Modelling And Optimization Of The Surface Roughness In The .
Modelling and Optimization of the Surface Roughness in the Dry Turning of the Cold Rolled Alloyed Steel Using Regression AnalysisDejan Tanikićdtanikic@tf.bor.ac.rsUniversity of BelgardeTechnical Faculty of BorV.J. 1219210 Bor, SerbiaVelibor Marinkovićvelmar@masfak.ni.ac.rsUniversity of NišFaculty of Mechanical EngineeringA. Medvedeva 14,18000 Niš, SerbiaModelling and Optimization of theSurface Roughness in the DryTurning of the Cold Rolled AlloyedSteel Using Regression AnalysisSurface quality of the machined parts is one of the most important product qualityindicators and one of the most frequent customer requirements. The average surfaceroughness (Ra) represents a measure of the surface quality, and it is mostly influenced bythe following cutting parameters: the cutting speed, the feed rate, and the depth of cut.Quantifying the relationship between surface roughness and cutting parameters is a veryimportant task. In this study regression analysis was used for modelling and optimizationof the surface roughness in dry single-point turning of the alloyed steel, using coatedtungsten carbide inserts. The experiment has been designed and carried out on the basis ofa three-level full factorial design. The linear, the quadratic and the power (non-linear)mathematical models were selected for the analysis. Obtained results are in goodaccordance with the experimentally obtained data, confirming the effectiveness ofregression analysis in modelling and optimization of surface roughness in the turningprocess. The general conclusion is that the surface roughness has a clear downward trendwith the cutting speed increase and decrease in the feed rate and the depth of cut.Keywords: turning, surface roughness, regression analysis, optimizationIntroduction1The key demands in the case of cutting technology include:reducing component size and weights, enhancing surface quality,tolerances and manufacturing accuracies, reducing costs andreducing batch sizes (Byrne, Dornfeld and Denkena, 2003).The surface roughness of the machined parts is one of the mostsignificant product quality characteristic. It is a key factor inevaluating the quality of a product and has the great importance onthe functional behaviour of the machined parts in exploitation aswell as manufacturing costs.The lack of good surface quality fails to satisfy one of the mostimportant technical requirements for mechanical products, whileextremely high level of surface quality causes higher productioncosts and lower overall productivity of cutting operations.The desired surface quality is a critical constraint in selectingthe optimal cutting parameters in the production process (Jacobs,Jacob and Kochan, 1972; Silva, Saramago and Machado, 2009;Pasam et al., 2010). Hence, it is of great importance to quantify therelationship between surface roughness and cutting conditions. Toolwear phenomenon, studied by a large number of scientists, directlyinfluences the quality of the machined surface (Rosa et al., 2010).The surface roughness also influences the tribologicalcharacteristics, the fatigue strength, the corrosion resistance and theaesthetic appearance of the machined parts.On the other side, the surface finish in the turning process isinfluenced by a number of factors, such as: cutting speed, feed rate,depth of cut, material characteristics, tool geometry, stability andstiffness of the machine tool – cutting tool – workpiece system,built-up edge, cutting fluid, etc. Therefore, the ideal surface qualitycould not be achieved even in the ideal cutting and environmentalconditions.The surface roughness always refers to deviation from thenominal surface. The actual surface profile is the superposition ofthe errors of the form, waviness and roughness.There are various parameters used to evaluate the surfaceroughness. In the present research the average surface roughness(Ra), also known as the Centerline Average (CLA), was selected forPaper received 1 March 2011. Paper accepted 29 June 2011.Technical Editor: Anselmo DinizJ. of the Braz. Soc. of Mech. Sci. & Eng.the characterization of the surface finish in the cutting process. It isthe most widely used surface finish parameter in industry.The turning process is one of the most fundamental amongvarious cutting processes, and it is also the most applied metalremoval operation in the real manufacturing environment.In order to achieve the best possible surface roughness manymachine tool operators rely on their own experience and/or theguidelines given in the machine tool manuals and handbooks. It hasalso been observed that experienced machine tool operators usetrial-and-error approach, i.e. they estimate surface quality byvisually comparing the actual surfaces on the machined part withthose on the measuring calibrator.Benardos and Vosniakos (2003) give a general review ofpredicting the surface roughness in machining. Also, a comprehensiveoverview of the optimization techniques in the metal cutting processesis presented by Mukherjee and Ray (2006). The determination of(near) optimal cutting conditions, using conventional and nonconventional optimization techniques, as well as in-process parameterrelationship modelling, are described in detail.Thangavel and Selladurai (2008) developed a mathematicalmodel to study the effect of cutting parameters on the surfaceroughness using the response surface methodology (RSM). After theregression analysis and the variance analysis, it was found that themodel is adequate and that all the main cutting parameters have asignificant impact on the surface roughness.Choudhury and El-Baradie (1997) utilized the samemethodology in order to develop the surface roughness model in dryturning of high-strength steel. Also, Sahin and Motorcu (2005)employed RSM for predicting the surface roughness in turning ofmild steel with the coated carbide tools.Arbizu and Perez (2003) employed a classic experimentaltechnique design to determine surface roughness in the turningprocess. The second-order mathematical model was adopted. It wasobserved that the feed rate and the depth of cut have negativeinfluences on the average surface roughness (Ra), while there is anoptimum cutting speed, which provides a minimum of the averagesurface roughness value.Cakir et al. (2009) investigated the influences of the cuttingparameters (the feed rate, the cutting speed and the depth of cut) andthe two-coated carbide inserts on the surface roughness in theturning process. The various mathematical models were developed,using a large experimental data set. It was pointed out that lowerCopyright 2012 by ABCMJanuary-March 2012, Vol. XXXIV, No. 1 / 41
Dejan Tanikić and Velibor Marinkovićvalues of the surface roughness are achieved when employing aPVD coated (TiAlN) insert instead of a CVD coated(TiCN Al2O3 TiN) insert.Davim (2001) and Davim et al. (2009) investigated the cuttingparameter effects on the surface finish in steel turning using thedesign of the experiment and the artificial neural network. For thepurpose of experimentation, the authors selected the standardL27(33) orthogonal array, based on the Taguchi experimentaldesign. The multiple linear regression and the three-layer backpropagation neural network models were developed to study theeffects of the cutting conditions on the surface roughness parameters(Ra and Rt). The good agreement exists between the experimentaland predicted results obtained from these models.In addition to the abovementioned, other methodologies arebeing employed for predicting the surface roughness, such asTaguchi method (Kopač, Bahor and Soković, 2002; Hascalic andCaydas, 2008), artificial neural networks (Karayel, 2009; Özel andKarpat, 2005; Lu, 2008; Marinković and Tanikić, 2011), neurofuzzy systems (Jiao et al., 2004; Kirby and Chen, 2007; Tanikić etal., 2010), genetic algorithms (Chen and Chen, 2003; Cus and Balic,2003), and artificial intelligence or soft computing techniques(Samanta, Erevelles and Omurtag, 2009).Research in this paper refers to dry turning process. In general,machining without the use of any cutting fluid (coolant andlubricant) is nowadays popular due to the concern regarding thesafety of the environment and the health protection (Sreejith andNgoi, 2001), (Klocke and Eisenblaetter, 1997). Besides everythingelse, the implementation of dry machining includes: non-pollutionof the atmosphere and no residue on the chip, which causes reduceddisposal and cleaning costs. It is harmless to skin and it is allergyfree. Moreover, it offers cost reduction in machining.NomenclatureabBb0bibiibijfRRa depth of cut, mm (k x 1) vector of the first-order regression coefficients (k x k) symmetric matrix, whose main diagonal elementsare the pure quadratic coefficients, while off-diagonalelements are one-half mixed quadratic coefficients free term (parameter) of the mathematical model linear terms quadratic terms interaction terms feed rate, mm/rev correlation coefficient average surface roughness, µmR̂aiV{wi}xxiXiyYye predicted average surface roughness, µm cutting speed, m/min canonical independent variables (factors) (k x 1) vector of the independent variables coded variables (factors) natural variables estimated response estimated natural response measured responseaverage surface roughness (Ra) was chosen for a target function(response, output). Since it is obvious that the effects of the factorsare non-linear, an experiment with factors at three levels was set up(Table 1).Table 1. Cutting factors and their levels.Cutting factorSymbolUnitCutting speedFeed rateDepth of cutV (X1)f (X2)a (X3)(m/min)(mm/rev)(mm)Level 1(Low)800.0710.5Factor levelsLevel 2(Middle)1100.1961.125Level 3(High)1400.3212.0The factor ranges were chosen with different criteria for eachfactor, aiming at the widest possible range of values, in order tohave a better utilization of the proposed models. At the same time,the characteristics of the mechanical system and manufacturer'srecommendations are taken into account.Table 2. Machining system, workpiece and measuring equipment.Machine toolCutting toolWorkpieceCutting fluidMeasuringequipmentProduction lathe PA-C-30 (Potisje-Ada), Three-phase 7.5 kWinduction electric motor, Speed range 20 2000 rpm, Longitudinal feedrate range 0.04 9.16 mm/rev, Max. workpiece diameter 600 mm,Distance from chuck to the tail stock 1500 mmCNMG 12 04 08 coated tungsten carbide inserts (SandvikCoromant), PCLNR 32 25 P12 tool holder (Sandvik Coromant)Č.4732 (AISI designation 4140) cold rolled steel; Chemicalcomposition: 0.40% C, 1.00% Cr, 0.20% Mo, 0.90% Mn, 0.25% Si,0.03% P, 0.10% S; Ultimate tensile strength 1050 N/mm2, Hardness205 BHN; Workpiece diameter 45 mm, Workpiece length 250 mmDry turningSurftest SJ-301 (Mitutoyo) surface profilometer, Cut-off length0.8 mm; MBS-9 optical microscopeProduction conditions used in the experiment are shown inTable 2. All of the trials have been conducted on the same machinetool, with the same cutting tool type and the same other cuttingconditions. Measuring equipment and surface roughness report areshown in Fig. 1.Greek Symbols δi absolute percentage error, %ε experimental error{λi} eigenvalues (canonical coefficients)Experimental WorkThe parameters (factors) considered in the present paper are: thecutting speed (V), the feed rate (f) and the depth of cut (a). The42 / Vol. XXXIV, No. 1, January-March 2012Figure 1. Measuring equipment (a) and surface roughness report (b).Profile of the machined surface for different cutting regimes ispresented in Fig. 2. Part of the experimental results, which refers tothe surface finish in the single-point turning process, is analysed inthis study.ABCM
Modelling and Optimization of the Surface Roughness in the Dry Turning of the Cold Rolled Alloyed Steel Using Regression AnalysisFigure 2. Profile of the machined surface for cutting regimes:a) V 110 m/min, a 1.25 mm, f 0.321 mm/revb) V 110 m/min, a 1.25 mm, f 0.196 mm/revc) V 110 m/min, a 1.25 mm, f 0.071 mm/revA design matrix was constructed on the basis of the selectedfactors and factor levels (Table 3). The method of coding the cuttingfactors is explained in the following chapter.Table 3. Experimental design and results.TrialNatural .252.000.501.252.00Coded eRa .8353.273.523.6053.66cutting process and neglects the effects of many process factors, aswell as environment factors (noise).Hence, various theoretical models that have been proposed arenot accurate enough and can be applied only to a limited range ofprocesses and cutting conditions. For these reasons, mostresearchers mainly use the empirical research.The regression analysis technique, based on the experimentaldata, is a powerful tool for modelling and analysing real processes,whose nature and behaviour cannot be explained using a theoreticalapproach. Many researchers use this method successfully in variousfields.Therefore, with the efficient regression analysis researcherscannot only rely on their perspicacity and intuition, but must have arelevant knowledge of the researched phenomenon and theexperimental techniques.Many experiments involve studying the effects of more factors.In these cases, generally, the design of experiment (DoE) is the mostefficient type of experiment, especially in relation to the traditionalone-factor-at-a-time experiment. The selection of a properexperimental design is essential for reducing the experimental costand time.The success of a regression analysis depends largely on thechoice of appropriate mathematical models. Many studies haveshown that the choice of mathematical models in the form ofpolynomials provides the most appropriate and effectiveapproximation of the experimental data. These are the followingmathematical models:a) linear mathematical modelky y e ε b0 b x(1a)i ii 1b) quasi-linear mathematical modelk 1ky y e ε b0 bi xi i 1k bij xi x j(1b)i 1 j i 1c) non-linear (quadratic) mathematical modelThe selected design matrix was a full factorial design consistingof 27 rows of coded/natural factors, corresponding to a number oftrials. This design provides a uniform distribution of experimentalpoints within the selected experimental hyper-space and theexperiment with high resolution. The experiment was conductedusing a new set of coated tungsten carbide inserts, preventingpossible mistakes caused by using a worn tool. The average surfaceroughness values (Ra), shown in Table 3, are the average values ofthree measurements.Regression AnalysisBrief overviewThe cutting processes based on the formation and removingchips from the workpiece surface are very complex and stillincompletely explored phenomenon.The extraordinary complexity of the mechanical, tribological,and thermodynamical phenomena in the cutting zone does not allowto determine a reliable and comprehensive theoretical model, whichcould explain the essence and the mechanism of chip formation andthe shaping of surface roughness.The theoretical approach is always based on simplifications andidealizations. It does not take into account any imperfections of theJ. of the Braz. Soc. of Mech. Sci. & Eng.ky ye ε b0 k 1 kkbi xi i 1 bii xi2 i 1 bijxi x j(1c)i 1 j i 1where y is the estimated response, ye is the measured response, ε isthe independent random variable (experimental error), normallydistributed with a mean of zero and a constant variance of σ2, b0 isthe free term (parameter) of the mathematical model, bi are thelinear terms, bii are the quadratic terms, bij are the interaction terms,and k is the number of the independent variables (factors). Theparameters of the mathematical model can only be statisticallyestimated on the bases of the experimental results.The relationship between dependent variable (response) andindependent variables (factors) can also be expressed in the form ofthe multiple power function:kbY c0 X 1b1 X 2b2 . X k k c0 Xbii(2a)i 1where Y is the estimated natural response, c0 and bi are constants tobe estimated.Copyright 2012 by ABCMJanuary-March 2012, Vol. XXXIV, No. 1 / 43
Dejan Tanikić and Velibor MarinkovićApplying the logarithmic transformation, the non-linearequation (2a) can be converted into the following linear equation:kln Y ln c0 b1 ln X 1 . bk ln X k ln c0 b ln Xii(2b)The stationary (optimal) point is obtained from the followingrelation:1x 0 B -1b2(5)i 1When the variables in logarithmic scale in Eq. (2b) are replacedwith the new variables, y lnY, xi lnXi (b0 lnc0), then it can berewritten in a linear form, defined by Eq. (1a). If the multiple powerfunction includes first-order factor interactions, then Eq. (2b)represents the quasi-linear mathematical model, defined by Eq. (1b).But, in this particular case, it is not necessary (Marinković andLazarević, 2010).In general, the mathematical models may also include higherorder factor interactions. Since the impact of higher-order factorinteractions is usually negligible, these terms of the mathematicalmodel may be omitted. On the other hand, in many cases, adding thehigh-order polynomial terms does not really improve the fit, butincreases the complexity of the mathematical model. Thus, it isuseful to try fitting using a lowest-order polynomial that adequatelydescribes the system/process.The statistical method often used to estimate the unknownparameters in a mathematical model is the method of least squares.The number of factor levels within the selected range istheoretically arbitrary, whereas practice confirms that it is sufficientto choose: two levels for (quasi) linear mathematical model, andthree levels for non-linear (quadratic) mathematical model.Since input factors may be various physical values (temperature,pressure, volume, velocity, etc.) it is useful to perform their coding.There are two ways of coding the independent variables (factors) onthree levels. It is accomplished by means of the transformingequations:a) for levels (–1 , 0, 1):xi 2X i X i min 1 ; (i 1, k )X i max X i minX i X i min 1 ; (i 1, k )X i max X i minkyˆ yˆ 0 λ wi2i(7)i 1where {wi} are the canonical independent variables (factors) and{λi} are their eigenvalues (canonical coefficients).Canonical coefficients are the roots of the characteristicequation:B λI 0(8)kk bi 1(3b)ii(9)i 1Canonical equations contain no linear effects or interactions,which makes them more suitable for the analysis of the surfaceresponse. The geometric form of the response surfaces is determinedby the stationary point, algebraic signs, and magnitudes of their ownvalues (Novik and Arsov, 1980).If the eigenvalues are all negative, the response surface has amaximum; if they are all positive, the response surface has aminimum; if they have mixed signs, the response surface has asaddle point.At least one eigenvalue equal to zero (or close to zero) indicatesthe presence of a "ridge" in the response surface.It should be noted that optimization of the real system/processmakes sense in a limited space of independent variables (factors).The constraints, in terms of the coded variables, are most commonspecified in the form of (in)equations as:(4)where x is a (k x 1) vector of the independent variables, b is a (k x1) vector of the first – order regression coefficients and B is a (k x k)symmetric matrix whose main diagonal elements are the purequadratic coefficients, while off-diagonal elements are one-halfmixed quadratic coefficients.44 / Vol.
regression analysis in modelling and optimization of surface roughness in the turning roughness has a clear downward trend feed rate and the depth of cut. Keywords: turning, surface roughness, regression analysis, optimization Introduction 1 The key demands in the case of cutting technology include: reducing component size and weights, enhancing surface quality, tolerances and manufacturing .
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