JQLNQLK7 QDH/thinkinglean.com/img/files/PAPER_7.pdf · · 2014-05-16À ÎÀ ±bF bOb À bÁ´´...
Transcript of JQLNQLK7 QDH/thinkinglean.com/img/files/PAPER_7.pdf · · 2014-05-16À ÎÀ ±bF bOb À bÁ´´...
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.
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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.
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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)
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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.
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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.
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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).
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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)
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
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
References
Baradie, M.A, 2006. Cutting fluids; Part 1 characterization, J. Mater process Technol 56,786-797.
Baychi T.P, Taguchi methods explained practical step to robust design, ”prentice hall of India,
New Delhi,1993
Chiang, K.T.,CFhang , F.P.,2006.Optimization of the WEDM process of particle reinforced material
with multiple performance characteristics using Grey relational analysis.,J.Mater.
process.Technol.108,96-101.
Davim, J.P., Reis, P. (2003). Drilling carbon fiber reinforced plastic manufactured by auto clave
experimental and statistical study. Materials and Design, vol. 24, no. 5, p. 315-324,
Deng, JL 2002 Introduction to grey system theory. Grey Syst.1, 1-24
Douglas C. Montgomery, cc Design and Analysis of Experiments, 5th Edition John Wiley 2007
Fung,C.P.,Huang C.H.,Doong,J.L.,2003.The study on the optimization of injection molding
process parameters with Grey relational nalysis.J.Reinf.Plast.Comp.22,51-66.
SREENİVASULU, RAO / International Journal of Lean Thinking Volume 3, Issue 2(December 2012)
78
Furness, R.J., Wu, C.L., Ulsoy, A.G. (1996). Statistical analysis of the effects of feed, speed, and
wear of hole quality in drilling. Journal of Manufacturing Science and Engineering, vol. 118, no. 3, p.
367-375
Gaitonde VN, Karnik SR, Achyutha BT, Siddeswarappa B (2007) Methodology of taguchi
optimization for multi-objective drilling problem to minimize burr size. Int J Adv Manuf Technol 34:1–
8
Korkut, I., Kucuk, Y. (2010). Experimental Analysis of the Deviation from Circularity of Bored
Hole Based on the Taguchi Method. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no.
5, p. 340-346.
Kurt, M., Bagci, E., Kaynak, Y. (2009). Application of Taguchi methods in the optimization of
cutting parameters for surface finish and hole diameter accuracy in dry drilling processes.
International Journal of Advanced Manufacturing Technology, vol.40, no. 5-6, p. 458-469
Nalbant, M., Gokkaya, H., Sur, G. (2007). Application of Taguchi method in the optimization of
cutting parameters for surface roughness in turning. Materials and Design, vol. 28, no. 4, p. 1379-
1385,.2006
Nayakamma k. and Arai m., ”Burr formation on mental cutting,” anals of the CIRP vol.36/1,1987
Pande. S. S., Relekar, H. P., “Investigations on Reducing Burr Formation inDrilling,” Int. J.
Machine Tool Design Research, Vol.26,No.3,pp339-348,1986
Phadke, M.S. (1989). Quality Engineering Using Robust Design. Prentice-Hall, New Jersey.
Risbood, K.A., Dixit, U.S., Sahasrabudhe, A.D. (2003).Prediction of surface roughness and
dimensional deviation by measuring cutting forces and vibrations in turning process. Journal of
Materials Processing Technology, vol. 132, no. 1-3, p. 203-214,
Tsao, C.C., Hocheng, H. (2008). Evaluation of thrust force and surface roughness in drilling
composite material using Taguchi analysis and neural network. Journal of Materials Processing
Technology,vol. 203, no. 1-3, p. 342-348,.2006
Yang, J.L., Chen, J.C. (2001). A systematic approach for identifying optimum surface roughness
performance in end-milling operations. Journal of Industrial Technology, vol. 17, no. 2, p. 1-8.
Zhang, J.Z., Chen, J.C., Kirby, E.D. (2007). Surface roughness optimization in an end-milling
operation using the Taguchi design method. Journal of Materials Processing Technology, vol. 184, no.
1-3, p. 233-39,.2006.