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Optimization of turning operations with multiple performance characteristics using the Taguchi method and Grey relational analysis
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2753–2759
journal homepage: www.elsevier.com/locate/jmatprotec
Review
Optimization of turning operations with multiple performance characteristics using the Taguchi method and Grey relational analysis Chorng-Jyh Tzeng a , Yu-Hsin Lin b , Yung-Kuang Yang a,∗ , Ming-Chang Jeng c a
Department of Mechanical Engineering, Minghsin University of Science and Technology, 1 Hsin Hsing Road, Hsin Feng, 304 Hsinchu, Taiwan b Department of Industrial Engineering and Management, Minghsin University of Science and Technology, 1 Hsin Hsing Road, Hsin Feng, 304 Hsinchu, Taiwan c Department of Mechanical Engineering, National Central University, Chung-Li 32054, Taiwan
a r t i c l e
i n f o
a b s t r a c t
Article history:
This study investigated the optimization of CNC turning operation parameters for SKD11 (JIS)
Received 12 June 2007
using the Grey relational analysis method. Nine experimental runs based on an orthogonal
Received in revised form 9 June 2008
array of Taguchi method were performed. The surface properties of roughness average and
Accepted 21 June 2008
roughness maximum as well as the roundness were selected as the quality targets. An optimal parameter combination of the turning operation was obtained via Grey relational analysis. By analyzing the Grey relational grade matrix, the degree of influence for each
Keywords:
controllable process factor onto individual quality targets can be found. The depth of cut
Grey relational analysis
was identified to be the most influence on the roughness average and the cutting speed
Optimization
is the most influential factor to the roughness maximum and the roundness. Additionally,
CNC turning
the analysis of variance (ANOVA) is also applied to identify the most significant factor; the
SKD 11
depth of cut is the most significant controlled factors for the turning operations according
ANOVA
to the weighted sum grade of the roughness average, roughness maximum and roundness. © 2008 Elsevier B.V. All rights reserved.
Contents 1. 2.
3.
∗
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grey relational analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Data preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Grey relational coefficients and Grey relational grades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental procedures and test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Schematic of machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Experimental parameters and design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Corresponding author. Tel.: +886 3 5593142x3001; fax: +886 3 5782822. E-mail address: [email protected] (Y.-K. Yang). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.06.046
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4.
5.
1.
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3.4. Measuring apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Best experimental run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Most influential factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Confirmation test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction
In modern industry the goal is to manufacture low cost, high quality products in short time. Automated and flexible manufacturing systems are employed for that purpose along with computerized numerical control (CNC) machines that are capable of achieving high accuracy and very low processing time. Turning is the most common method for cutting and especially for the finishing machined parts. Furthermore, in order to produce any product with desired quality by machining, cutting parameters should be selected properly. In turning process parameters such as cutting tool geometry and materials, the depth of cut, feed rates, cutting speeds as well as the use of cutting fluids will impact the material removal rates and the machining qualities like the surface roughness, the roundness of circular and dimensional deviations of the product (Kalpakjian and Schmid, 2001). Surface roughness of cutting process has been studied intensively, mostly through experiments. Yang and Tarng (1998) employed Taguchi method to investigate the cutting characteristics of S45C steel bars using tungsten carbide cutting tools. The optimal cutting parameters of the cutting speed, the feed rate and the depth of cut for turning operations with regard to performance indexes such as tool life and surface roughness are considered. Davim (2003) investigated the influence of cutting conditions (cutting velocity and feed) and cutting time on turning metal matrix composites. An orthogonal array and the analysis of variance are employed to investigate the cutting characteristics of flank wear (VB), power required (Pm) and surface roughness (Ra). Manna and Bhattacharyya (2004) took the significant cutting parameters into consideration and used multiple linear regression mathematical models relating the surface roughness height Ra and Rt to the cutting parameters for turning process of Al/SiC-MMC. Aslan et al. (2007) used an orthogonal array and the analysis of variance (ANOVA) to optimization of cutting parameters in turning hardened AISI 4140 steel (63 HRC) with Al2 O3 + TiCN mixed ceramic tool. The flank wear (VB) and surface roughness (Ra) had investigated a process optimization to determine optimal values of cutting parameters, such as cutting speed, feed rate and depth of cut. Nalbant et al. (2007) used Taguchi method to find the optimal cutting parameters for surface roughness in turning operations of AISI 1030 steel bars using TiN coated tools. Three cutting parameters, namely, insert radius, feed rate, and depth of cut, are optimized with considerations of surface roughness, and so on. However, very few studies have been conducted to investigate roundness under different turning parameter. Additionally, cutting fluids properly applied (Kalpakjian and Schmid, 2001; EI Baradie, 1996), can increase productivity and reduce costs by choosing higher
2756 2756 2756 2757 2759 2759 2759 2759
cutting speeds, higher feed rates and greater depths of cut. Effective application of cutting fluids can also increase tool life, decrease surface roughness, increase dimensional accuracy and decrease the amount of power consumed. The watersoluble (Water-miscible) cutting fluids are primarily used for high speed machining operations because they have better cooling capabilities (EI Baradie, 1996). There fluids are also best for cooling machined parts to minimize thermal distortions. Water-soluble cutting fluids are mixed with water at different ratios depending on the machining operation. Therefore, the effect of water-soluble cutting fluids under different ratios was also considered in this study. Recently, Deng (1989) proposed a Grey relational analysis. The Grey relational analysis is a method for measuring the degree of approximation among the sequences using a Grey relational grade. Theories of the Grey relational analysis have attracted considerable interest among researchers. Some other researchers have also examined the optimization of process parameters. For example, Huang and Lin (2002) applied the Grey relational analysis to design the die-sinking EDM machining parameters. Fung et al. (2003) studied the Grey relational analysis to obtain the optimal parameters of the injection molding process for mechanical properties of yield stress and elongation in polycarbonate/acrylonitrilebutadiene-styrene (PC/ABS) composites. Shen et al. (2004) studied different polymers (such as PP, PC, PS, POM) with various process parameters of the microgear. The simulation used the Taguchi method and the Grey relational analysis were provided. Lin (2004) employed the Taguchi method and the Grey relational analysis to optimize the turning operations with multiple performance characteristics. Chiang and Chang (2006) used the Grey relational analysis to optimize of the wire electric discharge machining process of particle-reinforced material with multiple performance characteristics. Yang et al. (2006) also applied the Taguchi method and the Grey relational analysis to optimize the dry machining parameters for high-purity graphite in end milling process, etc. Planning the experiments through the Taguchi orthogonal array has been used quite successfully in process optimization by Chen and Chen (2007), Fung and Kang (2005), Tang et al. (2007), Vijian and Arunachalam (2006), Yang (2007) as well as Zhang et al. (2007), etc. Therefore, this study applied a Taguchi L9 (34 ) orthogonal array to plan the experiments on turning operations. Four controlling factors including the cutting speed, the feed rate, the depth of cut, and the cutting fluid mixture ratios with three levels for each factor were selected. The Grey relational analysis is then applied to examine how the turning operation factors influence the quality targets of roughness average, roughness maximum and roundness. An optimal parameter combination was then obtained. Through analyzing the Grey relational grade matrix, the most influen-
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tial factors for individual quality targets of turning operations can be identified. Additionally, the ANOVA was also utilized to examine the most significant factors for the turning process as the roughness average, roughness maximum and roundness are simultaneously considered.
2.2. Grey relational coefficients and Grey relational grades
2.
Grey relational analysis
x0∗ (k), xi∗ (k) =
2.1.
Data preprocessing
(1)
(O)
(O)
(2)
(O)
max . xi (k) − min . xi (k)
However, if there is “a specific target value”, then the original sequence is normalized using,
xi∗ (k) = 1 −
max .
(O) xi (k) − OB (O)
(O)
max . xi (k) − OB, OB − min . xi (k)
(3) where OB is the target value. Alternatively, the original sequence can be normalized using the simplest methodology that is the values of the original sequence can be divided by the first value of the sequence, (O) xi (1). (O)
xi∗ (k) =
xi (k)
(4)
(O)
xi (1) (O)
where xi (k) is the original sequence, xi∗ (k) the sequence after (O)
(O)
the data preprocessing, max . xi (k) the largest value of xi (k), (O)
(5)
where oi (k) is the deviation sequence of reference sequence x0∗ (k) and comparability sequence xi∗ (k), namely,
0i (k) = x0∗ (k) − xi∗ (k),
max . =
(O)
min . xi (k): the smallest value of xi (k).
max . max . ∗ x0 (k) − xj∗ (k), ∀j ∈ i ∀k
min . min . ∗ x0 (k) − xj∗ (k), is the distinguishing ∀j ∈ i ∀k coefficient, ∈ [0,1] A Grey relational grade is a weighted sum of the Grey relational coefficients, and is defined as follows. min . =
x0∗ , xi∗ =
n
ˇk x0∗ (k), xi∗ (k)
k=1
ˇk = 1
(6)
k=1
max . xi (k) − xi (k) (O)
min . + max . 0i (k) + max .
0 < x0∗ (k), xi∗ (k) 1
n
(O) (O) xi (k) − min . xi (k) (O) (O) max . xi (k) − min . xi (k)
If the purpose is “the-smaller-the-better”, then the original sequence is normalized as follows
xi∗ (k) =
Grey data processing must be performed before Grey correlation coefficients can be calculated. A series of various units must be transformed to be dimensionless. Usually, each series is normalized by dividing the data in the original series by their average. Let the original reference sequence and sequence for comparison be represented as xo (k) and xi (k), i = 1, 2, . . ., m; k = 1, 2, . . ., n, respectively, where m is the total number of experiment to be considered, and n is the total number of observation data. Data preprocessing converts the original sequence to a comparable sequence. Several methodologies of preprocessing data can be used in Grey relation analysis, depending on the characteristics of the original sequence (Deng, 1989; Gau et al., 2006; You et al., 2007). If the target value of the original sequence is “the-larger-the-better”, then the original sequence is normalized as follows
xi∗ (k) =
Following the data preprocessing, a Grey relational coefficient can be calculated using the preprocessed sequences. The Grey relational coefficient is defined as follows.
Here, the Grey relational grade x0∗ , xi∗ represents the level of correlation between the reference and comparability sequences. If the two sequences are identical, then the value of the Grey relational grade equals to one. The Grey relational grade also indicates the degree of influence exerted by the comparability sequence on the reference sequence. Consequently, if a particular comparability sequence is more important to the reference sequence than other comparability sequences, the Grey relational grade for that comparability sequence and the reference sequence will exceed that for other Grey relational grades. The Grey relational analysis is actually a measurement of the absolute value of data difference between the sequences, and can be used to approximate the correlation between the sequences.
3.
Experimental procedures and test results
3.1.
Materials
SKD 11 is a high carbon high chromium alloy tool steel used in the production of dies, plastic injection molding dies, precision gauge, spindle, jigs and fixtures, etc. The composition of the SKD11 is 1.55 wt.% C–11.5 wt.% Cr–0.70 wt.% Mo–1.00 wt.% V–0.30 wt.% Mn–0.25 wt.% Si. The yielding stress of raw SKD11 is 330 MPa, the Young’s modulus is 200 GPa and hardness is 25 HRC. In this study, in order to properly control the depth of cut, the diameter of the workpieces has been fixed to 20 mm for bright steel bars.
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Table 1 – Experimental factors and factor levels Levels of experimental factors
Experimental control factors A/cutting speed (m/min)
1 2 3
3.2.
B/feed rate (mm/rev)
125 155 185
Schematic of machining
In this study, the experiments were carried out on a rigid CNC turning center with a 7.5 kW spindle motor at 4200 rpm (machine type of Vtum||–20, manufactured by VICTOR Taichung Machinery Works Co. in Taiwan). Fig. 1 shows the turning operation and the cutting length of workpiece is 40 mm. At the same time, the cutter tool is made of carbide and coated with titanium nitride (TiN) manufactured by Sumitomo Electric Industries, Ltd., Japan with a part number of TNMG160408-UG. Furthermore, the cutting speed (m/min), the feed rate (mm/rev), the depth of cut (mm) and the cutting fluids mixture ratio (%) are regulated in this experiment of turning operations.
3.3.
Experimental parameters and design
The effects of turning parameters on the surface roughness have been studied by Aslan et al. (2007), Davim (2003), Manna and Bhattacharyya (2004), Nalbant et al. (2007), Yang and Tarng (1998), and so on. In this study, further processing procedure for the roundness is investigated. Furthermore, an effect of turning parameters of cutting fluids under different mixture ratios was also considered. Therefore, the experiment is conducted with four controllable 3-level factors and three response variables. Nine experimental runs based on the orthogonal array L9 (34 ) are required. Table 1 presents four controlled factors of the cutting speed (i.e., A (m/min)), the feed rate (i.e., B (mm/rev)), the depth of cut (i.e., C (mm)), and the cutting fluid mixture ratios (i.e., D (%)) with three levels for each factor. Table 2 shows the nine cutting experimental runs according to the selected orthogonal table. Additionally, the water-soluble cutting fluids are mixed the water with differ-
C/cut depth (mm)
0.12 0.16 0.20
D/cutting fluid ratio (%)
0.50 0.65 0.80
4 8 12
ent ratios of synthetic oil (supplied by L & W international Co., USA). After turning, three quality objectives of the workpieces are chosen, including the roughness average (i.e., Ra (m)), roughness maximum (i.e., Rt (m)), and roundness (i.e., (m)). Typically, small values of roughness average, roughness maximum and roundness are desirable for the turning operations.
3.4.
Measuring apparatus
The roughness average (Ra) and roughness maximum (Rt) of surface after the turning process were measured by a surface analyzer of Form Talysurf 50 (Taylor Hobson Ltd., UK) and Form Talyrond 250 for the roundness () of circumference surface.
4.
Results and discussion
4.1.
Best experimental run
The experimental results for the Ra, the Rt and the are listed in Table 2. Typically, smaller values of the Ra, the Rt and the are desirable. Thus, the data sequences have a
Table 2 – Orthogonal array L9 (34 ) of the experimental runs and results Run no.
A
B
C
D
Ra (m)
Rt (m)
(m)
1 2 3 4 5 6 7 8 9
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1
3.2678 1.9245 1.7922 1.1112 1.7788 2.7283 1.0362 2.8740 3.9058
28.7636 15.9150 11.0371 6.6256 7.8608 10.8438 5.6975 11.1939 15.7113
4.70 2.90 1.90 0.85 1.10 1.95 0.75 2.10 2.55
Table 3 – The sequences after data preprocessing Comparability sequence
No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9
Fig. 1 – Scheme of turning operation.
Reference sequence Ra 1.0000
Rt 1.0000
1.0000
0.7777 0.3096 0.2635 0.0261 0.2588 0.5897 0.0000 0.6404 1.0000
1.0000 0.4430 0.2315 0.0402 0.0938 0.2231 0.0000 0.2383 0.4341
1.0000 0.5443 0.2911 0.0253 0.0886 0.3038 0.0000 0.3418 0.4557
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Table 4 – The calculated Grey relational coefficient and Grey relational grade for nine comparability sequences Orthogonal array L9 (34 )
Experimental run (comparability sequences) 1 2 3 4 5 6 7 8 9
A
B
C
D
Ra
Rt
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1
0.3913 0.6176 0.6549 0.9503 0.6590 0.4589 1.0000 0.4384 0.3333
0.3333 0.5302 0.6835 0.9255 0.8421 0.6915 1.0000 0.6772 0.5353
1 2 3
Factors A
B
C
D
0.5172 0.7723 0.6779
0.7651 0.6319 0.5705
0.5044 0.6496 0.8134
0.5334 0.7110 0.7231
Grey relational grade
0.3333 0.4788 0.6320 0.9518 0.8495 0.6220 1.0000 0.5940 0.5232
0.3527 0.5422 0.6568 0.9426 0.7835 0.5908 1.0000 0.5699 0.4639
provide the largest average response. In Table 5, the combination of A2 , B1 , C3 , and D3 shows the largest value of the Grey relational grade for the factors A, B, C, and D, respectively. Therefore, A2 B1 C3 D3 with a cutting speed of 155 m/min, a feed rate of 0.12 mm/rev, a depth of cut of 0.8 mm, and cutting fluid ratio of 12% is the optimal parameter combination of the turning operations.
Table 5 – The response table for Grey relational Levels
Grey relational coefficient
the-smaller-the-better characteristic, the “smaller-the-better” methodology, i.e. Eq. (2), was employed for data preprocessing. The values of the Ra, the Rt and are set to be the reference (O) sequence x0 (k), k = 1–3. Moreover, the results of nine experi-
4.2.
Most influential factor
In this study, the Grey relational analysis is applied to examine how the turning operation parameters influence the quality targets of workpieces. The values of the factor level in nine experimental runs are set to the comparability sequences for four controllable factors. Table 6 listed all of the sequences. Data preprocessing was performed based on Eq. (4), and Table 6 listed the normalized results. Subsequently, the deviation sequences were calculated using the method mentioned above. The deviation sequences and the distinguishing coefficient then were substituted into Eq. (5) to obtain the Grey relational coefficients. Additionally, the Grey relational coefficients are averaged using an equal weighting to obtain the Grey relational grade. Table 7 listed the Grey relational coefficients and the grade of the Ra of the reference sequence and comparability sequences. Table 8 gives the Grey relational coefficients and the grade of the Rt for the reference sequence and the comparability sequences. Similarly, Table 9 shows the Grey relational coefficients and the grade of the for the reference sequence and the comparability sequences.
(0)
ments were the comparability sequences xi (k), i = 1, 2, . . ., 9, k = 1–3 Table 3 listed all of the sequences after implementing the data preprocessing using Eq. (2). The reference and the comparability sequences were denoted as x0∗ (k) and xi∗ (k), respectively. Also, the deviation sequences 0i , max.(k) and min.(k) for i = 1–9, k = 1–3 can be calculated. The distinguishing coefficient can be substituted for the Grey relational coefficient in Eq. (5). If all the process parameters have equal weighting, is set to be 0.5. Table 4 listed the Grey relational coefficients and the grade for all nine comparability sequences. This investigation employs the response table of the Taguchi method to calculate the average Grey relational grades for each factor level, as illustrated in Table 5. Since the Grey relational grades represented the level of correlation between the reference and the comparability sequences, the larger Grey relational grade means the comparability sequence exhibiting a stronger correlation with the reference sequence. Based on this study, one can select a combination of the levels that
Table 6 – The sequences after data preprocessing for the reference sequences and comparability sequences Exp. run
1 2 3 4 5 6 7 8 9
Comparability sequences
Reference sequences
A
B
C
D
Ra
Rt
1 1 1 1.24 1.24 1.24 1.48 1.48 1.48
1 1.33 1.67 1 1.33 1.67 1 1.33 1.67
1 1.33 1.67 1.33 1.67 1 1.67 1 1.33
1 2 3 3 1 2 2 3 1
0.5889 0.5484 0.3400 0.5443 0.8349 0.3171 0.8795 1.1952 0.5889
0.5533 0.3837 0.2303 0.2733 0.377 0.1981 0.3892 0.5462 0.5533
0.6170 0.4043 0.1809 0.2340 0.4149 0.1596 0.4468 0.5426 0.6170
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Table 7 – The calculated Grey relational coefficient and Grey relational grade for experimental factors to experimental result of the Ra
Table 9 – The calculated Grey relational coefficient and Grey relational grade for experimental factors to experimental result of the
A
A
B
C
D
Grey relational coefficient 1.0000 1.0000 0.7742 0.6544 0.7574 0.5576 0.6103 0.6811 0.6696 0.6411 0.7768 0.6289 0.5479 0.6736 0.7013 0.7564 0.8319 0.7494
1.0000 0.6647 0.5727 0.5949 0.5718 0.8952 0.5235 0.9212 0.9308
1.0000 0.4997 0.3651 0.3464 0.7557 0.5475 0.4558 0.3993 0.8783
Grey relational grade 0.7410 0.7047
0.7416
0.5831
Table 8 – The calculated Grey relational coefficient and Grey relational grade for experimental factors to experimental result of the Rt A
B
C
D
Grey relational coefficient 1.0000 1.0000 0.7594 0.6438 0.6958 0.5235 0.5827 0.6468 0.5932 0.5708 0.6203 0.5222 0.5237 0.6374 0.5637 0.5989 0.6015 0.5571
1.0000 0.6537 0.5368 0.5686 0.5151 0.6935 0.5014 0.6977 0.6516
1.0000 0.4935 0.3501 0.3373 0.6598 0.4648 0.4389 0.3506 0.7565
Grey relational grade 0.6600 0.6334
0.6465
0.5391
The Grey relational grades in Tables 7–9 can be further arranged in a matrix form shown as follows:
⎡
⎤
(Ra, A) (Ra, B) (Ra, C) (Ra, D) = ⎣ (Rt, A) (Rt, B) (Rt, C) (Rt, D) ⎦ (, A) (, B) (, C) (, D)
⎡
⎤
0.7410 0.7047 0.7416 0.5831 = ⎣ 0.6600 0.6334 0.6465 0.5391 ⎦ 0.6632 0.6346 0.6500 0.5392
(7)
By comparing Row 1, Row 2 and Row 3, some conclusion can be drawn from this matrix. In the first row, (Ra, C) > (Ra, A) > (Ra, B) > (Ra, D), it means that the order of importance
B
C
D
Grey relational coefficient 1.0000 1.0000 0.7864 0.6631 0.7029 0.5275 0.5710 0.6325 0.5835 0.5618 0.6308 0.5296 0.5163 0.6265 0.5770 0.6139 0.6006 0.5563
1.0000 0.6736 0.5410 0.5574 0.5079 0.7067 0.4946 0.7182 0.6505
1.0000 0.5048 0.3519 0.3333 0.6479 0.4707 0.4337 0.3557 0.7550
Grey relational grade 0.6632 0.6346
0.6500
0.5392
for the controllable factors to the Ra, in sequence, is the factor C, A, B, and D. From the second row, (Rt, A) > (Rt, C) > (Rt, B) > (Rt, D), the order of importance for the controllable factors to the Rt, in sequence, is the factor A, C, B, and D. Similarly, based on the third row, (, A) > (, C) > (, B) > (, D), the order of importance for the controllable factors to the , in sequence, is the factor A, C, B, and D. Additionally, in the matrix, it also shows that the sequences for the (Rt) and the () are similar. The most influential factors that affect the output variables are determined by identifying the maximum values in each row. Hence, base on the maximum values in the matrix of the Grey relational ((Ra, C),(Rt, A),(, A)) = (0.7416, 0.6600, 0.6632), it can be found that the factor C, the depth of cut, has the most influence on the Ra with value of 0.7416. The factor A, the cutting speed, is the most influential factor to the Rt and the with values of 0.6600 and 0.6632, respectively. Additionally, Table 10 gives the results of the analysis of variance (ANOVA) for the Ra, the Rt, and the using the calculated values from the Grey relational grade of Table 4 and the response table of Table 5. According to Table 10, the factor C, the depth of cut with 38.73% of contribution, is the most significant controlled parameters for the turning operation; the cutting speed is with 29.95% contribution, the cutting fluid mixture ratios with 18.27%, and the feed rate with 16.04% of contribution if the minimization of the roughness average, roughness maximum and roundness are simultaneously considered.
Table 10 – ANOVA results for Ra, Rt, and Factor
Level 1
Level 2
Level 3
Degree of freedom
A B C D Error
0.5172 0.7651 0.5044 0.5334
0.7723 0.6319 0.6496 0.7110
0.6779 0.5705 0.8134 0.7231
2 2 2 2 0 8
Total
Mean square
F value
SS
Contribution (%)
0.0998 0.0594 0.1434 0.0677 0.0000
0.0499 0.0297 0.0717 0.0338
0.0499 0.0297 0.0717 0.0338
0.0998 0.0594 0.1434 0.0677
26.96 16.04 38.73 18.27
0.3702
0.0463
0.3702
100.00
Sum of squares
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2753–2759
4.3.
Confirmation test
After identifying the most influential parameters, the final phase is to verify the Ra, Rt, and the by conducting the confirmation experiments. The A2 B1 C3 D3 is an optimal parameter combination of the turning process via the Grey relational analysis. Therefore, the condition A2 B1 C3 D3 of the optimal parameter combination of the turning process was treated as a confirmation test. If the optimal setting with a cutting speed of 155 m/min, 0.12 mm/rev of the feed rate, a cut depth of 0.8 mm, and a cutting fluid ratio of 12% is used, the final workpiece gives the roughness average (i.e., Ra) of 1.0280 m, the roughness maximum (i.e., Rt) of 4.5302 m, and the roundness (i.e., ) of 0.74 m. In summary, the result of the confirmation test is better than the experiments in Table 2.
5.
Conclusions
The Grey relational analysis based on an orthogonal array of the Taguchi method was a way of optimizing the turning operations for SKD11. The analytical results are summarized as follows: 1. From the response table of the average Grey relational grade, it is found that the largest value of the Grey relational grade for the cutting speed of 155 m/min, the feed rate of 0.12 mm/rev, and the depth of cutting of 0.8 mm, and the cutting fluid ratio of 12%. It is the recommended levels of the controllable parameters of the turning operations as the minimization of the roughness average, roughness maximum and roundness are simultaneously considered. 2. The order of the importance for the controllable factors to the roughness average, in sequence, is the depth of cut, the cutting speed, the feed rate, and the cutting fluid mixture ratios. The order to the roughness maximum, in sequence, is the cutting speed, the depth of cutting, the feed rate, and the cutting fluid mixture ratios. Similarly, the order to the roundness, in sequence, is the cutting speed, the depth of cutting, the feed rate, and the cutting fluid mixture ratios. 3. Through ANOVA, the percentage of contribution to the turning process, in sequence, is the depth of cut, the cutting speed, the cutting fluid mixture ratios, and the feed rate. Hence, the depth of cut is the most significant controlled factor for the turning operation when the minimization of the roughness average, the roughness maximum and the roundness are simultaneously considered.
Acknowledgments The authors would like to thank the National Science Council of the Republic of China, for financially supporting this research (Contract No. NSC95-2622-E-159-001-CC3).
references
Aslan, E., Camuscu, N., Birgoren, B., 2007. Design optimization of cutting parameters when turning hardened AISI 4140 steel (63 HRC) with Al2 O3 + TiCN mixed ceramic tool. Mater. Des. 28, 1618–1622.
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Chen, D.C., Chen, C.F., 2007. Use of Taguchi method to study a robust design for the sectioned beams curvature during rolling. J. Mater. Process. Technol. 190, 130–137. Chiang, K.T., Chang, F.P., 2006. Optimization of the WEDM process of particle-reinforced material with multiple performance characteristics using Grey relational analysis. J. Mater. Process. Technol. 108, 96–101. Davim, J.P., 2003. Design of optimization of cutting parameters for turning metal matrix composites based on the orthogonal arrays. J. Mater. Process. Technol. 132, 340–344. Deng, J.L., 1989. Introduction to Grey system theory. J. Grey Syst. 1, 1–24. EI Baradie, M.A., 1996. Cutting fluids: part I characterization. J. Mater. Process. Technol. 56, 786–797. Fung, C.P., Kang, P.C., 2005. Multi-response optimization in friction properties of PBT composites using Taguchi method and principle component analysis. J. Mater. Process. Technol. 170, 602–610. Fung, C.P., Huang, C.H., Doong, J.L., 2003. The study on the optimization of injection molding process parameters with Gray relational analysis. J. Reinf. Plast. Comp. 22, 51–66. Gau, H.S., Hsieh, C.Y., Liu, C.W., 2006. Application of Grey correlation method to evaluate potential groundwater recharge sites. Stoch. Environ. Res. Risk Assess. 20, 407–421. Huang, J.T., Lin, J.L., 2002. Optimization of machining parameters setting of die-sinking EDM process based on the Grey relational analysis with L18 orthogonal array. J. Technol. 17, 659–664. Kalpakjian, S., Schmid, S.R., 2001. Manufacturing Engineering and Technology, International, Fourth ed. Prentice Hall Co., New Jersey, pp. 536–681. Lin, C.L., 2004. Use of the Taguchi method and Grey relational analysis to optimize turning operations with multiple performance characteristics. Mater. Manuf. Process. 19 (2), 209–220. Manna, A., Bhattacharyya, B., 2004. investigation for optimal parametric combination for achieving better surface finish during turning of Al/SiC-MMC. Int. J. Adv. Manuf. Technol. 23, 658–665. Nalbant, M., Gokkaya, H., Sur, G., 2007. Application of Taguchi method in the optimization of cutting parameters for surface roughness in turning. Mater. Des. 28, 1379–1385. Shen, Y.K., Chien, H.W., Lin, Y., 2004. Optimization of the micro-injection molding process using Grey relational analysis and MoldFlow analysis. J. Reinf. Plast. Comp. 23, 1799–1814. Tang, S.H., Tan, V.J., Sapuan, S.M., Sulaiman, S., Ismail, N., Samin, R., 2007. The use of Taguchi method in the design of plastic injection mould for reducing warpage. J. Mater. Process. Technol. 182, 418–426. Vijian, P., Arunachalam, V.P., 2006. Optimization of squeeze cast parameters of LM6 aluminium alloy for surface roughness using Taguchi method. J. Mater. Process. Technol. 180, 161–166. Yang, L.J., 2007. The effect of specimen thickness on the hardness of plasma surface hardened ASSAB 760 steel specimens. J. Mater. Process. Technol. 185, 113–119. Yang, W.H., Tarng, Y.S., 1998. Design optimization of cutting parameters for turning operations based on the Taguchi method. J. Mater. Process Technol. 84, 122–129. Yang, Y.K., Shie, J.R., Huang, C.H., 2006. Optimization of dry machining parameters for high-purity graphite in end milling process. Mater. Manuf. Process. 21 (8), 832–837. You, M.L., Wang, C.W., Yeh, C.K., 2007. The development of completed Grey relational analysis toolbox via Matlab. J. Grey Syst. 9 (1), 57–64. Zhang, J.Z., Chen, J.C., Kirby, E.D., 2007. Surface roughness optimization in a end-milling operation using the Taguchi design method. J. Mater. Process. Technol. 184, 233–239.
journal homepage: www.elsevier.com/locate/jmatprotec
Review
Optimization of turning operations with multiple performance characteristics using the Taguchi method and Grey relational analysis Chorng-Jyh Tzeng a , Yu-Hsin Lin b , Yung-Kuang Yang a,∗ , Ming-Chang Jeng c a
Department of Mechanical Engineering, Minghsin University of Science and Technology, 1 Hsin Hsing Road, Hsin Feng, 304 Hsinchu, Taiwan b Department of Industrial Engineering and Management, Minghsin University of Science and Technology, 1 Hsin Hsing Road, Hsin Feng, 304 Hsinchu, Taiwan c Department of Mechanical Engineering, National Central University, Chung-Li 32054, Taiwan
a r t i c l e
i n f o
a b s t r a c t
Article history:
This study investigated the optimization of CNC turning operation parameters for SKD11 (JIS)
Received 12 June 2007
using the Grey relational analysis method. Nine experimental runs based on an orthogonal
Received in revised form 9 June 2008
array of Taguchi method were performed. The surface properties of roughness average and
Accepted 21 June 2008
roughness maximum as well as the roundness were selected as the quality targets. An optimal parameter combination of the turning operation was obtained via Grey relational analysis. By analyzing the Grey relational grade matrix, the degree of influence for each
Keywords:
controllable process factor onto individual quality targets can be found. The depth of cut
Grey relational analysis
was identified to be the most influence on the roughness average and the cutting speed
Optimization
is the most influential factor to the roughness maximum and the roundness. Additionally,
CNC turning
the analysis of variance (ANOVA) is also applied to identify the most significant factor; the
SKD 11
depth of cut is the most significant controlled factors for the turning operations according
ANOVA
to the weighted sum grade of the roughness average, roughness maximum and roundness. © 2008 Elsevier B.V. All rights reserved.
Contents 1. 2.
3.
∗
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grey relational analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Data preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Grey relational coefficients and Grey relational grades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental procedures and test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Schematic of machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Experimental parameters and design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Corresponding author. Tel.: +886 3 5593142x3001; fax: +886 3 5782822. E-mail address: [email protected] (Y.-K. Yang). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.06.046
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4.
5.
1.
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3.4. Measuring apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Best experimental run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Most influential factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Confirmation test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction
In modern industry the goal is to manufacture low cost, high quality products in short time. Automated and flexible manufacturing systems are employed for that purpose along with computerized numerical control (CNC) machines that are capable of achieving high accuracy and very low processing time. Turning is the most common method for cutting and especially for the finishing machined parts. Furthermore, in order to produce any product with desired quality by machining, cutting parameters should be selected properly. In turning process parameters such as cutting tool geometry and materials, the depth of cut, feed rates, cutting speeds as well as the use of cutting fluids will impact the material removal rates and the machining qualities like the surface roughness, the roundness of circular and dimensional deviations of the product (Kalpakjian and Schmid, 2001). Surface roughness of cutting process has been studied intensively, mostly through experiments. Yang and Tarng (1998) employed Taguchi method to investigate the cutting characteristics of S45C steel bars using tungsten carbide cutting tools. The optimal cutting parameters of the cutting speed, the feed rate and the depth of cut for turning operations with regard to performance indexes such as tool life and surface roughness are considered. Davim (2003) investigated the influence of cutting conditions (cutting velocity and feed) and cutting time on turning metal matrix composites. An orthogonal array and the analysis of variance are employed to investigate the cutting characteristics of flank wear (VB), power required (Pm) and surface roughness (Ra). Manna and Bhattacharyya (2004) took the significant cutting parameters into consideration and used multiple linear regression mathematical models relating the surface roughness height Ra and Rt to the cutting parameters for turning process of Al/SiC-MMC. Aslan et al. (2007) used an orthogonal array and the analysis of variance (ANOVA) to optimization of cutting parameters in turning hardened AISI 4140 steel (63 HRC) with Al2 O3 + TiCN mixed ceramic tool. The flank wear (VB) and surface roughness (Ra) had investigated a process optimization to determine optimal values of cutting parameters, such as cutting speed, feed rate and depth of cut. Nalbant et al. (2007) used Taguchi method to find the optimal cutting parameters for surface roughness in turning operations of AISI 1030 steel bars using TiN coated tools. Three cutting parameters, namely, insert radius, feed rate, and depth of cut, are optimized with considerations of surface roughness, and so on. However, very few studies have been conducted to investigate roundness under different turning parameter. Additionally, cutting fluids properly applied (Kalpakjian and Schmid, 2001; EI Baradie, 1996), can increase productivity and reduce costs by choosing higher
2756 2756 2756 2757 2759 2759 2759 2759
cutting speeds, higher feed rates and greater depths of cut. Effective application of cutting fluids can also increase tool life, decrease surface roughness, increase dimensional accuracy and decrease the amount of power consumed. The watersoluble (Water-miscible) cutting fluids are primarily used for high speed machining operations because they have better cooling capabilities (EI Baradie, 1996). There fluids are also best for cooling machined parts to minimize thermal distortions. Water-soluble cutting fluids are mixed with water at different ratios depending on the machining operation. Therefore, the effect of water-soluble cutting fluids under different ratios was also considered in this study. Recently, Deng (1989) proposed a Grey relational analysis. The Grey relational analysis is a method for measuring the degree of approximation among the sequences using a Grey relational grade. Theories of the Grey relational analysis have attracted considerable interest among researchers. Some other researchers have also examined the optimization of process parameters. For example, Huang and Lin (2002) applied the Grey relational analysis to design the die-sinking EDM machining parameters. Fung et al. (2003) studied the Grey relational analysis to obtain the optimal parameters of the injection molding process for mechanical properties of yield stress and elongation in polycarbonate/acrylonitrilebutadiene-styrene (PC/ABS) composites. Shen et al. (2004) studied different polymers (such as PP, PC, PS, POM) with various process parameters of the microgear. The simulation used the Taguchi method and the Grey relational analysis were provided. Lin (2004) employed the Taguchi method and the Grey relational analysis to optimize the turning operations with multiple performance characteristics. Chiang and Chang (2006) used the Grey relational analysis to optimize of the wire electric discharge machining process of particle-reinforced material with multiple performance characteristics. Yang et al. (2006) also applied the Taguchi method and the Grey relational analysis to optimize the dry machining parameters for high-purity graphite in end milling process, etc. Planning the experiments through the Taguchi orthogonal array has been used quite successfully in process optimization by Chen and Chen (2007), Fung and Kang (2005), Tang et al. (2007), Vijian and Arunachalam (2006), Yang (2007) as well as Zhang et al. (2007), etc. Therefore, this study applied a Taguchi L9 (34 ) orthogonal array to plan the experiments on turning operations. Four controlling factors including the cutting speed, the feed rate, the depth of cut, and the cutting fluid mixture ratios with three levels for each factor were selected. The Grey relational analysis is then applied to examine how the turning operation factors influence the quality targets of roughness average, roughness maximum and roundness. An optimal parameter combination was then obtained. Through analyzing the Grey relational grade matrix, the most influen-
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tial factors for individual quality targets of turning operations can be identified. Additionally, the ANOVA was also utilized to examine the most significant factors for the turning process as the roughness average, roughness maximum and roundness are simultaneously considered.
2.2. Grey relational coefficients and Grey relational grades
2.
Grey relational analysis
x0∗ (k), xi∗ (k) =
2.1.
Data preprocessing
(1)
(O)
(O)
(2)
(O)
max . xi (k) − min . xi (k)
However, if there is “a specific target value”, then the original sequence is normalized using,
xi∗ (k) = 1 −
max .
(O) xi (k) − OB (O)
(O)
max . xi (k) − OB, OB − min . xi (k)
(3) where OB is the target value. Alternatively, the original sequence can be normalized using the simplest methodology that is the values of the original sequence can be divided by the first value of the sequence, (O) xi (1). (O)
xi∗ (k) =
xi (k)
(4)
(O)
xi (1) (O)
where xi (k) is the original sequence, xi∗ (k) the sequence after (O)
(O)
the data preprocessing, max . xi (k) the largest value of xi (k), (O)
(5)
where oi (k) is the deviation sequence of reference sequence x0∗ (k) and comparability sequence xi∗ (k), namely,
0i (k) = x0∗ (k) − xi∗ (k),
max . =
(O)
min . xi (k): the smallest value of xi (k).
max . max . ∗ x0 (k) − xj∗ (k), ∀j ∈ i ∀k
min . min . ∗ x0 (k) − xj∗ (k), is the distinguishing ∀j ∈ i ∀k coefficient, ∈ [0,1] A Grey relational grade is a weighted sum of the Grey relational coefficients, and is defined as follows. min . =
x0∗ , xi∗ =
n
ˇk x0∗ (k), xi∗ (k)
k=1
ˇk = 1
(6)
k=1
max . xi (k) − xi (k) (O)
min . + max . 0i (k) + max .
0 < x0∗ (k), xi∗ (k) 1
n
(O) (O) xi (k) − min . xi (k) (O) (O) max . xi (k) − min . xi (k)
If the purpose is “the-smaller-the-better”, then the original sequence is normalized as follows
xi∗ (k) =
Grey data processing must be performed before Grey correlation coefficients can be calculated. A series of various units must be transformed to be dimensionless. Usually, each series is normalized by dividing the data in the original series by their average. Let the original reference sequence and sequence for comparison be represented as xo (k) and xi (k), i = 1, 2, . . ., m; k = 1, 2, . . ., n, respectively, where m is the total number of experiment to be considered, and n is the total number of observation data. Data preprocessing converts the original sequence to a comparable sequence. Several methodologies of preprocessing data can be used in Grey relation analysis, depending on the characteristics of the original sequence (Deng, 1989; Gau et al., 2006; You et al., 2007). If the target value of the original sequence is “the-larger-the-better”, then the original sequence is normalized as follows
xi∗ (k) =
Following the data preprocessing, a Grey relational coefficient can be calculated using the preprocessed sequences. The Grey relational coefficient is defined as follows.
Here, the Grey relational grade x0∗ , xi∗ represents the level of correlation between the reference and comparability sequences. If the two sequences are identical, then the value of the Grey relational grade equals to one. The Grey relational grade also indicates the degree of influence exerted by the comparability sequence on the reference sequence. Consequently, if a particular comparability sequence is more important to the reference sequence than other comparability sequences, the Grey relational grade for that comparability sequence and the reference sequence will exceed that for other Grey relational grades. The Grey relational analysis is actually a measurement of the absolute value of data difference between the sequences, and can be used to approximate the correlation between the sequences.
3.
Experimental procedures and test results
3.1.
Materials
SKD 11 is a high carbon high chromium alloy tool steel used in the production of dies, plastic injection molding dies, precision gauge, spindle, jigs and fixtures, etc. The composition of the SKD11 is 1.55 wt.% C–11.5 wt.% Cr–0.70 wt.% Mo–1.00 wt.% V–0.30 wt.% Mn–0.25 wt.% Si. The yielding stress of raw SKD11 is 330 MPa, the Young’s modulus is 200 GPa and hardness is 25 HRC. In this study, in order to properly control the depth of cut, the diameter of the workpieces has been fixed to 20 mm for bright steel bars.
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Table 1 – Experimental factors and factor levels Levels of experimental factors
Experimental control factors A/cutting speed (m/min)
1 2 3
3.2.
B/feed rate (mm/rev)
125 155 185
Schematic of machining
In this study, the experiments were carried out on a rigid CNC turning center with a 7.5 kW spindle motor at 4200 rpm (machine type of Vtum||–20, manufactured by VICTOR Taichung Machinery Works Co. in Taiwan). Fig. 1 shows the turning operation and the cutting length of workpiece is 40 mm. At the same time, the cutter tool is made of carbide and coated with titanium nitride (TiN) manufactured by Sumitomo Electric Industries, Ltd., Japan with a part number of TNMG160408-UG. Furthermore, the cutting speed (m/min), the feed rate (mm/rev), the depth of cut (mm) and the cutting fluids mixture ratio (%) are regulated in this experiment of turning operations.
3.3.
Experimental parameters and design
The effects of turning parameters on the surface roughness have been studied by Aslan et al. (2007), Davim (2003), Manna and Bhattacharyya (2004), Nalbant et al. (2007), Yang and Tarng (1998), and so on. In this study, further processing procedure for the roundness is investigated. Furthermore, an effect of turning parameters of cutting fluids under different mixture ratios was also considered. Therefore, the experiment is conducted with four controllable 3-level factors and three response variables. Nine experimental runs based on the orthogonal array L9 (34 ) are required. Table 1 presents four controlled factors of the cutting speed (i.e., A (m/min)), the feed rate (i.e., B (mm/rev)), the depth of cut (i.e., C (mm)), and the cutting fluid mixture ratios (i.e., D (%)) with three levels for each factor. Table 2 shows the nine cutting experimental runs according to the selected orthogonal table. Additionally, the water-soluble cutting fluids are mixed the water with differ-
C/cut depth (mm)
0.12 0.16 0.20
D/cutting fluid ratio (%)
0.50 0.65 0.80
4 8 12
ent ratios of synthetic oil (supplied by L & W international Co., USA). After turning, three quality objectives of the workpieces are chosen, including the roughness average (i.e., Ra (m)), roughness maximum (i.e., Rt (m)), and roundness (i.e., (m)). Typically, small values of roughness average, roughness maximum and roundness are desirable for the turning operations.
3.4.
Measuring apparatus
The roughness average (Ra) and roughness maximum (Rt) of surface after the turning process were measured by a surface analyzer of Form Talysurf 50 (Taylor Hobson Ltd., UK) and Form Talyrond 250 for the roundness () of circumference surface.
4.
Results and discussion
4.1.
Best experimental run
The experimental results for the Ra, the Rt and the are listed in Table 2. Typically, smaller values of the Ra, the Rt and the are desirable. Thus, the data sequences have a
Table 2 – Orthogonal array L9 (34 ) of the experimental runs and results Run no.
A
B
C
D
Ra (m)
Rt (m)
(m)
1 2 3 4 5 6 7 8 9
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1
3.2678 1.9245 1.7922 1.1112 1.7788 2.7283 1.0362 2.8740 3.9058
28.7636 15.9150 11.0371 6.6256 7.8608 10.8438 5.6975 11.1939 15.7113
4.70 2.90 1.90 0.85 1.10 1.95 0.75 2.10 2.55
Table 3 – The sequences after data preprocessing Comparability sequence
No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9
Fig. 1 – Scheme of turning operation.
Reference sequence Ra 1.0000
Rt 1.0000
1.0000
0.7777 0.3096 0.2635 0.0261 0.2588 0.5897 0.0000 0.6404 1.0000
1.0000 0.4430 0.2315 0.0402 0.0938 0.2231 0.0000 0.2383 0.4341
1.0000 0.5443 0.2911 0.0253 0.0886 0.3038 0.0000 0.3418 0.4557
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Table 4 – The calculated Grey relational coefficient and Grey relational grade for nine comparability sequences Orthogonal array L9 (34 )
Experimental run (comparability sequences) 1 2 3 4 5 6 7 8 9
A
B
C
D
Ra
Rt
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1
0.3913 0.6176 0.6549 0.9503 0.6590 0.4589 1.0000 0.4384 0.3333
0.3333 0.5302 0.6835 0.9255 0.8421 0.6915 1.0000 0.6772 0.5353
1 2 3
Factors A
B
C
D
0.5172 0.7723 0.6779
0.7651 0.6319 0.5705
0.5044 0.6496 0.8134
0.5334 0.7110 0.7231
Grey relational grade
0.3333 0.4788 0.6320 0.9518 0.8495 0.6220 1.0000 0.5940 0.5232
0.3527 0.5422 0.6568 0.9426 0.7835 0.5908 1.0000 0.5699 0.4639
provide the largest average response. In Table 5, the combination of A2 , B1 , C3 , and D3 shows the largest value of the Grey relational grade for the factors A, B, C, and D, respectively. Therefore, A2 B1 C3 D3 with a cutting speed of 155 m/min, a feed rate of 0.12 mm/rev, a depth of cut of 0.8 mm, and cutting fluid ratio of 12% is the optimal parameter combination of the turning operations.
Table 5 – The response table for Grey relational Levels
Grey relational coefficient
the-smaller-the-better characteristic, the “smaller-the-better” methodology, i.e. Eq. (2), was employed for data preprocessing. The values of the Ra, the Rt and are set to be the reference (O) sequence x0 (k), k = 1–3. Moreover, the results of nine experi-
4.2.
Most influential factor
In this study, the Grey relational analysis is applied to examine how the turning operation parameters influence the quality targets of workpieces. The values of the factor level in nine experimental runs are set to the comparability sequences for four controllable factors. Table 6 listed all of the sequences. Data preprocessing was performed based on Eq. (4), and Table 6 listed the normalized results. Subsequently, the deviation sequences were calculated using the method mentioned above. The deviation sequences and the distinguishing coefficient then were substituted into Eq. (5) to obtain the Grey relational coefficients. Additionally, the Grey relational coefficients are averaged using an equal weighting to obtain the Grey relational grade. Table 7 listed the Grey relational coefficients and the grade of the Ra of the reference sequence and comparability sequences. Table 8 gives the Grey relational coefficients and the grade of the Rt for the reference sequence and the comparability sequences. Similarly, Table 9 shows the Grey relational coefficients and the grade of the for the reference sequence and the comparability sequences.
(0)
ments were the comparability sequences xi (k), i = 1, 2, . . ., 9, k = 1–3 Table 3 listed all of the sequences after implementing the data preprocessing using Eq. (2). The reference and the comparability sequences were denoted as x0∗ (k) and xi∗ (k), respectively. Also, the deviation sequences 0i , max.(k) and min.(k) for i = 1–9, k = 1–3 can be calculated. The distinguishing coefficient can be substituted for the Grey relational coefficient in Eq. (5). If all the process parameters have equal weighting, is set to be 0.5. Table 4 listed the Grey relational coefficients and the grade for all nine comparability sequences. This investigation employs the response table of the Taguchi method to calculate the average Grey relational grades for each factor level, as illustrated in Table 5. Since the Grey relational grades represented the level of correlation between the reference and the comparability sequences, the larger Grey relational grade means the comparability sequence exhibiting a stronger correlation with the reference sequence. Based on this study, one can select a combination of the levels that
Table 6 – The sequences after data preprocessing for the reference sequences and comparability sequences Exp. run
1 2 3 4 5 6 7 8 9
Comparability sequences
Reference sequences
A
B
C
D
Ra
Rt
1 1 1 1.24 1.24 1.24 1.48 1.48 1.48
1 1.33 1.67 1 1.33 1.67 1 1.33 1.67
1 1.33 1.67 1.33 1.67 1 1.67 1 1.33
1 2 3 3 1 2 2 3 1
0.5889 0.5484 0.3400 0.5443 0.8349 0.3171 0.8795 1.1952 0.5889
0.5533 0.3837 0.2303 0.2733 0.377 0.1981 0.3892 0.5462 0.5533
0.6170 0.4043 0.1809 0.2340 0.4149 0.1596 0.4468 0.5426 0.6170
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Table 7 – The calculated Grey relational coefficient and Grey relational grade for experimental factors to experimental result of the Ra
Table 9 – The calculated Grey relational coefficient and Grey relational grade for experimental factors to experimental result of the
A
A
B
C
D
Grey relational coefficient 1.0000 1.0000 0.7742 0.6544 0.7574 0.5576 0.6103 0.6811 0.6696 0.6411 0.7768 0.6289 0.5479 0.6736 0.7013 0.7564 0.8319 0.7494
1.0000 0.6647 0.5727 0.5949 0.5718 0.8952 0.5235 0.9212 0.9308
1.0000 0.4997 0.3651 0.3464 0.7557 0.5475 0.4558 0.3993 0.8783
Grey relational grade 0.7410 0.7047
0.7416
0.5831
Table 8 – The calculated Grey relational coefficient and Grey relational grade for experimental factors to experimental result of the Rt A
B
C
D
Grey relational coefficient 1.0000 1.0000 0.7594 0.6438 0.6958 0.5235 0.5827 0.6468 0.5932 0.5708 0.6203 0.5222 0.5237 0.6374 0.5637 0.5989 0.6015 0.5571
1.0000 0.6537 0.5368 0.5686 0.5151 0.6935 0.5014 0.6977 0.6516
1.0000 0.4935 0.3501 0.3373 0.6598 0.4648 0.4389 0.3506 0.7565
Grey relational grade 0.6600 0.6334
0.6465
0.5391
The Grey relational grades in Tables 7–9 can be further arranged in a matrix form shown as follows:
⎡
⎤
(Ra, A) (Ra, B) (Ra, C) (Ra, D) = ⎣ (Rt, A) (Rt, B) (Rt, C) (Rt, D) ⎦ (, A) (, B) (, C) (, D)
⎡
⎤
0.7410 0.7047 0.7416 0.5831 = ⎣ 0.6600 0.6334 0.6465 0.5391 ⎦ 0.6632 0.6346 0.6500 0.5392
(7)
By comparing Row 1, Row 2 and Row 3, some conclusion can be drawn from this matrix. In the first row, (Ra, C) > (Ra, A) > (Ra, B) > (Ra, D), it means that the order of importance
B
C
D
Grey relational coefficient 1.0000 1.0000 0.7864 0.6631 0.7029 0.5275 0.5710 0.6325 0.5835 0.5618 0.6308 0.5296 0.5163 0.6265 0.5770 0.6139 0.6006 0.5563
1.0000 0.6736 0.5410 0.5574 0.5079 0.7067 0.4946 0.7182 0.6505
1.0000 0.5048 0.3519 0.3333 0.6479 0.4707 0.4337 0.3557 0.7550
Grey relational grade 0.6632 0.6346
0.6500
0.5392
for the controllable factors to the Ra, in sequence, is the factor C, A, B, and D. From the second row, (Rt, A) > (Rt, C) > (Rt, B) > (Rt, D), the order of importance for the controllable factors to the Rt, in sequence, is the factor A, C, B, and D. Similarly, based on the third row, (, A) > (, C) > (, B) > (, D), the order of importance for the controllable factors to the , in sequence, is the factor A, C, B, and D. Additionally, in the matrix, it also shows that the sequences for the (Rt) and the () are similar. The most influential factors that affect the output variables are determined by identifying the maximum values in each row. Hence, base on the maximum values in the matrix of the Grey relational ((Ra, C),(Rt, A),(, A)) = (0.7416, 0.6600, 0.6632), it can be found that the factor C, the depth of cut, has the most influence on the Ra with value of 0.7416. The factor A, the cutting speed, is the most influential factor to the Rt and the with values of 0.6600 and 0.6632, respectively. Additionally, Table 10 gives the results of the analysis of variance (ANOVA) for the Ra, the Rt, and the using the calculated values from the Grey relational grade of Table 4 and the response table of Table 5. According to Table 10, the factor C, the depth of cut with 38.73% of contribution, is the most significant controlled parameters for the turning operation; the cutting speed is with 29.95% contribution, the cutting fluid mixture ratios with 18.27%, and the feed rate with 16.04% of contribution if the minimization of the roughness average, roughness maximum and roundness are simultaneously considered.
Table 10 – ANOVA results for Ra, Rt, and Factor
Level 1
Level 2
Level 3
Degree of freedom
A B C D Error
0.5172 0.7651 0.5044 0.5334
0.7723 0.6319 0.6496 0.7110
0.6779 0.5705 0.8134 0.7231
2 2 2 2 0 8
Total
Mean square
F value
SS
Contribution (%)
0.0998 0.0594 0.1434 0.0677 0.0000
0.0499 0.0297 0.0717 0.0338
0.0499 0.0297 0.0717 0.0338
0.0998 0.0594 0.1434 0.0677
26.96 16.04 38.73 18.27
0.3702
0.0463
0.3702
100.00
Sum of squares
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2753–2759
4.3.
Confirmation test
After identifying the most influential parameters, the final phase is to verify the Ra, Rt, and the by conducting the confirmation experiments. The A2 B1 C3 D3 is an optimal parameter combination of the turning process via the Grey relational analysis. Therefore, the condition A2 B1 C3 D3 of the optimal parameter combination of the turning process was treated as a confirmation test. If the optimal setting with a cutting speed of 155 m/min, 0.12 mm/rev of the feed rate, a cut depth of 0.8 mm, and a cutting fluid ratio of 12% is used, the final workpiece gives the roughness average (i.e., Ra) of 1.0280 m, the roughness maximum (i.e., Rt) of 4.5302 m, and the roundness (i.e., ) of 0.74 m. In summary, the result of the confirmation test is better than the experiments in Table 2.
5.
Conclusions
The Grey relational analysis based on an orthogonal array of the Taguchi method was a way of optimizing the turning operations for SKD11. The analytical results are summarized as follows: 1. From the response table of the average Grey relational grade, it is found that the largest value of the Grey relational grade for the cutting speed of 155 m/min, the feed rate of 0.12 mm/rev, and the depth of cutting of 0.8 mm, and the cutting fluid ratio of 12%. It is the recommended levels of the controllable parameters of the turning operations as the minimization of the roughness average, roughness maximum and roundness are simultaneously considered. 2. The order of the importance for the controllable factors to the roughness average, in sequence, is the depth of cut, the cutting speed, the feed rate, and the cutting fluid mixture ratios. The order to the roughness maximum, in sequence, is the cutting speed, the depth of cutting, the feed rate, and the cutting fluid mixture ratios. Similarly, the order to the roundness, in sequence, is the cutting speed, the depth of cutting, the feed rate, and the cutting fluid mixture ratios. 3. Through ANOVA, the percentage of contribution to the turning process, in sequence, is the depth of cut, the cutting speed, the cutting fluid mixture ratios, and the feed rate. Hence, the depth of cut is the most significant controlled factor for the turning operation when the minimization of the roughness average, the roughness maximum and the roundness are simultaneously considered.
Acknowledgments The authors would like to thank the National Science Council of the Republic of China, for financially supporting this research (Contract No. NSC95-2622-E-159-001-CC3).
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