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Case Study

Proc IMechE Part B:

J Engineering Manufacture

115IMechE 2015

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DOI: 10.1177/0954405415599927

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Analysis and optimization of cuttergeometric parameters for surface

integrity in milling titanium alloy usinga modified greyTaguchi method

Junxue Ren1, Jinhua Zhou1 and Jingwen Zeng2

Abstract

Surface integrity determines the performance and quality of the end product. It often needs to change the input para-

meters, such as cutting parameter, cutting tool geometry and material, and tool coating, to obtain the best machiningsurface integrity. This article presents and demonstrates the effectiveness for the multi-objective optimization of cuttergeometric parameters for surface integrity of milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy via grey relational analysiscoupled with the Taguchi method, entropy weight method, and analytic hierarchy process. The main influence factorsare chosen as radial rake angle, primary radial relief angle, and helix angle, while surface roughness and residual stressare taken as performance characteristics. Based on the Taguchi method, an L16 (4 3) orthogonal array is chosen for theexperiments. The effect of cutter geometric parameters on surface roughness and residual stress is analysed by signal-to-noise ratio. Then, the multiple objectives optimization problem is successfully converted to a single-objective optimi-zation of grey relational grade with the grey relational analysis. The weight coefficient for grey relational grade is deter-mined by entropy weight method integrated with analytic hierarchy process. The results show that the order ofimportance for controllable factor to the milling surface integrity, in sequence, is radial rake angle, primary radial relief

angle, and helix angle. The validation experiment verifies that the proposed optimization method has the ability to findout the optimal geometric parameters in terms of milling surface integrity.

Keywords

Surface integrity, Ti-5Al-5Mo-5V-1Cr-1Fe, cutter geometric parameter, multi-objective optimization, greyTaguchi,weight coefficient

Date received: 1 August 2014; accepted: 13 July 2015

Introduction

The use of titanium and its alloys has increased recentlydue to their superior properties and improvements in

machinability. Manufacturing of titanium alloys that

are critical structural components of the aerospace

industry is also a point of emphasis. Their poor machin-

ability often results in unfavourable accuracy of the

machined product dimensions or end product quality

issues such as surface integrity and lower lifetime prone-

ness. The final manufacturing process is decisive about

the product surface quality, so it should be controlled

and optimized. This study investigates the surface integ-

rity of finish milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium

alloy and explores possible way to adjust cutter geo-

metric parameters to achieve better surface integrity.Many researches focused on the machined surface

integrity in recent years. The research of Sun showed

that the machined surface exhibits an anisotropic

nature for end milling Ti-6Al-4V, and the b phase

experiences more deformation and volume shrinkage inthe near surface. The compressive residual stress in cut-

ting direction is about 30% larger than that in feed

direction and both increased with cutting speed.1 Hioki

et al.2 evaluated the influence of the cutting parameters

1The Key Laboratory of Contemporary Design and Integrated

Manufacturing Technology, Ministry of Education, School of Mechanical

Engineering, Northwestern Polytechnical University, Xian, China2Xian Microelectronics Technology Institute, Xian, China

Corresponding author:

Junxue Ren, The Key Laboratory of Contemporary Design and Integrated

Manufacturing Technology, Ministry of Education, School of MechanicalEngineering, Northwestern Polytechnical University, P.O. Box 552, Xian

710072, China.

Email: [email protected]

at Northwestern Polytechnical University on May 9, 2016pib.sagepub.comDownloaded from
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of high-speed milling on the surface integrity properties

of hardened AISI H13 steel. They found that the

engagement, feed per tooth, and cutting speed show

strong influence on the machined surface integrity.

Pawade et al.3 studied the effect of machining para-

meters and cutting edge geometry on surface integrity

of high-speed turned Inconel 718. They observed thatthe highest cutting speed, lowest feed rate, and moder-

ate depth of cut coupled with the use of honed cutting

edge can induce compressive surface residual stress.

Ezilarasan et al.4 found that a combination of 190m/

min cutting speed and 0.102 mm/rev feed rate is the crit-

ical condition for turning Nimonic C-263 alloy based

on surface roughness using whisker-reinforced ceramic

insert. Many researchers reported that cutting speed,

feed, and depth of cut are effective to some degree

increasing surface roughness, and increase in depth of

cut and feed has some effect on making the residual

stress more tensile at the surface and more compressivein the peak compressive depth.5 Additionally, appropri-

ate lubrication and inclination angles produce substan-

tial benefit in terms of milling surface integrity.6,7

These literature surveys focus on the surface integ-

rity and provide practical approach to obtain the opti-

mal process parameters. But it also has heighted the

dearth of information available to understand the effect

of cutter geometric parameters on surface integrity. In

addition, it is challenging to obtain excellent surface

integrity without losing production efficiency for the

cutting parameter optimization. A large material

removal rate improves production efficiency, but maybe

generates unfavourable surface integrity properties.8

Hence, it is the advantage to obtain a better surface

integrity by optimizing the cutter geometric parameters.

Many researches indicated that cutter geometry has

significant influence on the machining process and

quality characteristics. Different combinations of cutter

geometric parameters might produce large variations in

the final 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 sup-

pressing the machining chatter.912 Zain et al.13 applied

the genetic algorithm and regression model to find the

optimal solution of the cutting conditions (radial rakeangle, cutting speed, and feed rate) that yielded 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 contribu-

tions of tool grinding precision, geometric angle, and

cutting conditions to the 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 suggestedthat 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 influence the machining process

and performance significantly. Therefore, this study

attempts to determine the influence weight of these fac-

tors on multiple surface integrity properties.Considering the structure complexity and variety of

mill, the current techniques challenge is to design the

various cutter geometric parameters that yield opti-

mum surface integrity, which is a multi-objective opti-

mization problem.

The grey relational analysis (GRA) with the Taguchi

method (greyTaguchi) is an effective approach to

solve the multi-objective optimization problem. This

method has been widely applied in recent years for

optimal process parameter design of multiple perfor-

mance characteristics.1623 In the traditional machining,

Kopac and Krajnik24 applied the greyTaguchi method

to the robust design of flank milling parameters dealing

with the optimization of the cutting loads, milled sur-

face roughness, and the material removal rate. They

obtained optimal parameter combination of coolant

employment, number of end mill flutes, cutting speed,

feed, axial depth of cut, and radial depth of cut. Tsao25

adopted the greyTaguchi method to optimize the

milling parameters on A6061P-T651 aluminium alloy

with multiple performance characteristics. Haq et al.26

optimized drilling parameters with the considerations

of multiple responses such as surface roughness, cutting

force, and torque for drilling Al/SiC metal matrix com-

posite with the GRA in the Taguchi method. Ko klu27focused on the optimization of the continuous and

interrupted cylindrical grinding of AISI 4140 steel con-

sidering the effect of workpiece speed, depth of cut,

and the number of slots on the surface roughness and

roundness error using the grey-based Taguchi method.

To sum up, even though the effect of process para-

meters on the machined surface integrity has been accu-

mulated a lot, results are mainly dependent on

complicated factors. Furthermore, the factors that

these studies focused on are very dispersed and the sur-

face integrity is not integrately evaluated. The multi-

objective optimization of radial rake angle, primaryradial relief angle, and helix angle for milling surface

integrity is not yet available. More empirical studies

should be carried out to test the impact and optimiza-

tion processes of different combination of cutter geo-

metric parameters. Therefore, this research focuses on

the mill geometry optimization and machined surface

integrity for milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium

alloy and introduces the greyTaguchi method to

search the optimal cutter geometric parameters. The

design factors are selected as radial rake angle, primary

radial relief angle, and helix angle, while the surface

integrity are evaluated by surface roughness and sur-

face residual stress. Additionally, the influences of cut-ter geometric parameters on surface integrity are

analysed with the Taguchi method. Then, the

2 Proc IMechE Part B: J Engineering Manufacture



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correlations between the factors and surface integrity

are studied using the GRA method. Finally, a valida-

tion experiment verifies the effectiveness of this

approach. The multi-objective optimization flow dia-

gram of cutter geometric parameters using a modified

greyTaguchi method is illustrated in Figure 1.

Experimental procedureMachining setup

A set of milling experiments is conducted in a three-

coordinate vertical computer numerical control (CNC)

machining centreJOHNFORD VMC-850 with maxi-

mum 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 chemical composition is Al:

4.4-5.9wt%, Mo: 4.0-5.5wt%, V: 4.0-5.5wt%, Cr: 0.5-

1.5wt%, Fe: 0.5-1.5wt%, C: 0.1wt%, Si: 0.15wt%, Zr:

0.3wt%, N: 0.05wt%, H: 0.015wt%, O: 0.2wt%, and

the rest of Ti. The shapes of workpieces are oblong

blocks with the size of 71mm 3 55mm 3 49 mm.

The cutters are four-flute toroidal end mills with the

carbide body K40, diameter of 12 mm, circular arc

radius of 2 mm, and uncoated edge. To reduce the

influence of tool wear, a fresh cutter is used in each

experiment. The milling parameters in each experi-

ment are fixed at the level with spindle speed

s = 500 r/min, axial milling depth ap = 5 mm, radial

milling depth ae = 1 mm, and feed rate fz = 0.035

mm/z. The overhang length of toroidal end mill is

fixed as 44 mm. All cutting experiments are per-

formed in down milling using emulsified liquid.Figure 2 shows the milling process.

Experimental design

This study discusses the relationship between cutter

geometric parameters and the surface integrity of

milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy in order

to obtain the optimal geometric parameter combina-

tion. First, the objective performance characteristics

are focused on two aspects: surface roughness and sur-

face residual stress. The performance characteristics for

surface roughness contain the surface roughness of

machined bottom surface and side surface, denoted as

SRb and SRs respectively. The residual stresses are the

surface residual stress of machined bottom surface and

side surface, denoted as RSband RSs, respectively. The

machined bottom surface is formed by the end edges,

while the machined side surface is formed by the side

edges. Next, the control process parameters havinginfluence on the surface integrity properties are radial

Figure 1. Multi-objective optimization flow diagram of cutter geometric parameters.

Figure 2. Milling process.

Ren et al. 3



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rake angle (A), primary radial relief angle (B), and helix

angle (C). Table 1 lists the cutter geometric parameters

and their levels. Figure 3 diagrammatizes these three

kind of angles. Radial rake angle indicates the angle of

the flute face with respect to a line drawn from the cut-

ting edge at the outer diameter to the centre of the tool.

Most toroidal end mills are ground with positive rake

angles. In application, larger positive rake angles are

used on softer materials, and smaller positive rake

angles are used on harder materials. Primary radial

relief angle is ground for the length of cut to provideclearance behind the cutting edge. In general, larger

relief angle is favoured for softer materials, and smaller

relief angle are used for harder materials. Helix angle is

defined as the inclination of the cutting edges with

respect to the axis of the tool. Then, these experiments

are conducted with a three controllable four-level fac-

tors and four response variables. Therefore, the

Taguchi orthogonal array L16 (43) is used to reduce

the number of experiments, as shown in Table 2.

Measurement procedure

Surface integrity includes the mechanical properties,such as residual stress, hardness, and microstructural

changes, and topological parameters such as surface

Table 1. Cutter geometric parameters and their levels.

Symbol Geometric parameter Level 1 Level 2 Level 3 Level 4

A Radial rake angle () 4 8 12 16B Primary radial relief angle () 10 12 14 16C Helix angle () 30 40 50 60

Table 2. Taguchi L16 (43) orthogonal array and experimental results.

Experiment no. A B C SRb(mm) SRs(mm) RSb(Mpa) RSs(Mpa)

1 1 1 1 0.199 0.169 2335.4 2185.92 1 2 2 0.115 0.160 2201.4 2117.33 1 3 3 0.148 0.177 2276.6 2130.24 1 4 4 0.140 0.209 2217.7 2121.25 2 1 2 0.232 0.175 2267.7 297.26 2 2 1 0.246 0.147 2170.9 2133.37 2 3 4 0.225 0.196 2162.9 2137.58 2 4 3 0.140 0.123 2241.9 2140.19 3 1 3 0.262 0.201 2179.4 2142.310 3 2 4 0.280 0.199 2222.2 2167.411 3 3 1 0.226 0.132 2208.6 2149.812 3 4 2 0.362 0.117 2183 2130.813 4 1 4 0.119 0.199 2209.1 2122.914 4 2 3 0.159 0.167 2158.9 211615 4 3 2 0.248 0.160 2212.3 2120.316 4 4 4 0.347 0.173 2171.7 2147.5

Note: Values in bold face are idea values .

Figure 3. Geometrical parameters of a toroidal end mill.




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roughness. In this study, the surface roughness and resi-

dual stress are taken as assessment criteria for surface

integrity of milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium

alloy. The expressed surface roughness in this article is

the arithmetic mean deviation of the surface roughness

profile Ra. The surface roughness of machined surface

is measured in feed direction by surface roughness tester

MarSurf M 300 C, made by MAHR Co. Ltd, as shown

in Figure 4. An average value of five measurements of

surface roughness is used to evaluate geometric accu-

racy of machined surface. Measuring residual stress is

very difficult. X-ray diffraction (XRD) method stands

out as the reliable, nondestructive, and easily accessible

technique. In this method, the surface residual stress is

measured in PROTO LXRD MG2000, made by

PROTO Co. Ltd, with Gu-Ka radiation using XRD

method. Figure 5 illustrates the measurement process of

surface residual stress. The surface residual stress in

feed direction is used to evaluate the physical property

of machined surface. An average of two measurementsof surface residual stress is taken as the results.

Experimental results and discussion

Analysis of signal-to-noise ratio for single

performance characteristic

Table 2 shows the measurement results of surface

roughness and residual stress for the 16 experiments.

Negative sign of residual stress only represents that theresidual stress is compressive and is not taken in the cal-

culation. In order to study the effect of cutter geometry

on the surface integrity, the Taguchi method is used to

seek the optimal level combination of cutter geometric

parameters for single surface integrity property.

The Taguchi method is a simple and effective solu-

tion for parameter design and experiment planning.28 In

this method, Taguchi recommended analysing the per-

formance 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 ratiothe larger-the-better

model (LBM), the smaller-the-better model (SBM), andthe nominal-the-better model (NBM).29

1. LBM

Maximum response characteristic means that the

target extreme value is infinity. The S/N ratio is as

below

S=N = 10 log 1

N

XNi= 1

1

y2i

! 1

where yiis the response value of the ith test and N is

the number of measurements in each test.

2. SBM

Minimum response characteristic means that the

target extreme value will be 0. The S/N ratio with

a smaller-the-better characteristic is defined as fol-

lows

S=N = 10 log 1

N

XNi= 1

(yi)2

" # 2

3. NBM

Targeted response characteristic means that theresponse result is the target value. The S/N ratio

can be expressed as below

S=N=10log u2

s2

3

where

u = 1

NXN

i= 1

yi

and

Figure 4. Surface roughness measurement.

Figure 5. Surface residual stress measurement.

Ren et al. 5



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s2 = 1

N1

XNi= 1

(yiu)2

Obviously, smaller values of surface roughness are

desirable. Thus, the data sequences have a smaller-the-

better characteristic and the SBM, and equation (2) is

used to calculate the S/N ratio. Higher tensile residual

stress tends to present potential risk in terms of crack

initiation and propagation, and fatigue failure of end

products, but the compressive residual stress has the

opposite effect. Now that all these measurement results

present compressive surface residual stresses, and the

LBM of S/N ratio can be used to calculate the S/N ratio

for surface residual stress.

Table 3 shows the results of S/N ratio. 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 experi-

ment no. 2 has the maximum S/N ratio for bottom sur-

face roughness. It means the optimum combination of

cutter geometric parameters is A1B2C2 among the

experiment arrays. Side surface roughness has a higher

S/N ratio in experiment no. 12 than that in the others.

Therefore, the design factors A3B4C2should be selectedif only considering the side surface roughness for

milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy. As to

the surface residual stress, the largest value can beobtained from experiment no. 1 at levels A1B1C1among the 16 experiments.

The response table for the Taguchi method is used

to calculate the mean S/N ratios for each factor level.

First, group the S/N ratios by factor level for each col-

umn in the orthogonal array. Next, take their average.

For example, the S/N ratio for A at level 1 can be cal-

culated as follows

MA1=1

4(14:023+18:786+16:595+17:077)=16:620

4

The mean S/N ratios for each cutter geometric para-

meter level are calculated using the same process

method.

Based on the data presented in Table 4, the optimal

combination of parameters is A1B2C3 for the bottom

surface roughness, namely, radial rake angle is 4, pri-

mary radial relief angle is 12, and helix angle is 50.

Figure 6 shows the fluctuation of mean S/N ratio of

bottom surface roughness with the change in cutter

geometric parameters. The bottom surface roughness

increases with the radial rake angle and primary radial

relief angle on the overall trend. The reason could bethat larger rake angle and relief angle weaken the cutter

which leads to stronger cutter wear and increases

Table 3. The S/N ratio of the experimental results.

Experiment no. S/N (dB)

SRb SRs RSb RSs

1 14.023 15.442 50.511 45.3862 18.786 15.918 46.081 41.386

3 16.595 15.041 48.837 42.2924 17.077 13.597 46.757 41.6705 12.690 15.139 48.553 39.7536 12.181 16.654 44.655 42.4977 12.956 14.155 44.238 42.7668 17.077 18.202 47.673 42.9299 11.634 13.936 45.076 43.06410 11.057 14.023 46.935 44.47511 12.918 17.589 46.386 43.51012 8.826 18.636 45.249 42.33213 18.489 14.023 46.407 41.79114 15.972 15.546 44.023 41.28915 12.111 15.918 46.539 41.60516 9.193 15.239 44.695 43.376


Table 4. Mean S/N ratio for bottom surface roughness.

Factors Level (S/N) Maximumminimum

1 2 3 4

A 16.620 13.726 11.109 13.941 5.511B 14.209 14.499 13.645 13.043 1.456C 12.079 13.103 15.320 14.895 3.241





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vibration in axial direction. Simultaneously, a radial

rake angle also provides a better bottom surface finish

since it aids the chip to flow out from the workpiece.30

Therefore, the bottom surface roughness has obvious

decrease when radial rake angle reaches 16. From thefigure, it can be observed that the bottom surface

roughness decreases as the helix angle increases.

From Table 5, the optimum cutter geometric para-

meters for side surface roughness are as follows: radial

rake angle of 12, primary radial relief angle of 16, and

helix angle of 40. The mean S/N ratio plot of side sur-

face roughness with respect to radial rake angle, pri-mary radial relief angle, and helix angle is shown in

Figure 7. According to parallel shear zone theory,

Figure 6. S/N response graph for bottom surface roughness.

Figure 7. S/N response graph for side surface roughness.

Table 5. Mean S/N ratio for side surface roughness.


1 2 3 4

A 15.000 16.038 16.046 15.182 1.046B 14.635 15.535 15.676 16.419 1.784C 16.231 16.403 15.681 13.950 2.453


Ren et al. 7



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larger positive radial rake angle provides higher shear

angle.31 It also produces sharper cutting edges on the

periphery, which leads to diminishing peripheral milling

force or lateral cutting force. But the excessive rake

angle weakens the cutter and possibly increases accel-

eration amplitude in feed direction.32 Therefore, the

side surface roughness first decreases approaching a

value at a radial rake angle of 12 and then increases.

The side surface roughness decreases with primary

radial relief angle due to the fact that larger relief angle

weakens the friction effect between radial relief surface

and side surface of the workpiece by shortening the

contact length. It can be observed from Figure 7 that as

the helix angle increases, the side surface roughness alsoincreases. A possible reason is that higher helix angle

leads to more roughness heterogeneity bands due to the

grinding errors and high eccentricity of the cutters used

in experiment.33

As to the residual stress, Tables 6 and 7 illustrate the

results of mean S/N ratio for the machined bottom and

side surface. According to the Taguchi method, the

maximum compressive residual stress can be obtained

for bottom surface and side surface at the parameter

levels A1B1C2and A3B4C1, respectively. The mean S/N

ratios at each level are plotted as a response graph

shown in Figures 8 and 9. It can be seen that the resi-

dual compressive stress of the bottom surface monoto-

nically decreases with the radial rake angle. But the

other residual stress curves show no obvious regularity.

Generally, cutting residual stress can be affected bymechanical loading and thermal effects.34 In cutting

process, mechanical load caused by cutting force

Table 6. Mean S/N ratio for residual stress of bottom surface.


1 2 3 4

A 48.047 46.280 45.912 45.416 2.631B 47.637 45.424 46.500 46.094 2.213C 46.562 46.606 46.402 46.084 0.522


Table 7. Mean S/N ratio for residual stress of side surface.


1 2 3 4

A 42.684 41.986 43.345 42.015 1.359B 42.499 42.412 42.543 42.577 0.165C 43.692 41.269 42.394 42.676 2.423


Figure 8. S/N response graph for residual stress of bottom surface.




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induces residual compressive stress, while thermal load

caused by cutting temperature induces residual tensile

stress. Larger cutting force leads to higher cutting tem-

perature. Therefore, residual compressive stress may

increase or decrease with the change in cutting force

caused by varying these cutter geometric angles.

Multi-objective optimization of cutter geometric

parametersAnalysis of S/N ratios is available for single-objective

optimization problem, but ineffective for multi-

response characteristics. It often exists in multi-

objective optimization problem that the higher S/N

ratio for one performance characteristic may corre-

spond to a lower S/N ratio for another. So, it is essen-

tial to evaluate overall S/N ratios in multi-objective

optimization problem. In this study, the multiple per-

formance characteristics are evaluated using the GRA,

which converts a multiple response process optimiza-

tion into a single-objective optimization of the grey

relational grade (GRG).In the GRA, the performance characteristics are first

normalized, ranging from 0 to 1. 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 rep-

resents the correlation between the desired data

sequence and the actual experimental data sequence.

Finally, the GRG sequence can be obtained from the

weighted average of the GRC. The surface integrity of

milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy is eval-

uated by the GRG.

Grey relational generation. In the GRA, raw data prepro-

cessing is the first step, which is known as grey

relational generation. If the purpose is the larger-the-

better, then the normalized results can be expressed as

xi(k) =

x(0)i (k)minfx

(0)i (k)g

maxfx(0)i (k)g minfx(0)i (k)g

,

i= 1, . . . , m, k = 1, . . . , n

5

where xi(k) is the normalized value of the kth perfor-

mance characteristic in the ith experiment, while x(0)i (k)

is the original result of the kth performance characteris-

tic in the ith experiment;m is the total number of tests;

and n is equal to the number of performance

characteristics.

If the target value of the original sequence is the

smaller-the-better performance characteristic, then the

original sequence is normalized as follows

xi(k) =

maxfx(0)i (k)g x(0)i (k)

maxfx(0)i (k)g minfx(0)i (k)g

,

i= 1, . . . , m, k = 1, . . . , n

6

As mentioned above, a larger S/N ratio is desirable

and the larger-the-better is adopted. Consequently,

equation (5), a linear normalization, is used to prepro-

cess the origin response characteristic sequences. The

values of the surface roughness and surface residual

stress are set to be the origin sequence x(0)i (k), where k

is less than or equal to 4 corresponding to the number

of performance characteristics and i is not more than

16 corresponding to the number of experiments. Then,

the S/N ratios obtained by the Taguchi method are nor-

malized in the range of 01. The origin matrix O is the

composition of origin sequence x(0)i (k). After grey rela-

tional generation, the matrix S shows the normalizedresults for surface roughness and surface residual stress.

Basically, the larger normalized results correspond to

Figure 9. S/N response graph for residual stress of side surface.

Ren et al. 9



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the better performance and the best normalized results

should be equal to 1

O1634=

14:023 15:442 50:511 45:386

18:786 15:918 46:081 41:386

16:595 15:041 48:837 42:292

17:077 13:597 46:757 41:670

12:690 15:139 48:553 39:753

12:181 16:654 44:655 42:497

12:956 14:155 44:238 42:766

17:077 18:202 47:673 42:929

11:634 13:936 45:076 43:064

11:057 14:023 46:935 44:475

12:918 17:589 46:386 43:510

8:826 18:636 45:249 42:332

18:489 14:023 46:407 41:791

15:972 15:546 44:023 41:289

12:111 15:918 46:539 41:605

9:193 15:239 44:695 43:376

2

6666666666666666666666666666666664

3

7777777777777777777777777777777775

S1634=

0:522 0:366 1:000 1:000

1:000 0:461 0:317 0:290

0:780 0:287 0:742 0:451

0:828 0:000 0:421 0:340

0:388 0:306 0:698 0:000

0:337 0:607 0:097 0:487

0:415 0:111 0:033 0:535

0:828 0:914 0:563 0:564

0:282 0:067 0:162 0:588

0:224 0:085 0:449 0:838

0:411 0:792 0:364 0:667

0:000 1:000 0:189 0:458

0:970 0:085 0:367 0:362

0:717 0:387 0:000 0:273

0:330 0:461 0:388 0:329

0:037 0:326 0:104 0:643

26666666666666666666666666666666664

37777777777777777777777777777777775

GRC. After obtaining the normalized sequence, the

next step is to calculate the GRC. In the GRA, a higher

value of the GRC, ranging from 0 to 1, corresponds to

intense relational degree between the desired perfor-

mance characteristics and the actual performance char-

acteristics. The GRC is defined as follows

gi(k) =g(x0(k), x

i(k)) =

min8i

min8k

D0i(k) + zmax8i

max8k

D0i(k)

D0i(k) + zmax8i

max8k

D0i(k) ,

i= 1m, k = 1n

7

where

D0i(k) = jxi(k) x

0(k)j 8

0\g(x0(k), xi(k))\ 1

where x0(k) is the reference sequence, xi(k) is the com-

parability sequence, D0i(k) is the deviation sequence of

xi(k) and x

0(k), and z is the distinguishing coefficient

between 0 and 1.

The reference sequence indicates the expected

sequence. According to the normalized results, the ref-

erence sequence should be taken the maximum as

follows

x0= 1,1,1,1 9

The comparability sequencexi(k) has been obtained

from the previous step. Then, according to equation

(8), the maximum and minimum of deviation sequences

are calculated as follows

max8i

max8k

D0i(k) = j01j = 1 , 14i416,14k44 10

min8i

min8k

D0i(k) = j11j = 0 , 14i416,14k44 11

The value ofz is smaller and the identification abil-

ity is larger. In this study, it is set as 0.5.17 With equa-

tion (7), it is easy to obtain the GRC matrix R from the

normalized matrix S

R163 4=

0:511 0:441 1:000 1:0001:000 0:481 0:423 0:4130:694 0:412 0:660 0:477

0:744 0:333 0:463 0:4310:450 0:419 0:623 0:3330:430 0:560 0:356 0:4940:461 0:360 0:341 0:5180:744 0:853 0:534 0:5340:411 0:349 0:374 0:5480:392 0:353 0:476 0:7550:459 0:706 0:440 0:6000:333 1:000 0:381 0:4800:943 0:353 0:441 0:4390:639 0:449 0:333 0:4070:427 0:481 0:450 0:4270:342 0:426 0:358 0:583

2

666666666666666666666666664

3

777777777777777777777777775

Weight coefficient. In order to obtain the GRG sequence,

the weight of multi-performance characteristics needs

to be determined. It is also the weight of the column

vector of matrix R. The previous researchers prefer to

use the same weight, which ignores the difference of

multi-performance characteristics. The weight of vari-

ous performance is different from each other for the

current engineering problem due to variety of surface

integrity properties. In this section, a weight determina-

tion method is proposed to calculate the weight of

milling surface integrity by entropy weight method(EWM) combined with analytic hierarchy process




11/15

(AHP). The amalgamative method reflects the objective

competition level of multi-performance characteristics

by EWM and the specialistic evaluation for these

indexes by AHP.

The process of determining weight of multi-

performance characteristics is as follows:

Step 1. Calculate the objective weight by EWM.

First, calculate the weight of ith experiment for each

performance characteristic by equation (12). In other

words, calculate the weight of ith row by column. The

matrix P can be obtained from the matrix R

Pij= RijPm

i= 1

Rij

(i=1,2, . . . , m;j=1,2, . . . , n) 12

where the Pijis the weight ofith experiment forjth per-

formance characteristic, m is the total number of test,

andn is the number of performance characteristics

P1634=

0:057 0:055 0:131 0:1180:111 0:060 0:055 0:0490:077 0:052 0:086 0:0570:083 0:042 0:060 0:0510:050 0:053 0:081 0:0390:048 0:070 0:047 0:0590:051 0:045 0:045 0:0610:083 0:107 0:070 0:0630:046 0:044 0:049 0:0650:044 0:044 0:062 0:0890:051 0:089 0:057 0:071

0:037 0:125 0:050 0:0570:105 0:044 0:058 0:0520:071 0:056 0:044 0:0480:048 0:060 0:059 0:0510:038 0:053 0:047 0:069

2666666666666666666666666664

3777777777777777777777777775

Second, calculate entropy value of the jth perfor-

mance characteristic. The entropy row vector e can be

obtained from the matrix P by equation (13)

ej= 1

ln m

Xmi= 1

PijlnPij (j=1,2, . . . , n) 13

where e

j is the entropy of the jth performancecharacteristic

e = 0:9782 0:9778 0:9821 0:9861

Finally, determine the entropy weight vector a for

the multi-performance characteristics by equation (14)

aj= 1 ej

nPnj= 1

ej

(j=1,2, . . . , n) 14

where aj is the entropy weight vector for the multi-

performance characteristics

a= 0:288 0:292 0:235 0:183

Step 2. Calculate the subjective weight by AHP.

The subjective weight depends on the specialistic eva-

luation on the specific engineering problems. Table 8

shows the relative importance degree by pairwise com-

parison of the multi-performance characteristics.

Therefore, the judgment matrix J is as follows

J434=

1 1 1

3

1

3

1 1 1

3

1

33 3 1 1

3 3 1 1

2666664

3777775

The weight vector b for multi-performance charac-

teristics can be easily calculated by asymptotic normali-

zation coefficient method

b= 0:125 0:125 0:375 0:375

Step 3. Determine the amalgamative weight vector.

The amalgamative weight of each performance charac-

teristic can expressed as follows

vj=ajbj

Pn1 a

jbj

15

where vj is the weight of the jth performance

characteristic.

The amalgamative weight vector v is calculated by

equation (15) as follows

v= 0:157 0:159 0:384 0:299

GRG. The GRG expresses the correlation between the

comparability sequence and the reference sequence. A

higher GRG presents that the corresponding multi-

performance characteristics are closer to the ideal value.The GRG ranges from 0 to 1 and equals to 1 when the

two sequences agree with each other completely. The

GRG can be expressed as follows

gi(x0, x

i) =

Xnk = 1

vkgi(k), i= 1m, k = 1n

or

g=R3vT 16

where v is the weight factor of the kth performance

characteristic.

The GRG is used to evaluate the overall surfaceintegrity. The parametric combination with highest

GRG implies that the corresponding experimental run

Table 8. Comparison of importance degree.

SRb SRs RSb RSs

SRb 1 1 1/3 1/3SRs 1 1 1/3 1/3RSb 3 3 1 1

RSs 3 3 1 1

Ren et al. 11



12/15

is closest to the optimal value of the desired multiple

performance characteristics.23 The GRG vector g can

be determined by equation (16) as follows. It is clearly

observed that g1 has the largest value among the com-

ponents of vector g. It also suggests that the experi-

ment no. 1 has the optimal surface integrity among the

16 experiments

g=

0:8330:5190:571

0:4760:4760:4410:4150:6170:4270:5260:5330:5010:5050:4210:444

0:433

2

666666666666666666666666664

3

777777777777777777777777775

The average GRGs for each factor level have been

calculated using the process approach similar to that of

the mean S/N ratios, as shown in Table 9. The average

of GRG at each level is plotted as a response shown in

Figure 10. Since the GRG reflects the level of correla-

tion between the comparability and the reference

sequences, a larger GRG represents the comparability

sequence exhibiting a stronger correlation with the ref-

erence sequence [1, 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 A1, B1, and C1 exhibits the largest

value of the GRG for the design factors A, B, and C,

respectively. Consequently, A1B1C1 with a radial rake

angle of 4, primary radial relief angle of 10, and helix

angle of 30is the optimum cutter geometric parameter

combination.

From Table 9, the difference between the maximum

and minimum values of the GRG of the cutter geo-

metric parameters is 0.149 for A, 0.084 forB, and 0.080

for C. 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 milling sur-face integrity. It can be easily observed that the maxi-

mum value among 0.149, 0.084, and 0.080 is 0.149,

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

Factors GRG Maximumminimum Rank

1 2 3 4

A 0.600 0.487 0.497 0.451 0.149 1B 0.560 0.477 0.491 0.507 0.084 2C 0.560 0.485 0.509 0.481 0.080 3

Note: Values in bold face are idea values

GRG: grey relational grade.

Total mean value of the GRG was 0.509.

Figure 10. Response graph of average grey relational grade.




13/15

which means radial rake angle has the most remarkable

effect on the multiple performance characteristics

among the cutter geometric parameters. That is to say

the order of optimization for cutter geometric para-

meters should be A (radial rake angle) . B (primary

radial relief angle) . C(helix angle) in this study.

Validation tests

The estimated GRG gusing the optimum cutter geo-

metric parameters can be expressed as

g=gm+Xni= 1

(gi gm) 17

wheregm is the total mean of the GRG, gis the mean

of the GRG at the optimal level, and n is the number

of control factors that significantly affects the multiple

performance characteristics.

Generally, the GRG under optimal parameters can

be calculated by equation (17) in greyTaguchi method.

As mentioned above, the GRG reaches its maximum

value at A1B1C1 which coincidentally corresponds to

experiment no. 1 in the Taguchi orthogonal array L16

(43). Therefore, one more validation test is superfluous.

The effectiveness of the modified greyTaguchi method

can be verified by comparing the response results of the

parameter combination A1B1C1 and initial parameter

combination. The initial cutter geometric parameters

are selected as A2B1C2 with a radial rake angle of 8,primary radial relief angle of 10, and helix angle of 40

according to engineering experience.

Table 10 illustrates the comparison of the experi-

mental results using the initial and optimal cutter geo-

metric parameters. Under the condition with the levels

A1B1C1of the optimum parameters, the GRG has been

improved by 0.357; the bottom and side surface rough-

ness are decreased to 0.199 (an improvement of 14.2

%) and 0.169 mm (an improvement of 3.40 %), respec-

tively; and the compressive residual stress of bottom

and side surface is improved from 267.7 and 97.2MPa

to 335.4 and 185.9 MPa, respectively. In summary, it isclearly shown that the surface integrity of milling Ti-

5Al-5Mo-5V-1Cr-1Fe titanium alloy can be

significantly improved by optimization of cutter geo-

metric parameters.

Conclusion

This study applies the GRA integrated with the

Taguchi method, EWM, and AHP to optimize the cut-

ter geometric parameters in terms of surface integrity

for milling Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy.

Conclusions are summarized as follows:

1. The validation experiment indicates that the grey

Taguchi method is an effective approach of multi-

objective optimization to the cutter geometry for

machined surface integrity. With this method, the

GRG of the multiple performance characteristics

is significantly improved by 0.357.

2. With the analysis of S/N ratio, the optimum radialrake angle, primary radial relief angle, and helix

angle for bottom surface roughness are 4, 12, and

50, respectively; the optimal controllable factors for

side surface roughness are radial rake angle of 12,

primary radial relief angle of 16, and helix angle of

40; the optimum radial rake angle, primary radial

relief angle, and helix angle for residual stress of bot-

tom surface are 4, 10, and 40, respectively; the

optimal controllable factors for residual stress of

side surface are radial rake angle of 12, primary

radial relief angle of 16, and helix angle of 30.

3. The radial rake angle is the most significant con-trol factor for the milling surface integrity among

the three cutter geometric parameters. The largest

value of GRG is obtained at the combination of

cutter geometric parameters with a radial rake

angle of 4, primary radial relief angle of 10, and

helix angle of 30 It is the recommended levels of

cutter geometric parameters in terms of surface

roughness and residual stress for milling Ti-5Al-

5Mo-5V-1Cr-1Fe titanium alloy.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interestwith respect to the research, authorship, and/or publi-

cation of this article.

Table 10. Comparison results of the initial and optimal cutter geometric parameters.

Initial cutter geometric parameters Optimal cutter geometric parameters Improvement rate (%)

Prediction Validation tests

Level A2B1C2 A1B1C1SRb(mm) 0.232 0.199 14.2SRs(mm) 0.175 0.169 3.40RSb(MPa) 2267.7 2335.4 25.3RSs(MPa) 297.2 2185.9 91.3GRG 0.476 0.702 0.833 75.0

GRG: grey relational grade.

Improvement in the GRG is 0.357.

Ren et al. 13



14/15

Funding

The author(s) disclosed receipt of the following finan-

cial support for the research, authorship, and/or publi-

cation of this article: This work was supported by the

National Science and Technology Major Project of

China (no. 2013ZX04001081) and the Doctorate

Foundation of Northwestern Polytechnical University(no. CX201514).

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Appendix 1

Notationap axial milling depth

ae radial milling depth

A radial rake angle

B primary radial relief angle

C helix angle

e entropy row vector

fz feed rate

J judgment matrix

m total number of tests

n number of performance characteristics

N number of measurements in each test

O matrix composed of origin resultsx(0)

i (k)

Pij weight of theith experiment for thejth

performance characteristic

R matrix composed of the grey relational

coefficients

RSb residual stress of bottom surface

RSs residual stress of side surface

s spindle speedS matrix composed of normalized results of

performance characteristicsxi(k)

S/N signal-to-noise ratio

SRb bottom surface roughness

SRs side surface roughness

x(0)i (k) original result of thekth performance

characteristic in theith experiment

xi(k) normalized value of thekth performance

characteristic in theith experiment

xi(k) comparability sequence

x0(k) reference sequence

yi response value of theith test

a entropy weight vector calculated by EWM

b weight vector calculated by AHP

gi grey relational grade of theith experiment

gi(k) grey relational coefficient of theith

performance characteristic in theith

experiment

g estimated grey relational grade

D0i(k) deviation sequence ofxi(k) andx

0(k)

z distinguishing coefficient

v amalgamative weight vector

Ren et al. 15

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