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     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

    DrillingSurface RoughnessRoundness ErrorTaguchi 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 surfaceroughness 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 toreduce 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

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    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 holequality 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 Ncoated 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 mixtureratio are regulated in this experiment.

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    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 processingprocedure 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.

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    Table 1. Factors and Levels of the Experiment

    Levels of

    experimental

    factors

    Cutting

    Speed

    (m/min.) A

    Feed rate

    (mm/rev)B

    Drill

    diameterC

    Point

    angle( ◦ )D

    Cutting

    Fluid

    MixtureRatio (%)

    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

    R 1 (µm)  R 2 (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

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    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 (R 2 ). 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 isenormous, 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) x max (K)minx (K) x (k) x 

    i * 

      (1)

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

    (K)minx (K) x max 

    (K) x (K) x (k) x 

    i * 

      max  (2)

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

    form.

    0 0 

    i * 

    i  x (K) x max 

     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 

    i * 

    1

      (4)

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     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 x n 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 )(k oi  is the deviation sequence of the reference sequence (k) x * o and the comparability sequence

    (k) x * i  , namely

    )(k oi  = ||   (k) x * o -   (k) x 

    i ||

    max  = ||)()(||  **

    maxmax   k  x k  x  i k i  j 

     

    min = ||)()(||  **

    0minmin   k  xk  x ik i j

       

     

     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

    i i    k n   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

    n

    i k i    w k w n   11

    11

    )(.     (7)

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

    and (7) are equal.

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    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.

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    ∆o1(1)=│ x o*(1)-x 1

    *(1)│=│1.00-0.4117=0.5883│ ∆o1(2)=│ x o

    *(2)-x 1*(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). Ifall the process parameters have equal weighting, ζ is 0.5.

    Table 4: Grey Relational Coefficients and Grey Relational gradesRuns Grey Relational Coefficients Grey Relational Grade

    R 1  R 2 

    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 0.412011 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 L 18 orthogonal array by

    applying equations (5) and (6).

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    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=0.5698γ(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

       a   v   e   r   a   g   e    g

       r   e   y

       r   e    l   a   t   i   o   n   a

        l   g   r   a    d   e 

    experimental runs

    Graph for Grey Relational Grade

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    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 studyselects 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

    ve

    r

    a

    g

    e

     

    G

    R

    G

     

    levels

    feed rate (B)

    0

    0,2

    0,4

    0,6

    0,8

    1 2 3

    av

    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)

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     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 therecommended 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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