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International Journal of Lean Thinking Volume 3, Issue 2 (December 2012)

Lean Thinkingjournal homepage: www.thinkinglean.com/ijlt

APPLICATION OF GRAY RELATIONAL ANALYSIS FOR SURFACE ROUGHNESS AND

ROUNDNESS ERROR IN DRILLING OF AL 6061 ALLOY

Reddy Sreenivasulu* Dept of

Mechanical Engineering,RVR&JC College of Engineering,Guntur, Andhra Pradesh,

India. Email: [email protected]

Dr.Ch.SrinivasaRao Dept of Mechanical Engineering ,University college of Engineering.,

Andhra University, Visakhapatnam, Andhra Pradesh, India.

A B S T R A C T K E Y W O R D S

A R T I C L E I N F O

Drilling Surface Roughness

Roundness Error

Taguchi method,

Gray relational analysis,

Al6061 Alloy

Received 07 June 2012

Accepted 15 June 2012

Available online 01 October 2012

In this study, the effects of drilling parameters on surface

roughness and roundness error were investigated in drilling of

AI6061 alloy with HSS twist drills. In addition, optimal control

factors for the hole quality were determined by using Taguchi -

Gray relational analysis. Cutting speed, feed rate, drill diameter,

point angle and cutting fluid mixture ratio were considered as

control factors, and L18 (3*5) orthogonal array was determined for

experimental trials. Gray relational analysis was employed to

minimize the surface roughness and roundness error achieved via

experimental design. Minimum surface roughness and roundness

error were obtained with treated drills at 25.13 m/min cutting

speed and 0.3 mm/rev feed rate,10mm drill diameter, 110 degrees

point angle and 12% cutting fluid mixture ratio. Confirmation

experiments showed that Gray relational analysis precisely

optimized the drilling parameters in drilling of Al6061 alloy.

________________________________

* Corresponding Author

1. Introduction

To provide cost effectiveness in manufacturing and especially machining operations,

there is a continuous need to reduce tooling costs. The most well-known methods used to

reduce tooling costs are various applications of more resistant tool materials, heat treatments,

cutting fluids, speed and feed rates, and the development of coated cutting tool. But also

provides significant benefits for machining conditions. The surface quality is an important

parameter to evaluate the productivity of machine tools as well as machined components.

Hence, achieving the desired surface quality is of great importance for the functional behavior

of the mechanical parts. A reasonably good surface finish is desired for improving the

tribological properties, fatigue strength, corrosion resistance and aesthetic appeal of the

product. Excessively better surface finish may involve more cost of manufacturing. The surface

roughness and roundness error are affected by several factors including cutting tool geometry,

cutting speed, feed rate, the microstructure of the work piece and the rigidity of the machine

tool. These parameters affecting the surface roughness and drilled hole qualities (roundness,

cylindricality and hole diameter) can be optimized in various ways such as Taguchi method and

multiple regression models.

SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)

68

multiple regression models. Therefore, a number of Researchers have been focused on an appropriate

prediction of surface roughness and roundness error. The Taguchi method has been widely used in

engineering analysis and is a powerful tool to design a high quality system. Moreover, the Taguchi method

employs a special design of orthogonal array to investigate the effects of the entire machining parameters

through the small number of experiments. Recently, the Taguchi method has been widely employed in

several industrial fields, and research works. By applying the Taguchi technique, the time required for

experimental investigations can be significantly reduced, as it is effective in the investigation of the effects

of multiple factors on performance as well as to study the influence of individual factors to determine

which factor has more influence, which one less. Yang and Chen used the Taguchi parameter design in

order to identify optimum surface roughness performance on an aluminum material with cutting

parameters of depth of cut, cutting speed, feed rate and tool diameter. It was found that tool diameter is

not a significant cutting factor affecting the surface roughness. Davim and Reis presented an approach

using the Taguchi method and ANOVA to establish a correlation between cutting speed and feed rate with

the de lamination in a composite laminate. A statistical analysis of hole quality was performed by Furness

et al. They found that feed rate and cutting speed have a relatively small effect on the measured hole

quality features. With the expectation of hole location error, the hole quality was not predictably or

significantly affected by the cutting conditions. Tsao and Hocheng performed the prediction and

evaluation of thrust force and surface roughness in drilling of composite material. The approach used

Taguchi and the artificial neural network methods. The experimental results show that the feed rate and

the drill diameter are the most significant factors affecting the thrust force, while the feed rate and spindle

speed contribute the most to the surface roughness. Zhan get al. performed a study of the Taguchi design

application to optimize surface quality in a CNC face milling operation. Taguchi design was successful in

optimizing milling parameters for surface roughness. Nalbant et al. utilized the Taguchi technique to

determine the optimal cutting parameters for surface roughness in turning of AISI 1030 steel with Ti N

coated inserts. Three cutting parameters such as insert radius, feed rate, and depth of cut, are optimized

for minimum surface roughness. Kurt et al. employed the Taguchi method in the optimization of cutting

parameters for surface finish and hole diameter accuracy in dry drilling processes. The validity of the

Taguchi approach to process optimization was well established. The objective of this study is to investigate

the effects of the drilling parameters on surface roughness and roundness error, and is to determine the

optimal drilling parameters using the Taguchi - Gray relational analysis in drilling

2. Experimental Procedure:

2.1 Material:

Al 6061 is one of the 6000 series Aluminum alloy used in the aircraft and aerospace components,

marine fittings, bicycle frames ,camera lenses ,brake components, electrical fittings and connectors, valves,

couplings etc.. . The composition of Al 6061 is 0.63% Si, o.466% Fe, 0.096% Cu, 0.179% Mn, 0.53% Mg,

0.091% Zn, 0.028% Cr,0.028% Ti and remaining aluminum. The young’s modulus is 80 G pa and hardness

98 BHN. In this study 600x50x10mm rectangular bar was used.

2.2 Schematic machining:

In this study, the experiments were carried out on a CNC vertical machining center (KENT and

ND Co. Ltd, Taiwan make) to perform different size of holes on Al6061 work piece by alter the point angle

on standard HSS drill bits of point angle 118 degrees and maintain constant Helix angle of 30 degrees.

Furthermore the cutting speed (m/min), the feed rate (mm/Rev) and Percentage of cutting fluid mixture

ratio are regulated in this experiment.


69

Fig (1).Shows CNC Machining Center, Controller ,fixing of work piece in a vice

Fig (2), Shows HSS twist drills and work piece with drilled holes

Fig(3) ,Shows alter the point angles on HSS twist drills made on tool & cutter grinder ,surf tester to

measure surface roughness, CMM to measure roundness error.

2.3 Experimental parameters and design:

The effects of drilling parameters on burr size have been studied by S.S Pande and H.P Relekar (1986),

Nayakamma k etal (1987), V.N.Gaitonde etal (2007), and so on. In this study, further processing

procedure for optimize the surface roughness and roundness error is investigated. Furthermore, an effect

of drilling parameters of cutting fluids under different mixture ratio was also considered. Therefore the

experiment is conducted with 5 controllable 3 level factors and two response variables 18 experimental

runs based on the orthogonal array L18 are required. Table (1) presents 5 controlled factors of the cutting

speed (i e (A m/ min)), the feed rate (i e (B mm/rev)), drill diameter in mm (C ) point angle (D(degrees))

and cutting fluid mixture ratio ( i e E (%)) with 3 levels for each factor.


70

Table 1. Factors and Levels of the Experiment

Levels of

experimental

factors

Cutting

Speed

(m/min.)

A

Feed rate

(mm/rev)

B

Drill

diameter

C

Point

angle(◦)

D

Cutting

Fluid

Mixture

Ratio (%)

E

1 15.08 0.3 8 118 12

2 25.13 0.5 10 110 18

3 37.70 0.6 12 100 24

Table 2. Experimental runs &Responses

Runs A B C D E Measured Responses

R1 (µm) R2 (mm)

1 1 1 1 1 1 2.39 0.053

2 1 2 2 2 2 1.16 0.073

3 1 3 3 3 3 4.50 0.082

4 2 1 1 2 2 1.25 0.066

5 2 2 2 3 3 3.36 0.058

6 2 3 3 1 1 3.72 0.092

7 3 1 2 1 3 4.15 0.017

8 3 2 3 2 1 3.45 0.036

9 3 3 1 3 2 2.29 0.074

10 1 1 3 3 2 3.33 0.008

11 1 2 1 1 3 2.25 0.109

12 1 3 2 2 1 1.06 0.027

13 2 1 2 3 1 3.26 0.019

14 2 2 3 1 2 3.60 0.041

15 2 3 1 2 3 1.56 0.032

16 3 1 3 2 3 3.54 0.026

17 3 2 1 3 1 2.45 0.094

18 3 3 2 1 2 4.38 0.035


71

Table (2) shows the experimental runs according to the selected orthogonal table. After drilling, two

quality objectives of the work pieces are chosen, including the average surface roughness (R1) and

roundness error (R2). Typically, small values of average surface roughness and roundness error are

desirable for the drilled hole.

3. Grey relational analyses:

In grey relational analysis, black represents having no information and white represents having all

information. A grey system has a level of information between black and white. This analysis can be used

to represent the grade of correlation between two sequences so that the distance of two factors can be

measured discretely. In the case when experiments are ambiguous or when the experimental method

cannot be carried out exactly, grey analysis helps to compensate for the shortcoming in statistical

regression .Grey relation analysis is an effective means of analyzing the relationship between sequences

with less data and can analyze many factors that can overcome the disadvantages of statistical method.

3.1 Data Pre-Processing:

In grey relational analysis, when the range of the sequence is large or the standard value is

enormous, the function of factors is neglected. However, if the factors goals and directions are different,

the grey relational might produce incorrect results. Therefore, one has to pre-process the data which are

related to a group of sequences, which is called ‘grey relational generation’

Data pre-processing is a process of transferring the original sequence to a comparable sequence.

For this purpose the experimental results are normalized in the range between zero and one. The

normalization can be done form three different approaches.

If the target value of original sequence is infinite, then it has a characteristic of “the larger-the –

better”. The original sequence can be normalized as follows.

(K)minx(K)xmax

(K)minx(K)x(k)x

0

i

0

i

0

i

0

i*

i

(1)

If the expectancy is the smaller-the better, then the original sequence should be normalized as follows.

(K)minx(K)xmax

(K)x(K)x(k)x

0

i

0

i

0

i

0

i*

i

max (2)

However, if there is a definite target value to be achieved, the original sequence will be normalized in the

form.

0

i

0

i

00

i*

ix(K)xmax

x(K)x(k)x

||1

(3)

Or the original sequence can be simply normalized by the most basic methodology i.e., let the values of

original sequence be divided by the first value of sequence

)(x

(K)x(k)x

0

i

0

i*

i1

(4)


72

Where (k)x*

i is the value after the grey relational generation (data pre-processing), max (k)x i

0 is the

largest value of (k)x i

0 , min (k)x i

0 is the smallest value of (k)x i

0 and xn is the desired value.

3.2 Grey relational coefficient and grey relational grade:

Following data pre-processing, a grey relational coefficient is calculated to express the

relationship between the ideal and actual normalized experimental results. They grey relational coefficient

can be expressed as follows:

max

maxmin

.)(

.

k(k)

oi

i (5)

Where )(koi is the deviation sequence of the reference sequence (k)x*

o and the comparability sequence

(k)x*

i , namely

)(koi = || (k)x*

o - (k)x*

i ||

max = ||)()(|| **

maxmax kxkx i

kij

0

min = ||)()(|| **

0minmin kxkx ikij

is distinguishing or identification coefficient to [0,1]. =0.5 is generally used.

After obtaining the grey relational coefficient, we normally take the average of the grey relational

coefficient as the grey relational grade. The grey relational grade is defined as follows.

n

k

ii kn 1

1)( (6)

However, since in real application the effect of each factor on the system is not exactly same. Eq.(6) can be

modified as

n

k

k

n

k

iki wkwn 11

11

)(. (7)

Where wk represents the normalized weighting value of factor ‘k’. Given same weights. Equations (6)

and (7) are equal.


73

In the grey relational analysis, the grey relational grade is sued to show the relationship among the

sequences. If the two sequences are identical, then the value of grey relational grade is equal to 1. The

grey relational grade also indicates the degree of influence that the comparability sequence could exert

over the reference sequence. Therefore, if a particular comparability sequence is more important than the

other comparability sequences to the reference, then the grey relational grade for that comparability

sequence and reference sequence will be higher than other grey relational grades.

4. Analysis and discussion of Experimental results:

In the present study, average surface roughness and roundness error of drilled hole in different

parameters and experimental runs are listed in table 2.Typically, lower values of average Surface

roughness and roundness error as the target values are desirable. Therefore, the data sequences have the

smaller-the-better characteristic. The values of average surface roughness and roundness error are set to be

the reference sequence. More over the results of 18 experiments were the comparability sequences x i*(k),

i = 1 – 18, k= 1 – 3.

Table3 : Sequences after data pre processing

Comparability sequence R1

R2

1 0.6153 0.6086

2 0.9709 0.3913

3 0.0000 0.2934

4 0.9447 0.4673

5 0.3313 0.5543

6 0.2267 0.1847

7 0.1067 1.0000

8 0.3052 0.7934

9 0.6424 0.3804

10 0.3401 0.2282

11 0.6540 0.0000

12 1.0000 0.8913

13 0.3604 0.9782

14 0.2616 0.7391

15 0.8546 0.8369

16 0.2790 0.9021

17 0.5959 0.1630

18 0.0348 0.8043

Table3 Lists all of the sequences following data pre processing using equation(2) .Also, the deviation

sequences ∆oi , ∆max(k) and ∆min(k) for i = 1 – 18, k= 1 – 3 can be calculated asfollows.


74

∆o1(1)=│ xo*(1)-x1

*(1)│=│1.00-0.4117=0.5883│

∆o1(2)=│ xo*(2)-x1

*(2)│=│1.00-0.6020=0.3980│

∆max=∆08(1)= ∆10(2)=1.0000

∆min=∆15(1)= ∆17(2)=0.0000

The distinguishing coefficient ζ can be substituted for the grey relational coefficient in equation (5). If

all the process parameters have equal weighting, ζ is 0.5.

Table 4: Grey Relational Coefficients and Grey Relational grades

Runs Grey Relational Coefficients Grey Relational Grade

R1 R2

1 0.5638 0.5609 0.5623

2 0.9450 0.4509 0.6979

3 0.3333 0.4143 0.3738

4 0.9004 0.4841 0.6922

5 0.4278 0.5287 0.4782

6 0.3926 0.3801 0.3863

7 0.3575 1.0000 0.6787

8 0.4184 0.7076 0.5630

9 0.5830 0.4465 0.5147

10 0.4310 0.3931 0.4120

11 0.5910 0.3333 0.4621

12 1.0000 0.8214 0.9107

13 0.4387 0.9582 0.6984

14 0.4037 0.6571 0.5304

15 0.7747 0.7540 0.7643

16 0.4095 0.8362 0.6228

17 0.5530 0.3739 0.4634

18 0.3412 0.7187 0.5299

Table 4 lists the grey relational coefficient and grade for each experiment of the L18 orthogonal array by

applying equations (5) and (6).


75

Fig 4. Graph for Grey Relation Grade

According to the performed experiment design it is clearly observed from table 4 and fig (4)That the

drilling process parameter setting of experiment no.12 has the highest grey relational grade. Thus the

experiment no12 gives the best multi-performance characteristics among the 18 experiments. The

response table of Taguchi method was employed here to calculate the average grey relational grade for

each factor level. The procedure was to group the relational grades firstly by factor level for each column

in the orthogonal array and then to average them. For example the grey relational grades for factors A & B

at level 1 can be calculated as follows.

γ(A)1=0.5623+0.6979+0.3738+0.4120+0.4621+0.9107=0.5698

γ(B)1=0.5623+0.6922+0.6787+0.4120+0.6984+0.6228=0.6110

Using the same method, calculations were performed for each factor level and response table was

generated, as shown in table6.

Table 5. Average Grey Relational Grade for Factor and Levels of the Experiment

Levels A B C D E

1 0.5698 0.6110 0.5765 0.5249 0.5973

2 0.5916 0.5325 0.6656 0.7084 0.5628

3 0.5620 0.5799 0.4813 0.4900 0.5633

0

0,2

0,4

0,6

0,8

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ave

rage

gre

y re

lati

on

al g

rad

e

experimental runs

Graph for Grey Relational Grade


76

Grey relational grade graphs for drilling parameters :

Fig.(5): Graphs for levels of controllable facters and average gray relational grades

Since the grey relational grades represented the level of correlation between the reference and

comparability sequences, the larger grey relational grade means the comparability sequence exhibits a

stronger correlation with reference sequence. Therefore, the comparability sequence has a larger value of

grey relational grade for average surface roughness and roundness error. Based on this premise the study

selects the level that provides the largest average response. In table 6, A2 B1 C2 D2 E1 show the largest

0,54

0,56

0,58

0,6

1 2 3

a

v

e

r

a

g

e

G

R

G

levels

cutting speed(A)

0,45

0,5

0,55

0,6

0,65

1 2 3

a

v

e

r

a

g

e

G

R

G

levels

feed rate (B)

0

0,2

0,4

0,6

0,8

1 2 3

a

v

e

r

a

g

e

G

R

G

levels

Drill diameter(C)

0

0,2

0,4

0,6

0,8

1 2 3

a

v

e

r

a

g

e

G

R

G

levels

Point angle (D)

0,5

0,55

0,6

0,65

0,7

1 2 3

a

v

e

r

a

g

e

G

R

G

levels

Cutting fluid mixture ratio (E)


77

value of grey relational grade for factors A, B, C, D and E respectively. Therefore A2 B1 C2 D2 E1 is the

condition for the optimal parameter combination of the drilling of a hole to minimize average surface

roughness and roundness error. The influence of each cutting parameter can be more clearly presented by

means of the grey relational grade graph. It shows the change in the response, when the factors go for

their level 1 to level 3. The response graph for the drilling parameters is presented in fig. (5). In this

figure, the greater values average grey relational grades gives the low surface roughness and roundness

error

5. Conclusion:

The Grey relational analysis based on an orthogonal array of the Taguchi methods was a way of

optimizing the process parameters in drilling for Al6061 alloy. The analytical results summarized as

follows:

1. From the response table of the average grey relational grade, it is found that the largest

value of the GRA for the cutting speed of 25.13 m/min, the feed rate of 0.3 mm/rev, the drill

diameter 10 mm, point angle110 deg, and % cutting fluid mixture ratio12 %. It is the

recommended levels of the controllable parameters for the process of drilling as the minimization

of average surface roughness and roundness error.

2. The order of the importance of influential factors based on the Taguchi response table in

sequence is point angle, drill diameter, feed rate, % cutting fluid mixture ratio and cutting speed

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