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journa l homepage: www.e lsev ier .com/ locate / jmatprotec

ptimizing power consumption for CNC turned parts usingesponse surface methodology and Taguchi’s technique—Aomparative analysis

man Aggarwala,∗, Hari Singhb, Pradeep Kumarc, Manmohan Singhd

Mechanical and Automation Engineering Department, Maharaja Agrasen Institute of Technology, Rohini, Delhi 110085, IndiaMechanical Engineering Department, National Institute of Technology, Kurukshetra 136119, IndiaDepartment of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee 247267, IndiaSolid State Physics Lab, DRDO, Delhi, India

r t i c l e i n f o

rticle history:

eceived 22 September 2006

eceived in revised form

2 August 2007

ccepted 11 September 2007

eywords:

a b s t r a c t

This paper presents the findings of an experimental investigation into the effects of cutting

speed, feed rate, depth of cut, nose radius and cutting environment in CNC turning of AISI

P-20 tool steel. Design of experiment techniques, i.e. response surface methodology (RSM)

and Taguchi’s technique, have been used to accomplish the objective of the experimental

study. L27 orthogonal array and face centered central composite design have been used for

conducting the experiments. Taguchi’s technique as well as 3D surface plots of RSM revealed

that cryogenic environment is the most significant factor in minimizing power consumption

followed by cutting speed and depth of cut. The effects of feed rate and nose radius were

found to be insignificant compared to other factors. Though both the techniques predicted

esponse surface methodology

entral composite design

aguchi technique

27 orthogonal array

ryogenic cooling

near similar results, RSM technique seems to have an edge over the Taguchi’s technique.

© 2007 Elsevier B.V. All rights reserved.

widely used in place of one-factor-at-a-time experimentalapproach which is time consuming and exorbitant in cost.

ISI P-20 tool steel

. Introduction

t has long been recognized that cutting conditions suchs feed rate, cutting speed and depth of cut in machiningperation should be selected to optimize the economics ofachining operations as assessed by productivity, total manu-

acturing cost per component or some other suitable criteria.ecause of the high cost of numerically controlled machineools compared to their conventional counterparts, there is

n economic need to operate these machines as efficiently asossible in order to obtain the required payback.

∗ Corresponding author. Tel.: +91 130 2249465; fax: +91 11 25489494.E-mail address: aman aggarwal28@yahoo.co.uk (A. Aggarwal).

924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.09.041

In machinability studies investigations, statistical designof experiments is used quite extensively. Statistical design ofexperiments refers to the process of planning the experimentso that the appropriate data can be analyzed by statisti-cal methods, resulting in valid and objective conclusions(Montgomery, 1997). DOE methods such as factorial design,response surface methodology and Taguchi methods are now

Thomas et al. (1997) used a full factorial design involving sixfactors to investigate the effects of cutting and tool parameters

374 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t

Nomenclature

A first factor or input variable investigated—cutting speed (m/min)

A1 average power consumption at the first level ofcutting speed

Adeq. precision adequate precisionAdj. R2 adjusted R2

B second factor or input variable investigated—feed (mm/rev)

C third factor or input variable investigated—depth of cut (mm)

C1 average power consumption at the first level ofdepth of cut

Cor. total totals of all information corrected for themean

CV coefficient of variationD fourth factor or input variable investigated—

cutting environmentD3 average power consumption at the third level

of environmentDOF degrees of freedomE fifth factor or input variable investigated—nose

radiusfe error DOFF˛;(1,fe) F-ratio required for ˛

neff effective number of replicationsN total number of experimentsPc power consumption (W)Pred. R2 predicted R2

PRESS predicted residual error sum of squaresProb. > F proportion of time or probability one would

expect to get the stated F-valueR number of repetitions for confirmation experi-

mentR2 coefficient of determinationS.D square root of the residual mean squareTPc overall mean of power consumptionVe error variance

Greek symbol

model equation containing the said input variables by min-

˛ risk

on the resulting surface roughness and built-up edge forma-tion in the dry turning of carbon steel. The Taguchi methodwas used by Yang and Tarng (1998) to find the optimal cuttingparameters for turning operations. Choudhury and EI-Baradie(1997) used RSM for predicting surface roughness when turn-ing high-strength steel. Thiele and Melkote (1999) used acomplete factorial design to determine the effects of workpiece hardness and cutting tool edge geometry on surfaceroughness and machining forces. Antony (2000) presents acase study for optimizing multi-responses in industrial exper-iments using Taguchi’s quality loss function in conjunctionwith principal component analysis. A polynomial network

was used by Lee et al. (2000) to develop a machining databasefor turning operations. Lin et al. (2001) used an adductive net-work to construct a prediction model for surface roughness

e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384

and cutting force. In their study, cutting speed, feed rate anddepth of cut were the primary factors investigated.

One of the most important parameters in tool geometry isthe nose radius. It strengthens the tool point by thinning thechip where it approaches the point of tool and by spreadingthe chip over larger area of point. It also produces better finishbecause tool marks are not as deep as formed by sharp tool(Lindberg, 1990). In this study, nose radius has been taken intoconsideration along with cutting speed, feed rate and depthof cut. The fifth factor taken into consideration is the cuttingenvironment. Machining is done under three different envi-ronmental conditions—dry, wet (conventional coolant ILO cut154 Indian Oil recommended for CNC machine) and cryogenic(liquid nitrogen as coolant).

A cryocan was used for pouring liquid nitrogen in theform of jet on machining area. Some work has recently beendone (Alexender et al., 1998; Thomas and Chanderasekaran,1994; Chattopadhaya et al., 1985; Paul et al., 1993; Paul andChattopadhaya, 1995) on cryogenic cooling by liquid nitrogenjet in machining and grinding of some commonly used steels.Compared to dry and wet grinding with conventional fluid,cryogenically cooled grinding provided better surface integrity,lower cutting forces and longer wheel life, though in differentdegrees for different kinds of steels, mainly through reduc-ing temperature, preventing wheel loading and retaining grithardness. Dhar et al. (2002) have studied the effect of cryogeniccooling in machining of AISI 1040 steel and AISI 4320 steel andreported similar findings.

The objective of this experimental investigation is to ascer-tain the effects of cutting speed, feed rate, depth of cut, noseradius and cutting environment on power consumption inCNC turning of AISI P-20 tool steel. Design of experiment tech-niques, i.e. response surface methodology (RSM) and Taguchi’stechnique, have been used to accomplish the objective. L27

orthogonal array and face centered central composite designhave been used for conducting the experiments.

2. Design of experiment techniques—abrief review

2.1. Response surface methodology

RSM is a collection of mathematical and statistical techniquesthat are useful for modeling and analysis of problems in whicha response of interest is influenced by several variables andthe objective is to optimize this response (Montgomery, 1997).RSM also quantifies relationships among one or more mea-sured responses and the vital input factors. The version 7 ofthe Design-Expert Software was used to develop the experi-mental plan for RSM (Design-Expert Software, 2006). The samesoftware was also used to analyze the data collected. A regres-sion is performed on the data collected wherein the observedvariable (response) is approximated based on a functional rela-tionship between the estimated variable and one or moreinput variables. The least square technique is used to fit a

imizing the residual error measured by the sum of squaredeviations between the actual and the estimated responses.This involves the calculation of estimates for the regres-

t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384 375

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Table 1 – Process parameters with their values at threelevels

Factors Process parameters Level 1 Level 2 Level 3

A Cutting speed (m/min) 120 160 200B Feed rate (mm/rev) 0.10 0.12 0.14C Depth of cut (mm) 0.20 0.35 0.50

Tool length 100 mmCutting edge length 9 mm

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

ion coefficients, i.e. the coefficients of the model variablesncluding the intercept or constant terms. However, the cal-ulated coefficients of the model equation need to be testedor statistical significance. In this respect, three tests areerformed—test for significance of the regression model, testor significance on individual model coefficients and test forack-of-fit (Steppan et al., 1998).

Additionally, checks need to be made in order to deter-ine whether the model actually describes the experimental

ata (Steppan et al., 1998). The checks performed here includeetermining the various coefficients of determination (R2).hese R2 coefficients have values between 0 and 1. In addi-

ion to this, the adequacy of the model is also investigatedy the examination of residuals (Montgomery, 1997). Theesiduals are the differences between the observed and theredicted responses and these are examined using the nor-al probability plots of the residuals and the plots of the

esiduals versus the predicted response. If the model is ade-uate, the points on the normal probability plots of theesiduals should form a straight line. On the other hand, thelots of the residuals versus the predicted response shoulde structure less, that is, they should contain no obviousatterns.

.2. Taguchi’s technique

aguchi’s parameter design is an important tool for robustesign. It offers a simple and systematic approach to opti-ize design for performance, quality and cost. Two major

ools used in robust design are signal to noise ratio, whicheasures quality with emphasis on variation, and orthogonal

rray, which accommodates many design factors simulta-eously (Park, 1996; Unal and Dean, 1991; Phadke, 1989).aguchi’s design is a fractional factorial matrix that ensuresbalanced comparison of levels of any factor. In this design

nalysis each factor is evaluated independent of all otheractors.

Taguchi has built upon W.E. Deming’s observation that5% of poor quality is attributable to the manufacturingrocess and only 15% to the worker. When a critical qual-

ty characteristic deviates from the target value, it causes aoss (Unal and Dean, 1991). Continuously pursuing variabilityeduction from the target value in critical quality charac-eristics is the key to achieve high quality and reduce cost.y applying this technique one can significantly reduce theime required for experimental investigation, as it is effectiven investigating the effects of multiple factors on perfor-

ance as well as to study the influence of individual factorso determine which factor has more influence and whichas less (Singh and Kumar, 2003, 2004a,b, 2005, 2006; Lin,002).

. Experimental details

.1. Work material

he work material selected for the study was AISI P-20 toolteel. It is used extensively for making injection moulds andccasionally compression moulds. The steel is supplied in

D Environment Dry Wet CryoE Nose radius (mm) 0.4 0.8 1.2

hardness range of about 32–36 HRc and there is no need ofsubsequent heat treatment. It is a cold worked tool steel, hard-ened and tempered. It has an excellent polish ability and issuitable for texturing. The chemical composition of this mate-rial is 0.4% C, 1.5% Mn, 1.9% Cr, 1.0% Ni and 0.2% Mo.

3.2. Cutting inserts

The cutting tool selected for machining AISI P-20 tool steelwas TiN coated tungsten carbide inserts of Kennametal make(Kennametal Inc., 1999). The tungsten carbide inserts usedwere of ISO coding CNMG 120404, CNMG 120408 and CNMG120412 and tool holder of ISO coding PCLNR 1616H07. The pro-vision of a functional TiN outer layer reduces the tendencyto built-up edges. Furthermore, the generation of heat is lessowing to the reduction of friction. This results in less thermalcracks and increased tool life. In addition, any wear patterncan be easily recognized with the yellow TiN layer (Walter,1996). The tool geometry of the insert and tool holder is asfollows.

Insert shape Diamond 80◦

Insert clearance angle 0◦

Tolerance ±0.002Cutting edge length 12 mmInsert thickness 4 mmNose radius 0.4, 0.8 and 1.2 mm.Holder style Offset shank 5◦ SCEAInsert clearance angle 0◦

Shank height 16 mmShank width 16 mm

Fig. 1 – Photograph of experimental setup.

n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384

Table 2 – Experimental data of power consumption forTaguchi technique

Trial no. Power consumption (W) S/N ratio (dB)

R1 R2 R3

1 840 880 880 −58.762 1560 1560 1560 −63.863 1080 1080 1040 −60.564 1480 1480 1520 −63.485 960 1000 1000 −59.886 1200 1160 1200 −61.487 920 960 1000 −59.658 1120 1160 1120 −61.099 1800 1800 1840 −65.1710 1600 1560 1600 −64.0111 1000 1040 1000 −60.1112 1240 1280 1200 −61.8713 880 920 880 −59.0214 1240 1280 1240 −61.9615 1800 1800 1760 −65.0416 1080 1120 1120 −60.8817 1520 1520 1560 −63.7118 1360 1360 1400 −62.7619 1080 1040 1080 −60.5620 1400 1360 1360 −62.7621 2080 2120 2080 −66.4222 1300 1260 1300 −62.1923 1840 1880 1880 −65.4224 1600 1600 1640 −64.1625 1600 1560 1560 −63.9426 1440 1480 1440 −63.2527 1680 1680 1640 −64.44

Total 36700 36940 36900 −1686.45

376 j o u r n a l o f m a t e r i a l s p r o c e s s i

3.3. Experimental plan and cutting conditions

The experimental work was carried out at Solid State PhysicsLab (SSPL), Delhi under Ministry of Defence on a Scaublin makeCNC turning center. P-20 bars (65 mm diameter and 275 mmlength) were used for the experimentation. Canned cycle wasused for machining and the machining was done in absolutemode. A set of wattmeters was used for measuring power con-sumption. Readings of both the wattmeters were taken andmultiplied by suitable multiplying factor and added to get thetotal power consumed. The experimental setup is shown inFig. 1. Cutting conditions were selected based on some pre-liminary investigations and are given in Table 1.

3.3.1. Taguchi’s experimental design—L27 orthogonalarrayAs per Taguchi’s method the total DOF of the selected OA mustbe greater than or equal to the total DOF required for the exper-iment. So, an L27 (313) OA (a standard three-level orthogonalarray) having 26 DOF was selected for the present work. Thenon-linear relationship among the process parameters, if itexists, can only be revealed if more than two levels of theparameters are considered (Park, 1996). Thus each selectedparameter was analyzed at three levels. The process parame-ters and their values at three levels are given in Table 1. Powerconsumption being a ‘lower the better’ type of machiningquality characteristic, the S/N ratio for this type of responsewas used and is given below (Roy, 1990):

S/N ratio = −10 log[

1n

(y21 + y2

2 + · · · + y2n)]

(1)

where y1, y2, . . ., yn are the responses of the machining char-acteristic, for a trial condition repeated n times. The S/N ratioswere computed using Eq. (1) for each of the 27 trials and thevalues are reported in Table 2.

3.3.2. RSM experimental technique—central compositedesignThe turning process was studied with a standard RSM designcalled a central composite design (CCD) wherein the factorialportion is a full factorial design with all factors at three levels,the star points are at the face of the cube portion on the designwhich correspond to ˛-value of 1. This is commonly referredto as a face centered CCD. The center points, as implied bythe name, are points with all levels set to coded level 0, themidpoint of each factor range, and this is repeated six times.Thirty experiments were performed for each of the dry, wetand cryogenic cutting environment. The design layout is asshown in Table 3. For each experimental trial, a new cuttingedge was used. Due to the limited number of inserts available,each trial was repeated twice.

4. Analysis and discussion

4.1. Taguchi’s technique

It is evident from Fig. 1 that power consumption is minimumat the first level of feed (B), first level of depth of cut (C) and

TPc , overall mean of power consumption = 1364.69 W.

first level of cutting speed (A). The effect of nose radius is notvery clearly defined but lower nose radius favors lesser powerconsumption. As far as environment is concerned, cryogenicenvironment favors reduction of power consumption followedby dry environment.

The interaction analysis in Fig. 2 clearly shows that A1B1

and A1C1 are the optimal combinations. Thus first level of cut-ting speed, first level of feed and first level of depth of cut, firstlevel of nose radius and cryogenic environment represent theoptimal levels of various turning process parameters to yieldan optimal value of the power consumption. The S/N plots (notshown) also reveal the same results.

In order to quantify the influence of process parametersand interactions on the selected machining characteristic,analysis of variance (ANOVA) was performed. The pooledANOVA of the raw data and the S/N pooled ANOVA are givenin Tables 4 and 5, respectively.

It is evident that cutting speed, depth of cut and cuttingenvironment are significant at 95% confidence level in both theANOVAs, and thus affects mean value and variation aroundthe mean value of the power consumption. The depth of cutis significant in ANOVA for raw data only, and thus affects

the mean value of the power consumption. The nose radiusis not significant in either of the ANOVAs and thus affectsnothing. It can be selected based on some economic con-siderations. It is also clear that cutting environment is the

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377

Table 3 – Experimental data for power consumption (dry, wet and cryogenic) for RSM technique

S. no. Cutting speed(m/min)

Feed(mm/rev)

Depth ofcut (mm)

Nose radius(mm)

Power consumption(dry) (W)

Power consumption(wet) (W)

Power consumption(cryogenic) (W)

R1 R2 R̄ S1 S2 S̄ T1 T2 T̄

1 120 0.10 0.20 0.4 840 880 860 1520 1520 1520 640 680 6602 200 0.10 0.20 0.4 1100 1140 1120 1660 1700 1680 1020 980 10003 120 0.14 0.20 0.4 940 900 920 1520 1560 1540 840 800 8204 200 0.14 0.20 0.4 1400 1360 1380 1760 1800 1780 1120 1200 11605 120 0.10 0.50 0.4 1120 1160 1140 1580 1620 1600 920 960 9406 200 0.10 0.50 0.4 1500 1540 1520 2000 2040 2020 1460 1500 14807 120 0.14 0.50 0.4 1160 1200 1180 1600 1640 1620 1100 1140 11208 200 0.14 0.50 0.4 1700 1660 1680 2100 2140 2120 1620 1660 16409 120 0.10 0.20 1.2 900 860 880 1500 1460 1480 760 800 780

10 200 0.10 0.20 1.2 1200 1160 1180 1660 1620 1640 1100 1180 114011 120 0.14 0.20 1.2 980 980 980 1520 1480 1500 980 940 96012 200 0.14 0.20 1.2 1380 1420 1400 1760 1720 1740 1260 1300 128013 120 0.10 0.50 1.2 1140 1180 1160 1580 1540 1560 1040 1080 106014 200 0.10 0.50 1.2 1660 1620 1640 1940 2020 1980 1620 1620 162015 120 0.14 0.50 1.2 1240 1320 1280 1540 1620 1580 1240 1240 124016 200 0.14 0.50 1.2 1800 1800 1800 2040 2120 2080 1800 1760 178017 120 0.12 0.35 0.8 1160 1080 1120 1500 1540 1520 940 900 92018 200 0.12 0.35 0.8 1440 1520 1480 1880 1840 1860 1340 1380 136019 160 0.10 0.35 0.8 1140 1180 1160 1680 1640 1660 1100 1060 108020 160 0.14 0.35 0.8 1300 1340 1320 1740 1700 1720 1220 1260 124021 160 0.12 0.20 0.8 1040 1080 1060 1580 1620 1600 980 940 96022 160 0.12 0.50 0.8 1320 1360 1340 1840 1800 1820 1360 1320 134023 160 0.12 0.35 0.4 1240 1280 1260 1720 1680 1700 1060 1100 108024 160 0.12 0.35 1.2 1240 1280 1260 1640 1680 1660 1220 1180 120025 160 0.12 0.35 0.8 1260 1300 1280 1660 1700 1680 1120 1160 114026 160 0.12 0.35 0.8 1280 1280 1280 1680 1680 1680 1160 1120 114027 160 0.12 0.35 0.8 1260 1220 1240 1680 1720 1700 1120 1200 116028 160 0.12 0.35 0.8 1280 1240 1260 1660 1700 1680 1160 1120 114029 160 0.12 0.35 0.8 1240 1280 1260 1660 1700 1680 1140 1140 114030 160 0.12 0.35 0.8 1260 1260 1260 1680 1720 1700 1160 1160 1160

378 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384

Fig. 2 – Effects of process parameters on power consumption (raw data).

Table 4 – Pooled ANOVA (raw data: power consumption)

Source SS DOF V F-ratio SS′ P

A 1721313.61 2 860656.8 33.5* 1674034.3 16.81B 160780.27 2 80390.14 3.13* 113500.93 1.14C 1313787.67 2 656893.84 25.57* 1266508.3 12.73D 4908513.61 2 2454256.8 95.52* 4861234.3 48.83E 74261.76 (2) – Pooled Pooled PooledAB 73797.66 (4) – Pooled Pooled PooledAC 243990.19 (4) – Pooled Pooled PooledBC 86656.85 (4) – Pooled Pooled Pooled

T 9954202.5 80 100691.76

1. *Sig

e 1371100.87 72 25

Tabulated F-ratio at 95% confidence level: F0.05;2;72 = 3.12; F0.05;4;72 = 2.5

most significant factor followed by cutting speed and depth ofcut.

The percent contribution of parameters as quantifiedunder column P of Tables 4 and 5 reveals that the influence of

Table 5 – S/N pooled ANOVA (power consumption)

Source SS DOF V F-ratio SS′ P

A 21.89 2 10.945 21.93* 20.01 17.56B 1.9 (2) – Pooled Pooled PooledC 20.91 2 10.45 20.92* 19.03 16.7D 61.19 2 30.59 61.24* 59.31 52.04E 2.56 (2) – Pooled Pooled PooledAB 0.46 (4) – Pooled Pooled PooledAC 1.26 (4) – Pooled Pooled PooledBC 0.06 (4) – Pooled Pooled Pooled

T 113.98 26 100e 15.61 20 0.4995 15.61 15.61

Tabulated F-ratio at 95% confidence level: F0.05;2;20 = 3.4928;F0.05;4;20 = 2.8661. *Significant at 95% confidence level.

75.6107 20.48

nificant at 95% confidence level.

environment in affecting power consumption is significantlylarger. It is attributed to the fact that no pump is requiredin cryogenic cutting environment. Also in cryogenic cooling,cutting temperature is reduced which results in heat reduc-tion. Owing to this, their are lower stresses which result inreduction of cutting forces and hence reduction in power con-sumption. Next significant factor is cutting speed followed bydepth of cut.

4.1.1. Estimation of optimum value of power consumptionThree factors were found to be significant in both raw data andS/N data analysis that is cutting environment, cutting speedand depth of cut. Lowest level of cutting speed and depth of cutare the most desired conditions as far as power consumption isconsidered. Also cryogenic environment favors reduced powerconsumption.

The estimated mean of the power consumption can becomputed as:

�Pc = A1 + C1 + D3 − 2TPc (2)

t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384 379

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j o u r n a l o f m a t e r i a l s p r o c e s s i n g

here TPc = 1364.69, A1 = 1207.4, C1 = 1203.7 and D3 =136.29

Hence �Pc = 818 W.A confidence interval for the predicted mean on a confirma-

ion run can be calculated using the following equation (Ross,996):

I =√

F˛(1,fe)Ve

[1

neff+ 1

R

](3)

eff = N

1 + [total DOF associated in the estimate of mean]= 11

here Ve = 25691.75, fe = 72, ˛ = 0.05 and F0.05;(1,72) = 3.98 (tabu-ated).

The calculated CI is: CI = ±207.16.The predicted mean of power consumption is: �Pc = 818 W.The 95% confidence interval of the predicted optimal power

onsumption is:

�Pc − CI] < �Pc < [�Pc + CI], i.e. 610.84 < �Pc (W) < 1025.16

.2. RSM technique

he results from the machining trials performed as per thexperimental plan are shown in Table 3. These results werenput into the Design-Expert Software for further analysis.

ithout performing any transformation on the response,xamination of the fit summary output revealed that theuadratic model is statistically significant for all the threenvironmental conditions and, therefore, it has been used forurther analysis.

Test for significance of the regression model, test for signif-cance on individual model coefficients and test for lack-of-fit

eed to be performed. An ANOVA table (not shown) is com-only used to summarize the tests performed. The value of

P > F” for models is less than 0.05, which indicates that theodel is significant which is desirable as it indicates that the

Table 6 – ANOVA for response surface reduced quadratic model

Source Sum of squares DOF M

Model 1.097E+006 8A 5.832E+005 1B 1.089E+005 1C 3.417E+005 1E 1422.22 1AB 400000.00 1AC 4187.83 1A2 1323.31 1C2 10768.48 1

Residual 1853.03 21Lack-of-fit 719.70 16Pure error 1133.33 5Cor. total 1.099E+006 29

Std. dev. 27.09Mean 1256.67CV (%) 2.16PRESS 62215.30

Fig. 3 – Normal probability plot of residuals for powerconsumption (dry) data.

terms in the model have a significant effect on the response.The value of P < 0.0001 indicates that there is only a 0.01%chance that a “model F-value” this large could occur due tonoise. Values greater than 0.1000 indicate the model termsare not significant. Some of the model terms were found tobe significant. For dry environment A–D, AB, AC, A2 and C2 aresignificant model terms wheras for wet environment A–C, AB,AC and C2 are significant model terms. Likewise for cryogenicenvironment A–D, AB, AC and B2 are significant model terms.The insignificant model terms can be removed and may result

in an improved model. The lack-of-fit was also found to beinsignificant in all the three cases. Insignificance of lack-of-fit signifies that it is not significant relative to the pure error.This is desirable, as we want a model that fits. By selecting the

(dry)

ean square F-value p-Value Prob. > F

1.371E+005 1554.14 <0.0001 significant5.832E+005 6609.28 <0.00011.089E+005 1234.01 <0.00013.417E+005 3872.29 <0.0001

1422.22 16.12 0.0006400000.00 453.31 0.00014187.83 47.46 0.00011323.31 15.00 0.0009

10768.48 122.04 0.0001

88.2444.98 0.20 0.994 not significant

226.67

R-squared 0.9921Adj. R-squared 0.9848Pred. R-squared 0.9555Adeq. precision 48.949

380 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384

Fig. 4 – Plot of residuals vs. predicted response for powerconsumption (dry) data.

backward elimination procedure to automatically reduce theterms that are not significant, the resulting ANOVA tables forthe reduced quadratic model for power consumption (dry, wetand cryogenic) are shown in Tables 4–6, respectively. Resultsshow that the models are still significant. However, the maineffect of cutting speed was found to be the most significant fac-tor followed by depth of cut and feed for dry, wet and cryogenicenvironment. Also for all the three environmental conditionslevel of significance of nose radius was comparatively muchless. Besides this, some of the second-order effects and thetwo-level interaction were also found to be significant modelterms. The lack-of-fit can still be said to be insignificant. Inall the three cases the R2 value is high, close to 1, which is

desirable. The predicted R2 is in reasonable agreement withthe adjusted R2. The adjusted R2 value is particularly usefulwhen comparing models with different number of terms. Thiscomparison is, however, done in the background when model

Fig. 5 – 3D surface graph in feed and cutting speed for Pc

(dry).

Fig. 6 – 3D surface graph in depth of cut and cutting speedfor Pc (dry).

reduction is taking place. Adequate precision compares therange of the predicted values at the design points to the aver-age prediction error. Ratios greater than 4 indicate adequatemodel discrimination. In all the three environmental condi-tions the value was well above 4. The following equations arethe final empirical models for the power consumption.

Power consumption (dry)

Pdry = 1075.18 − 10.99A − 2444.44B + 1918.52C + 72.22E

+37.50AB+4.58AC+0.03A2 − 2222.22C2 ± 1133.33 (4)

Power consumption (wet)

Pwet = 1832.28 − 2.67A − 1805.55B − 2191.36C + 23.44AB

+11.04AC + 1580.25C2 ± 600 (5)

Fig. 7 – 3D surface graph in nose radius and cutting speedfor Pc (dry).

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384 381

tion

P

osooAuaiwaf

Fig. 8 – Ramp func

Power consumption (cryogenic)

cryo = 320.92 + 3.33A − 7888.88B − 51.85C + 161.11E

−6.25AB + 8.33AC + 54166.66B2 ± 533.33 (6)

The normal probability plots of the residuals and the plotsf the residuals versus the predicted response for power con-umption (dry) are shown in Figs. 3 and 4, respectively. A checkn the plots in Fig. 3 revealed that the residuals generally falln a straight line implying that errors are distributed normally.lso Fig. 4 revealed that they have no obvious pattern andnusual structure. This implies that the models proposed aredequate and there is no reason to suspect any violation of the

ndependence or constant variation assumption. Similar plotsere drawn for wet and cryogenic environment (not shown)nd they also predicted similar results. The 3D surface graphsor power consumption (dry) are shown in Figs. 5–7.

Fig. 9 – Ramp function

graph for Pc (dry).

All of them have curvilinear profile in accordance tothe quadratic model fitted. From the 3D surface plots itis clear that lowest power consumption is at lowest levelof cutting speed, feed, depth of cut and nose radius. Sim-ilar plots were drawn for wet and cryogenic environment(not shown) and they also predicted similar results as faras response of parameters are concerned but 3D graphs ofcryogenic environment on a whole showed highest powerconsumption followed by dry environment. The highestpower consumption is for wet environment. Ramp functiongraph for dry, wet and cryogenic environment are given inFigs. 8–10.

The desirability value of 1 corresponds to lowest valueof power consumption in the given range of parameters

as given in Table 1. Ramp function graphs shows whatshall be the value of parameters to obtain lowest valueof power consumption for different cutting environmentconditions.

graph for Pc (wet).

382 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384

Fig. 10 – Ramp function graph for Pc (cryogenic).

Table 7 – Confirmation experiments

S. no. Cutting speed(m/min)

Feed(mm/rev)

Depth of cut(mm)

Nose radius(mm)

Cuttingenvironment

Actual Pc(W)

Predicted Pc(W)

Residual Error

1 120 0.1 0.20 0.4 Dry 880 841.30 38.70 4.42 160 0.14 0.35 0.8 Wet 1760 1721.11 38.89 2.263 200 0.14 0.2 1.2 Cryo 1280 1286.11 −6.11 −0.48

4 120 0.12 0.5 1.25 160 0.12 0.35 0.46 200 0.1 0.35 0.8

5. Confirmation test

5.1. RSM technique

In order to verify the adequacy of the model developed, sixconfirmation experiments were performed (Table 7). The testconditions for first three confirmation experiments are among

Table 8 – ANOVA for response surface reduced quadratic model

Source Sum of squares DOF M

Model 7.611E+005 7A 4.608E+005 1B 27222.22 1C 1.881E+005 1AB 5625.00 70225.00 1AC 9102.22 1C2 1

Residual 7661.11 22Lack-of-fit 7061.11 17Pure error 600.00 5Cor. total 7.687E+005 29

Std. dev. 18.66Mean 1701.33CV (%) 1.10PRESS 16473.94

Wet 1600 1593.75 6.25 0.39Cryo 1040 1080.55 −40.55 −3.90Dry 1440 1400.08 39.92 2.77

the cutting conditions that were taken previously whilst forthe remaining three confirmation experiments, there werecutting conditions that have not been used previously butare within the specified range of the parameters defined

previously. Using the point prediction capability of the soft-ware, the power consumption of the selected experimentswas predicted together within the 95% prediction interval.The predicted values and the associated prediction interval

(wet)

ean square F-value p-Value Prob. > F

1.087E+005 312.22 <0.0001 significant4.608E+005 1323.25 <0.0001

27222.22 78.17 <0.00011.881E+005 540.12 <0.0001

5625.00 16.15 0.000670225.00 201.66 <0.00019102.22 26.14 <0.0001

348.23415.36 3.48 0.0874 not significant120.00

R-squared 0.9900Adj. R-squared 0.9869Pred. R-squared 0.9786Adeq. precision 62.725

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 373–384 383

Table 9 – ANOVA for response surface reduced quadratic model (cryo)

Source Sum of squares DOF Mean square F-value p-Value Prob. > F

Model 1.777E+006 7 2.538E+005 4085.36 <0.0001 significantA 8.712E+005 1 8.712E+005 14024.20 <0.0001B 1.217E+005 1 1.217E+005 1958.89 <0.0001C 6.651E+005 1 6.651E+005 10706.31 <0.0001E 74755.56 1 74755.56 1203.38 <0.0001AB 400.00 1 400.00 6.44 0.0188AC 40000.00 1 40000.00 643.90 <0.0001B2 3380.00 1 3380.00 54.41 <0.0001

Residual 1366.67 22 62.12Lack-of-fit 833.33 17 49.02 0.46 0.8948 not significantPure error 533.33 5 106.67Cor. total 1.778E+006 29

Std. dev. 7.88 R-squared 0.9992Mean 1158.00 Adj. R-squared 0.9990CV (%) 0.68 Pred. R-squared 0.9986PRESS 2502.19 Adeq. precision 274.632

terac

avta

deadwt

5

Apa

significant effect in reducing power consumption. The low-

Fig. 11 – Effects of process parameters in

re based on the model developed previously. The predictedalue and the actual experimental value were compared andhe residual and the percentage error calculated. These valuesre presented in Table 7.

The percentage error range between the actual and pre-icted value for Pc is −3.9 to 4.4%. It can be said that thempirical models developed were reasonably accurate. All thectual values for the confirmation run are within the 95% pre-iction interval. The 95% prediction interval is the range inhich we can expect any individual value to fall into 95% of

he time.

.2. Taguchi technique

confirmation test was performed at predicted level of all thearameters, i.e. lowest level of cutting speed, feed, depth of cutnd nose radius and cryogenic environment. Power consump-

tions on power consumption (raw data).

tion was 680 W which falls between the predicted interval, i.e.610.84 < �Pc (W) < 1025.16.

6. Conclusions

1. The analysis of the results for power consumption showsthat the techniques, RSM and Taguchi methodology, givesimilar results. Taguchi’s technique revealed that cryo-genic environment is the most significant factor followedby cutting speed and depth of cut. The 3D surface plotsof RSM also revealed that cryogenic environment has very

est value of power consumption in the given range ofparameters as depicted by ramp function graphs are dryenvironment (858.07), wet environment (1479.87) and cryo-genic environment (658.79).

n g t

r

384 j o u r n a l o f m a t e r i a l s p r o c e s s i

2. Significance of interactions and square terms of param-eters is more clearly predicted in RSM. The RSM showssignificance of all possible combinations of interactionsand square terms as depicted in Tables 6, 8 and 9. InTaguchi’s technique only three interactions (AB, AC and BC)are normally studied. Also square of parameters are ana-lyzed in RSM whereas none of them is done in Taguchi’stechnique. This is owing to the fact that in Taguchi’s design,interactions between control factors are aliased with theirmain effects.

3. Time required for conducting experiments using RSM tech-nique was almost twice as that needed through Taguchitechnique. It is attributed to the fact that 180 (30 × 2, 30 × 2,30 × 2) were performed using face centered central com-posite design for three (dry, wet and cryogenic) cuttingenvironments whereas only 81 (27 × 3) experiments wereperformed using L27 orthogonal array.

4. As evident from Eqs. (4)–(6), RSM technique can model theresponse in terms of significant parameters, their inter-actions and square terms. This facility is not provided byTaguchi’s technique.

5. 3D surfaces generated by RSM (Figs. 5–14) can help invisualizing the effect of parameters on response in theentire range specified whereas Taguchi’s technique givesthe average value of response at given level of parameters(Figs. 2 and 11). Also ramp function graphs tell the exactlevel of parameters for desired level of response. Thus RSMcan better predict the effect of parameters on response andis a better tool for optimization.

Acknowledgements

The authors acknowledge with thanks permission given bySSPL, Delhi, under Ministry of Defence, for carrying out thenecessary experimental work.

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