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Optimization of turning operations with multiple performance characteristics
Journal of Materials Processing Technology 95 (1999) 90±96
Optimization of turning operations with multiple performance characteristics C.Y. Niana, W.H. Yangb, Y.S. Tarngb,* a Department of Automatic Engineering, Fushin Institute of Technology, I-Lan, Touchen 261, Taiwan Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, 106, Taiwan
b
Received 4 April 1998
Abstract The optimization of turning operations based on the Taguchi method with multiple performance characteristics is proposed in this paper. The orthogonal array, multi-response signal-to-noise ratio, and analysis of variance are employed to study the performance characteristics in turning operations. Three cutting parameters namely, cutting speed, feed rate, and depth of cut, are optimized with considerations of multiple performance characteristics including tool life, cutting force, and surface ®nish. Experimental results are provided to illustrate the effectiveness of this approach. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Analysis of variance; Orthogonal array; Cutting speed; Feed rate; Depth of cut; Tool life; Cutting force; Surface ®nish
1. Introduction The Taguchi method [1±3] is a systematic application of design and analysis of experiments for the purpose of designing and improving product quality. In recent years, the Taguchi method has become a powerful tool for improving productivity during research and development so that high quality products can be produced quickly and at low cost. A lot of applications of the Taguchi method have been reported in a world-wide range of industries and nationalities [4]. This is because the Taguchi method is universally applicable to all engineering ®elds. However, most published Taguchi applications to date have been concerned with the optimization of a single performance characteristic. Handling the more demanding multiple performance characteristics is seldom considered in the literature [5]. In this paper, the application of the parameter design of the Taguchi method for improving the multiple performance characteristics in turning operations is reported. In the past, several optimization methods for turning operations have been documented [6±9]. To determine the optimal cutting parameters, reliable mathematical models based on a large amount of machining data have to be *Corresponding author. Tel.: +886-2-2737-6456; fax: +886-2-27376460 E-mail address: [email protected] (Y.S. Tarng)
formulated to associate the cutting parameters with machining performance. Sophisticated optimization algorithms are then applied to the mathematical models for solving the optimal cutting parameters. It is shown by this study that the use of the parameter design of the Taguchi method can greatly simplify the optimization procedure for determining the optimal cutting parameters in turning operations. As a result, from the practical viewpoint, the parameter design of the Taguchi method seems to be the most suitable approach to determine the optimal cutting parameters for turning operations in a machine shop. The paper is organized in the following manner. An overview of the parameter design based on the Taguchi method is given ®rst. Then, the parameter design with the multiple performance characteristics is introduced. The experimental details of using the parameter design to determine and analyze the optimal cutting parameters in turning operations is described next. Finally, the paper concludes with a summary of this study. 2. Parameter design based on the Taguchi method The objective of the parameter design [10] is to optimize the settings of the process parameter values for improving performance characteristics and to identify the product parameter values under the optimal process parameter
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C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
values. In addition, it is expected that the optimal process parameter values obtained from the parameter design are insensitive to the variation of environmental conditions and other noise factors. Therefore, the parameter design is the key step in the Taguchi method to achieving high quality without increasing cost. Basically, classical parameter design, developed by Fisher [11], is complex and not easy to use. Especially, a large number of experiments have to be carried out when the number of the process parameters increases. To solve this task, the Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with a small number of experiments only. A loss function is then de®ned to calculate the deviation between the experimental value and the desired value. Taguchi recommends the use of the loss function to measure the performance characteristic deviating from the desired value. The value of the loss function is further transformed into a signal-to-noise (S/ N) ratio. Usually, there are three categories of the performance characteristic in the analysis of the S/N ratio, that is, the lower-the-better, the higher-the-better, and the nominalthe-better. The S/N ratio for each level of process parameters is computed based on the S/N analysis. Regardless of the category of the performance characteristic, the larger S/N ratio corresponds to the better performance characteristic. Therefore, the optimal level of the process parameters is the level with the highest S/N ratio. Furthermore, a statistical analysis of variance (ANOVA) is performed to see which process parameters are statistically signi®cant. With the S/N and ANOVA analyses, the optimal combination of the process parameters can be predicted. Finally, a con®rmation experiment is conducted to verify the optimal process parameters obtained from the parameter design. In this paper, the cutting parameter design by the Taguchi method is adopted to obtain optimal machining performance in turning. 3. Parameter design with multiple performance characteristics As mentioned earlier, most published Taguchi applications to date have been concerned with the optimization of a single performance characteristic. Handling the more demanding multiple performance characteristics is seldom considered in the literature [5]. The usual recommendation for the optimization of a process with multiple performance characteristics is left to engineering judgement and veri®ed by con®rmation experiments [3]. In this paper, an attempt to deal with the optimization of a turning operation with multiple performance characteristics is investigated. Basically, several problems are encountered in the optimization of a process with multiple performance characteristics. For example, each performance characteristic may belong to a different category in the analysis of the S/N ratio. The engineering unit for describing each performance char-
91
acteristic may not be the same. The importance of each performance characteristic in the overall performance evaluation may be different. As a result, the application of the parameter design of the Taguchi method in a process with multiple performance characteristics cannot be straightforward. To solve these problems, the loss function corresponding to each performance characteristic is ®rst normalized, i.e, Sij
Lij ; Li
(1)
where Sij is the normalized loss function for the ith performance characteristic in the jth experiment, Lij the loss function for the ith performance characteristic in the jth experiment and Li is the average loss function for the ith performance characteristic. A weighting method is then used to determine the importance of each normalized loss function. Based on the weighting method, the total loss function TLj in the jth experiment is de®ned as TLj
m X
wi Sij ;
(2)
i1
where wi is the weighting factor for the ith performance characteristic and m is the number of performance characteristics. The total loss function is further transformed into a multiresponse S/N ratio. In the Taguchi method, the S/N ratio is used to measure the performance characteristic deviating from the desired value. Therefore, the multi-response S/N ratio j in the jth experiment can be expressed as j ÿ10 log TLj :
(3)
Based on the discussion of Sections 2 and 3, the use of the parameter design of the Taguchi method to optimize a process with multiple performance characteristics includes the following steps: (1) identify the performance characteristics and select process parameters to be evaluated; (2) determine the number of levels for the process parameters and possible interactions between the process parameters; (3) select the appropriate orthogonal array and assignment of process parameters to the orthogonal array; (4) conduct the experiments based on the arrangement of the orthogonal array; (5) calculate the total loss function and the multiresponse S/N ratio; (6) analyze the experimental results using the multi-response S/N ratio and ANOVA; (7) select the optimal levels of process parameters; and (8) verify the optimal process parameters through the con®rmation experiment. 4. Turning process experiments Turning is a widely used machining process in which a single-point cutting tool removes material from the surface of a rotating cylindrical workpiece. Three cutting para-
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C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
meters, i.e., cutting speed, feed rate, and depth of cut, must be determined in a turning operation. Common methods of evaluating machining performance in a turning operation are based on the following performance characteristics: tool life, cutting force, and surface roughness. Basically, tool life, cutting force, and surface roughness are strongly correlated with cutting parameters such as cutting speed, feed rate, and depth of cut [12]. Proper selection of the cutting parameters can obtain a longer tool life, a lower cutting force, and better surface roughness. Hence, optimization of the cutting parameters based on the parameter design of the Taguchi method is adopted in this paper to improve the tool life, cutting force, and surface roughness in a turning operation. 4.1. Selection of cutting parameters and their levels The cutting experiments were carried out on an engine lathe using tungsten carbide with the grade of P-10 for the machining of S45C steel bars. The initial cutting parameters were as follows: cutting speed of 210 m/min, a feed rate of 0.20 mm/rev, and a depth of cut of 1.1 mm. The feasible range for the cutting parameters was recommended by a machining handbook, i.e., cutting speed in the range 135±285 m/min, feed rate in the range 0.08±0.32 mm/rev, and depth of cut in the range 0.6±1.6 mm. Therefore, three levels of the cutting parameters were selected as shown in Table 1. 4.2. Machining performance measure Tool life is de®ned as the period of cutting time at which the average ¯ank wear land VB of the tool is equal to 0.3 mm or the maximum ¯ank wear land VBmax is equal to 0.6 mm. This tool life criterion is recommended by the International Standard Organization (ISO). In the experiments, the ¯ank wear land was measured by using a toolmaker's microscope (Isoma). The cutting force acting on the cutting tool in the X, Y, and Z directions was measured by a three-component piezo-electric dynamometer (Kistler 5257A) under the tool holder. The resultant cutting force is then calculated to evaluate the machining performance in this study. The machined surface roughness was measured by a pro®le meter (3D-Hommelewerk). The average surface roughness Ra, which is the most widely used surface ®nish parameter in industry, is selected in this study, being the arithmetic average of the absolute value of the heights of roughness Table 1 Cutting parameters and their levels Symbol
Cutting parameter
Unit
Level 1
Level 2
Level 3
A B C
Cutting speed Feed rate Depth of cut
m/min mm/rev mm
135 0.08 0.6
210a 0.20a 1.1a
285 0.32 1.6
a
Initial cutting parameters.
irregularities from the mean value measured within the sampling length of 8 mm. 5. Determination of optimal cutting parameters In this section, the use of an orthogonal array to reduce the number of cutting experiments for determining the optimal cutting parameters is reported. Results of the cutting experiments are studied by using the S/N and ANOVA analyses. Based on the results of the S/N and ANOVA analyses, optimal cutting parameters with considerations of the multiple performance characteristics including tool life, cutting force, and surface roughness are obtained and veri®ed. 5.1. Orthogonal array experiment To select an appropriate orthogonal array for experiments, the total degrees of freedom need to be computed. The degrees of freedom are de®ned as the number of comparisons between process parameters that need to be made to determine which level is better and speci®cally how much better it is. For example, a three-level process parameter counts for two degrees of freedom. The degrees of freedom associated with interaction between two process parameters are given by the product of the degrees of freedom for the two process parameters. In the present study, the interaction between the cutting parameters is neglected. Therefore, there are six degrees of freedom owing to the three cutting parameters in turning operations. Once the degrees of freedom required are known, the next step is to select an appropriate orthogonal array to ®t the speci®c task. Basically, the degrees of freedom for the orthogonal array should be greater than or at least equal to those for the process parameters. In this study, an L9 orthogonal array with four columns and nine rows was used. This array has eight degrees of freedom and it can handle three-level process parameters. Each cutting parameter is assigned to a column and nine cutting parameter combinations are available. Therefore, only nine experiments are required to study the entire parameter space using the L9 orthogonal array. The experimental layout for the three cutting parameters using the L9 orthogonal array is shown in Table 2. Since the L9 orthogonal array has four columns, one column of the array is left empty for the error of experiments. Orthogonality is not lost by letting one column of the array remain empty. Table 3 shows the experimental results of tool life, cutting force, and surface roughness. 5.2. Analysis of the multi-response signal-to-noise (S/N) ratio As mentioned earlier, there are three categories of performance characteristics, i.e., the lower-the-better, the higher-the-better, and the nominal-the-better. To obtain
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Table 2 Experimental layout using an L9 orthogonal array
Table 4 Multi-response signal-to-noise ratio with different weighting factors
Experiment number
Experiment number
1 2 3 4 5 6 7 8 9
Cutting parameter level A
B
C
D
Case 1
Case 2
Cutting speed
Feed rate
Depth of cut
Error
w15, w22, w33
w13, w25, w32
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 3 1 2 2 3 1
1.807 ÿ4.464 ÿ11.715 ÿ4.840 ÿ5.606 ÿ10.501 ÿ4.351 ÿ8.703 ÿ16.402
0.194 ÿ7.752 ÿ13.199 ÿ6.696 ÿ5.457 ÿ11.102 ÿ4.037 ÿ10.173 ÿ14.549
1 2 3 4 5 6 7 8 9
optimal machining performance, the higher-the-better performance characteristic for tool life must be taken. On the other hand, the lower-the-better performance characteristic for cutting force and surface roughness should be taken for obtaining optimal machining performance. For the higherthe-better performance characteristic, the loss function can be expressed as Lij
n 1X 1 n k1 y2ijk
(4)
where Lij is the loss function of the ith performance characteristic in the jth experiment, n the number of tests, and yijk is the experimental value of the ith performance characteristic in the jth experiment at the kth test. The loss function Lij for the lower-the-better performance characteristic can be expressed as Lij
Multi-response S/N Ratio (dB)
n 1X y2 : n k1 ijk
(5)
Table 4 shows the multi-response S/N ratio with different combinations of the weighting factors, calculated by Eq. (1)±Eq. (5). For case 1, the importance order of the performance characteristics is tool life (w15), then surface roughness (w23), and then cutting force (w32). However, the importance order of the performance characteristics for
case 2 is changed to cutting force (w15), then tool life (w23), and then surface roughness (w32). Since the experimental design (Table 2) is orthogonal, it is then possible to separate out the effect of each cutting parameter at different levels. For example, the mean of the multiresponse S/N ratio for the cutting speed at level 1, 2, and 3 can be calculated by averaging the multi-response S/N ratios for the experiments 1±3, 4±6, and 7±9, respectively (Table 2). The mean of the multi-response S/N ratio for each level of the other cutting parameters can be computed in a similar manner. The mean of the multi-response S/N ratio for each level of the cutting parameters is summarized and it is called the multi-response S/N table (Tables 5 and 6). In addition, the total mean of the multi-response S/N ratio for the nine experiments is also calculated and listed in Tables 5 and 6. Figs. 1 and 2 show the multi-response S/N Table 5 Multi-response signal-to-noise table for w15, w22, w33 Symbol
A B C
Cutting parameter
Mean multi-response S/N ratio (dB) Level 1
Level 2
Cutting speed Feed rate Depth of cut
ÿ4.79 ÿ2.46 ÿ6.73
ÿ6.98 ÿ6.26 ÿ6.44
Level 3 ÿ9.82 ÿ12.87 ÿ8.42
Max±min 5.03 10.41 1.98
Total mean multi-response S/N ratioÿ7.20 dB Table 3 Experimental results for tool life, cutting force, and surface roughness Experiment number
Tool life (s)
Cutting force (N)
Surface roughness (mm)
Table 6 Multi-response signal-to-noise table for w13, w25, w32
1 2 3 4 5 6 7 8 9
2645 2060 1733 1310 1198 734 854 765 216
263 704 1198 593 389 854 335 857 464
1.239 1.921 9.443 2.641 4.513 7.490 0.908 4.184 9.695
Symbol
A B C
Cutting parameter
Mean multi-response S/N ratio (dB) Level 1
Level 2
Cutting speed Feed rate Depth of cut
ÿ6.84 ÿ3.51 ÿ6.60
ÿ7.75 ÿ7.72 ÿ7.55
Total mean multi-response S/N ratioÿ8.06 dB
Level 3 ÿ9.59 ÿ12.95 ÿ10.02
Max-min 2.74 9.44 3.42
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C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
Fig. 1. Multi-response signal-to-noise graph for w15, w22, and w33.
Fig. 2. Multi-response signal-to-noise graph for w13, w25, and w32.
graph for cases 1 and 2. As shown in Eq. (1)±Eq. (5), regardless of the lower-the-better or the higher-the-better performance characteristic, the larger is the multi-response S/N ratio, the smaller is the variance of performance characteristics around the desired value. However, the relative importance amongst the cutting parameters for the multiple performance characteristics still needs to be known so that the optimal combinations of the cutting parameter levels can be determined more accurately. This will be discussed in Section 5.3 using ANOVA.
where p is the number of experiments in the orthogonal array and j is the mean of the multi-response S/N ratio for the jth experiment. The total sum of the squared deviations SST is decomposed into two sources: the sum of the squared deviations SSd due to each process parameter and the sum of the squared error SSe. The percentage contribution by each of the process parameters in the total sum of the squared deviations SST can then be calculated. Statistically, there is a tool called the F-test named after Fisher [11] to see which process parameters have a signi®cant effect on the performance characteristic. In performing the F-test, the mean of the squared deviations SSm due to each process parameter needs to be calculated. The mean of the squared deviations SSm is equal to the sum of the squared deviations SSd divided by the number of degrees of freedom associated with the process parameter. Then, the F value for each process parameter is simply a ratio of the mean of the squared deviations SSm to the mean of the squared error SSe. Usually, the larger the F value, the greater the effect on the performance characteristic due to the change of the process parameter. Table 7 shows the results of ANOVA for case 1. It can be found that the feed rate and cutting speed are the signi®cant cutting parameters for affecting the multiple performance characteristics. The change of the depth of cut in the range
5.3. Analysis of variance The purpose of the ANOVA is to investigate which of the process parameters signi®cantly affect the performance characteristics. This is accomplished by separating the total variability of the multi-response S/N ratios, which is measured by the sum of the squared deviations from the total mean of the multi-response S/N ratio, into contributions by each of the process parameters and the error. First, the total sum of the squared deviations SST from the total mean of the multi-response S/N ratio m can be calculated as SST
p X j ÿ m 2 ;
(6)
j1
Table 7 Results of the analysis of variance for w15, w22, w33 Symbol
Cutting parameter
Degrees of freedom
Sum of squares
Mean square
F
Contribution (%)
A B C
Cutting speed Feed rate Depth of cut
2 2 2
38.13 166.55 6.85
19.06 83.28 3.43
3.31 14.47 0.06
17.10 74.67 3.07
Error
2
11.51
5.75
Total
8
223.04
5.16 100
C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
95
Table 8 Results of the analysis of variance for w13, w25, w32 Symbol
Cutting parameter
Degrees of freedom
Sum of squares
Mean square
F
Contribution (%)
A B C
Cutting speed Feed rate Depth of cut
2 2 2
11.73 134.12 18.69
5.86 67.06 9.35
1.07 12.26 1.71
6.68 76.43 10.65
Error
2
10.94
5.47
Total
8
223.04
given by Table 1 has an insigni®cant effect on the de®ned multiple performance characteristics of case 1. Therefore, based on the S/N and ANOVA analyses, the optimal cutting parameters for case 1 are the cutting speed at level 1, the feed rate at level 1, and the depth of cut at level 2. Table 8 shows the results of ANOVA for case 2. Feed rate is the most signi®cant cutting parameter for affecting the multiple performance characteristic of case 2. The optimal cutting parameters for case 2 are the cutting speed at level 1, the feed rate at level 1, and the depth of cut at level 1. 5.4. Confirmation tests Once the optimal level of the process parameters is selected, the ®nal step is to predict and verify the improvement of the performance characteristic using the optimal level of the process parameters. The estimated S/N ratio ^ using the optimal level of the process parameters can be calculated as q X i ÿ m ; (7) ^ m i1
where m is the total mean of the multi-response S/N ratio, i the mean of the multi-response S/N ratio at the optimal level, and q is the number of the process parameters that signi®cantly affect the multiple performance characteristics. The estimated multi-response S/N ratio using the optimal cutting parameters can then be obtained. Table 9 shows the results of the con®rmation experiment using the optimal cutting parameters of case 1. Good agreement between the predicted machining performance and actual machining performance is shown. The increase of the multi-response S/N ratio from the initial cutting parameters to the optimal Table 9 Results of the confirmation experiment for w15, w22, w33 Initial cutting parameters
Level A2B2C2 A1B1C2 Tool life (s) 1059 Cutting force (N) 622 Surface roughness (mm) 2.754 S/N ratio (dB) ÿ5.73 ÿ0.06 Improvement multi-response S/N ratio4.91 dB
Experiment A1B1C2 2604 454 1.084 ÿ0.82
100
cutting parameters is 4.91 dB. The improvement of the S/N ratio for the individual performance characteristic is shown in Table 10. Based on the result of the con®rmation test, the tool life is increased 2.46 times, the cutting force is decreased by 1.37 times, and surface roughness is decreased by 2.54 times. Therefore, the machining performance for case 1 is improved signi®cantly. Table 11 shows the results of the con®rmation experiment using the optimal cutting parameters of case 2. The predicted machining performance is consistent with the actual machining performance. For individual performance characteristic, the increase of the S/N ratio from the initial cutting parameters to the optimal cutting parameters is shown in Table 12. The cutting force is decreased by 2.37 times because the cutting force is the largest weighting factor for the multiple performance characteristics of case 2. In addition, the tool life is increased by 2.50 times, and the surface roughness is decreased by 2.22 times. Once again, the machining performance of case 2 is improved greatly. In the foregoing discussion, the experimental results con®rm the prior parameter design for the optimal cutting parameters with the multiple performance characteristics in turning operations. Table 10 Improvement of the individual signal-to-noise ratio for w15, w22, w33
Initial cutting parameters (A2B2C2) Optimal cutting parameters (A1B1C2) Improvement S/N ratio
Tool life (dB)
Cutting force (dB)
Surface roughness (dB)
60.50
ÿ55.88
ÿ8.80
68.31
ÿ53.14
ÿ0.70
7.81
2.73
8.10
Table 11 Results of the confirmation experiment for w13, w25, w32
Optimal cutting parameters Prediction
6.23
Level Tool life (s) Cutting force (N) Surface roughness (mm) S/N ratio (dB)
Initial cutting parameters
Optimal cutting parameters Predication
Experiment
A2B2C2 1059 622 2.754 ÿ7.30
A1B1C1
A1B1C1 2645 263 1.239 0.19
0.07
Improvement multi-response S/N ratio7.49 dB
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C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
Table 12 Improvement of the individual signal-to-noise ratio for w13, w25, w32
Initial cutting parameters (A2B2C2) Optimal cutting parameters (A1B1C1) Improvement S/N ratio
Tool life (dB)
Cutting force (dB)
Surface roughness (dB)
60.50
ÿ55.88
ÿ8.80
68.50
ÿ48.40
ÿ1.86
8.00
7.48
6.94
6. Conclusions This paper has presented an application of the parameter design of the Taguchi method in the optimization of turning operations with multiple performance characteristics. It is found that the parameter design of the Taguchi method provides a simple, systematic, and ef®cient methodology for the optimization of the cutting parameters. Furthermore, the multiple performance characteristics such as tool life, cutting force, and surface roughness can be improved simultaneously through this approach instead of using engineering judgement. Therefore, a useful technical tool for the quality optimization of manufacturing systems with considerations of multiple performance characteristics has been proposed and veri®ed in this study. Acknowledgements Financial support from the National Science Council of the Republic of China, Taiwan, under grant number NSC872216-E011-025 is acknowledged.
References [1] G. Taguchi, Introduction to Quality Engineering, Asian Productivity Organization, Tokyo, 1990. [2] P.J. Ross, Taguchi Techniques for Quality Engineering, McGrawHill, New York, 1988. [3] M.S. Phadke, Quality Engineering Using Robust Design, PrenticeHall, Englewood Cliffs, NJ, 1989. [4] A. Bendell, J. Disney, W.A. Pridmore, Taguchi Methods: Applications in World Industry, IFS Publications, UK, 1989. [5] E.A. Elsayed, A. Chen, Optimal levels of process parameters for products with multiple characteristics, Int. J. Prod. Res. 31(5) (1993) 1117±1132. [6] A.M. Abuelnaga, M.A. El-Dardiry, Optimization methods for metal cutting, Int. J. Mach. Tool Design Res. 24(1) (1984) 11±18. [7] G. Chryssolouris, M. Guillot, A comparison of statistical and AI approaches to the selection of process parameters in intelligent machining, ASME J. Eng. Ind. 112 (1990) 122±131. [8] C. Zhou, R.A. Wysk, An integrated system for selecting optimum cutting speeds and tool replacement times, Int. J. Machi. Tools Manuf. 32(5) (1992) 695±707. [9] M.S. Chua, M. Rahman, Y.S. Wong, H.T. Loh, Determination of optimal cutting conditions using design of experiments and optimization techniques, Int. J. Machi. Tools Manuf. 33(2) (1993) 297±305. [10] D.C. Montgomery, Design and Analysis of Experiments, Wiley, Singapore, 1991. [11] R.A. Fisher, Statistical Methods for Research Worker, Oliver & Boyd, London, 1925. [12] M.C. Shaw, Metal Cutting Principle, Oxford University Press, New York, 1984.
Optimization of turning operations with multiple performance characteristics C.Y. Niana, W.H. Yangb, Y.S. Tarngb,* a Department of Automatic Engineering, Fushin Institute of Technology, I-Lan, Touchen 261, Taiwan Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, 106, Taiwan
b
Received 4 April 1998
Abstract The optimization of turning operations based on the Taguchi method with multiple performance characteristics is proposed in this paper. The orthogonal array, multi-response signal-to-noise ratio, and analysis of variance are employed to study the performance characteristics in turning operations. Three cutting parameters namely, cutting speed, feed rate, and depth of cut, are optimized with considerations of multiple performance characteristics including tool life, cutting force, and surface ®nish. Experimental results are provided to illustrate the effectiveness of this approach. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Analysis of variance; Orthogonal array; Cutting speed; Feed rate; Depth of cut; Tool life; Cutting force; Surface ®nish
1. Introduction The Taguchi method [1±3] is a systematic application of design and analysis of experiments for the purpose of designing and improving product quality. In recent years, the Taguchi method has become a powerful tool for improving productivity during research and development so that high quality products can be produced quickly and at low cost. A lot of applications of the Taguchi method have been reported in a world-wide range of industries and nationalities [4]. This is because the Taguchi method is universally applicable to all engineering ®elds. However, most published Taguchi applications to date have been concerned with the optimization of a single performance characteristic. Handling the more demanding multiple performance characteristics is seldom considered in the literature [5]. In this paper, the application of the parameter design of the Taguchi method for improving the multiple performance characteristics in turning operations is reported. In the past, several optimization methods for turning operations have been documented [6±9]. To determine the optimal cutting parameters, reliable mathematical models based on a large amount of machining data have to be *Corresponding author. Tel.: +886-2-2737-6456; fax: +886-2-27376460 E-mail address: [email protected] (Y.S. Tarng)
formulated to associate the cutting parameters with machining performance. Sophisticated optimization algorithms are then applied to the mathematical models for solving the optimal cutting parameters. It is shown by this study that the use of the parameter design of the Taguchi method can greatly simplify the optimization procedure for determining the optimal cutting parameters in turning operations. As a result, from the practical viewpoint, the parameter design of the Taguchi method seems to be the most suitable approach to determine the optimal cutting parameters for turning operations in a machine shop. The paper is organized in the following manner. An overview of the parameter design based on the Taguchi method is given ®rst. Then, the parameter design with the multiple performance characteristics is introduced. The experimental details of using the parameter design to determine and analyze the optimal cutting parameters in turning operations is described next. Finally, the paper concludes with a summary of this study. 2. Parameter design based on the Taguchi method The objective of the parameter design [10] is to optimize the settings of the process parameter values for improving performance characteristics and to identify the product parameter values under the optimal process parameter
0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 9 9 ) 0 0 2 7 1 - X
C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
values. In addition, it is expected that the optimal process parameter values obtained from the parameter design are insensitive to the variation of environmental conditions and other noise factors. Therefore, the parameter design is the key step in the Taguchi method to achieving high quality without increasing cost. Basically, classical parameter design, developed by Fisher [11], is complex and not easy to use. Especially, a large number of experiments have to be carried out when the number of the process parameters increases. To solve this task, the Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with a small number of experiments only. A loss function is then de®ned to calculate the deviation between the experimental value and the desired value. Taguchi recommends the use of the loss function to measure the performance characteristic deviating from the desired value. The value of the loss function is further transformed into a signal-to-noise (S/ N) ratio. Usually, there are three categories of the performance characteristic in the analysis of the S/N ratio, that is, the lower-the-better, the higher-the-better, and the nominalthe-better. The S/N ratio for each level of process parameters is computed based on the S/N analysis. Regardless of the category of the performance characteristic, the larger S/N ratio corresponds to the better performance characteristic. Therefore, the optimal level of the process parameters is the level with the highest S/N ratio. Furthermore, a statistical analysis of variance (ANOVA) is performed to see which process parameters are statistically signi®cant. With the S/N and ANOVA analyses, the optimal combination of the process parameters can be predicted. Finally, a con®rmation experiment is conducted to verify the optimal process parameters obtained from the parameter design. In this paper, the cutting parameter design by the Taguchi method is adopted to obtain optimal machining performance in turning. 3. Parameter design with multiple performance characteristics As mentioned earlier, most published Taguchi applications to date have been concerned with the optimization of a single performance characteristic. Handling the more demanding multiple performance characteristics is seldom considered in the literature [5]. The usual recommendation for the optimization of a process with multiple performance characteristics is left to engineering judgement and veri®ed by con®rmation experiments [3]. In this paper, an attempt to deal with the optimization of a turning operation with multiple performance characteristics is investigated. Basically, several problems are encountered in the optimization of a process with multiple performance characteristics. For example, each performance characteristic may belong to a different category in the analysis of the S/N ratio. The engineering unit for describing each performance char-
91
acteristic may not be the same. The importance of each performance characteristic in the overall performance evaluation may be different. As a result, the application of the parameter design of the Taguchi method in a process with multiple performance characteristics cannot be straightforward. To solve these problems, the loss function corresponding to each performance characteristic is ®rst normalized, i.e, Sij
Lij ; Li
(1)
where Sij is the normalized loss function for the ith performance characteristic in the jth experiment, Lij the loss function for the ith performance characteristic in the jth experiment and Li is the average loss function for the ith performance characteristic. A weighting method is then used to determine the importance of each normalized loss function. Based on the weighting method, the total loss function TLj in the jth experiment is de®ned as TLj
m X
wi Sij ;
(2)
i1
where wi is the weighting factor for the ith performance characteristic and m is the number of performance characteristics. The total loss function is further transformed into a multiresponse S/N ratio. In the Taguchi method, the S/N ratio is used to measure the performance characteristic deviating from the desired value. Therefore, the multi-response S/N ratio j in the jth experiment can be expressed as j ÿ10 log TLj :
(3)
Based on the discussion of Sections 2 and 3, the use of the parameter design of the Taguchi method to optimize a process with multiple performance characteristics includes the following steps: (1) identify the performance characteristics and select process parameters to be evaluated; (2) determine the number of levels for the process parameters and possible interactions between the process parameters; (3) select the appropriate orthogonal array and assignment of process parameters to the orthogonal array; (4) conduct the experiments based on the arrangement of the orthogonal array; (5) calculate the total loss function and the multiresponse S/N ratio; (6) analyze the experimental results using the multi-response S/N ratio and ANOVA; (7) select the optimal levels of process parameters; and (8) verify the optimal process parameters through the con®rmation experiment. 4. Turning process experiments Turning is a widely used machining process in which a single-point cutting tool removes material from the surface of a rotating cylindrical workpiece. Three cutting para-
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meters, i.e., cutting speed, feed rate, and depth of cut, must be determined in a turning operation. Common methods of evaluating machining performance in a turning operation are based on the following performance characteristics: tool life, cutting force, and surface roughness. Basically, tool life, cutting force, and surface roughness are strongly correlated with cutting parameters such as cutting speed, feed rate, and depth of cut [12]. Proper selection of the cutting parameters can obtain a longer tool life, a lower cutting force, and better surface roughness. Hence, optimization of the cutting parameters based on the parameter design of the Taguchi method is adopted in this paper to improve the tool life, cutting force, and surface roughness in a turning operation. 4.1. Selection of cutting parameters and their levels The cutting experiments were carried out on an engine lathe using tungsten carbide with the grade of P-10 for the machining of S45C steel bars. The initial cutting parameters were as follows: cutting speed of 210 m/min, a feed rate of 0.20 mm/rev, and a depth of cut of 1.1 mm. The feasible range for the cutting parameters was recommended by a machining handbook, i.e., cutting speed in the range 135±285 m/min, feed rate in the range 0.08±0.32 mm/rev, and depth of cut in the range 0.6±1.6 mm. Therefore, three levels of the cutting parameters were selected as shown in Table 1. 4.2. Machining performance measure Tool life is de®ned as the period of cutting time at which the average ¯ank wear land VB of the tool is equal to 0.3 mm or the maximum ¯ank wear land VBmax is equal to 0.6 mm. This tool life criterion is recommended by the International Standard Organization (ISO). In the experiments, the ¯ank wear land was measured by using a toolmaker's microscope (Isoma). The cutting force acting on the cutting tool in the X, Y, and Z directions was measured by a three-component piezo-electric dynamometer (Kistler 5257A) under the tool holder. The resultant cutting force is then calculated to evaluate the machining performance in this study. The machined surface roughness was measured by a pro®le meter (3D-Hommelewerk). The average surface roughness Ra, which is the most widely used surface ®nish parameter in industry, is selected in this study, being the arithmetic average of the absolute value of the heights of roughness Table 1 Cutting parameters and their levels Symbol
Cutting parameter
Unit
Level 1
Level 2
Level 3
A B C
Cutting speed Feed rate Depth of cut
m/min mm/rev mm
135 0.08 0.6
210a 0.20a 1.1a
285 0.32 1.6
a
Initial cutting parameters.
irregularities from the mean value measured within the sampling length of 8 mm. 5. Determination of optimal cutting parameters In this section, the use of an orthogonal array to reduce the number of cutting experiments for determining the optimal cutting parameters is reported. Results of the cutting experiments are studied by using the S/N and ANOVA analyses. Based on the results of the S/N and ANOVA analyses, optimal cutting parameters with considerations of the multiple performance characteristics including tool life, cutting force, and surface roughness are obtained and veri®ed. 5.1. Orthogonal array experiment To select an appropriate orthogonal array for experiments, the total degrees of freedom need to be computed. The degrees of freedom are de®ned as the number of comparisons between process parameters that need to be made to determine which level is better and speci®cally how much better it is. For example, a three-level process parameter counts for two degrees of freedom. The degrees of freedom associated with interaction between two process parameters are given by the product of the degrees of freedom for the two process parameters. In the present study, the interaction between the cutting parameters is neglected. Therefore, there are six degrees of freedom owing to the three cutting parameters in turning operations. Once the degrees of freedom required are known, the next step is to select an appropriate orthogonal array to ®t the speci®c task. Basically, the degrees of freedom for the orthogonal array should be greater than or at least equal to those for the process parameters. In this study, an L9 orthogonal array with four columns and nine rows was used. This array has eight degrees of freedom and it can handle three-level process parameters. Each cutting parameter is assigned to a column and nine cutting parameter combinations are available. Therefore, only nine experiments are required to study the entire parameter space using the L9 orthogonal array. The experimental layout for the three cutting parameters using the L9 orthogonal array is shown in Table 2. Since the L9 orthogonal array has four columns, one column of the array is left empty for the error of experiments. Orthogonality is not lost by letting one column of the array remain empty. Table 3 shows the experimental results of tool life, cutting force, and surface roughness. 5.2. Analysis of the multi-response signal-to-noise (S/N) ratio As mentioned earlier, there are three categories of performance characteristics, i.e., the lower-the-better, the higher-the-better, and the nominal-the-better. To obtain
C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
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Table 2 Experimental layout using an L9 orthogonal array
Table 4 Multi-response signal-to-noise ratio with different weighting factors
Experiment number
Experiment number
1 2 3 4 5 6 7 8 9
Cutting parameter level A
B
C
D
Case 1
Case 2
Cutting speed
Feed rate
Depth of cut
Error
w15, w22, w33
w13, w25, w32
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 3 1 2 2 3 1
1.807 ÿ4.464 ÿ11.715 ÿ4.840 ÿ5.606 ÿ10.501 ÿ4.351 ÿ8.703 ÿ16.402
0.194 ÿ7.752 ÿ13.199 ÿ6.696 ÿ5.457 ÿ11.102 ÿ4.037 ÿ10.173 ÿ14.549
1 2 3 4 5 6 7 8 9
optimal machining performance, the higher-the-better performance characteristic for tool life must be taken. On the other hand, the lower-the-better performance characteristic for cutting force and surface roughness should be taken for obtaining optimal machining performance. For the higherthe-better performance characteristic, the loss function can be expressed as Lij
n 1X 1 n k1 y2ijk
(4)
where Lij is the loss function of the ith performance characteristic in the jth experiment, n the number of tests, and yijk is the experimental value of the ith performance characteristic in the jth experiment at the kth test. The loss function Lij for the lower-the-better performance characteristic can be expressed as Lij
Multi-response S/N Ratio (dB)
n 1X y2 : n k1 ijk
(5)
Table 4 shows the multi-response S/N ratio with different combinations of the weighting factors, calculated by Eq. (1)±Eq. (5). For case 1, the importance order of the performance characteristics is tool life (w15), then surface roughness (w23), and then cutting force (w32). However, the importance order of the performance characteristics for
case 2 is changed to cutting force (w15), then tool life (w23), and then surface roughness (w32). Since the experimental design (Table 2) is orthogonal, it is then possible to separate out the effect of each cutting parameter at different levels. For example, the mean of the multiresponse S/N ratio for the cutting speed at level 1, 2, and 3 can be calculated by averaging the multi-response S/N ratios for the experiments 1±3, 4±6, and 7±9, respectively (Table 2). The mean of the multi-response S/N ratio for each level of the other cutting parameters can be computed in a similar manner. The mean of the multi-response S/N ratio for each level of the cutting parameters is summarized and it is called the multi-response S/N table (Tables 5 and 6). In addition, the total mean of the multi-response S/N ratio for the nine experiments is also calculated and listed in Tables 5 and 6. Figs. 1 and 2 show the multi-response S/N Table 5 Multi-response signal-to-noise table for w15, w22, w33 Symbol
A B C
Cutting parameter
Mean multi-response S/N ratio (dB) Level 1
Level 2
Cutting speed Feed rate Depth of cut
ÿ4.79 ÿ2.46 ÿ6.73
ÿ6.98 ÿ6.26 ÿ6.44
Level 3 ÿ9.82 ÿ12.87 ÿ8.42
Max±min 5.03 10.41 1.98
Total mean multi-response S/N ratioÿ7.20 dB Table 3 Experimental results for tool life, cutting force, and surface roughness Experiment number
Tool life (s)
Cutting force (N)
Surface roughness (mm)
Table 6 Multi-response signal-to-noise table for w13, w25, w32
1 2 3 4 5 6 7 8 9
2645 2060 1733 1310 1198 734 854 765 216
263 704 1198 593 389 854 335 857 464
1.239 1.921 9.443 2.641 4.513 7.490 0.908 4.184 9.695
Symbol
A B C
Cutting parameter
Mean multi-response S/N ratio (dB) Level 1
Level 2
Cutting speed Feed rate Depth of cut
ÿ6.84 ÿ3.51 ÿ6.60
ÿ7.75 ÿ7.72 ÿ7.55
Total mean multi-response S/N ratioÿ8.06 dB
Level 3 ÿ9.59 ÿ12.95 ÿ10.02
Max-min 2.74 9.44 3.42
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C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
Fig. 1. Multi-response signal-to-noise graph for w15, w22, and w33.
Fig. 2. Multi-response signal-to-noise graph for w13, w25, and w32.
graph for cases 1 and 2. As shown in Eq. (1)±Eq. (5), regardless of the lower-the-better or the higher-the-better performance characteristic, the larger is the multi-response S/N ratio, the smaller is the variance of performance characteristics around the desired value. However, the relative importance amongst the cutting parameters for the multiple performance characteristics still needs to be known so that the optimal combinations of the cutting parameter levels can be determined more accurately. This will be discussed in Section 5.3 using ANOVA.
where p is the number of experiments in the orthogonal array and j is the mean of the multi-response S/N ratio for the jth experiment. The total sum of the squared deviations SST is decomposed into two sources: the sum of the squared deviations SSd due to each process parameter and the sum of the squared error SSe. The percentage contribution by each of the process parameters in the total sum of the squared deviations SST can then be calculated. Statistically, there is a tool called the F-test named after Fisher [11] to see which process parameters have a signi®cant effect on the performance characteristic. In performing the F-test, the mean of the squared deviations SSm due to each process parameter needs to be calculated. The mean of the squared deviations SSm is equal to the sum of the squared deviations SSd divided by the number of degrees of freedom associated with the process parameter. Then, the F value for each process parameter is simply a ratio of the mean of the squared deviations SSm to the mean of the squared error SSe. Usually, the larger the F value, the greater the effect on the performance characteristic due to the change of the process parameter. Table 7 shows the results of ANOVA for case 1. It can be found that the feed rate and cutting speed are the signi®cant cutting parameters for affecting the multiple performance characteristics. The change of the depth of cut in the range
5.3. Analysis of variance The purpose of the ANOVA is to investigate which of the process parameters signi®cantly affect the performance characteristics. This is accomplished by separating the total variability of the multi-response S/N ratios, which is measured by the sum of the squared deviations from the total mean of the multi-response S/N ratio, into contributions by each of the process parameters and the error. First, the total sum of the squared deviations SST from the total mean of the multi-response S/N ratio m can be calculated as SST
p X j ÿ m 2 ;
(6)
j1
Table 7 Results of the analysis of variance for w15, w22, w33 Symbol
Cutting parameter
Degrees of freedom
Sum of squares
Mean square
F
Contribution (%)
A B C
Cutting speed Feed rate Depth of cut
2 2 2
38.13 166.55 6.85
19.06 83.28 3.43
3.31 14.47 0.06
17.10 74.67 3.07
Error
2
11.51
5.75
Total
8
223.04
5.16 100
C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
95
Table 8 Results of the analysis of variance for w13, w25, w32 Symbol
Cutting parameter
Degrees of freedom
Sum of squares
Mean square
F
Contribution (%)
A B C
Cutting speed Feed rate Depth of cut
2 2 2
11.73 134.12 18.69
5.86 67.06 9.35
1.07 12.26 1.71
6.68 76.43 10.65
Error
2
10.94
5.47
Total
8
223.04
given by Table 1 has an insigni®cant effect on the de®ned multiple performance characteristics of case 1. Therefore, based on the S/N and ANOVA analyses, the optimal cutting parameters for case 1 are the cutting speed at level 1, the feed rate at level 1, and the depth of cut at level 2. Table 8 shows the results of ANOVA for case 2. Feed rate is the most signi®cant cutting parameter for affecting the multiple performance characteristic of case 2. The optimal cutting parameters for case 2 are the cutting speed at level 1, the feed rate at level 1, and the depth of cut at level 1. 5.4. Confirmation tests Once the optimal level of the process parameters is selected, the ®nal step is to predict and verify the improvement of the performance characteristic using the optimal level of the process parameters. The estimated S/N ratio ^ using the optimal level of the process parameters can be calculated as q X i ÿ m ; (7) ^ m i1
where m is the total mean of the multi-response S/N ratio, i the mean of the multi-response S/N ratio at the optimal level, and q is the number of the process parameters that signi®cantly affect the multiple performance characteristics. The estimated multi-response S/N ratio using the optimal cutting parameters can then be obtained. Table 9 shows the results of the con®rmation experiment using the optimal cutting parameters of case 1. Good agreement between the predicted machining performance and actual machining performance is shown. The increase of the multi-response S/N ratio from the initial cutting parameters to the optimal Table 9 Results of the confirmation experiment for w15, w22, w33 Initial cutting parameters
Level A2B2C2 A1B1C2 Tool life (s) 1059 Cutting force (N) 622 Surface roughness (mm) 2.754 S/N ratio (dB) ÿ5.73 ÿ0.06 Improvement multi-response S/N ratio4.91 dB
Experiment A1B1C2 2604 454 1.084 ÿ0.82
100
cutting parameters is 4.91 dB. The improvement of the S/N ratio for the individual performance characteristic is shown in Table 10. Based on the result of the con®rmation test, the tool life is increased 2.46 times, the cutting force is decreased by 1.37 times, and surface roughness is decreased by 2.54 times. Therefore, the machining performance for case 1 is improved signi®cantly. Table 11 shows the results of the con®rmation experiment using the optimal cutting parameters of case 2. The predicted machining performance is consistent with the actual machining performance. For individual performance characteristic, the increase of the S/N ratio from the initial cutting parameters to the optimal cutting parameters is shown in Table 12. The cutting force is decreased by 2.37 times because the cutting force is the largest weighting factor for the multiple performance characteristics of case 2. In addition, the tool life is increased by 2.50 times, and the surface roughness is decreased by 2.22 times. Once again, the machining performance of case 2 is improved greatly. In the foregoing discussion, the experimental results con®rm the prior parameter design for the optimal cutting parameters with the multiple performance characteristics in turning operations. Table 10 Improvement of the individual signal-to-noise ratio for w15, w22, w33
Initial cutting parameters (A2B2C2) Optimal cutting parameters (A1B1C2) Improvement S/N ratio
Tool life (dB)
Cutting force (dB)
Surface roughness (dB)
60.50
ÿ55.88
ÿ8.80
68.31
ÿ53.14
ÿ0.70
7.81
2.73
8.10
Table 11 Results of the confirmation experiment for w13, w25, w32
Optimal cutting parameters Prediction
6.23
Level Tool life (s) Cutting force (N) Surface roughness (mm) S/N ratio (dB)
Initial cutting parameters
Optimal cutting parameters Predication
Experiment
A2B2C2 1059 622 2.754 ÿ7.30
A1B1C1
A1B1C1 2645 263 1.239 0.19
0.07
Improvement multi-response S/N ratio7.49 dB
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C.Y. Nian et al. / Journal of Materials Processing Technology 95 (1999) 90±96
Table 12 Improvement of the individual signal-to-noise ratio for w13, w25, w32
Initial cutting parameters (A2B2C2) Optimal cutting parameters (A1B1C1) Improvement S/N ratio
Tool life (dB)
Cutting force (dB)
Surface roughness (dB)
60.50
ÿ55.88
ÿ8.80
68.50
ÿ48.40
ÿ1.86
8.00
7.48
6.94
6. Conclusions This paper has presented an application of the parameter design of the Taguchi method in the optimization of turning operations with multiple performance characteristics. It is found that the parameter design of the Taguchi method provides a simple, systematic, and ef®cient methodology for the optimization of the cutting parameters. Furthermore, the multiple performance characteristics such as tool life, cutting force, and surface roughness can be improved simultaneously through this approach instead of using engineering judgement. Therefore, a useful technical tool for the quality optimization of manufacturing systems with considerations of multiple performance characteristics has been proposed and veri®ed in this study. Acknowledgements Financial support from the National Science Council of the Republic of China, Taiwan, under grant number NSC872216-E011-025 is acknowledged.
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