Ren 2014

Hindawi Publishing Corporation Advances in Mechanical Engineering Article ID 721093

Research Article Optimization of Cutter Geometric Parameters in End Milling of Titanium Alloy Using the Grey-Taguchi Method Junxue Ren,1,2 Jinhua Zhou,1 and Jianwei Wei3 1

School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China The Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, P.O. Box 552, Xi’an 710072, China 3 China Gas Turbine Establishment, Chengdu 621703, China 2

Correspondence should be addressed to Junxue Ren; [email protected] Received 30 June 2014; Accepted 8 October 2014 Academic Editor: Hyung Hee Cho Copyright © Junxue Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Further progress in control of manufacturing process and performance depends on the innovativeness of machine tools after cutting parameter optimization. This paper presents a multiobjective optimization of cutter geometric parameters in end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy via Taguchi method in integration with grey relational analysis. Sixteen experiments are conducted by the Taguchi method and analyzed based on the signal-to-noise ratio. Then, the multiple objectives optimization is successfully converted to a single objective optimization of the grey relational grade by the grey relational analysis. The cutter geometric parameters, namely, fluting rake angle, gash angle, helix angle, gash rake angle, and pitch angle difference, are optimized to minimize cutting force, surface roughness, and the acceleration. According to the results of Analysis of variance, the order of importance for the control factors to the multiperformance characteristics, in sequence, is helix angle, gash angle, gash rake angle, pitch angle difference, and fluting rake angle. Experimental results indicate that the multiperformance characteristics can be improved effectively with the grey-Taguchi method.

1. Introduction Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy is considered as a kind of hard-to-cut material and has very poor machinability. However, it offers high strength and wide processing window compared to traditional hard steels and plays an extremely important role in gas turbines, aircraft, marine, rocket engines, and other high temperature applications. Therefore, recent design considerations in aerospace and aviation industry rejuvenate the interest for Ti-5Al-5Mo5V-1Cr-1Fe titanium alloy as large-size and load-bearing components. Many researches focused on cutting parameters to improve the machining quality for turning, milling, drilling, grinding, and other machining operations. Pawade and Joshi [1] obtained better high-speed turning performance of Inconel 718 in terms of cutting forces and surface roughness by optimizing the cutting parameters. Shi et al. [2] recently employed the grey-Taguchi relational analysis to accomplish the multiobjective optimization of surface integrity

for milling TB6. Lebaal et al. [3] obtained the optimal cutting parameters that improve the surface roughness with maximizing the volume of material removal and cutting tool life. Prasanna et al. [4] optimized the thrust force, overcut, circularity, and taper by controlling the drilling parameters for small hole dry drilling of Ti-6Al-4V. Thepsonthi and ¨ [5] identified optimum process parameters for microend Ozel milling of Ti-6Al-4V titanium alloy, which minimized the surface roughness and burr formation. These literature surveys in traditional machining focus on the machining parameters optimization and provide practical approach to obtain the optimal parameters. However, the effect of cutter geometric parameters on quality characteristics of machining was not given enough attention by the previous researchers. Some investigations indicate that cutter structures have significant influence on the machining process and quality characteristics. Different combinations of cutter geometric parameters might produce large variations in the final

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

2

Advances in Mechanical Engineering

product quality. For instance, a variable pitch or helix milling tool can be used to reduce the cutting force and improve the machined surface quality by suppressing the machining chatter [6–12]. Zain et al. [13] applied the genetic algorithm and regression model to find the optimal solution of the cutting conditions (radial rake angle, cutting speed, and feed rate) that yield the minimum value surface roughness. Wang et al. [14] built an analysis model of parameters affecting performance in high-speed milling of AISI H13 tool steel considering cutter geometric parameters and cutting parameters. Their experimental results indicated that the contributions of tool grinding precision, geometric angle, and cutting conditions to the multiple performance characteristics are 11.8%, 9.8%, and 73.1%, respectively. Arunachalam et al. [15] studied the effect of insert shape, cutting edge preparation, type, and nose radius on both residual stresses and surface finish. They suggested that coated carbide cutting tool inserts of round shape, chamfered cutting edge preparation, negative type and small nose radius (0.8 mm), and coolant would generate primarily compressive residual stress. From the above analyses, it can be seen that cutter geometric parameters have some influences on the machining process and performance. Therefore, the current study attempts to determine the influence weight of these factors on multiple performance characteristics. Furthermore, the effect of the pitch angle difference of end mill on the stability of machining process is especially considered. Considering the structure complexity and variety of end mill, a current technique challenge is to design the various cutter geometric parameters that yield optimum multiple performance characteristics, which is a multiobjective optimization problem. Taguchi method integrated with grey relational analysis (GRA) is an effective approach to solve the multiobjective optimization problem. Grey-Taguchi method has been widely applied in recent years for optimal process parameter design of multiple performance characteristics [16–24]. In the traditional machining, Kopac and Krajnik [25] applied grey-Taguchi to the robust design of flank milling parameters dealing with the optimization of the cutting loads, milled surface roughness, and the material removal rate in the machining of an Al-alloy casting plate for injection moulds. Tsao [26] adopted grey-Taguchi method to optimize the milling parameters on A6061P-T651 aluminum alloy with multiple performance characteristics. Haq et al. [27] optimized drilling parameters with the considerations of multiresponses for drilling Al/SiC metal matrix composite with the GRA in the Taguchi method. K¨okl¨u [28] completed the optimization of the continuous and interrupted cylindrical grinding of AISI 4140 steel considering the effect of workpiece speed, depth of cut, and the number of slot on the multiple performance characteristics using grey-based Taguchi method. By looking at previous studies, as far as they have been reviewed, it seems that the application of grey-Taguchi optimization techniques for optimizing the cutter geometric parameters in end milling is still not given consideration by researchers. Therefore, the current research focuses on the structure design of end mill for end milling of Ti-5Al5Mo-5V-1Cr-1Fe titanium alloy and introduces the GRA to

search the optimal cutter geometric parameters. The design factors are selected as fluting rake angle, gash angle, helix angle, gash rake angle, and pitch angle difference while the multiple performance characteristics are evaluated by cutting force, surface roughness, and the acceleration. Additionally, the correlations between the factors and their influences on performance are studied using the grey-Taguchi method. Then, the influence of the design factors on multiple performance characteristics are analyzed using analysis of variance (ANOVA). Finally, a validation experiment is conducted to verify the effectiveness of this approach.

2. Analysis Methods 2.1. Taguchi Method. Generally, traditional experimental design methods require a dense mass of sample points when the number of process parameters increases. In order to reduce the number of trials, Taguchi method is employed to seek the optimal combination of cutter geometric parameters in end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. Taguchi method is a simple and effective solution for parameter design and experiment planning [29]. In this method, Taguchi recommended analyzing the performance of process response using signal-to-noise (𝑆/𝑁) ratio, in which the largest value of 𝑆/𝑁 is required. There are three types of 𝑆/𝑁 ratio—the larger-the-better model, the smallerthe-better model, and the nominal-the-better [30]. (1) The Larger-the-Better Model (LBM). Maximum response characteristic means that the target extreme value is infinity. The 𝑆/𝑁 ratio is as follows: 1 𝑛 𝑆/𝑁 = 10 lg ( ∑𝑦𝑖 2 ) , 𝑛 𝑖=1

(1)

where 𝑦𝑖 is the 𝑖th test and 𝑛 is the total number of tests. (2) The Smaller-the-Better Model (SBM). Minimum response characteristic means that the target extreme value will be zero. The 𝑆/𝑁 ratio with a smaller-the-better characteristic is defined as follows: 1 𝑛 2 𝑆/𝑁 = −10 lg [ ∑ (𝑦𝑖 ) ] . 𝑛 𝑖=1

(2)

(3) The Nominal-the-Best Model (NBM). Targeted response characteristic means that the response result is the target value. The 𝑆/𝑁 ratio can be expressed as follows: 𝑆/𝑁 = 10 lg [

𝑢2 ], 𝜎2

(3)

where 𝑢=

1 𝑛 ∑𝑦 , 𝑛 𝑖=1 𝑖

1 𝑛 2 𝜎2 = ∑ (𝑦 − 𝑢) . 𝑛 − 1 𝑖=1 𝑖

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

(4)

Advances in Mechanical Engineering

3

2.2. Grey Relational Analysis. Analysis of 𝑆/𝑁 ratios is available for single performance characteristic, but ineffective for multiresponse characteristics. It often exists in multiobjective optimization problem that the higher 𝑆/𝑁 ratio for one performance characteristic may correspond to a lower 𝑆/𝑁 ratio for another. So, it is essential to evaluate overall 𝑆/𝑁 ratios in multiobjective optimization problem. In this study, the multiple performance characteristics are evaluated using the GRA, which converts a multiple response process optimization into a single objective optimization of the grey relational grade (GRG). In the GRA, the quality characteristics are first normalized, ranging from zero to one. This experiment data process is called grey relational generation. The second step is to calculate the grey relational coefficient (GRC) based on the normalized experimental data, which represents the correlation between the desired data sequence and the actual experimental data sequence. Finally, the GRG sequence can be obtained by taking the weighted average of the GRC sequence. The multiple performance characteristics are evaluated by the GRG. (1) Grey Relational Generation. If the purpose is the largerthe-better, then the normalized results can be expressed as 𝑥𝑖∗ (𝑘) =

𝑥𝑖(0) (𝑘) − min {𝑥𝑖(0) (𝑘)} max {𝑥𝑖(0) (𝑘)} − min {𝑥𝑖(0) (𝑘)} 𝑖 = 1 ∼ 𝑚,

,

(5)

𝑘 = 1 ∼ 𝑛,

𝑥𝑖∗ (𝑘)

is the normalized value of the 𝑘th performance where characteristic in the 𝑖th experiment, while 𝑥𝑖(0) (𝑘) is the original result of the 𝑘th performance characteristic in the 𝑖th experiment, m is the total number of test, and 𝑛 is equal to the number of performance characteristics. If the target value of the original sequence is the smallerthe-better performance characteristic, then the original sequence is normalized as follows: 𝑥𝑖∗ (𝑘) =

max {𝑥𝑖(0) (𝑘)} − 𝑥𝑖(0) (𝑘) max {𝑥𝑖(0) (𝑘)} − min {𝑥𝑖(0) (𝑘)} 𝑖 = 1 ∼ 𝑚,

,

(6)

𝑘 = 1 ∼ 𝑛.

(2) Grey Relational Coefficient. A higher value of the GRC, ranging from zero to one, corresponds to intense relational degree between the desired performance characteristics and the actual performance characteristics. The GRC is defined as follows: 𝛾 (𝑥0∗ (𝑘) , 𝑥𝑖∗ (𝑘)) =

min∀𝑖 min∀𝑘 Δ 0𝑖 (𝑘) + 𝜁max∀𝑖 max∀𝑘 Δ 0𝑖 (𝑘) , Δ 0𝑖 (𝑘) + 𝜁max∀𝑖 max∀𝑘 Δ 0𝑖 (𝑘) 𝑖 = 1 ∼ 𝑚,

where

(7)

𝑘 = 1 ∼ 𝑛,

󵄨 󵄨 Δ 0𝑖 (𝑘) = 󵄨󵄨󵄨𝑥𝑖∗ (𝑘) − 𝑥0∗ (𝑘)󵄨󵄨󵄨 ,

(8)

0 < 𝛾 (𝑥0∗ (𝑘) , 𝑥𝑖∗ (𝑘)) < 1,

(9)

Table 1: Design factors and their levels. Levels 1 2 3 4

𝐴, ∘ 4 6 8 10

Experimental control factors 𝐵, ∘ 𝐶, ∘ 𝐷, ∘ 25 30 2 30 35 4 35 40 6 40 45 8

𝐸, ∘ 0 3 5 7

where 𝑥0∗ (𝑘) is reference sequence, 𝑥𝑖∗ (𝑘) is comparability sequence, Δ 0𝑖 (𝑘) is the deviation sequence of 𝑥𝑖∗ (𝑘) and 𝑥0∗ (𝑘), and 𝜁 is a distinguishing coefficient between zero and one. (3) Grey Relational Grade. A higher GRG presents that the corresponding performance characteristics are closer to the ideal normalized value. The GRG can be calculated as follows: 𝛾 (𝑥0∗ , 𝑥𝑖∗ ) =

1 𝑛 ∑ 𝛾 (𝑥0∗ (𝑘) , 𝑥𝑖∗ (𝑘)) , 𝑛 𝑘=1

𝑘 = 1 ∼ 𝑛,

(10)

where 𝑥0∗ is reference sequence vector, while 𝑥𝑖∗ is comparability sequence vector. Here, the GRG 𝛾(𝑥0∗ , 𝑥𝑖∗ ) ∈ [0, 1] represents the level of correlation between the reference sequence vector and comparability sequence vector. The flow diagram of cutter geometric parameters using the Taguchi method in integration with the GRA is illustrated in Figure 1.

3. Experiment Procedures A set of end milling experiments are conducted in a threecoordinate vertical CNC machining center-VMC850 with maximum spindle speed of 8000 rpm, maximum feed rate of 12 m/min, and spindle power of 10 hp. The workpiece material used in all experiments is Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. The cutters are four flutes flat-end mills with the carbide body K40, diameter of 12 mm, and uncoated edge. To reduce the influence of tool wear, a fresh cutter is used in each experiment. The overhang length of end mill is fixed as 32 mm in each experiment. The milling parameter in each experiment is fixed at the level with spindle speed 𝑛 = 4000 r/min, axial milling depth 𝑎𝑝 = 0.3 mm, radial milling depth 𝑎𝑒 = 4 mm, and feed rate𝑓𝑧 = 0.02 mm/z. This study discusses the relationship between cutter geometric parameters and the performance characteristics for end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy in order to obtain optimal combination of the parameters. First, the objective performance characteristics are focused on three aspects: cutting force, surface roughness, and the acceleration. Next, five cutter geometric parameters (fluting rake angle, gash angle, helix angle, gash rake angle, and pitch angle difference, denoted as 𝐴, 𝐵, 𝐶, 𝐷, and 𝐸, resp.) are selected as control factors with four levels, denoted as 1, 2, 3, and 4, as shown in Table 1. An end mill with pitch angle difference of 3∘ corresponds to the fact that the four pitch angle is 87∘ , 93∘ , 87∘ , and 93∘ , respectively. These cutter geometrical parameters are illustrated in Figure 2.

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

4

Advances in Mechanical Engineering

Taguchi orthogonal experiment array

Selection of cutter geometric parameters and their levels

Conduct of experiments to obtain the multiresponses Single objective optimization Data analysis by S/N Multiple objective optimization Normalization of the original multiresponse sequence ANOVA and determination of significant parameters Calculation of GRC

Confirmation test

Calculation of GRG and determination of optimal parameters

Figure 1: Flowchart of grey-Taguchi method.

Table 2: Taguchi L16(45 ) orthogonal array. Experiment number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

𝐴 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4

𝐵 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

𝐶 1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1

𝐷 1 2 3 4 3 4 1 2 4 3 2 1 2 1 4 3

𝐸 1 2 3 4 4 3 2 1 2 1 4 3 3 4 1 2

The selection of levels of design parameters is based on the experience of engineers and previous experimental study. In general, the rake angle is no more than 10∘ in machining process. According to previous experimental investigation, a pitch angle difference between 0∘ and 7∘ may be beneficial to suppressing the machining chatter in end milling the titanium alloy. Larger gash angle leads to lower rigidity of cutting edge while an end mill with smaller gash angle is bad for separation of chip. Helix angle ranging from 30∘ to 45∘ is often used for milling titanium alloy. Then, a Taguchi orthogonal array L16(45 ) is employed to reduce the number of experiments, as shown in Table 2. All experiments are performed in down milling using emulsified liquid. Figure 3 presents the process of end milling.

The average lateral cutting force and axial cutting force are measured with a Kistler dynamometer (Model 9255B), respectively. Then the resultant cutting force is calculated as the results to evaluate the cutting force by the Pythagorean Theorem. The expressed surface roughness in this paper is the arithmetic mean deviation of the surface roughness profile Ra. The surface roughness of machined surfaces is measured in feed direction by surface roughness tester TR240, made by Bei Jing Time Technologies Co. Ltd. An average value of five measurements of surface roughness is taken to use in the multicriteria optimization. As shown in Figure 3, the acceleration sensor is cemented on the machine tool spindle head. The vibrations are monitored using a Kistler piezoelectric Accelerometer (Model 3055B2) and the average values of the amplitude in a stable data stage are taken as the results.

4. Experimental Results and Discussion 4.1. Analysis of Signal-to-Noise (𝑆/𝑁) Ratio. Table 3 presents the experimental results of cutting force, surface roughness, and the acceleration. Apparently, smaller values of these responses are desirable. Thus, the data sequences have a smaller-the-better characteristic and the SB model (equation (2)) is employed to calculate the 𝑆/𝑁 ratio. The results of 𝑆/𝑁 ratio are illustrated in Table 3. The 𝑆/𝑁 ratios of cutting force, surface roughness, and the acceleration can be used for performance analysis and a higher 𝑆/𝑁 ratio value represents that the response value is closer to the expected performance characteristic. According to this criterion, it is obviously observed that experiment number 7 has the maximum of 𝑆/𝑁 ratio for cutting force, which means the optimum combination of cutter geometric parameters is 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸2 among the experiment arrays. Similarly, surface roughness has a higher 𝑆/𝑁 ratio in experiment number 7 than that in the others. Therefore, the design factors 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸2 should

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

Advances in Mechanical Engineering

5 Table 3: Experimental results and their 𝑆/𝑁 ratio. CF

Experiment number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

SR 𝑆/𝑁 (dB) −32.119 −31.193 −30.256 −30.381 −32.922 −32.217 −30.203 −30.683 −32.061 −31.711 −32.262 −30.719 −31.698 −32.531 −31.464 −32.881

Results (N) 40.36 36.28 32.57 33.04 44.27 40.82 32.37 34.21 40.09 38.51 41.03 34.35 38.45 42.32 37.43 44.06

Ra (𝜇m) 0.248 0.311 0.268 0.272 0.240 0.228 0.186 0.271 0.357 0.208 0.195 0.249 0.239 0.240 0.237 0.214

AC 𝑆/𝑁 (dB) 12.111 10.145 11.437 11.309 12.396 12.841 14.610 11.341 8.947 13.639 14.199 12.076 12.432 12.396 12.505 13.392

Results (g) 0.675 0.491 0.579 0.829 0.922 0.580 0.506 0.524 0.758 0.603 0.664 0.478 0.322 0.593 0.939 0.649

𝑆/𝑁 (dB) 3.414 6.178 4.746 1.629 0.705 4.731 5.910 5.613 2.407 4.394 3.561 6.411 9.843 4.539 0.547 3.755

CF: cutting force; SR: surface roughness; AC: acceleration; g: the acceleration of gravity.

A

R

Fluting rake angle

Second relief face Primary relief face

90∘

Gash rake angle

Rake face of end tooth

Primary radial relief angle

Helix angle

Gash angle

A

Pitch angle difference

A-A

Figure 2: Geometrical parameters of an end mill.

be selected if only considering the surface roughness for the end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. The smallest acceleration can be obtained from experiment number 13 at levels 𝐴 4 𝐵1 𝐶4 𝐷2 𝐸3 among the 16 experiments. The response table for the Taguchi method is used to calculate the mean 𝑆/𝑁 ratios for each factor level. First step is to calculate the sum of the 𝑆/𝑁 ratios for each factor level in the orthogonal array. Next step is to take the average of the sum. The mean 𝑆/𝑁 ratios are equal to the average. For example, the 𝑆/𝑁 ratio for 𝐴 at level 1 can be calculated as follows:

Accelerator

Dynamometer

𝑀𝐴1 =

Figure 3: End milling experiment.

(−32.119 − 31.193 − 30.256 − 30.381) = −30.987. 4 (11)

The mean 𝑆/𝑁 ratios for each cutter geometric parameter level are calculated using the same process method. A higher

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

6

Advances in Mechanical Engineering A

B

C

D

E

7

−31.2

S/N ratios of AC (dB)

S/N ratios of CF (dB)

−31.0 −31.4 −31.6 −31.8 −32.0 −32.2

C

D

E

6 5 4 3

4 6 8 10 25 30 35 40 30 35 40 45 2 4 6 8 0 3 5 7

4 6 8 10 25 30 35 40 30 35 40 45 2 4 6 8 0 3 5 7

Figure 6: 𝑆/𝑁 response graph for the acceleration.

Figure 4: 𝑆/𝑁 response graph for cutting force.

S/N ratios of SR (dB)

B

2

−32.4

13.5

A

A

B

C

D

E

Table 4: The mean signal-to-noise (𝑆/𝑁) ratio for cutting force. Factors

13.0

𝐴 𝐵 𝐶 𝐷 𝐸

12.5 12.0 11.5 11.0 4 6 8 10 25 30 35 40 30 35 40 45 2 4 6 8 0 3 5 7

1 −30.987 −32.200 −32.370 −31.393 −31.494

Factors

4.2. Multiple Objective Optimization of Cutter Geometric Parameters. As mentioned in Section 2, the multiple performance characteristics for ending milling Ti-5Al-5Mo5V-1Cr-1Fe titanium alloy are evaluated using the GRA. The objective is to convert the optimization of multiple performance characteristics into the optimization of single GRG. The following steps are considered for the GRA. 4.2.1. Grey Relational Generation. In the GRA, raw data preprocessing is the first step, which is known as grey

4 −32.144 −31.166 −30.998 −31.531 −32.024

Max–min 1.157 1.154 1.372 0.550 0.801

Table 5: The mean signal-to-noise (𝑆/𝑁) ratio for surface roughness.

Figure 5: 𝑆/𝑁 response graph for surface roughness.

𝑆/𝑁 ratio corresponds to a lower value of these performance characteristics. For the cutting force, the optimal combination of parameters is 𝐴 1 𝐵3 𝐶4 𝐷1 𝐸3 based on the data presented in Table 4; namely, fluting rake angle is 4∘ , gash angle is 35∘ , helix angle is 45∘ , gash rake angle is 2∘ , and pitch angle difference is 5∘ . Figure 4 shows the fluctuation of mean 𝑆/𝑁 ratio of performance characteristics with the change of cutter geometric parameters. As to the surface roughness, the optimum cutter geometric parameters are as follows based on the data shown in Table 5: fluting rake angle of 6∘ , gash angle of 35∘ , helix angle of 30∘ , gash rake angle of 2∘ , and pitch angle difference of 7∘ . The mean 𝑆/𝑁 ratio plot of surface roughness with respect to front angle, gash angle, helix angle, gash rake angle, and pitch angle difference is shown in Figure 5. According to the 𝑆/𝑁 analysis, it is clearly observed from Table 6 and Figure 6 that the acceleration reaches the minimum at 𝐴 4 𝐵2 𝐶4 𝐷2 𝐸3 .

Level (𝑆/𝑁) 2 3 −31.506 −31.688 −31.913 −31.046 −31.575 −31.383 −31.459 −31.943 −31.585 −31.223

𝐴 𝐵 𝐶 𝐷 𝐸

1 11.251 11.472 13.136 12.798 12.399

Level (𝑆/𝑁) 2 3 12.797 12.215 12.255 13.188 11.781 11.030 12.029 12.716 11.774 12.197

4 12.681 12.030 12.998 11.401 12.575

Max–min 1.546 1.716 2.106 1.397 0.801

Table 6: The mean signal-to-noise (𝑆/𝑁) ratio for the acceleration. Factors 𝐴 𝐵 𝐶 𝐷 𝐸

1 3.992 4.092 3.865 5.069 3.492

Level (𝑆/𝑁) 2 3 4.240 4.193 4.961 3.691 3.460 4.326 6.299 3.400 4.563 6.433

4 4.671 4.352 5.444 2.329 2.609

Max–min 0.679 1.270 1.984 3.970 3.824

relational generation. As mentioned above, a larger 𝑆/𝑁 ratio is desirable. Consequently, (5), a linear normalization, is employed to preprocess the original response characteristic sequences. The values of the cutting force, surface roughness, and the acceleration are set to be the original sequence 𝑥𝑖(0) (𝑘), where 𝑘 is less than or equal to three corresponding to the number of performance characteristics and 𝑖 is no more than sixteen corresponding to the number of experiments. Then, the 𝑆/𝑁 ratios obtained by Taguchi’s method are normalized in the range of zero and one. Table 7 shows the normalized

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

Advances in Mechanical Engineering

7

Table 7: Normalized experimental results. Experiment number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

CF 0.295 0.636 0.981 0.935 0.000 0.259 1.000 0.823 0.317 0.445 0.243 0.810 0.450 0.144 0.536 0.015

SR 0.559 0.212 0.440 0.417 0.609 0.688 1.000 0.423 0.000 0.829 0.927 0.553 0.615 0.609 0.628 0.785

AC 0.31 0.61 0.45 0.12 0.02 0.45 0.58 0.54 0.20 0.41 0.32 0.63 1.00 0.43 0.00 0.35

results for cutting force, surface roughness, and the acceleration. Basically, the larger normalized results correspond to the better performance and the best-normalized results should be equal to one. 4.2.2. Grey Relational Coefficient and Grey Relational Grade. After obtaining the normalized sequence, the next step is to calculate the GRC and the GRG. Since the 𝑆/𝑁 ratio is the larger-the-better, the reference sequence should take the maximum as follows: 𝑥0∗ = [1, 1, 1] .

(12)

The comparability sequence 𝑥𝑖∗ (𝑘) has been obtained from the previous step. Then, according to (8), the maximum and minimum of deviation sequences are calculated as follows: max max Δ 0𝑖 (𝑘) = |0 − 1| = 1,

1 ≤ 𝑖 ≤ 16, 1 ≤ 𝑘 ≤ 3,

min min Δ 0𝑖 (𝑘) = |1 − 1| = 0,

1 ≤ 𝑖 ≤ 16, 1 ≤ 𝑘 ≤ 3.

∀𝑖

∀𝑖

∀𝑘

∀𝑘

(13) Suppose the performance characteristics have equal weights, and set the distinguish coefficient 𝜁 as 0.5 in the current study [31]. The value of 𝜁 is smaller and the identification ability is larger. With (10), it is easy to obtain the GRG. Table 8 lists the grey relational coefficients and the grades for all sixteen comparability sequences. In this investigation, a higher GRG means the corresponding cutter geometric parameters combination is closer to the optimum. In other words, the larger the GRG is, the better the multiple performance characteristics will be [26]. Owing to the fact that experiment number 7 has the highest GRG, it has the best multiple performance characteristics among all experiments. The average grey relational grades for each factor level have been calculated using the process approach similar

Table 8: Grey relational coefficients, grey relational grades, and their order. Experiment number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

CF 0.415 0.579 0.963 0.885 0.333 0.403 1.000 0.739 0.423 0.474 0.398 0.725 0.476 0.369 0.519 0.337

GRC SR 0.531 0.388 0.472 0.462 0.561 0.616 1.000 0.464 0.333 0.745 0.873 0.528 0.565 0.561 0.573 0.699

AC 0.42 0.56 0.48 0.36 0.34 0.48 0.54 0.52 0.38 0.46 0.42 0.57 1.00 0.47 0.33 0.43

GRG

Rank

0.455 0.509 0.638 0.569 0.411 0.500 0.847 0.574 0.379 0.560 0.564 0.608 0.680 0.467 0.474 0.489

14 9 3 6 15 10 1 5 16 8 7 4 2 13 12 11

to the calculation process of mean 𝑆/𝑁 ratios, as shown in Table 9. Figure 7 demonstrates their fluctuation with the change of cutter geometric parameters. Since the GRG reflects the level of correlation between the comparability and the reference sequences, a larger GRG represents the comparability sequence exhibiting a stronger correlation with the reference sequence [1, 1, 1]. Based on this basic criterion of grey system theory, one can select a combination of the design factor levels that provide the largest average performance characteristics. As listed in Table 9, the combination of 𝐴 2 , 𝐵3 , 𝐶4 , 𝐷1 , and 𝐸3 shows the largest value of the GRG for the design factors 𝐴, 𝐵, 𝐶, 𝐷, and 𝐸, respectively. Consequently, 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸3 with a fluting rake angle of 6∘ , gash angle of 35∘ , helix angle of 45∘ , gash rake angle of 2∘ , and pitch angle difference of 5∘ is the optimum cutter geometric parameter combination. From Table 9, the difference between the maximum and minimum value of the GRG of the milling parameters is 0.055 for 𝐴 (fluting rake angle), 0.150 for 𝐵 (gash angle), 0.184 for 𝐶 (helix angle), 0.113 for 𝐷 (gash rake angle), and 0.104 for 𝐸 (pitch angle difference). These difference values reflect the level of effect of cutter geometric parameters on the performance characteristics. In other words, the comparison among the difference values will qualitatively give the level of significance of the control factors over the multiple performance characteristics. It can be easily observed that the maximum value among 0.055, 0.150, 0.184, 0.113, and 0.104 is 0.184, which means the helix angle has the most remarkable effect on the multiple performance characteristics among the cutter geometric parameters. 4.2.3. Analysis of Variance (ANOVA). In this paper, ANOVA is employed to investigate which cutter geometric parameters significantly affect the integrated performance of end mill Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. It is accomplished by

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

8

Advances in Mechanical Engineering A

Table 9: Response table of the average grey relational grade.

𝐴 𝐵 𝐶 𝐷 𝐸

1 0.543 0.481 0.480 0.594 0.516

2 0.583 0.509 0.523 0.582 0.556

C

D

E

0.65

GRG 3 0.528 0.631 0.515 0.525 0.607

4 0.528 0.560 0.664 0.481 0.503

Max–min

Rank

0.055 0.150 0.184 0.113 0.104

5 2 1 3 4

GRG

Factors

B

0.60 0.55 0.50

Total mean value of the grey relational grade = 0.545.

4 6 8 10 25 30 35 40 30 35 40 45 2 4 6 8 0 3 5 7

Table 10: ANOVA results for grey relational grade. Factors 𝐴 𝐵 𝐶 𝐷 𝐸 Error Total

DF 3 3 3 3 3 0 15

SS 0.0082 0.0518 0.0757 0.0335 0.0262 0 0.1952

MS 0.0027 0.0173 0.0252 0.0111 0.0087 — 0.0130

𝐹 — 6.30 9.22 4.07 3.19 —

Figure 7: Response graph of average grey relational grade. 𝜌 (%) 4.21 26.51 38.76 17.12 13.41 — 100

DF: degree of freedom; SS: sum of squares; 𝜌: percentage of contribution. Significance is at 95% confidence level.

separating the total variability of the grey relational grade, which is measured by the sum of the squared deviations from the total mean of the grey relational grade, into contributions by each cutter geometric parameter and the error. According to the results of ANOVA, the influential degree of each cutter geometric parameter on the GRG can be estimated by the percent contribution. The results of ANOVA are obtained using statistical software MINITAB 17, as illustrated in Table 10. The effects of design factors on the grey relational grades are plotted in Figure 8. It can be clearly observed that the main contribution percentages for fluting rake angle, gash angle, helix angle, gash rake angle, and pitch angle difference are 4.21%, 26.51%, 38.76%, 17.12%, and 13.41%. Furthermore, helix angle is the most significant cutter geometric parameter due to its 𝐹 statistics value. That is to say, it should be the prior control factor of end mill to simultaneously minimize cutting force, surface roughness, and the acceleration for end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. 4.3. Validation Test. A validation experiment is conducted to verify the improvement of the performance characteristics using the optimum cutter geometric parameter combination 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸3 . The estimated grey relational grade 𝛾̂ using the optimum milling parameters can be expressed as 𝑛

𝛾̂ = 𝛾𝑚 + ∑ (𝛾𝑖 − 𝛾𝑚 ) ,

(14)

𝑖=1

where 𝛾𝑚 is the total mean of the grey relational grade, 𝛾𝑖 is the mean of the grey relational grade at the optimal level, and 𝑛 is the number of milling parameters that significantly affect the multiple performance characteristics.

The initial cutter geometric parameters are selected as 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸2 due to the largest GRG of experiment number 7 among the sixteen experiments. Table 11 illustrates the comparison of the experimental results using the initial and optimal cutter geometric parameters. Under the condition with the levels 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸3 of the optimum parameters, the grey relational grade has been improved 0.122; cutting force is greatly reduced from 32.37 N to 25.57 N; surface roughness is decreased to 0.170 𝜇m, an improvement of 8.60%; the acceleration has been improved from 0.506 g to 0.340 g. Optimal parameter settings obtained by individually analyzing 𝑆/𝑁 ratio in Section 4.1 are 𝐴 1 𝐵3 𝐶4 𝐷1 𝐸3 for cutting force, A2 B3 C1 D1 E4 for surface roughness, and 𝐴 4 𝐵2 𝐶4 𝐷2 𝐸3 for the acceleration. The corresponding GRGs are 0.608, 0.558, and 0.578, respectively, which are less than the GRG under the condition with the optimum parameter level 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸3 . It demonstrates the effectiveness of the greyTaguchi method for the multiobjective optimization compared with the analysis of 𝑆/𝑁 ratio. In summary, it is clearly shown that multiobjective quality characteristics for end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy can be significantly improved by optimization of cutter geometric parameters.

5. Conclusions This study applies the grey relational analysis integrating with the Taguchi method to optimize the cutter geometric parameters with multiple performance characteristics (cutting force, surface roughness, and the acceleration) for end milling of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. Conclusions are summarized as follows. (1) The validation experiment indicates that greyTaguchi method is an effective approach of multiobjectives optimization to the structural parameters of end mill for machining Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. With this method, the grey relational grade of the multiple performance characteristics is significantly improved by 0.122. (2) Through the analysis of 𝑆/𝑁 ratio, the optimal controllable factors for cutting force are fluting rake angle of 4∘ , gash angle of 35∘ , helix angle of 45∘ , gash rake angle of 2∘ , and pitch angle difference of 5∘ ; the

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

Advances in Mechanical Engineering

9

Table 11: The comparing results of the initial and optimal cutter geometric parameters. Initial milling factors Level CF (N) SR (𝜇m) AC (g) GRG

𝐴 2 𝐵3 𝐶4 𝐷1 𝐸2 32.37 0.186 0.506 0.847

Optimal cutter geometric parameters Prediction Validation tests 𝐴 2 𝐵3 𝐶4 𝐷1 𝐸3 25.57 0.170 0.340 0.899 0.969

Improvement rate, (%)

21.01 8.60 32.81 14.40

Improvement of the grey relational grade = 0.122.

Pitch angle difference (E) 13.41%

Fluting rake angle (A) 4.21% Gash angle (B) 26.51%

Gash rake angle (D) 17.12%

Helix angle (C) 38.76%

Figure 8: Effects of the factors according to ANOVA results on grey relational grade (%).

optimum fluting rake angle, gash angle, helix angle, gash rake angle, and pitch angle difference for surface roughness are 6∘ , 35∘ , 30∘ , 2∘ , and 7∘ ; the optimized fluting rake angle, gash angle, helix angle, gash rake angle, and pitch angle difference for the acceleration are 10∘ , 30∘ , 45∘ , 4∘ , and 5∘ . (3) According to results of ANOVA, the percentage of contribution to the end milling operation, in sequence, is the helix angle, the gash angle, the gash rake angle, the pitch angle difference, and the fluting rake angle. Hence, the helix angle is the most significant control factor for the end milling process when the minimization of the cutting force, surface roughness, and the acceleration are simultaneously considered. (4) The largest value of grey relational grade is obtained at the combination of cutter geometric parameters with a fluting rake angle of 6∘ , gash angle of 35∘ , helix angle of 45∘ , gash rake angle of 2∘ , and pitch angle difference of 5∘ . It is the recommended levels for end milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy when simultaneously optimizing the five structural parameters of an end mill.

Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments This work was supported by the National Science and Technology Major Project of China (no. 2013ZX04001081) and Graduate Starting Seed Fund of Northwestern Polytechnical University (Z2013031).

References [1] R. S. Pawade and S. S. Joshi, “Multi-objective optimization of surface roughness and cutting forces in high-speed turning of Inconel 718 using Taguchi grey relational analysis (TGRA),” International Journal of Advanced Manufacturing Technology, vol. 56, no. 1-4, pp. 47–62, 2011. [2] K. Shi, D. Zhang, J. Ren, C. Yao, and Y. Yuan, “Multiobjective optimization of surface integrity in milling TB6 alloy based on Taguchi-grey relational analysis,” Advances in Mechanical Engineering, vol. 2014, Article ID 280313, 7 pages, 2014. [3] N. Lebaal, M. Nouari, and A. Ginting, “A new optimization approach based on Kriging interpolation and sequential quadratic programming algorithm for end milling refractory titanium alloys,” Applied Soft Computing Journal, vol. 11, no. 8, pp. 5110–5119, 2011. [4] J. Prasanna, L. Karunamoorthy, M. V. Raman, S. Prashanth, and D. R. Chordia, “Optimization of process parameters of small hole dry drilling in Ti-6Al-4V using Taguchi and grey relational analysis,” Measurement, vol. 48, no. 1, pp. 346–354, 2014. ¨ [5] T. Thepsonthi and T. Ozel, “Multi-objective process optimization for micro-end milling of Ti-6Al-4V titanium alloy,”

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015

10

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

Advances in Mechanical Engineering International Journal of Advanced Manufacturing Technology, vol. 63, no. 9-12, pp. 903–914, 2012. P. Huang, J. Li, J. Sun, and M. Ge, “Milling force vibration analysis in high-speed-milling titanium alloy using variable pitch angle mill,” International Journal of Advanced Manufacturing Technology, vol. 58, no. 1–4, pp. 153–160, 2012. E. Budak, “An analytical design method for milling cutters with nonconstant pitch to increase stability. Part I. Theory,” Journal of Manufacturing Science and Engineering, vol. 125, no. 1, pp. 29– 34, 2003. E. Budak, “An analytical design method for milling cutters with nonconstant pitch to increase stability, Part 2: application,” Journal of Manufacturing Science and Engineering, Transactions of the ASME, vol. 125, no. 1, pp. 35–38, 2003. N. D. Sims, B. Mann, and S. Huyanan, “Analytical prediction of chatter stability for variable pitch and variable helix milling tools,” Journal of Sound and Vibration, vol. 317, pp. 664–686, 2008. S. Turner, D. Merdol, Y. Altintas, and K. Ridgway, “Modelling of the stability of variable helix end mills,” International Journal of Machine Tools and Manufacture, vol. 47, no. 9, pp. 1410–1416, 2007. A. R. Yusoff and N. D. Sims, “Optimisation of variable helix tool geometry for regenerative chatter mitigation,” International Journal of Machine Tools and Manufacture, vol. 51, no. 2, pp. 133– 141, 2011. K. Takuya, N. Suzuki, R. Hino, and E. Shamoto, “A novel design method of variable helix cutters to attain robust regeneration suppression,” Procedia CIRP, vol. 8, pp. 363–367, 2013. A. M. Zain, H. Haron, and S. Sharif, “Application of GA to optimize cutting conditions for minimizing surface roughness in end milling machining process,” Expert Systems with Applications, vol. 37, no. 6, pp. 4650–4659, 2010. Y.-C. Wang, C.-H. Chen, and B.-Y. Lee, “Analysis model of parameters affecting cutting performance in high-speed machining,” The International Journal of Advanced Manufacturing Technology, vol. 72, no. 1–4, pp. 521–530, 2014. R. M. Arunachalam, M. A. Mannan, and A. C. Spowage, “Surface integrity when machining age hardened Inconel 718 with coated carbide cutting tools,” International Journal of Machine Tools and Manufacture, vol. 44, no. 14, pp. 1481–1491, 2004. A. Al-Refaie, “Grey-data envelopment analysis approach for solving the multi-response problem in the Taguchi method,” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 224, no. 1, pp. 147–158, 2010. C.-J. Tzeng, Y.-H. Lin, Y.-K. Yang, and M.-C. Jeng, “Optimization of turning operations with multiple performance characteristics using the Taguchi method and Grey relational analysis,” Journal of Materials Processing Technology, vol. 209, no. 6, pp. 2753–2759, 2009. S. Pattnaik, D. B. Karunakar, and P. K. Jha, “Optimization of multiple responses in the lost wax process using Taguchi method and grey relational analysis,” Proceedings of the Institution of Mechanical Engineers Part L: Journal of Materials: Design and Applications, vol. 227, no. 2, pp. 156–167, 2013. M.-Y. Lin, C.-C. Tsao, C.-Y. Hsu, A.-H. Chiou, P.-C. Huang, and Y.-C. Lin, “Optimization of micro milling electrical discharge machining of Inconel 718 by Grey-Taguchi method,” Transactions of Nonferrous Metals Society of China, vol. 23, no. 3, pp. 661–666, 2013.

[20] S. Dharmalingam, R. Subramanian, and M. K¨ok, “Optimization of abrasive wear performance in aluminium hybrid metal matrix composites using Taguchi-grey relational analysis,” Proceedings of the Institution of Mechanical Engineers Part J: Journal of Engineering Tribology, vol. 227, no. 7, pp. 749–760, 2013. [21] E. Kuram and B. Ozcelik, “Multi-objective optimization using Taguchi based grey relational analysis for micro-milling of Al 7075 material with ball nose end mill,” Measurement, vol. 46, no. 6, pp. 1849–1864, 2013. [22] M. Y. Lin, C. C. Tsao, H. H. Huang, C. Y. Wu, and C. Y. Hsu, “Use of the grey-Taguchi method to optimise the micro-electrical discharge machining (micro-EDM) of Ti-6Al-4V alloy,” International Journal of Computer Integrated Manufacturing, 2014. [23] M. K. Sahu, A. Valarmathi, S. Baskaran, V. Anandakrishnan, and R. K. Pandey, “Multi-objective optimization of upsetting parameters of Al-TiC metal matrix composites: a grey Taguchi approach,” Proceedings of the Institution of Mechanical Engineers Part B: Journal of Engineering Manufacture, 2014. [24] Q. D. Fannian Meng, P. Wang, and Y. Wang, “Multiobjective optimization for the impeller of centrifugal fan based on response surface methodology (RSM) with grey relational analysis method,” Advances in Mechanical Engineering, vol. 2014, Article ID 614581, 13 pages, 2014. [25] J. Kopac and P. Krajnik, “Robust design of flank milling parameters based on grey-Taguchi method,” Journal of Materials Processing Technology, vol. 191, no. 1–3, pp. 400–403, 2007. [26] C. C. Tsao, “Grey-Taguchi method to optimize the milling parameters of aluminum alloy,” International Journal of Advanced Manufacturing Technology, vol. 40, no. 1-2, pp. 41–48, 2009. [27] A. N. Haq, P. Marimuthu, and R. Jeyapaul, “Multi response optimization of machining parameters of drilling Al/SiC metal matrix composite using grey relational analysis in the Taguchi method,” The International Journal of Advanced Manufacturing Technology, vol. 37, no. 3-4, pp. 250–255, 2008. [28] U. K¨okl¨u, “Optimisation of machining parameters in interrupted cylindrical grinding using the Grey-based Taguchi method,” International Journal of Computer Integrated Manufacturing, vol. 26, no. 8, pp. 696–702, 2013. [29] W. H. Yang and Y. S. Tarng, “Design optimization of cutting parameters for turning operations based on the Taguchi method,” Journal of Materials Processing Technology, vol. 84, no. 1–3, pp. 122–129, 1998. [30] A. W. L. Yao and S. C. Chi, “Analysis and design of a TaguchiGrey based electricity demand predictor for energy management systems,” Energy Conversion and Management, vol. 45, no. 7-8, pp. 1205–1217, 2004. [31] H. S. Jailani, A. Rajadurai, B. Mohan, A. S. Kumar, and T. Sornakumar, “Multi-response optimisation of sintering parameters of Al-Si alloy/fly ash composite using Taguchi method and grey relational analysis,” International Journal of Advanced Manufacturing Technology, vol. 45, no. 3-4, pp. 362–369, 2009.

Downloaded from ade.sagepub.com at WESTERN OREGON UNIVERSITY on June 8, 2015