dimensional quality optimisation of high-speed cnc milling process with dynamic quality...

7/27/2019 Dimensional Quality Optimisation of High-speed CNC Milling Process With Dynamic Quality Characteristic

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greater potential in the dry turning and milling of

ALSi10MG casting alloy compared with PCD and K10.

Vieira et al. [11] investigated the performance of cutting

fluids during HS face milling of steels. They reported

that semi-synthetic cutting fluid exhibited the best

cooling effects in the HS machining process, followed

by the emulsion-based mineral fluid, and the 10%concentration of synthetic fluids. The converse observa-

tion was made on the power consumption. Avila et al.

[12] investigated the effects of the HS cutting fluids on

turning hardened AISI 4340 steel using mixed alumina

(Al2O3+TiC). They found that appropriate use of

emulsion without mineral oil led to better tool life,

surface finish and chip control. Su et al. [1315] studied

the effects of the coated materials on HS milling process

using Taguchi static approach. Their results showed that

multi-layer coating construction has better performance

on the cutting tool wear than single layer at the same

thickness basis.

The research for investigating factors effects of HS

cutting process and improving its performance have

continuously received much attention worldwide. Of the

various study methodologies, Taguchi method is the

preferred approach to undertake the present study as it

has been proved to be an effective and efficient

approach. However, most past Taguchi experiments

concentrated on the optimisation of static or single

quality characteristic, indicating that only a fixed output

target instead of a wide range is developed. A new

parameter design has to be developed whenever a new

process/product is planned, leading to a waste of time

and money.Nowadays the international market in the mold and

die manufacture industry becomes increasingly compe-

titive. To meet customer requirements for short delivery,

high quality, and low cost, the high-speed CNC milling

process must have the capability of versatility, flexibility,

and robustness. Taguchi dynamic approach can be far

more powerful in developing a robust process design

with dynamic quality characteristic. Hence, the main

objective of this study is an attempt to apply Taguchi

dynamic approach to optimise the dimensional quality

of high-speed CNC milling process with dynamic quality

characteristic.

2. Equipments and materials

Feeler QM-22 CNC 3-axis milling machine with the

maximum spindle revolution 30000 rpm was used

throughout the experiments coupled with a c 6 mm

end-milling cutter. Mitutoyo MF Series toolmakers

microscope and SJ-301 surface profiler were used to

measure the dimension and surface roughness of the

machined products, respectively. Tool steels SKD61 and

SKD11 were selected as the materials with the chemical

compositions as displayed in Table 1.

3. Experimental

3.1. Engineered system and Taguchi robust design

As shown in Fig. 1, any man-made machine or

equipment is regarded by Taguchi methods as an

engineered system with a specific function, requested

by customers. The system consists mainly of four

components including control, noise, signal factors,

and output response. A control factor is a factor that

can be selected and fixed to a certain level after

parameter design. However, a noise factor is a factor

that cannot be controlled, due to either practical or

economical reasons. Noise entering a system may take

many forms, and is a true disturbance to the engineered

system. Signal factor is a factor to change the output

response which is what the system is designed toproduce. When the output response of an engineered

system can dynamically vary with the input signal to

generate a range of responses, it has the so-called

dynamic quality characteristic [17].

Engineered system starts to use energy transformation

to carry out its function when the input signal is

received. The process of energy transformation is

governed by the control factors to convert input energy

into intended output energy by using laws of physics.

The engineered system reaches its ideal function when

all of its applied energy is transformed efficiently into

creating desired output energy. However, noise factorsusually cause variability in the energy transformations

leading to unintended outputs.

In every engineered system, there exists some form of

ideal relationship between its input signal and output

response. However, correct identification of an ideal

function is not easy, and ideal function may differ from

case to case. One of the most common ways of

expressing a designs ideal function is

Y fM bM, (1)

where a linear relationship with a slope b exists between

Y (=ideal output response) and M (=input signal) as

ARTICLE IN PRESS

Table 1

The chemical compositions of tool steel [16]

Material Chemical composition (%)

C Si Mn P S Cr Mo V Cu

SKD11 1.5 0.4 0.6 0.03 0.03 12 1.0 0.35 0.25

SKD61 0.37 1.0 0.5 0.03 0.03 5.0 1.25 1.0 0.25

T. Yih-fong, J. Ming-der / Robotics and Computer-Integrated Manufacturing 21 (2005) 506517 507


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shown in Fig. 2(a). However, in reality, energy

transformation of any system does not happen as

designed or intended, because there might be noise

factors disturbing the system. The reality of the system

function consists of nonlinear effects between the input

and output that can be mathematically described as

follows:

Yr fM; C1; C2; C3;. . .

; Cm; N1; N2; N3;. . .

; Nn bMferrorM; C1; C2; C3; . . . ; Cm; N1; N2; N3; . . . ; Nn

YferrorM; C1; C2; C3; . . . ; Cm; N1; N2; N3; . . . ; 2Nn,

2

where Yr is the real output response, C1; C2; C3; . . . ; Cmthe control factors, N1; N2; N3; . . . ; Nn the noise factors,and ferror the difference between the ideal function

and the reality. The real function is demonstrated by

Fig. 2(b).

Orthogonal array is well known as one of the most

important tools used in Taguchi robust design because it

provides a fair comparison of any factor. This enablessufficient information to be collected by conducting only

partial series of experiments. Taguchi parameter design

strategy separates the control factors from both the

noises and the signals by using inner and outer arrays,

respectively. Noise factors coupled with signal factor are

assigned to the outer array for exposing the process to

varying noise conditions. An experiment is conducted

for all combinations between the inner and the outer

arrays. The tendencies of control factors, and how these

may affect robustness are evaluated. The best combina-

tion of control factor levels is therefore sought so that

the system becomes most insensitive to noise factors.

When such a technology is developed, it has a robust

function [17].

Taguchi robust design seeks to attain the ideal state of

an engineered system, referred to as the designs ideal

function. Proper level settings of control factors will not

only make the design robust against noise factors, but

also can adjust the output response to the desired target.Therefore, ferror stably gets close to its minimum, and

then Yr approaches to Y bM:

3.2. Proposed ideal function model for CNC milling

system

Fig. 3 is the application of Taguchis concept about an

engineering system in the high-speed CNC machining

process. The high-speed CNC milling system is essen-

tially designed to perform material removal for produ-

cing high-dimensional quality of products requested by

the customers. The input signal, reflecting the intent of

the customers, to the CNC milling system represents

the factor informing system of exactly what job to do. It

can be perceived as the programmed geometrical

dimension of product to be machined for driving

the machining function to transform the solid model

on the PC to the work piece. If there is no energy loss

due to noise factors to create symptoms of poor

function, such as tool wear, vibration, noise, lubricant

aging, etc., the geometrical shape of solid model on the

PC will be accurately duplicated on the work piece.

Hence, the ideal function of the CNC milling systemcan be defined in terms of transformability. The ideal

function Y bM is modelled as Y being the desired

product dimension, M the programmed dimension,

and b 1:

3.3. Robustness evaluation using signal/noise ratio

The signal-to-noise (S/N) ratio originated in the

communication field. Taguchi methods expanded its

function into quality engineering area including staticand dynamic characteristics. As for the dynamic-type

S/N ratio, it is written based on the ideal function of a

product or process that is related with input/output

energy transformation. For any engineered system, as

the input signal, control factors, and noise factors come

together to perform its designed function, their com-

bined impacts on the output response can be evaluated

using the dynamic-type S/Nratio to measure the quality

of energy transformation. As shown in Fig. 3, the output

response of high-speed CNC milling system consists

of the so-called useful and harmful outputs. For a

dynamic quality characteristic application, the concept

ARTICLE IN PRESS

Control Factors

Engineered

SystemsOutput Response

Noise Factors

Signal Factors

Fig. 1. An engineered system model used by Taguchi methods.

Fig. 2. (a) The systems ideal function and (b) its reality.

T. Yih-fong, J. Ming-der / Robotics and Computer-Integrated Manufacturing 21 (2005) 506517508


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of S/N ratio is [17]

Z Useful output

Harmful output

10 logLinear relationship between M and Y

Variability around the linear relationship

10 logb2

s2 , 3

where b is the slope of best-fit line between the measured

values and the inputs, and s2 the variability around the

best-fit line.

The S/N ratio measures the level of system perfor-

mance and the effects of noise factors on performance so

that it can be employed as an indicator of the

consistency of a given system. The higher this ratio,

the more the system is doing what is intended to do

regardless of noise factors and the system is more robust

against noise.

3.4. Control factors and their levels

An L18 is selected for arranging the overall experi-

mental tests. Eight dominant process conditions

of the high-speed CNC milling process are identi-

fied as the control factors, which are listed in Table 2

together with their alternative levels. It is noted

that most of the factors has three levels except factor

A, which has two. All levels are selected for proper

reasons.

3.5. Noise factors

Generally, there are a lot of noise factors associated

with the high-speed CNC milling process, such as,

material lot, machine setting variability, material hard-

ness variability, lubricant condition, tool wear, and

manufacturing variability of milling machine, etc. Due

to hard control, Taguchi methods suggested the use of

the compounding strategy to arrange them to be two

extreme conditions. For the simplification of experi-

mentation, only material hardness variability is chosen

as the noise factor. The identified two noise conditions

of N1 and N2 are displayed in Table 3. It is designed so

ARTICLE IN PRESS

Fig. 3. The schematic of an engineering system as a high-speed CNC milling system.

Table 2

Control factors and their levels

Control

factors

Level

1 2 3

A Milling type Downward

mill

Upward

mill

B Cutting speed

(m/min)

150 225 300

C Feed per tooth

(mm/tooth)

0.03 0.04 0.05

D Film material TiCN TiN TiAlN

E Tool material K10 (Co 8%) K20 (Co

10%)

K30 (Co

12%)

F Number of tooth 2 3 4

G Rake angle 41 71 101

H Helix angle 301 351 451



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because that from the standpoint of energy the softer

material is easier to be machined, and vice versa.

3.6. Test piece and signal arrangements

How to vary the signals experimentally is also one of

the most important steps in the Taguchi robust design.Since some of the research objectives are to develop

versatility and flexibility into the high-speed CNC mill-

ing process, the optimised technology development must

be applicable to a family of products and future pro-

ducts. Therefore, it is most effective to specify the signal

levels so that the range covers all usage conditions.

In view of this goal, test piece with a range of

geometrical characteristics is designed for the study. Allof the test workpieces is finish machined with a constant

depth of cut of 0.1 mm. The test piece is easier to

measure dimensions and would allow them to evaluate

multiple levels of the signal easily. Fig. 4 illustrates

the test piece we designed for the study. As shown in

Fig. 4(a), the test piece has three typical of geometrical

characteristics to be machined, including rectangular,

circle, and triangle on each of three layers with a volume

ratio of 1:2:3.

ARTICLE IN PRESS

Table 3

Noise factors arranged as two extreme conditions

Noise factors Material Hardness (HRC)

N1 (positive side extreme condition) SKD11 2123

N2 (negative side extreme condition) SKD61 1719

Fig. 4. The designed test piece for experimentations: (a) solid modeling, (b) top view with the programmed vertices, diameters, and circle center, (c)

side view.



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As illustrated in Fig. 4(b), the zero point is fixed on

the (0,0) point on the southwest corner. All locations on

the rectangular and triangles are defined by positive X

and Y coordinates relative to the fixed origin. The

diameters of three circles are defined in the same

fashion, but in relation to their fixed center point (Pi;i=2527). The programmed dimensions for positioning

the various vertices, diameters, and the common circle

center are listed in Table 4. There are a total of 51 of the

programmed dimensions used as the input signals in an

incremental way.

4. Experimental results and analysis

4.1. General effects of control factors

Fig. 5 plots the entire experimental results as the

input/output relationship that shows slight scattering

phenomena due to noise effects. Table 5 displays a

complete experimental layout, resultant data, and

performance evaluation. The linearity effects of each

experimental arrangement are evaluated by computing

their dynamic S/N ratios as shown in Table 5. The

slopes of the best-fit line for the defined ideal function

model are calculated using simple linear regression

analysis and listed in Table 5. Another importantmeaning of the combination and S/N ratio and slope

here is that it represents the input/output transform-

ability of high-speed CNC milling system under the

defined experimental conditions. That is, the larger S/N

ratio coupled with near-one slope, the higher both the

linear effects and the transformability between input and

output. Those S/N data can be further translated into

the effect each control factor has on S/N by computing

their average values as listed in Table 6. Fig. 6 is its

response graph.

Table 6 suggests that the best levels for each control

factors are A1; B1; C3; D3; E2; F3; G1; and H1 due to

their maximum S/N ratios. The maxmin value is

equal to the range of S/N ratio variance due to the

change in the level setting. The larger the range,

the more powerful impact the control factor has on

the dimensional precision. The ranking in Table 6

demonstrates that factor A (milling type), factor B

(cutting speed), and factor F (number of tooth) have

relatively strong impacts on the dimensional precision,

while C, D, E, G, and H have relatively weak impacts.

Factors A, B, and F should be strictly controlled for

high-dimensional precision during the high-speed CNC

milling process.

Factor B (cutting speed) has been found to be the

most important factor governing process robustness

(dimensional quality) because of the maximum changein S/Nratios. It is due to cutting speed directly affecting

tool wear. This is why the lowest speed level B1 results

in the best dimensional quality. Factor A (milling type)

is identified as the second due to its significant influence

in vibration. A1 is downward milling type, causing

smaller vibration. Factor F (number of tooth) is the

third. F3 is the best level setting due to smaller cutting

force.

The slope of the best-fit line in the study technically

denotes the overcutting or undercutting effects of

the machined products. When the slope is greater

than 1, the machined product has the undercuttingeffects, the larger the more serious, and vice versa.

It is noted in Table 5 that all of the arranged

experimental conditions in L18 array led to under-

cutting effects. Table 7 shows the average effects

each control factors have on slope and Fig. 7 is its

response graph. The same observation about under-

cutting effects is made for all of the control factors.

The ranking in Table 7 displays that control factors A,

B, and F have stronger cutting effects on the dimen-

sional accuracy of machined products. Of the control

factors, factor A is the most important due to its largest

impact.

ARTICLE IN PRESS

Table 4

Input signals, and their corresponding positions and programmed dimensions

Input signal M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14Position P1X P1Y P6Y P7X P19Y P2X P8X P2Y P5Y P20Y P3X P9X P3Y P6Y

Programmed dimension (mm) 2.4 2.4 2.4 2.4 2.4 5.55 5.55 6.4 6.4 6.4 9.06 9.06 12.4 12.4

Input signal M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27 M28

Position P19Y P24 P13Y P14Y P15Y P25Y P26Y P27Y P23 P6X P12X P5X P11X P23Programmed dimension (mm) 12.4 19.2258 24.9 24.9 24.9 24.9 24.9 24.9 27.1894 29.04 29.04 32.55 32.55 33.3

Input signal M29 M30 M31 M32 M33 M34 M35 M36 M37 M38 M39 M40 M41 M42

Position P4X P10X P9Y P12Y P18Y P8Y P11Y P17Y P7Y P10Y P16Y P25X P26X P27XProgrammed dimension (mm) 35.7 35.7 37.4 37.4 37.4 43.4 43.4 43.4 47.4 47.4 47.4 58.425 58.425 58.425

Input signal M43 M44 M45 M46 M47 M48 M49 M50 M51

Position P13X P14X P15X P21X P21X P17X P20X P18X P19XProg rammed dimensi on ( mm) 81. 15 84. 3 87. 81 1 07 .79 10 7. 79 1 11 .3 1 11 .3 114 .4 5 11 4.4 5



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4.2. Analysis of variance (ANOVA)

The analysis of variance (ANOVA) on the experi-

mental results is performed to evaluate the source of

variation during the high-speed CNC milling process.

From the analysis, it is easy to identify which factors are

the most important in terms of quality characteristic.

Consequently, those important factors have to be

carefully monitored during the process for a consistently

high-quality product.

Table 8 shows the ANOVA that is done on

the S/N ratios. It is therefore easy to see that

factors A, B, and F are the most important in terms

of dimensional quality. These three factors account

for about 65 percent of the experimental variance.

The observation agrees well with those reflected in

ARTICLE IN PRESS

Table 5

Experimental layout, resultant data, and performance evaluation

NO Control factors M1 (2.4mm) M2 (2.4mm) M50 (114.45mm) M51 (114.45mm) Performance evaluation

A B C D E F G H N 1 N2 N1 N2 N1 N2 N1 N2 S/N (db) Slope (b)

1 1 1 1 1 1 1 1 1 2.3392 2.3474 2.3547 2.3565 114.5024 114.4947 114.4930 114.4514 26.3816 1.000001

2 1 1 2 2 2 2 2 2 2.3426 2.3960 2.3956 2.3908 114.4463 114.5182 114.4510 114.4645 30.0520 1.000051

3 1 1 3 3 3 3 3 3 2.4030 2.3968 2.3848 2.4046 114.5107 114.4803 114.5012 114.4508 31.5543 1.000270

4 1 2 1 1 2 2 3 3 2.2512 2.3144 2.2703 2.3849 114.5619 114.5108 114.5201 114.4604 21.4463 1.000260

5 1 2 2 2 3 3 1 1 2.3269 2.3904 2.3280 2.3733 114.5227 114.4910 114.5659 114.4735 26.1627 1.000324

6 1 2 3 3 1 1 2 2 2.2854 2.3493 2.3074 2.3755 114.6139 114.6169 114.6715 114.6003 21.1510 1.000929

7 1 3 1 2 1 3 2 3 2.1593 2.3501 2.2139 2.3792 114.6374 114.4911 114.6078 114.4749 19.6770 1.000283

8 1 3 2 3 2 1 3 1 2.3809 2.3657 2.3372 2.3376 114.5573 114.4899 114.5087 114.4664 24.1879 1.000105

9 1 3 3 1 3 2 1 2 2.3296 2.3652 2.3396 2.3929 114.5438 114.4695 114.5461 114.4281 23.6981 1.000300

10 2 1 1 3 3 2 2 1 2.3458 2.3863 2.3265 2.3925 114.5476 114.4933 114.5326 114.4704 24.0331 1.000273

11 2 1 2 1 1 3 3 2 2.3134 2.3033 2.3096 2.3656 114.5829 114.4428 114.6165 114.5200 20.7488 1.000213

12 2 1 3 2 2 1 1 3 2.3379 2.3653 2.3447 2.3524 114.6115 114.5321 114.6151 114.5331 22.4899 1.000859

13 2 2 1 2 3 1 3 2 2.1212 2.3235 2.0641 2.3146 114.8699 114.5506 114.8776 114.5712 14.0266 1.001444

14 2 2 2 3 1 2 1 3 2.3485 2.3645 2.3459 2.3810 114.5181 114.4941 114.5665 114.4937 21.7157 1.000340

15 2 2 3 1 2 3 2 1 2.3382 2.3878 2.3158 2.3966 114.5993 114.4978 114.6720 114.4842 24.3425 1.000624

16 2 3 1 3 2 3 1 2 2.3256 2.3925 2.3223 2.3645 114.5560 114.5319 114.5801 114.5310 25.4485 1.000453

17 2 3 2 1 3 1 2 3 2.0989 2.2817 2.1220 2.3633 114.7854 114.5193 114.7802 114.4915 13.8235 1.001144

18 2 3 3 2 1 2 3 1 2.1808 2.3856 2.1357 2.2879 114.8085 114.5074 114.7783 114.5056 16.4607 1.001239

Table 6

S/N ratio response table

Level A B C D E F G H

1 24.9234 25.8766 21.8355 21.7401 21.0225 20.3434 24.3161 23.5947

2 20.3433 21.4741 22.7818 21.4781 24.6612 22.9010 22.1798 22.5208

3 20.5493 23.2828 24.6817 22.2164 24.6556 21.4041 21.7845

Maxmin 4.5802 5.3274 1.4472 3.2036 3.6387 4.3122 2.9120 1.8103Ranking 2 1 8 5 4 3 6 7

0

10

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Programmed dimension(mm)

Product

dimension(mm)

Fig. 5. The complete results plotted as the input/output relationship.



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Table 6 and Fig. 6. Additionally, error contributing

about 3.4% to total variance indicates that experi-

mentation is fairly successful and reliable. It is also

found that ANOVA has almost the same function as

Table 6 except for the provision of more detailed

information.

4.3. High-speed CNC milling process optimisation

The goal for study is to seek a robust process design

for which the high-speed CNC milling process can

always produce a variety of products with high-

dimensional quality. To meet this goal, Taguchi

proposed a two-step optimisation strategy in obtaining

the best process conditions. The two-step optimisation

strategy reduces the variations in the product dimension

in the first step and then adjusts the slope of the bestfitting line to the desired level. The optimisation is:

Step 1: reduce dimensional variability. To produce the

strongest linear relation between signal factor (M=pro-

grammed dimension) and output response (Y=product

dimension), it is necessary to reduce dimensional

variability. As such, the optimal levels for each control

factors are those levels that maximise S/Nratios leading

to a robust machining performance, i.e. high-dimen-

sional precision. The selected levels are A1; B1; C3; D3;E2; F3; G1; and H1:

Step 2: adjust slope to the desired level. According to

the dynamic formula Y bM; it appears to select the

ARTICLE IN PRESS

26.6333

A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3

Controlfactors and their levels

S/Nratio(db)

22.6333

18.6333

Fig. 6. S/N ratio response graph.

Table 7

Slope response table

Level A B C D E F G H

1 1.000280 1.000278 1.000452 1.000424 1.000501 1.000747 1.000379 1.000428

2 1.000732 1.000653 1.000363 1.000700 1.000392 1.000410 1.000551 1.000565

3 1.000587 1.000703 1.000395 1.000626 1.000361 1.000588 1.000526

Max-min 0.000452 0.000376 0.000341 0.000305 0.000234 0.000386 0.000209 0.000137Ranking 1 3 4 5 6 2 7 8

1.000206

1.000506

1.000806

A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3

Control factors and their levels

Slope

Fig. 7. Slope response graph.

Table 8

Analysis of variance

Control factors S F V r (%)

A 94.4012 1 94.4012 24.5815

B 97.2363 2 48.6181 25.3198

C 6.4818 2 3.2409 1.6878

D 37.9696 2 18.9848 9.8871

E 41.2854 2 20.6427 10.7505

F 56.4299 2 28.2149 14.6940

G 27.2900 2 13.6450 7.1062

H 9.9452 2 4.9726 2.5897

Error 12.9939 2 6.4970 3.3835

Total 384.0333 100



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slope (b) closer to 1 for higher machining accuracy.

However, it must be noted that the adjustment of the

slope is best not to affect the process robustness. Based

on this principle, since all other control factors working

at the optimal level have already achieved both highest

S/N ratios and smallest slopes, the slope for control

factor C (feed per tooth) is the best choice foradjustment. It is therefore predicted that the change

from C3 to C2 leads to a highest machining accuracy

without significantly affecting process robustness. Thus,

the predicted optimal combination is selected as A1; B1;C2; D3; E2; F3; G1; and H1:

4.4. Optimal performance forecasting

Taguchi methods require a confirmation run to check

for both the validity of experimentation and, also the

reproducibility of the experimental results. It is im-

portant to predict the performance under the optimal

conditions before running the confirmation. The pre-

dictions of S/N ratio and slope for the optimal

conditions can be calculated by means of the additively

law as follows:

For the optimal conditions: A1; B1; C2; D3; E2; F3; G1;H1

Zopt A1 B1 C2 D3 E2 F3 G1 H1 7TZ

24:9234 25:8766 23:2828 24:6817 24:6612

24:6556 24:3161 23:5947 7 22:6333

37:5588 db,

bopt A1 B1 C2 D3 E2 F3 G1 H1 7Tb

1:000280 1:000278 1:000363 1:000395

1:000392 1:000361 1:000379 1:000428

7 1:000506

0:999334.

For the initial conditions: A1; B1; C1; D1; E1; F1; G1; H1

Zinitial A1 B1 C1 D1 E1 F1 G1 H1 7TZ

24:9234 25:8766 21:8355 21:7401 21:0225

20:3434 24:3161 23:5947 7 22:6333

25:2190 db,

binitial A1 B1 C1 D1 E1 F1 G1 H1 7Tb

1:000280 1:000278 1:000452 1:000424

1:000501 1:000747 1:000379 1:000428

7 1:000506

0:999946,

where TZ and Tb represented the average effects of the

overall control factors.

As a result, 12.3398 db db gain in S/N ratio is

predicted.

4.5. Confirmation run

Fig. 8 is plotted from confirmation results for the

optimal conditions. Table 9 is the comparison of the

prediction and the confirmation between the initial and

the optimal conditions. It is noted that the confirmed

S/N ratio 37.2933 db for the optimal conditions is still

the best when compared to the entire results in Table 5.

The actual gain is 10.9117 db that is very close to the

predicted 12.3398 db. This indicates the best combina-

tion of the control factors level setting is robust enough

against noise effects and results in high reproducibility.

Accordingly, as demonstrated in Fig. 8, there is a very

strong linear relationship between the input pro-

grammed dimension and the product dimension.

Furthermore, the % variability range improved can be

ARTICLE IN PRESS

y = 1.000101 x

0

10

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

Programmed dimension (mm)

Productdimension(m

m)

Fig. 8. Plot of the confirmation results as input/output relationship.



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calculated by the equation

% variabilityrange improved 1

2

gain=6

% variability rangeinitial. 4

So the gain of 10.9117 db is equivalent to reducing thevariation range by 10.5(10.9117/6)=71.6508 which in-

dicates that the process robustness has improved 3.53

times.

It is also noted in Fig. 8 that using simple regression

analysis of the confirmation run data generates the best-

fit line equation Y=1.000101X. This is in practice the

best functional relationship between input signal and

output response of the high-speed CNC milling system

under the optimal conditions. It can be estimated

through the equation Y=1.000101M that the under-

cutting of the machined product dimension is

1:000101 M M=M 100% 0:0101%.

If there is still a need to adjust the product dimension for

suitable dimensional allowance for meeting post-proces-

sing and customer requirements, the input programmed

dimension can be modified through the following

mathematical relationship:

adjusted 1

1:000101Yfinal, (5)

where Madjusted is the adjusted input programmeddimension, and Yfinal is the desired final product

dimension.

4.6. Cutter flank wear and work piece surface roughness

analysis

Table 10 shows the cutter flank wear and the work

piece surface roughness analysis comparison between

the raw experimental runs and the confirmation trial.

Flank wear values are the average of the data mea-

sured on each tooth of the milling cutter. Roughness

values are the average of 18 data measured on thesurface of the machined product. It is clear that

the average flank wear values are among the range

of 132.43411887.0565mm for N1 condition and of

60.9085375.2826mm for N2 condition. The average

surface roughness values are found among the range of

0.25330.4833mm for N1 and of 0.18330.3617mm for

N2 condition. The results indicate that for both the

cutter flank wear and the work piece surface roughness,

N2 is appreciably better than N1 because of their lower

values plus with narrower ranges. This is due to that

material used in N1 is harder, causing more cutting tool

wear and then worse surface quality.

ARTICLE IN PRESS

Table 9

The comparison between the prediction and the confirmation

Level combination Prediction Confirmation

S/N (db) Slope (b) S/N (db) Slope (b)

Initial A1B1C1D1E1F1G1H1 25.2190 0.999946 26.3816 1.000001

Optimum A1B1C2D3E2F3G1H1 37.5588 0.999334 37.2933 1.000101

Gain 12.3398 10.9117

Table 10

Cutter flank wear and work piece surface roughness results

NO Control factors Average flank wear (mm) Average roughness: Ra (mm)

A B C D E F G H N 1 N2 N1 N2

1 1 1 1 1 1 1 1 1 323.8422 215.8492 0.2533 0.1844

2 1 1 2 2 2 2 2 2 417.3984 140.2617 0.4028 0.1911

3 1 1 3 3 3 3 3 3 136.6434 133.7832 0.3983 0.3617

4 1 2 1 1 2 2 3 3 275.0565 194.1669 0.2556 0.1833

5 1 2 2 2 3 3 1 1 477.6723 158.6058 0.3600 0.2461

6 1 2 3 3 1 1 2 2 729.1758 60.9085 0.2856 0.2361

7 1 3 1 2 1 3 2 3 945.8786 177.0516 0.3867 0.3189

8 1 3 2 3 2 1 3 1 537.9706 86.3831 0.2756 0.2811

9 1 3 3 1 3 2 1 2 1283.2963 167.0189 0.4394 0.3344

10 2 1 1 3 3 2 2 1 132.4341 97.5158 0.3178 0.2767

11 2 1 2 1 1 3 3 2 323.2417 154.5529 0.2694 0.2733

12 2 1 3 2 2 1 1 3 725.3799 273.2197 0.3778 0.2739

13 2 2 1 2 3 1 3 2 1470.6875 375.2826 0.4833 0.2250

14 2 2 2 3 1 2 1 3 229.2672 338.1873 0.3289 0.3039

15 2 2 3 1 2 3 2 1 202.1113 67.3019 0.3667 0.3106

16 2 3 1 3 2 3 1 2 620.2814 119.4116 0.3428 0.3261

17 2 3 2 1 3 1 2 3 747.5027 117.9605 0.3806 0.2378

18 2 3 3 2 1 2 3 1 1887.0565 124.0422 0.3472 0.3578

Confirmed 1 1 2 3 2 3 1 1 180.6815 79.9970 0.3111 0.2244



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It is noted in Figs. 9(a), (c), (e), and (g) that the

optimal conditions results in better form shape at the

corners of the machined products. It is also observed in

Figs. 9(b), (d), (f), and (h) that flank wear has been

significantly improved at the optimal conditions which

has 180.6815mm for N1 condition, and 79.9970 mm for

N2 condition. Compared to the entire results in the L18

array, they are better than most of the data. Similar

observation is made on the surface roughness analysis.

It seems to point out that the optimised processparameters developed in terms of dimension vs. dimen-

sion also works in both the reduction in tool wear and

the improvement in surface roughness.

4.7. Conclusion remarks

The study using Taguchi dynamic experiment coupled

with the ideal function model of programmed dimension

vs. product dimension has been very successful in

developing a robust, versatile, high-dimensional quality

of high-speed CNC milling technology. Based on the

experimental results, conclusions can be drawn as

follows:

1. The optimised control factors are: A1 (milling type),

B1 (cutting speed), C2 (feed per tooth), D3 (film

material), E2 (tool material), F3 (number of tooth),

G1 (rake angle), and H1 (helix angle).

2. The most important factors identified by S=N andANOVA analysis affecting the process robustness are

in a decreasing manner: factor B (cutting speed),factor A (milling type), and F (number of tooth).

They account for about 65% of total variance.

3. Actual gain 10.9117 db is very close to the predicted

12.3398 db. It shows very good reproducibility and

confirms the success of the experiment.

4. Dimensional variability after process optimization

has been significantly improved to be 28.3492% of

the initial conditions, leading to 3.55903 times

improvement in the process robustness.

5. The optimal function between input signal and

output response can be linearly described as

Y=1.000101M.

ARTICLE IN PRESS

Fig. 9. OM photographs of the form shape of the machined products and the flank wear of the cutting tools. (a), (b), (c), and (d) are for the initialconditions and (e), (f), (g), (h) for the optimal conditions.



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References

[1] Fallbohmer P, Rodriguez CA, Ozel T, Altan T. High-speed

machining of cast iron and alloy steels for die and mold

manufacturing. J. Mater. Process. Technol. 2000;98:10415.

[2] Ning Y, Rahman M, Wong YS. Investigation of chip formation

in high speed end milling. J. Mater. Process. Technol. 2001;113:

3607.[3] He N, Lee TC, Lau WS, Chan SK. Assessment of deformation of

a shear localized chip in high speed machining. J. Mater. Process.

Technol. 2002;129:1014.

[4] Gu J, Barber G, Tung S, Gu RJ. Tool life and mechanism of

uncoated and coated milling inserts. Wear 1999;225:27384.

[5] Jawaid A, Koksal S, Sharif S. Cutting performance and wear

characteristics of PVD coated and uncoated carbide tools in face

milling Inconel 718 aerospace alloy. J. Mater. Process. Technol.

2001;116:29.

[6] Smith S, Dvorak D. Tool path strategies for high speed milling

aluminum workpieces with thin webs. Mechatronics 1998;8:

291300.

[7] Dolinsek S, Sustarsic B, Kopac J. Wear mechanism of cutting

tools in high-speed cutting processes. Wear 2001;250:34956.

[8] Diniz AE, Micaroni R. Cutting condition for finish turningprocess aiming: the use of dry cutting. Int. J. Mach. Tools Manuf.

2002;42:899904.

[9] Gunter KL, Sutherland JW. An experimental investigation

into the effect of process conditions on the mass concentra-

tion of cutting fluid mist in turning. J. Cleaner Product. 1999;7:

34150.

[10] Lahres M, Jorgensen G. Properties and dry cutting perfor-

mance of diamond-coated tools. Surf. Coat. Technol. 1997;96:

198204.

[11] Vieira JM, Machado AR, Ezugwu EO. Performance of cuttingfluids during face milling of steels. J. Mater. Process. Technol.

2001;116:24451.

[12] Avila RF, Abrao AM. The effect of cutting fluids on the

machining of hardened AISI 4340 steel. J. Mater. Process.

Technol. 2001;119:216.

[13] Su YL, Yao SH, Wei CS, Wu CT. Analyses and design

of a WC milling cutter with TiCN coating. Wear 1998;215:

5966.

[14] Su YL, Yao SH, Wei CS, Wu CT, Kao WH. Design of a titanium

nitride-coated WC milling cutter. J. Mater. Process. Technol.

1999;86:2336.

[15] Su YL, Kao WH. Optimum multiplayer TiNTiCN coatings for

wear resistance and actual application. Wear 1998;223:11930.

[16] Huang JC. Metal Handbook, Machinery, 2nd ed. Taiwan: Taipei;

2001.[17] Robust Design Using Taguchi Methods, Workshop Manual, 3rd

Version, 2000, ASI.

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