams of experments related to manufacturng s to acheve the desred surface roughness and cuttng force components wth the optmal cuttng parameters. To attan ths end, the explotaton of the RSM optmzaton seems to be a helpful technque. Here, the goal s to mnmze surface roughness (Ra) and cuttng forces (Fa, Fr and Ft), the parameter ranges defned for the optmzaton processes are summarzed n Table. Table Goals and parameter ranges for optmzaton of cuttng condtons. Condton Goal Lower lmt Upper lmt Cuttng speed, s n range Feed rate, f s n range Depth of cut, ap s n range Ra (µm) mnmze Fa (N) mnmze Fr (N) mnmze Ft (N) mnmze To resolve ths type of parameter desgn problem, an objectve functon, F(x), s defned as follows (Myers & Montgomery, 2): () n n w DF d w j F( x) DF where d s the desrablty defned for the th targeted output and w s the weghtng of d. For varous goals of each targeted output, the desrablty, d, s defned n dfferent forms. If a goal s to reach a specfc value of T, the desrablty d s: d 0 f Low Y Low d f Low T Low Y T (2) Y Hgh d f T Hgh d 0 f Hgh T Y Hgh For a goal to fnd a maxmum, the desrablty s shown as follows: d 0 f Low Y Low d f Hgh Low d f Hgh Low Y Hgh (3) For a goal to search for a mnmum, the desrablty can be defned by the followng formulas:

15 H. Zaha et al. / Internatonal Journal of Industral Engneerng Computatons 6 (205) 28 d f Low Hgh Y d f Low Hgh Low Y Hgh (4) d 0 f Hgh where the Y s the found value of the th output durng optmzaton processes; the Low and the Hgh are, respectvely, the mnmum and the maxmum values of the expermental data for the th output. In Eq. (), w s set to one snce the d s equally mportant n ths study. The DF s a combned desrablty functon (Myers & Montgomery, 2), and the objectve s to choose an optmal settng that maxmzes a combned desrablty functon DF,.e., mnmzes F(x). From the results shown n Fg. 9 and Table 2, t can be underlned that optmal cuttng parameters found to be cuttng speed () of 80m/mn, feed rate (f) of 0.08mm/rev, cuttng depth (ap) of 0.5mm. The optmzed surface roughness Ra = 0.23µm. Also, the optmzed cuttng force components are: [feed force (Fa) s decreased to 29.87N wth a reducton of 6.88%, thrust force (Fr) s decreased to 6.87N wth a reducton of 3.65%, tangental force (Ft) s decreased to 34.83N wth a reducton of 9.05%. Table2 Response optmzaton for surface roughness and cuttng force components. (m/mn) f (mm/rev) ap (mm) Surface roughness Cuttng forces Ra, μm Fa, N Fr, N Ft, N Desrablty 0.99 Composte desrablty = 0.99 Fg.9. Response optmzaton for surface roughness and cuttng force components

16 Conclusons Ths paper proposes the RSM approach to predcted and optmzed surface roughness and cuttng forces based on cuttng parameters (cuttng speed, feed rate and depth of cut). The mportant fndngs are summarzed as follows: ) In general, the hgher s the work materal hardness, the hgher s the machnng forces. The thrust force presents hgher values followed by the tangental and feed force. 2) The machnng force components ncrease almost lnearly as the feed rate and depth of cut are elevated. 3) Feed rate and depth of cut have the greatest nfluence on surface roughness and cuttng forces, respectvely. 4) Based on the analyss of the varance (ANOVA) results, the hghly effectve parameters on both the surface roughness and cuttng forces were determned. Namely, the feed rate parameter s the man factor that has the hghest mportance on the surface roughness and accounts for 77.92% contrbuton n the total varablty of the model. The cuttng speed has a secondary contrbuton of 5.47%, whereas the depth of cut affects farly the surface roughness. The feed force, thrust force and cuttng force are affected strongly by the depth of cut and account for 90.22%, 67.64%, 69.44% contrbuton n the total varablty of model, respectvely. 5) An mprovement n surface qualty and lower cuttng forces are observed at hgher cuttng speed wth lower feed rate and depth of cut. 6) Predcton accuracy of surface roughness and cuttng forces by RSM developed models s effcent both for the tranng and testng data set. 7) The developed model has hgh square values of the regresson coeffcents whch ndcated hgh assocaton wth varances n the predctor values. 8) Comparson of expermental and predcted values of the surface roughness and cuttng forces show that a good agreement has been acheved between them. 9) Response optmzaton show that the optmal combnaton of cuttng parameters are found to be cuttng speed of 80m/mn, feed rate of 0.08mm/rev, cuttng depth of 0.5mm. For machnng AISI 440 steel n the hard turnng process, the optmal values of the surface roughness (Ra) = 0.23µm and cuttng force components (feed, thrust and cuttng forces) represent a reducton of (6.88%, 3.65% and 9.05%), respectvely. These values were compared to results of ntal cuttng parameters. In ths study, the optmzaton methodology proposed s a powerful approach and can offer to scentfc researchers as well ndustral metalworkng a helpful optmzaton procedure for varous combnatons of the workpece and the cut materal tool. Acknowledgements Ths work was acheved n the laboratores LMS (Unversty of Guelma Algera) n collaboraton wth LaMCoS (CNRS, INSA-Lyon, France). The authors would lke to thank the Algeran Mnstry of Hgher Educaton and Scentfc Research (MESRS) and the Delegated Mnstry for Scentfc Research (MDRS) for grantng fnancal support for CNEPRU Research Project, CODE: (Unversty 08 May 945, Guelma).

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