Optimizing multi-machiningcharacteristics through Taguchis

approach and utility conceptHari Singh

Mechanical Engineering Department, National Institute of Technology,Kurukshetra, India, and

Pradeep KumarDepartment of Mechanical and Industrial engineering, Indian Institute of

Technology, Roorkee, India

Abstract

Purpose Taguchis technique is best suited to optimize a single performance characteristic yieldingan optimal setting of process parameters. A single setting of process parameters may be optimal forone quality characteristics but the same setting may yield detrimental results for other qualityfeatures. Thus the purpose of this paper is to describe simultaneous optimization ofmulti-characteristics.

Design/methodology/approach The multi-machining characteristics have been optimizedsimultaneously using Taguchis parameter design approach and the utility concept. The paper useda single performance index, utility value, as a combined response indicator of several responses.

Findings A simplified model based on Taguchis approach and utility concept is used to determinethe optimal settings of the process parameters for a multi-characteristic product. The model is used topredict optimal settings of turning process parameters to yield the optimum quality characteristics ofEn24 steel turned parts using TiC coated carbide inserts. The optimal values obtained using themulti-characteristic optimization model have been validated by confirmation experiments. The modelcan be extended to any number of quality characteristics provided proper utility scales for thecharacteristics are available from the realistic data.

Practical implications The proposed methodology can be applied to those industrial situationswhere a number of responses are to be optimized simultaneously.

Originality/value The paper discusses a case study on En24 steel turned parts using titaniumcarbide coated tungsten carbide inserts. The material, En24 steel, has wide applications in aerospace,machine tools, automobiles, etc. The proposed algorithm is easy to apply.

Keywords Taguchi methods, Utility theory, Production processes

Paper type Case study

IntroductionThe Taguchis approach for determining the optimal settings of controllable parametersthrough offline experiments focuses on products with a single quality characteristic. Butmost of the products have several quality features of interest. A single setting of processparameters may be optimal for one response but the same setting may yield detrimentalresults for other responses. In such cases, a need arises to obtain an optimal setting of theprocess parameters so that the product can be produced with optimum or near optimumresponses. This problem has been investigated by researchers who developedapproaches for products with multiple characteristics.

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1741-038X.htm

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Received August 2004Revised March 2005Accepted May 2005

Journal of Manufacturing TechnologyManagement

Vol. 17 No. 2, 2006pp. 255-274

q Emerald Group Publishing Limited1741-038X

DOI 10.1108/17410380610642304

Literature review on multi-response optimizationA number of techniques have been developed by the researchers for optimizingmultiple characteristics of the products. Taraman (1974) investigates multi machiningoutput multi independent variable turning research by response surfacemethodology. The purpose of this research was to develop a methodology whichwould allow determination of the cutting conditions (cutting speed, feed rate and depthof cut) such that specified criterion for each of the several machining dependentparameters (surface finish, tool force and tool life TL) could be achievedsimultaneously. A central composite design was used to develop mathematical modelscorrelating the dependent and independent parameters of the process. Disposableinserts of tungsten carbide were used to turn SAE1018 cold rolled steel. Byrne andTaguchi (1987) illustrate a case of the optimization of two quality characteristics: theforce required to insert the tube into the connector and the pull off force. The selectedquality characteristics were independently optimized using Taguchi approach andthen the results were compared subjectively to select the best levels in terms of thequality characteristics of interest. Phadke (1989) presents a case of products withmultiple characteristics such as surface defects and thickness in his example ofpolysilicon deposition. In order to estimate the loss caused by quality characteristics,he assigned a weight from experience to each quality characteristic. Elsayed and Chen(1993) present a model using loss function approach to determine the optimal settingsof the process parameters of the production process for products with multiplecharacteristics. Tong et al. (1997) propose a procedure on the basis of the quality loss ofeach response so as to achieve the optimization on multi-response problems in theTaguchi method. The procedure is a universal approach which can simultaneouslydeal with continuous and discrete data. A plasma-enhanced chemical vapor depositionprocess experiment was evaluated to prove that the proposed procedure yields asatisfactory result. Su and Tong (1997) propose an effective procedure on the basis ofprincipal component analysis (PCA) to optimize the multi-response problems in theTaguchi method. With the PCA, a set of original responses can be transformed into aset of uncorrelated components. Therefore, the conflict for determining the optimalsettings of the design parameters for the multi-response problems can be reduced.Reddy et al. (1997) present an approach to optimize multi responses simultaneouslyusing goal programming in conjunction with Taguchis robust design methodology.A case study for optimizing an injection moulding process is first carried out usingTaguchi robust design methodology. The optimization study revealed that theoptimum conditions obtained for one response are not completely compatible withthose of other responses. So trade offs were made in selection of levels for factors usingengineering judgment which increased the uncertainty in the decision-making process.The further optimization study on the injection moulding process revealed that theoptimum conditions obtained using goal programming in conjunction with Taguchismethodology have better goal attainment properties compared to robust design.Antony (2000) presents a case study for optimizing multi-responses in industrialexperiments using Taguchis quality loss function in conjunction with PCA. Theapproach is able to eliminate the uncertainty and subjectivity in the decision-makingprocess. Tarang et al. (2000) report the use of fuzzy logic in the Taguchi method tooptimize the submerged arc welding process with multiple performancecharacteristics. An orthogonal array (OA), the signal-to-noise ratio, multi response

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performance index and analysis of variance (ANOVA) are employed to study theperformance characteristics in the submerged arc welding process. The processparameters, namely arc current, arc voltage, welding speed, electrode protrusion, andpreheat temperature are optimized with considerations of the performancecharacteristics, including deposition rate and dilution. Experimental results confirmthe effectiveness of the approach. Antony (2001) has developed a simple and practicalstep-by-step approach for tackling multiple response or quality characteristic problemsin Taguchis parameter design experiments. The methodology uses the Taguchisquality loss function for identifying the significant factor/interaction effects and alsofor determining the optimal condition of the process. In order to demonstrate thepotential of the proposed methodology, a simple case study was carried out foroptimizing three quality characteristics, namely solder paste mass, solder paste height,and glue torque, for a double-sided surface mounting technology electronic assemblyoperation. Six controllable factors and one interaction effect were studied using anL8 OA experiment advocated by Taguchi. Lu and Antony (2002) present a robust andpractical approach which takes advantage of both the Taguchi method and afuzzy-rule based inference system. A case study illustrates the potential of thispowerful integrated approach for tackling multiple response optimization problems.The variance analysis used in the study identifies the most critical and statisticallysignificant parameters. Liao (2003) proposes an effective procedure called PCR-TOPSISthat is based on process capability ratio theory and on the theory of order preference bysimilarity to the ideal solution (TOPSIS) to optimize multi-response problems. UsingPCR-TOPSIS, multiple responses in each experiment are transformed into aperformance index and the optimal factors/levels combinations for themulti-responses can thus be determined. The results of two case studies indicatethat the approach can yield a satisfactory solution for multi-response problems.

In this paper, a simplified methodology based on Taguchis approach and utilityconcept has been developed for determining optimal settings of the process parametersfor multi-characteristic product. The trade off between conflicting qualitycharacteristics is made objective in the developed model through utility concept.A case study on En24 steel turned parts, utilizing a simplified multi-characteristicoptimization model based on Taguchis technique and utility concept, is also discussed.

Process parameters of turning operationIn order to identify the process parameters that affect the quality of the turned parts, anIshikawa cause-effect diagram was constructed as shown in Figure 1. The Ishikawacause-effect diagram depicts that the following process parameters may affect thequality of the turned parts:

. Cutting parameters: cutting speed, feed rate, depth of cut.

. Environment parameters: wet, dry.

. Cutting tool parameters: tool geometry, tool material.

. Work piece material: hot worked, cold worked, difficult to machine.

The following process parameters were identified as potentially important in affectingthe quality features of the turned parts under study (Singh, 2000; Singh et al., 2001;Singh and Kumar, 2000, 2003a, b, c, 2004):

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. cutting speed;

. feed rate;

. depth of cut;

. tool material WIDADUR TG inserts;

. work material En24 steel; and

. environment dry.

En24 steel is a difficult-to-machine material and finds its typical applications in themanufacturing of automobile and machine tool parts (Mottram and WoolMan, 1966).Because of its wide application En24 steel has been selected as the work material inthis case study. The recently developed tool materials like coated carbides haveimproved the productivity levels of difficult-to-machine materials. Thus coated carbidetool Widadur TG of Widia India Limited has been selected to turn En24 steel. Theranges of the selected process parameters were decided by conducting the experimentsand using one variable at a time approach (Singh, 2000; Singh and Kumar, 2000). Theprocess parameters, their designated symbols and ranges are given in Table I. Eachparameter was studied at three levels.

Quality characteristics of turned partsMetal cutting processes consist of independent or input variables, dependent variables,and independent-dependent interactions. The independent variables are broadlygrouped into the cutting tool parameters, the work piece parameters and the cuttingparameters (Figure 1). One can select the independent parameters while setting up thecutting process. The dependent variables are determined by the process, based on the

Figure 1.Ishikawa cause-effectdiagram of a turningprocess

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prior selection of independent parameters. The important dependent parameters forturning process are cutting force (CF), power consumption (PC), dimensional accuracy,surface finish, tool wear and TL. The following features were selected to evaluate thequality of En24 steel turned parts:

. surface roughness (SR);

. tool life;

. cutting force; and

. power consumption.

SR, CF and PC are lower the better type of responses whereas TL is higher thebetter type of quality characteristic. In the present case study, a simplifiedmethodology based on Taguchis approach and utility concept has been used fordetermining optimal settings of the process parameters for multi-characteristicproduct. In fact, the methodology is an extension of Byrne and Taguchi (1987).

The utility conceptA customer evaluates a product based on a number of different quality characteristics.The evaluations of different characteristics should then be combined to give acomposite index. Such a composite index represents the utility of the product. Theutility of a product on a particular characteristic measures the usefulness of thatparticular characteristic of the product. In this paper it is assumed that the overallutility of a product is the sum of utilities of each of the quality characteristics.

Thus if Xi is the measure of effectiveness of an attribute (characteristic) i and thereare n attributes evaluating the outcome space, then the joint utility function can beexpressed as (Derek, 1982):

U X1;X2; . . . ;Xn f U 1X1;U 2X2; . . . ;UnXn 1where Ui(Xi) is the utility of the ith attribute. Assuming that the attributes areindependent and have no interactions between themselves, and the overall utilityfunction is a linear sum of individual utilities, the function becomes:

U X1;X2; . . . ;Xn Xni1

UiXi 2

The attributes may be given priorities as per customers requirements andcorresponding weights for the individual utility index. The overall utility functioncan then be written as

LevelsProcess parameters Designation L1 L2 L3

Cutting speed (m/min) A 190 250 310Feed (mm/rev) B 0.14 0.16 0.18Depth of cut (mm) C 0.70 0.85 1.00

Table I.Process parameters

and their levels

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U X1;X2; . . . ;Xn Xni1

WiUiXi 3

Where Wi is the weight assigned to the attribute i and the sum of the weights for allattributes is equal to 1. The utility function is of higher the better type. If thecomposite measure (the overall utility) is maximized, the quality characteristicsconsidered for the evaluation of utility will be optimized (maximized or minimized).

Determination of utility valueTo determine the utility value for a number of quality characteristics, a preferencescale for each quality characteristic is constructed. Later these scales are weighted toobtain a composite number (overall utility). The weighting is done to satisfy the test ofindifference on the various quality characteristics. The preference scale should be alogarithmic one (Gupta and Murthy, 1980). The minimum acceptable quality level foreach quality characteristic is set at a preference number of 0 and the best availablequality is assigned a preference number of 9. If a log scale is chosen, the preferencenumber (Pi) is given by Gupta and Murthy (1980):

Pi A log XiX 0i

4

where Xi is the value of quality characteristic or attribute i, X0i is the minimum

acceptable value of the quality characteristic or attribute i and A is a constant.Arbitrarily, we may choose A such that Pi 9 at Xi X*, where X* is the optimum

value of Xi assuming such a number exists.

So; A 9log X*

X 0i

5

The next step is to assign weights or relative importance to the quality characteristics.This assignment is subjective and based on experience. Moreover, it depends on theend use of the product or customers requirements. The weights should be assignedsuch that the following condition holds:

Xni1

Wi 1 6

The overall utility can be calculated as:

U Xni1

WiPi 7

The multi-characteristic optimization algorithmIn this paper, the following algorithm is suggested based on Taguchis technique andutility concept.

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. Find optimal values of the selected quality characteristics separately usingTaguchi experimental design and analysis.

. Using the optimal values and the minimum quality levels for the characteristicsfrom the experimental data, construct preference scale for each qualitycharacteristic. Use equations (4) and (5).

. Assign weights Wi, i 1,2, . . . , n based on experience and end use of the productsuch that equation (6) is satisfied.

. Find utility values for each product against each trial condition of the experimentusing equation (7).

. Use these values as a response of the trial conditions of the selected experimentalplan.

. Analyze results using the procedure suggested by Taguchi (Roy, 1990).

. Find the optimal settings of the process parameters for optimum utility (meanand minimum deviation around the mean) based on the analysis in step 6.

. Predict the individual characteristic values considering the optimal significantparameters determined in step 7.

. Conduct confirmation experiment at the optimal setting and compare thepredicted optimal values of the quality characteristics with the actual ones.

The flow chart of the methodology is shown in Figure 2.

Optimization of an individual quality characteristicTaguchis technique is applied to identify the optimum levels of turning processparameters for each of the selected machining characteristics individually. Theselection of an appropriate OA is a critical step in Taguchis experimental design. TheOA selected should satisfy the following inequality (Ross, 1996):

Degree of freedom (DOF) of OA $ Total DOF required for the experiments.Along with the three parameters (A, B and C), three interactions (A B, B C,

A C) were also selected (Singh, 2000; Singh and Kumar, 2000). With the threeparameters each at three-levels and three two factor interactions, the total DOFrequired was 18 ((3 2) (3 4)), the DOF of a three-level factor is 2 (number oflevels-1) and that of two factor interaction is 4 (product of DOF of interacting factors).Thus L27 (3

13) OA was selected for the experiments. The L27 OA is a three-level OAhaving 27 trial conditions and can accommodate 13 parameters. Using a linear graphand a triangular table (Ross, 1996), the selected process parameters and interactionswere assigned to the columns of the OA. The linear graph with main and interactioneffects of interest is shown in Figure 3.

The entire experimentation has been carried out in a phase manner. In phase I, thethree process parameters viz cutting speed, feed rate and depth of cut were varied(Table I) to investigate their effects on SR, CF and PC of turned parts and subsequentlyto optimize the characteristics individually. A total of 81 experiments (three repetitionsat each trial condition) were conducted according to the test conditions given inTable II. En24 steel rods (90 mm diameter and 500 mm length) were turned on an H-22center lathe using TiC coated carbide inserts. The SR was measured by Philipsroughness measuring equipment (PR9150) having a least count of 1 ru (0.025m). The CF

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Figure 2.Flow chart of proposedalgorithm forsimultaneous optimizationof multiple responses

Figure 3.Linear graph of L27 OAwith factors andinteraction assigned

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was measured with a three dimensional turning dynamometer which waspre-calibrated on a vertical milling machine. The PC was recorded with the help of apower meter.

In phase II, the selected process parameters and their levels were the same as inphase I (Table I). In this phase of experimentation, 81 cutting edges (21 inserts, fouredges each) of Widadur TG TiC coated carbide inserts were used according to the trialconditions specified in the L27 OA and given in Table II. Each experiment wasreplicated three times. The trials were conducted on En24 steel rods (90 mm diameterand 500 mm length) on H-22 center lathe to measure TL of carbide inserts. For TLassessment, flank wear width was measured at an interval of 1 min and the flank wearcriterion of 0.45 mm against one TL was applied.

The observed values of SR, CF, PC (phase I) and TL (phase II) are given in Table III.

The analysis and optimal resultsUsing Taguchis analysis and the ANOVA, the optimal settings of turning processparameters for SR, CF, PC and TL were obtained separately and the optimal values ofthe selected characteristics were predicted. The average values of the machining

Column A B A B A B C A C A C B C B C Trial 1 2 3 4 5 6 7 8 9 10 11 12 13

1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 2 2 2 2 2 2 2 2 23 1 1 1 1 3 3 3 3 3 3 3 3 34 1 2 2 2 1 1 1 2 2 2 3 3 35 1 2 2 2 2 2 2 3 3 3 1 1 16 1 2 2 2 3 3 3 1 1 1 2 2 27 1 3 3 3 1 1 1 3 3 3 2 2 28 1 3 3 3 2 2 2 1 1 1 3 3 39 1 3 3 3 3 3 3 2 2 2 1 1 1

10 2 1 2 3 1 2 3 1 2 3 1 2 311 2 1 2 3 2 3 1 2 3 1 2 3 112 2 1 2 3 3 1 2 3 1 2 3 1 213 2 2 3 1 1 2 3 2 3 1 3 1 214 2 2 3 1 2 3 1 3 1 2 1 2 315 2 2 3 1 3 1 2 1 2 3 2 3 116 2 3 1 2 1 2 3 3 1 2 2 3 117 2 3 1 2 2 3 1 1 2 3 3 1 218 2 3 1 2 3 1 2 2 3 1 1 2 319 3 1 3 2 1 3 2 1 3 2 1 3 220 3 1 3 2 2 1 3 2 1 3 2 1 321 3 1 3 2 3 2 1 3 2 1 3 2 122 3 2 1 3 1 3 2 2 1 3 3 2 123 3 2 1 3 2 1 3 3 2 1 1 3 224 3 2 1 3 3 2 1 1 3 2 2 1 325 3 3 2 1 1 3 2 3 2 1 2 1 326 3 3 2 1 2 1 3 1 3 2 3 2 127 3 3 2 1 3 2 1 2 1 3 1 3 2

Table II.Design matrix (L27 OA)

with parameters andinteractions

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characteristics at each level and against each parameter were calculated and arereported in Table IV. The summary results are given in Table V.

Table V displays the individual optimal values of the selected characteristics andcorresponding optimal settings of the process parameters for En24 steel turned partsusing TiC coated carbide inserts.

Surface roughness(ru)

Tool life(min)

Cutting force(N)

Power consumption(kW)

Trial no. R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3

1 80 80 90 18 18 17 336 395 358 1.064 1.251 1.1342 90 100 90 15 14 15 427 438 430 1.352 1.387 1.3623 100 110 100 13 13 12 493 484 504 1.561 1.533 1.5964 100 120 110 14 15 14 435 416 377 1.378 1.317 1.1945 100 100 100 11 10 11 459 492 460 1.454 1.558 1.4576 110 100 110 10 10 10 558 538 564 1.767 1.704 1.7867 110 110 110 8 10 9 463 410 428 1.466 1.298 1.3558 120 130 120 14 12 13 516 504 482 1.634 1.596 1.5269 130 130 120 8 9 10 617 573 549 1.954 1.815 1.739

10 80 90 80 22 24 22 354 349 369 1.475 1.454 1.53811 80 90 90 19 21 20 472 423 437 1.967 1.763 1.82112 90 100 90 16 16 14 486 417 435 2.025 1.738 1.81313 110 100 90 20 22 20 375 389 362 1.563 1.621 1.50814 100 100 110 14 13 15 506 423 484 2.108 1.763 2.01715 100 110 110 11 12 10 505 536 479 2.104 2.233 1.99616 100 100 100 17 18 17 413 412 409 1.721 1.717 1.69217 110 110 120 16 15 16 542 511 546 2.258 2.129 2.27518 130 120 120 11 10 10 549 526 555 2.288 2.192 2.31319 80 70 70 8 8 7 347 322 334 1.793 1.664 1.72620 90 80 80 15 16 15 370 361 412 1.912 1.865 2.12921 90 100 90 8 10 7 470 528 467 2.428 2.728 2.41322 100 90 90 14 14 12 373 346 361 1.927 1.788 1.86523 90 110 100 11 10 13 418 444 434 2.16 2.294 2.24224 100 110 100 6 8 10 508 511 505 2.625 2.64 2.60925 90 100 100 11 12 10 392 367 390 2.025 1.896 2.01526 100 110 110 12 12 10 441 498 460 2.279 2.573 2.37727 110 110 120 5 7 5 572 551 589 2.955 2.847 3.043

Table III.Observed values ofquality characteristics

Average valuesof SR (ru)

Average valuesof TL (min)

Averagevalues

of CF (N)Average values

of PC (kW)Process parameterdesignation L1 L2 L3 L1 L2 L3 L1 L2 L3 L1 L2 L3

A 106.3 101.1 95.9 12.33 16.33 10.22 471 454 436 1.490 1.892 2.252B 88.1 102.6 112.6 14.93 12.59 11.37 415 454 491 1.722 1.877 2.036C 94.4 101.1 107.8 14.85 14.00 10.04 381 459 521 1.572 1.898 2.165A B 101.1 100.0 102.2 13.31 12.81 12.76 452 457 452 1.891 1.890 1.891B C 100.4 100.9 102.0 12.56 13.31 13.02 458 453 450 1.898 1.872 1.865A C 101.9 100.7 100.7 12.69 12.67 13.54 456 449 456 1.923 1.864 1.849

Table IV.Average values of qualitycharacteristics atdifferent levels

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Preference scale constructionSurface roughness

X* optimum value of SR 76.18 ru (refer to Table V)X0 minimum acceptable value of SR 130 ru (assumed, as all the observed

values of SR in Table III are in between 70 and 130 ru)

Using these values and the equations (4) and (5), the preference scale for SR wasconstructed as

PSR 38:78 log XSR130

8

Tool life

X* optimum value of TL 20.19 min (refer to Table V)X0 minimum acceptable value of TL 5 min (assumed, as all the observed

values of TL in Table III are in between 5 and 25 min)

The preference scale for TL was constructed as:

PTL 14:85 log XTL5

9

Cutting force

X* optimal value of CF 324.88 N (refer to Table V)X0 minimum acceptable value of CF 620 N (assumed, as all the values of CF in

Table III lie in between 320 and 620 N)

Using these values in equations (4) and (5), the preference scale for CF has beenconstructed as:

PCF 232:10 log XCF620

10

Qualitycharacteristic

Optimal settings ofprocess parameters

Significant process parameters(at 95 percent confidence level)

Predicted optimal valueof quality characteristics

SR A3 B1 C1 A, B, C 76.18 ruTL A2 B1 C1 A, B, C 20.19 minCF A3 B1 C1 A, B, C 324.88 NPC A1 B1 C1 A, B, C 1.028 kW

Note: Subscripts represent levels of the process parameters

Table V.Optimal settings ofprocess parameters(phase I and II) and

optimal values ofindividual quality

characteristics

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Power consumption

X* optimum value of PC (when optimized individually) 1.028 kW (Table V)X0 minimum acceptable value of PC 3.050 kW (assumed, all the PC values in

Table III are in between 1.060 and 3.050 kW)

Using these values, the preference scale for PC has been found to be:

PPC 219:06 log XPC3:050

11

Weight of quality characteristicsThe weights to the selected quality characteristics were assigned as given below:

WSR weight assigned to SR 0.25WCF weight assigned to CF 0.25WTL weight assigned to TL 0.25WPC weight assigned to PC 0.25

It has been assumed that all the quality characteristics are equally important and henceequal weights have been assigned. However, there is no constraint on the weights andit can be any value between 0 and 1 subject to the condition specified in equation (6).The customers requirements and priorities should be taken into consideration whiledeciding the weights of quality characteristics.

Utility value calculationThe utility value of each turned part was calculated using the following relation(overall utility function):

U n;R PSRn;R W SR PCFn;R WCF PTLn;R WTL PPCn;R WPC 12

where, n trial number, n 1, 2, . . . , 27; R replication number, R 1,2,3The utility values thus calculated are reported in Table VI.

Analysis of the data and determination of optimal settings of processparametersThe data (utility values) were analyzed both for mean response (mean of utility at eachlevel of each parameter) and signal-to-noise (S/N) ratio. Since utility is a higher thebetter (HB) type of characteristic, (S/N)HB has been used (Ross, 1996):

S=N HB 210 log 1RXRj1

1

y2j

" #13

where, yj value of the characteristic at observation j; R number of replicationsin a trial.

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The S/N ratios are also given in Table VI. The mean responses and main effects interms of utility values are calculated and reported in Table VII.

The average values of S/N ratios and the S/N main effects are also calculated andreported in Table VIII. The data from Tables VII and VIII are plotted in Figure 4.

It is clear from the Figure 4 that the second level of cutting speed (A2), the first levelof feed (B1) and the first level of depth of cut (C1) would yield best performance in termsof utility value and S/N ratio within the selected range of parameters.

Raw data (utility values) S/N ratiosR1 R2 R3 (dB)

8.43 7.52 7.48 17.816.30 5.60 6.27 15.614.83 4.52 4.57 13.325.64 5.24 6.03 14.984.95 4.42 4.94 13.533.32 3.91 3.26 10.794.00 5.03 4.62 13.043.93 3.47 4.19 11.661.70 2.29 3.04 6.687.88 7.61 7.66 17.756.05 6.32 6.08 15.775.13 5.52 5.53 14.626.07 6.42 7.13 16.254.23 5.10 4.19 12.973.86 3.27 3.60 11.015.67 5.78 5.74 15.163.67 3.88 3.27 11.082.28 2.71 2.42 7.796.07 6.90 6.49 16.206.09 6.82 5.97 15.933.75 3.01 3.56 10.615.48 6.35 5.86 15.374.90 3.57 4.52 12.492.39 2.43 3.26 8.355.27 5.32 4.70 14.104.72 3.22 3.38 11.181.11 1.79 1.52 2.85

Table VI.Utility data based on

quality characteristics (a)SR (b) TL (c) CF (d) PC

Average utility values Main effectsProcess parameters designation L1 L2 L3 L2-L1 L3-L2

A 4.80 5.08 4.35 0.28 20.73B 6.00 4.61 3.62 21.39 20.99C 6.16 4.82 3.24 21.34 21.58A B 4.80 4.73 4.70 20.07 20.03B C 4.70 4.79 4.74 0.09 20.05A C 4.63 4.75 4.84 0.12 0.09

Table VII.Average values and

main effects (raw data:SR, CF, TL and PC)

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The pooled versions of ANOVA for raw data (utility) and S/N ratio are given inTables IX and X, respectively. It is clear from the Tables IX and X that feed (B) anddepth of cut (C) affect significantly the variation of utility value since these aresignificant in both the ANOVAs. The Table IX also reveals that the relative power ofdepth of cut (C: 51.82 percent) and feed (B: 34.61 percent) is significantly quite larger

Average S/N values S/N main effectsProcess parameters designation L1 L2 L3 L2-L1 L3-L2

A 13.05 13.60 11.35 0.55 22.25B 15.29 12.86 9.85 22.43 23.01C 15.63 13.36 9.01 22.27 24.35A B 12.62 12.60 12.78 20.02 0.18B C 12.17 12.56 13.27 0.39 0.71A C 12.30 12.60 13.10 0.30 0.50

Table VIII.Average S/N values andmain effects (raw data:SR, CF, TL and PC)

Figure 4.Effects of processparameters on utilityvalue and S/N ratio (themain effects)

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than the relative power of cutting speed (A: 3.02 percent) and interaction betweencutting speed and depth of cut (A C: 0.81 percent) in affecting the utility value. Thecutting speed (A) and the interaction between cutting speed and depth of cut (A C)are significant in ANOVA for raw data only, hence affect the mean utility value.

The optimal setting of the turning process parameters for the multi-characteristicsoptimization (SR, TL, CF and PC) of En24 steel turned parts using TiC coated carbideinserts is given in Table XI.

Predicted means (optimal values of quality characteristics)Surface roughnessThe average values of SR at the second level of cutting speed A2; the first level of feed B1 and the first level of depth of cut C1 are given in Table XII. The overall mean ofSR TSR is 101.11 ru. The predicted mean (optimal value) of SR (mSR) is:

Source SS DOF V F ratio SS0 P

A 7.253 2 3.627 13.58 * 6.677 3.02B 77.169 2 38.585 144.51 * 76.593 34.61C 115.251 (4) 57.626 215.83 * 114.675 51.82A B (0.426) (4) Pooled B C (0.393) 4 Pooled A C 2.934 0.734 2.75 * 1.782 0.81T 221.280 80 221.280 100.00e (pooled) (18.673) (70) 0.267 21.553 9.74

Notes: SS Sum of squares, DOF Degrees of freedom, V Variance, SS0=Pure sum of squares,P Percent contribution, T=Total, e error, A Cutting speed, B Feed, C Depth of cut;*Significant at 95 percent confidence level; F0.05;2;70 3.13 (tabulated); F0.05;4;70 2.50 (tabulated)

Table IX.Pooled ANOVA (raw

data: SR, CF, TL and PC)

Source SS DOF V F ratio SS0 P

A (24.689) (2) Pooled B 133.841 2 66.921 13.78 * 121.521 27.36C 203.466 2 101.733 20.95 * 191.146 43.04A B (2.330) (4) Pooled B C (15.157) (4) Pooled A C (15.350) 4 Pooled T 444.111 26 444.111 100.00e (pooled) (106.804) (22) 4.855 131.444 29.60

Notes: *Significant at 95 percent confidence level; F0.05;2;22 3.44 (tabulated)Table X.

Pooled S/N ANOVA (rawdata: SR, CF, TL and PC)

Cutting speed * (A2, second level) 250 m/minFeed * (B1, first level) 0.14 mm/revDepth of cut * (C1, first level) 0.70 mm

Note: *Significant at 95 percent confidence level

Table XI.Optimal settings ofprocess parameters

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mSR A2 B1 C1 2 2 TSR 81:38 ruThe 95 percent confidence interval of confirmation experiments (CICE) was calculatedby using the following equation (Ross, 1996):

CICE Fa1; f e 1

neff 1R

sVe 14

where,

Fa(1, fe) the F-ratio at a confidence level of (1 2 a) against DOF 1 and error degreeof freedom, fe;

neffN

1Total DOF associated in the estimate of mean ;

N total number of results;

R sample size for confirmation experiment;

Ve error variance.

The specific values as required in equation (14) are:

f e error DOF 70; Ve error variance 36:720

N 81; neff 81=7calculated

R 3; F0:051; 70 3:98Tabulated F valueSo, CICE ^7.83

The predicted optimal range (for a confirmation run of three experiments) of SR is:

73:55 , mSRru , 89:21

Tool lifeThe average values of TL at the second level of cutting speed A2; the first level offeed B1 and the first level of depth of cut C1 are given in Table XII. The overallmean of TL TTL is 12.96 min. So, the predicted mean of TL (mTL) is:

mTL A2 B1 C1 2 2 TTL 20:19 min:

Levels SR (ru) * TL (min) * CF (N) * PC (kW) *

A2 101.1 16.33 454 1.892B1 88.1 14.93 415 1.722C1 94.4 14.85 381 1.572

Note: *The above average values are taken from Table IV

Table XII.Average values of qualitycharacteristics atoptimum levels

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The 95 percent confidence interval of confirmation experiments (CICE) was calculatedby using the following values in equation (14):

f e error DOF 62; Ve error variance 2:277

N 81; neff 81=7calculated

R 3; F0:051; 62 4:00tabulated F valueSo, CICE ^2.16

The predicted optimal range (for a confirmation run of three experiments) of TL is:

18:03 , mTLmin , 22:35

Cutting forceThe average values of CF at the second level of cutting speed A2; the first level of feed B1 and the first level of depth of cut C1 are given in Table XII.

The overall mean of CF TCF is 453.56 N. So, the predicted mean of CF (mCF) is:mCF A2 B1 C1 2 2 TCF 342:88 N

The 95 percent CICE (for three confirmation experiments) of the predicted mean hasbeen calculated using equation (14). The specific values as required in equation (14) are:

f e error DOF 70; Ve error variance 488:49

N 81; neff 81=7calculated

R 3; F0:051; 70 3:98Tabulated; from F TableSo, CICE ^28.57.

The predicted optimal range (for a confirmation run of three experiments) of CF is:

314:31 , mCFN , 371:45

Power consumptionThe average values of PC at the second level of cutting speed A2; the first level of feed B1 and the first level of depth of cut C1 are given in Table XII.

The overall mean of PC TPC is 1.878 kW. So, the predicted mean of PC (mPC) is:mPC A2 B1 C1 2 2 TPC 1:43 kW

The 95 percent CICE (for three confirmation experiments) of the predicted mean hasbeen calculated by using the following values in equation (14):

f e error DOF 70; Ve error variance 9:87243 1023

N 81; neff 81=7calculated

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R 3; F0:051; 70 3:98tabulated; from F tableSo, CICE ^0.128.

The predicted optimal range (for a confirmation run of three experiments) of PC is:

1:302 , mPCkW , 1:558The values of the error DOF and the error variance for all the above calculations havebeen taken from the pooled ANOVAs of raw data (not reported here) when the qualitycharacteristics are optimized individually by Taguchis approach.

Confirmation experimentsThree confirmation experiments were conducted at the optimal settings of turningprocess parameters. The following average values have been found for the qualitycharacteristics considered:

. Average SR 83.33 ru

. Average CF 358 N

. Average TL 21.67 min

. Average PC 1.489 kWThese average values of the quality characteristics are lying within the 95 percent CICEof the optimal range.

Summary results and comparison with single characteristic optimizationThe summary results and comparison with single characteristic optimization arereported in Table XIII.

Conclusions. A simplified model based on Taguchis approach and utility concept is used

to determine the optimal settings of the process parameters for amulti-characteristic product. The model is used to predict optimal settings ofturning process parameters to yield the optimum quality characteristics of En24steel turned parts using TiC coated carbide inserts.

Method Characteristic Optimal condition Optimal value

Single characteristic optimization SR A3 *, B1 *,C1 * 76.18 ruTL A2 *, B1 *,C1 * 20.19 minCF A3 *, B1 *,C1 * 324.88 NPC A1 *, B1 *, C1 * 1.028 kW

Multi-characteristic optimization SR, TL, CF, PC A2 *, B1 *,C1 * SR 81.38 ruTL 20.19 minCF 342.88 NPC 1.43 kW

Notes: Quality characteristics: surface roughness (SR), tool life (TL), cutting force (CF), powerconsumption (PC); Weights: WSR 0.25, WTL 0.25, WCF 0.25, WPC 0.25; Type: LB, HB, LB, LB,respectively; *Significant at 95 percent confidence level

Table XIII.Summary andcomparison results

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. The optimal values obtained using the multi-characteristic optimization modelhave been validated by confirmation experiments.

. The weights assigned to the selected quality characteristics have been assumedequal. However, with a different set of weights, a different set of optimalparameters for the quality characteristics will result. The optimal set predictedwill be closer to the optimal set predicted for the single characteristic which ishaving the largest weight.

. The model can be extended to any number of quality characteristics providedproper utility scales for the characteristics are available from the realistic data.

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Further reading

Tsui, K.L. (1999), Robust design optimization for multiple characteristics problems,International Journal Production Research, Vol. 37, pp. 433-45.

Corresponding authorHari Singh can be contacted at: hsingh_nitk@rediffmail.com

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