Multi Response Optimization of Process Parameters ... - World Scientific

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Journal of Advanced Manufacturing Systems Vol. 14, No. 2 (2015) 107–121 c World Scientific Publishing Company
DOI: 10.1142/S0219686715500080

Multi Response Optimization of Process Parameters of Abrasive Water Jet Machining for Stainless Steel AISI 304 Using VIKOR Approach Coupled with Signal to Noise Ratio Methodology Vedansh Chaturvedi∗,† and Diksha Singh∗,‡ ∗Department of Mechanical Engineering Madhav Institute of Technology & Science Gwalior 474005, Madhya Pradesh, India †[email protected] ‡[email protected]

As the population of the world is continuously increasing, demand of the mechanical manufactured products is also increasing. Machining is the most important process in any mechanical manufacturing, and in machining two factors, i.e. material removal rate (MRR) and surface roughness (SR) are the most important responses. If the MRR is high, the product will get desired shape in minimum time so the production rate will be high, but we could not scarify with the surface finishing also because in close tolerance limit parts like in automobile industry, if the surface is rough exact fit cannot take place. The term optimization is intensively related to the field of quality engineering. Abrasive water jet machining is an important unconventional machining, In order to obtain better response, i.e. material removal rate and surface roughness. Various process parameters of AWJM need to be observed and selected to improve machining characteristics. Better machining characteristics can be achieved by optimizing various process parameters of AWJM. This study considers four process control parameters such as transverse speed, standoff distance, abrasive flow rate and water pressure. The response is taken to be material removal rate and surface roughness. The work piece for stainless steel AISI 304 material of size 15 cm × 10 cm × 2 cm is selected for experiments. Sixteen experimental runs (two trials for each experimental runs) were carried out for calculating MRR and SR and average value of these two trials have been taken for analysis. MRR is normalized according to higher-is-better and SR is normalized according to lower is better. The experiment data analysis is done and VIKOR index is found. Finally, the analysis of VIKOR index using S/N ratio is done and found the most significant factor for AWJM and predicted optimal parameters setting for higher material removal rate and lower surface roughness. Verification of the improvement in quality characteristics has been made through confirmation test with the predicted optimal parameters setting. It is found that the determined optimum combination of AWJM parameters gives the lowest VIKOR INDEX which shows the successful implementation of VIKOR Method coupled with S/N ratio in AWJM. Keywords: AWJM; stainless steel; MRR; SR; VIKOR method; S/N ratio.

‡ Corresponding

author.

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1. Introduction Abrasive water jet machining (AWJM) process is one of the nontraditional machining processes that have been used extensively in various industry related applications. The AWJM process provides a single tool that is suitable for machining a wide range of composite material. It is a noncontact, inertia less and faster cutting process that offers some advantages like narrow key width, negligible heat affected zone reduced waste material and flexibility to machining process in different ways by Hashish.1 The basic principle of AWJM was reviewed in details by Momber and Kovacevic.2 Ramulu and Arola3 used regression analysis to predict depth of cut due to cutting and deformation wear for graphite/epoxy composite materials. It is also a cost effective and environmental friendly technique that can be adopted for processing number of engineering materials, particularly difficult to cut materials such as ceramic reported by Siores et al.4 This technology is less sensitive to material properties as it does not cause chatter, has no thermal effects, impose minimal stresses on the work piece and has high machinery versatile and high flexibility, but it has some drawbacks especially it may generated loud noise and a messy working environment. The influence of AWJM condition on surface quality of graphite is introduced by Wang and Wong.6 Akkurt et al.7 showed the effect of feed rate on surface roughness of AISI 304 steel in abrasive water jet cutting, feed rate, and reduction in abrasive water jet cutting of AISI 304 stainless steel results in better surface quality only for 5 mm thickness specimen. Azmir and Ahsam8 found that the type of abrasive materials, hydraulic pressure, standoff distance and traverse rate were the significant control factors and the cutting orientation was the insignificant control factor in controlling the Ra. For noise factors effect, the forms of glass fibers and thickness of composite laminate showed the greatest influence on Ra. A Mathematical model was developed using piecewise linear regression analysis to predict the performance of Ra in terms of the cutting parameters of AWJM. The models successfully predicted the Ra of an AWJ machined glass/epoxy laminate within the limit of this study. It was confirmed that the determined optimum combination of AWJM parameters satisfy the real need for machining of glass fiber reinforced epoxy composites in practice. Caydas et al.9 used artificial neural network and regression analysis for study of surface roughness of AA7075 aluminum in abrasive water jet machining. ANOVA is used to check the validity of regression model and to determine the significant parameters affecting the surface roughness. Also SEM investigation revealed that AWJM produce three distinct zones along the cut surface of AA7075 aluminum alloy and surface striations and waviness were increased significantly with jet pressure. Tsai et al.10 has introduced the Taguchi experimental investigation into the optimal processing condition for the abrasive jet polishing of SKD61 mold steel and found that the optimal polishing effect is attained using 8000 SK abrasive particles and a 1:1 mixture of water solvent machining oil and pure water. Iqbal et al.11 used full factorial design of experiments to optimize the process parameters of abrasive water

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jet machining of high strength low alloy steel and aluminum 2219. Four variables jet pressure, abrasive mixing rate, cutting feed and plate thick are taken and three response variable are considered. It was found that cutting speed and thickness were highly influential parameters, while abrasive mixing rate is influential upon surface roughness only. Strong interaction was found between jet pressure and work piece material. Karakurt et al. (2011) showed the effect of the process parameters on the cut depth and kerf width. Analysis of varience (ANOVA) used and found that transverse speed is highly significant factor in cut depth and kerf width of granite. As in the case of every machining process, the quality of process in AWJM is significantly affected by the process turning parameters. There are several process parameters in this technique, among which water pressure, standoff distance, abrasive flow rate, jet transverse rate and diameter of focusing nozzle are of great importance and precisely controllable. The main process quality measure include depth of cut, key width material removal rate and its regularly surface roughness. Therefore, it is of great importance to study the effect of process parameters on the process response characteristics. In this study, four process variables are considered, i.e. traverse speed, standoff distance, abrasive flow rate, water pressure and two responses are taken as MRR and SR is considered for performance measures as in many industrial applications these are the main constraints on the process applicable. Few attempts have been made to model and optimize the process variables in AWJM. Rowland et al.3 introduced an application of Taguchi experimental design for process optimization. Reid14 described a methodology for solving parameter design (PD) problems in production and business systems of considerable complexity. The solution is aimed at determining optimum settings to system critical parameters so that each system response is at its optimum performance level with least amount of variability. When approaching such problem, analysts are often faced with four major challenges: representing the complex parameter design problem, utilizing an effective search method that is able to explore the problem’s complex and large domain, making optimization decisions based on multiple and, often, conflicting objectives, and handling the stochastic variability of system response as an integral part of the search method. To tackle such challenges, this paper proposes a solution methodology that integrates four state-of-the-art modules of proven methods: simulation modeling (SM), genetic algorithm (GA), entropy method (EM), and robustness module (RM). The approaches are employed in this direction includes design of experiment (DOE), regression modeling, ANOVA, fuzzy logic, artificial neutral network, Taguchi and Grey relational analysis, etc. A number of attempts have been made to optimize the process parameters of AWJM for different materials, but not any kind of experimental analysis have been made earlier by using VIKOR method coupled with S/N ratio methodology. Opricovic had developed the basic idea of VIKOR. Visekriferijumska optimizacija I Kompromusno Resenje, that means: Multicriteria optimization and compromise solution with Pronunciation: VIKOR. The real applications were presented by Opricovic.15 The paper by Opricovic and Tzeng15 contributed to the international recognition

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of the VIKOR method. In this paper multi criteria decision making of AWJM is done by using VIKOR method coupled with signal to noise ratio.

2. Scheme of Investigation In order to maximize and minimize the quality characteristics, the present investigation has been made in the following sequence. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x)

Selection of base material (i.e. Stainless steel AISI 304). Identify the important AWJM process parameters. Find the upper and lower limit (i.e. Range) of identified process parameters. Select the orthogonal array for available factors and their range. Conduct experiment according to design of matrix. Record the quality characteristic (i.e. material removal rate and surface roughness). Find the optimal condition for AWJM. Identified the significant factors. Conduct the confirmation test. Check the adequacy of developed model.

3. Methodology 3.1. VIKOR method The MCDM method is very popular technique widely applied for determining the best solution among several alternatives having multiple attributes or alternatives. A MCDM problem can be represented by a decision matrix (D) as follows:   Cx 1 Cx 2 · · · Cx n A1    x11 x12 · · · x1n    A2  x21 x22 · · · x2n    ·   · · · · · .  · (1) ·   · ··· ·   ·  ·   · · ··· ·   ·   · · ··· ·  Am xm1 xm2 · · · xmn Here, A1 represents ith alternative, i = 1, 2, . . . , m. Cx j represents the jth criterion, j = 1, 2, . . . , n. xij is the individual performance of an alternative. The procedures for evaluating the best solution to an MCDM problem include computing the utilities of alternatives and ranking these alternatives. The alternative solution with the highest utility is considered to be the optimal solution. The following steps are involved in VIKOR methods.

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Step 1. Representation of normalized decision matrix The normalized decision matrix can be expressed as follows: F = [fij ]mxn . x Here, fij = √Pmij

i=1

x2ij

(2)

, I = 1, 2, . . . , m; and xij is the performance of alternative

Ai with respect to the jth criterion. Step 2. Determination of ideal and negative-ideal solution The ideal solution A∗ and the negative ideal solution A− are determined as follows:  (max fij | j ∈ J) or (min fjj | j ∈ JK 1 ), ∗ A = i = 1, 2, . . . , m = {f1∗ , f2∗ , . . . fn∗ } A− =

 (min fij | j ∈ J) or (max fjj | j ∈ JK 1 ),

(3)

i = 1, 2, . . . , m

= {f1− , f2− , . . . fn− }

(4)

Here, J = {j = 1, 2, . . . , n\fij , if desired response is large}, J = {j = 1, 2, . . . , n\fij , if desired response is small}. Step 3. Calculation of utility measure and regret measure The utility measure and the regret measure for each alternative are given as Si =

n  j=1

wj

(fj∗ − fij )

(fj∗ − fj− )



Ri = Max wj

,

(5)

(fj∗ − fij )

(fj∗ − fj− )

,

(6)

where Si and Ri represent the utility measure and the regret measure, respectively, and wj is the weight of the jth criterion. Step 4. Computation of VIKOR index The VIKOR index can be expressed as follows:   Si − S ∗ Ri − R∗ Qi = v + (1 − v) . S− − S∗ R− − R∗ Here, Qi , represents the ith alternative VIKOR value, i = 1, 2, . . . , m; S − = Max(Si ); i

S ∗ = Min(Si ); R∗ = Min(Ri ); i

(7)

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R− = Max(Ri ) and v is the weight of the maximum i group utility (usually it is to be set to 0.5). The alternative having smallest VIKOR value is determined to be the best solution. 3.1.1. Optimization procedure adopted Step 1. Estimation of quality loss Taguchi defined quality loss estimates for response using lower-the-better (LB) and higher-the-better (HB) criterion are given below. (a) For an LB response r

Lij = k1 ×

1 1 2 . r yijk

(8)

k=1

(b) For an HB response r

Lij = k2 ×

1 1 2 . r yijk

(9)

k=1

Here, Lij is the quality loss associated with the jth response in the ith experiemental run; Yijk is the objserved kth repetition datum for the jth response in the ith experimental run; r is the number of repetition for each experimental run. K1 and K2 are quality loss coefficients, i = 1, 2, . . . , m; j = 1, 2, . . . , n; k = 1, 2, . . . , r. Step 2. Calculation of normalized quality loss (NQL) for individual responses in each experimental run. The NQL can be obtained as follows: Lij fij =  m

i=1

L2ij

,

i = 1, 2, . . . , m; j = 1, 2, . . . , n.

(10)

Here Fij represents the NQL of the jth response in the ith experimental run. Step 3. Evaluation of ideal and negative-ideal solution. A∗ = {min fij | i = 1, 2, . . . , m} = {f1∗ , f2∗ , . . . , fj∗ , . . . , fn∗ },

(11)

A− = {max fij | i = 1, 2, . . . , m} = {f1− , f2− , . . . , fj− , . . . , fn− }.

(12)

A smaller NQL is preferred, so the ideal and negative-ideal solutions which represent the minimum and maximum NQL of all experimental runs are as follows: Step 4. Calculation of the utility and regret measures for each response in each experimental run using Eqs. (5) and (6), respectively. Step 5. Calculation of VIKOR index of the ith experimental run. Substituting Si and Ri into Eq. (7) yields the VIKOR index of the ith experimental run as follows. A smaller VIKOR index produces better multi-response performance. Step 6. Determination of optimal parametric combination.

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The multi-response quality scores for each experimental run can be determined from the VIKOR index obtained in Step 5, and the effects of the factors can be estimated from the calculated VIKOR values. The optimal combination of factorlevel called optimal parametric combination is finally determined, in view of the fact that a smaller VIKOR value indicates a better quality. Signal to method is to be applied finally to evaluate this optimal setting by minimizing the VIKOR index. Optimal result is to be verified through confirmatory tests. 3.2. Signal to noise ratio calculation S/N characteristics formulated for three different categories are as follows: 3.2.1. Larger is best characteristic Data sequence for MRR, which are higher-the-better performance characteristic are pre-processed as Eq. (13)   t 1 (13) S/N = −10 log 1/n i=1 2 . y 3.2.2. Nominal and smaller is best characteristic Data sequence for surface roughness, which are lower-the-better performance characteristic are pre-processed as per Eqs. (14) and (15).   t (14) S/N = −10 log 1/n t=1 y 2 ,   S/N = −10 log((1/n) (15) (y 2 ) , where y 2 is average of observed data y, sy 2 is variance of y, and n is the number of observations. 4. Experimental Study 4.1. Material selection In this experiment the work piece of AISI 304 stainless steel is used with a dimension of 2 cm thickness, 15 cm length, and 10 cm width as shown in Fig. 1. Two measurements have been taken for MRR and surface roughness for each experimental run and average was taken as a final reading. The general composition of stainless steel AISI 304 is shown in Table 1. The physical, mechanical and electrical properties of the work material are shown in Table 2. 4.2. Machine setup The equipment Abrasive water jet machine was used for machining the samples, model no. 2626 OMAX jet machining centre equipped with OMAX-high pressure

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Fig. 1.

Modeled image of work piece to be machined.

Table 1. COMPOSITION Weight %

C

Composition of stainless steel AISI 304. Cr

Fe

Mn

Ni

P

S

Si

Max. 0.08 18–20 66.345–74 Max. 2 8–10.5 Max 0.045 Max 0.03 Max 1

Table 2.

Properties of stainless steel AISI 304.

S. No.

Features

Metric

Physical and mechanical properties

Density Tensile strength ultimate Elongation of break Modulus of elasticity Poisson ratio Shear modulus

8 g/cc 505 mpa 70% 193–200 Gpa 0.29 86 Gpa

Electrical properties

Electrical resistivity Magnetic permeability

7.2e-0.05 ohm-cm 1.008 CRT

pump of 3376.43 bar. The OMAX high pressure pump is an electrically driven, positive displacement. Variable speed crank shaft drive triplex pump designed for use with the OMAX precision jet machining system and other application requiring high pressure water by the OMAX jet machining system to operate. The pump control panel provides a keypad display screen, and the pump provides start/stop controls. When the pump is attached to an OMAX jet machining center, controls sheared between controller and the pump. The specifications of OMAX 2626 AMJM are shown in Table 3. 4.3. Experimental design Design of experiments (DOE) is the process of planning the experiments considering the process parameters at different levels. Experimental design using Taguchi’s method provides a simple, efficient and systematic approach for an optimal design of

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(a)

(b)

(c)

(d)

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Fig. 2. Abrasive water jet machining overview of parts. (a) Working table of AWJM, (b) abrasive feeder (c) control Penal and (d) machine set-up. Table 3.

Specification of OMAX 2626 AWJM.

Position Accuracy

Table Size

Foot Print

Weight (Empty Tank)

X-Y Cutting

Ceiling Height Requirement

0.003 (0.08 gm)

46 ∗ 3 (1168 mm ∗ 787 mm)

116 L ∗ 72 W (2946 mm ∗ 1829 mm)

3000 lbs-table only(1364 ks)

29 ∗ 26 (737 mm ∗ 660 mm)

8 ft (2.44 m)

Table 4.

Design scheme of experiment of parameters and level.

S. No.

Parameters

Notation

Units

Level 1

Level 2

Level 3

Level 4

1 2 3 4

Transverse speed Standoff distance Abrasive flow rate Water pressure

T S A W

(mm/min) (mm) (g/min) (MPa)

70 1.5 300 320

90 2 350 340

100 2.5 400 360

120 3 450 380

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V. Chaturvedi & D. Singh Table 5.

S. No.

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

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Design of experiment and collected response data.

Design of Experiments T

S

A

W

MRR1 (g/min)

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1

1 2 3 4 3 4 1 2 4 3 1 2 2 1 4 3

0.265 0.354 0.332 0.291 0.293 0.538 0.210 0.431 0.425 0.410 0.261 0.288 0.310 0.277 0.301 0.275

Response Data/Observed Values MRR2 Average SR 1 SR 2 (g/min) MRR(g/min) (Ra) (Ra) 0.269 0.352 0.331 0.291 0.295 0.531 0.212 0.432 0.428 0.413 0.263 0.287 0.313 0.278 0.303 0.270

0.267 0.353 0.331 0.291 0.294 0.534 0.211 0.431 0.426 0.411 0.262 0.287 0.311 0.277 0.302 0.272

3.25 4.36 4.13 3.89 3.91 5.43 2.90 4.39 4.31 3.91 3.12 3.90 3.19 3.46 3.10 2.86

3.23 4.36 4.11 3.88 3.90 5.42 2.95 4.35 4.31 3.91 3.10 3.88 3.20 3.47 3.12 2.85

Average SR(Ra) 3.24 4.36 4.12 3.88 3.90 5.42 2.92 4.37 4.31 3.91 3.11 3.89 3.19 3.46 3.11 2.85

experiments to assess the performance. The experimental layout for the machining parameters using the L16 orthogonal array was used in this study. This array consists of four variables and four levels. The experimental domains for AWJM are shown in Table 4. The observed values of material removal rate (MRR), and surface roughness (SR) were normalized according to “Higher is better” and “Lower is better”, respectively. The analysis of observed value is done using VIKOR method coupled with S/N ratio and found the predicted optimal parameter setting and most significant factor.

5. Observed Data Collections and Results 5.1. Multi-criteria decision making in AWJM using VIKOR approach Quality loss estimates for individual response have been calculated using Eqs. (8) and (9) and furnished in Table 6. For material removal rate (HB) and for surface roughness (LB) criterion have been selected. Normalized quality loss estimates have been determined using Eq. (10) and shown in Table 7. Table 8 represents utility measure of individual response. It has been assumed that all responses are equally important. Therefore, 50% weightage has been assigned to each response. Utility and regret measure for each alternative have been tabulated in Table 9. VIKOR index of each alternative have been presented in Table 10. Analysis of VIKOR index has been done using signal to noise ratio (S/N ratio) and predicted optimal parameter setting found.

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Table 6. Calculated quality loss estimates. S. No.

Quality Loss Estimates MRR

SR

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

14.0274 8.0251 9.0998 11.8090 11.5692 3.5002 22.4613 5.3707 5.4974 5.9055 14.5679 12.0982 10.3058 12.9859 10.9644 13.4668

10.4976 19.0096 16.9744 15.0932 15.2490 29.4306 8.5556 19.0969 18.5761 15.2881 9.6721 15.1321 10.2080 12.0062 9.6721 8.1510

Table 7. Normalized quality loss estimates. S. No.

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

Normalized Quality Loss Estimates MRR

SR

0.3016 0.1725 0.1956 0.2539 0.2488 0.0752 0.4830 0.1154 0.1182 0.127 0.3132 0.2601 0.2216 0.2792 0.2357 0.2896

0.1695 0.3070 0.2741 0.2437 0.2462 0.4753 0.1381 0.3084 0.3049 0.2469 0.1562 0.2443 0.1648 0.1939 0.1562 0.1316

The ideal and negative ideal solutions which represents the minimum and maximum NQL of all experimental runs are calculated by using Eq. (3) and Eq. (4) are as follows: A∗ = {min fij | i = 1, 2, } = {f1∗ , f2∗ } = {0.0752, 1316}, A− = {max fij | i = 1, 2, } = {f1− , f2− } = {0.4830, 0.4753}.

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

Utility Measure of Each Criteria (w = 0.50) UM (MRR)

UM (SR)

0.2775 0.1192 0.1476 0.2191 0.2128 0.0000 0.5 0.0492 0.0527 0.0635 0.2918 0.2267 0.1794 0.2501 0.1967 0.2628

0.0551 0.2551 0.2074 0.1630 0.1668 0.5 0.00945 0.2572 0.2449 0.1677 0.0357 0.1640 0.0482 0.0906 0.0357 0.0000

Table 9. Utility measure (Si ) and regret measure (Ri ) of individual alternatives. S. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Si

Ri

0.3326 0.3743 0.355 0.3821 0.3796 0.5 0.50945 0.3064 0.2976 0.2312 0.3275 0.3907 0.2276 0.3407 0.2324 0.2628

0.2775 0.2551 0.2074 0.2191 0.2128 0.5 0.5 0.2572 0.2449 0.1677 0.2918 0.2267 0.1794 0.2501 0.1967 0.2628

The S/N ratio for VIKOR index has been calculated using LB criterion.   t S/N = −10 log 1/n t=1 y 2 . Here n is the number of measured ith characteristic value, i.e. ith quality indicator. The S/N ratio plot for the VIKOR index is represented graphically.

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Table 10. VIKOR index of individual alternatives. S. No.

VIKOR Index

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

0.3515 0.3917 0.2857 0.3514 0.3374 0.9833 1.0000 0.2744 0.2403 0.0063 0.3639 0.378 0.0176 0.3245 0.0525 0.2054

Table 11. S/N ratio for different VIKOR index. S. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

VIKOR Index

S/N Ratio

0.3515 0.3917 0.2857 0.3514 0.3374 0.9833 1.0000 0.2744 0.2403 0.0063 0.3639 0.378 0.0176 0.3245 0.0525 0.2054

9.0815 8.1409 10.8818 9.0840 9.4371 0.1463 0.0000 11.2323 12.3849 44.0132 8.7804 8.4502 35.0897 9.7757 25.6632 13.7480

6. Interpretation of Results The optimum condition represents the combination of control factor levels that is expected to produce the best performance. The average S/N for each factor level indicate the relative effects of the various factors on quality characteristics of MRR and SR during machining of AISI304 stainless steel Taguchi analysis observe the higher value of mean S/N ratio are better quality characteristics. Therefore, based on the average S/N ratio for each factor level as illustrated in based on Fig. 4 the optimum machining performance for both MRR and SR was obtained at level 4 Transverse speed (120 mm/min), level 1, for standoff distance (1.5 mm), level 4 for abrasive flow rate (450 gm/min), level 3 for water

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Fig. 3.

Average S/N ratio by control factor for VIKOR index.

Table 12.

Response table for S/N ratio.

Level

A

B

C

D

1 2 3 4 Delta Rank

9.297 5.204 18.407 21.069 15.865 1

16.498 15.519 11.331 10.629 5.870 4

7.939 12.923 11.069 22.047 14.108 2

6.827 15.811 19.520 11.820 12.693 3

pressure (360 MPa). The optimum parametric combination for both MRR and SR is A4B1C4D3. Table 12 is the response table for S/N ratio, which shows the most significant factor for MRR and SR of AISI 304 stainless steel. Transverse speed having rank 1, which is the most significant factor and standoff distance having rank 4, which is the less significant factor. 6.1. Taguchi analysis: VIKOR index versus A, B, C, D 6.1.1. Response table for signal to noise ratios 7. Conclusion In this study, the effects of process parameters setting on abrasive water jet machining of stainless steel AISI304 have been investigated. Four process parameters such as transverse speed, standoff distance, abrasive flow rate, and water pressure at four

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levels are selected for experimental runs, and experiment is conducted according to orthogonal array L16 . MRR and SR are selected as a quality target, using VIKOR method the responses have been normalized and VIKOR index found. Signal to noise ratio is calculated according to lower-is-better by MINITAB-15 software and predicted optimal parameter setting found to be A4B1C4D3 and factor A (transverse speed) is found most significant parameter. According to predicted optimal parameter setting the confirmation test has been done and VIKOR INDEX 0.0049 is found, as per methodology VIKOR INDEX should be minimum so the successful implementation of VIKOR approach has been done. The aforesaid method can be applied for continuous quality improvement of the product and off line quality control.

References 1. M. Hashish, Advances in composite machining with abrasive-waterjets, Process. Manuf. Comput. Mater. 49(27) (1991) 93–111. 2. A. W. Momber and R. Kovacevic, Principle of Abrasive Water Jet Machining (Springer Verlag limited, London, 1992). 3. M. Ramulu and D. Arola, The influences of AWJM condition on the surface quality of graphite, Int. J. Mach. Tools Manuf. 34(3) (1994) 295–313. 4. E. Siores, W. C. K. Wong, L. Chen and J. C. Wager, Enhancing abrasive water jet cutting of ceramic by head oscillation technique, Ann. CIRP 45(1) (1996) 215–218. 5. S. Opricovic, Multicriteria Optimization in Civil Engineering (in Serbian) (Faculty of Civil Engineering, Belgrade, 1998), pp. 302, ISBN 86-80049-82-4. 6. J. Wang and W. C. K. Wong, A study of water jet cutting of metallic coated sheet steels, Int. J. Mach. Tool Manuf. 39 (1999) 855–870. 7. A. Akkurt, M. K. Kulekci, U. Seker and F. Ercan, Effect of feed rate on surface roughness in abrasive water jet cutting application, J. Mater. Process. Technol. 147 (2004) 389–396. 8. M. A. Azmir and A. K. Ahsam, Investigation on glass/epoxy composite surface machined by abrasive water jet machining, J. Mater. Process. Technol. 198(1) (2008) 122–128. 9. U. Caydas and A. Hascalik, A study on surface roughness in AWJM process using artificial neural network and regression analysis methodology, J. Mater. Process. Technol. 202 (2008) 574–582. 10. F. C. Tsai, B. H. Yan, C. Y. Kuan and F. Y. Huang, A Taguchi and experimental investigation into the optimal processing condition for the abrasive jet polishing of SKD61 mold steel, Int. J. Mach. Tool Manuf. 48 (2008) 932–945. 11. A. Iqbal, N. V. Dar and G. Hussain, Optimization of abrasive water jet cutting of ductile materials, J. Wuhan Univ. Technol., Mater. Sci. 26(1) (2011) 88–92. 12. I. Karakut, G. Aydin and K. Aydiner, A machinability study of granite using abrasive water jet cutting technology, Gazi Univ. J. Sci. 24 (2011) 143–151. 13. H. Rowland’s, J. Antony and G. Knowler, An application of experimental design for process optimization, TQM Mag. 12(2) (2000) 78–83. 14. A. Aomar and Reid, A robust simulation-based multicriterion optimization methodology, Proc. 2002 Winter Simulation Conf. 15. S. Opricovic and G.-H. Tzeng, The compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, Eur. J. Oper. Res. 56(2) (2004) 445–455.