Multiple process parameter optimization of wire

Int J Adv Manuf Technol DOI 10.1007/s00170-013-5081-z

ORIGINAL ARTICLE

Multiple process parameter optimization of wire electrical discharge machining on Inconel 825 using Taguchi grey relational analysis G. Rajyalakshmi & P. Venkata Ramaiah

Received: 30 August 2011 / Accepted: 20 May 2013 # Springer-Verlag London 2013

Abstract In this paper, an effective approach, Taguchi grey relational analysis, has been applied to experimental results of wire cut electrical discharge machining (WEDM) on Inconel 825 with consideration of multiple response measures. The approach combines the orthogonal array design of experiment with grey relational analysis. The main objective of this study is to obtain improved material removal rate, surface roughness, and spark gap. Grey relational theory is adopted to determine the best process parameters that optimize the response measures. The experiment has been done by using Taguchi’s orthogonal array L36 (21 ×37). Each experiment was conducted under different conditions of input parameters. The response table and the grey relational grade for each level of the machining parameters have been established. From 36 experiments, the best combination of parameters was found. The experimental results confirm that the proposed method in this study effectively improves the machining performance of WEDM process. Keywords Inconel 825 . Wire cut EDM . Taguchi grey relational analysis . Optimization

G. Rajyalakshmi (*) School of Mechanical and Building Sciences, VIT University, Vellore, Tamilnadu 632014, India e-mail: [email protected] P. Venkata Ramaiah Department of Mechanical Engineering, Sri Venkateswara University, Tirupati, Andhra Pradesh 517 502, India e-mail: [email protected]

1 Introduction 1.1 Wire EDM Wire electrical discharge machining (WEDM) is one of the important nontraditional machining processes which are used for machining difficult to machine materials like composites and intermetallic materials. Intricate profiles used in prosthetics and biomedical applications can also be done in WEDM. WEDM involves complex physical and chemical process including heating and cooling. The electrical discharge energy affected by the spark plasma intensity and the discharging time will determine the crater size, which in turn will influence the machining efficiency and surface quality. In WEDM, also known as wire cut EDM and wire cutting, a thin single-strand metal wire, usually brass, is fed through the workpiece and submerged in a tank of dielectric fluid, typically deionized water. Wire cut EDM is typically used to cut plates as thick as 300 mm and to make punches, tools, and dies from hard metals that are difficult to machine with other methods. The wire, which is constantly fed from a spool, is held between upper and lower diamond guides. The guides, usually CNC controlled, move in the x–y plane. On most machines, the upper guide can also move independently in the z–u–v axis, giving rise to the ability to cut tapered and transitioning shapes (circle on the bottom square at the top for example). The upper guide can control axis movements in x–y–u–v–i–k–l. This allows the wire cut EDM to be programmed to cut very intricate and delicate shapes. The upper and lower diamond guides are usually accurate to 0.004 mm and can have a cutting path or kerf as small as 0.12 mm using a Ø 0.1 mm wire, though the average cutting

Int J Adv Manuf Technol

kerf that achieves the best economic cost and machining time is 0.335 mm using Ø 0.25 brass wire. The reason that the cutting width is greater than the width of the wire is because sparking occurs from the sides of the wire to the workpiece, causing erosion. This “overcut” is necessary; for many applications, it is adequately predictable and therefore can be compensated for (for instance in micro-EDM, this is not often the case). Spools of wire are long—an 8-kg spool of 0.25 mm wire is just over 19 km in length. Wire diameter can be as small as 20 μm and the geometry precision is not far from ±1 μm. The wire cut process uses water as its dielectric fluid, controlling its resistivity and other electrical properties with filters and deionizer units. The water flushes the cut debris away from the cutting zone. Flushing is an important factor in determining the maximum feed rate for a given material thickness (Fig. 1). Along with tighter tolerances, multi-axis EDM wire cutting machining center has added features such as multiheads for cutting two parts at the same time, controls for preventing wire breakage, automatic self-threading features in case of wire breakage, and programmable machining strategies to optimize the operation. Wire cutting EDM is commonly used when low residual stresses are desired because it does not require high cutting forces for removal of material. If the energy/power per pulse is relatively low (as in finishing operations), little change in the mechanical properties of a material is expected due to these low residual stresses, although material that has not been stress relieved can distort in the machining process. The workpiece may undergo a significant thermal cycle; its severity depending on the technological parameters used. Such thermal cycles may cause formation of a recast layer on the part and residual tensile stresses on the workpiece. With the introduction and increased use of newer and harder materials like titanium, hardened steel, high-strength temperature-resistant alloys, fiber-reinforced composites, and ceramics in aerospace, nuclear, missile, turbine, automobile, and tool and die making industries, a different class

Fig. 1 Wire cut EDM process [2]

of machining process has emerged. Better finish, low tolerance, higher production rate, miniaturization, etc. are also the present demands of the manufacturing industries. In recent years, wire EDM has become an important nontraditional machining process, which is widely used in the aerospace and automotive industries. However, selection of cutting parameters for obtaining higher cutting efficiency or accuracy in wire EDM is still not fully solved, even with the most up-to-date CNC wire EDM machine. This is mainly due to the complicated stochastic process mechanisms in wire EDM. As a result, the relationships between the cutting parameters and cutting performance are hard to model accurately. 1.2 Literature survey In EDM, it is important to select machining parameters for achieving optimal machining performance [1]. Usually, the desired machining parameters are determined based on experience or on handbook values. However, this does not ensure that the selected machining parameters result in optimal or near optimal machining performance for that particular electrical discharge machine and environment. Mahapatra et al. [2] explained the method of optimization of WEDM process parameters using Taguchi method. It has been shown that the grey-based Taguchi method can optimize the multi-response processes through the settings of the process parameters [3] but, in this paper, the grey relational analysis is not used for calculating the S/N ratio. This is because grey relational analysis based on the grey system theory [4] is used for solving the complicated interrelationships among the multiple responses. A grey relational grade is then obtained for analyzing the relational degree of the multiple responses. The fuzzy-based Taguchi method can also be used to optimize the multi-response process through the settings of process parameters [5]. Chung-Feng et al. [6] examined multiple quality optimization of the injection molding for polyether ether ketone. This study looked into the dimensional deviation and strength of screws produced by the injection molding. This study applied the Taguchi method to cut down on the number of experiments and combined grey relational analysis to determine the optimal processing parameters for multiple quality characteristics. Tosun [7] used the grey relational analysis for the determination of optimal drilling parameters with the objective of minimization of surface roughness and burr height. Lin et al. [8] used the grey relational analysis method for optimization of the EDM process. Most of the applications of Taguchi method concentrate on the optimization of single response problems [4]. The grey relational analysis based on grey system theory can be used for solving the complicated interrelationships among the multi-responses [4, 9, 10]. A grey relational grade is obtained to evaluate the multiple responses. As a

Int J Adv Manuf Technol

result, optimization of the multiple responses can be converted into optimization of a single relational grade. In short, there is an ample scope of applying the proposed methodology of grey relational analysis and Taguchi method with the multiple responses for the optimization. It may be noted that most of the prevailing approaches have used complex mathematical or statistical methods such as ANN, dual response approach, genetic algorithm, simulated annealing, and linear or nonlinear or dynamic programming. These approaches are difficult to implement by individuals with little background in mathematics/statistics and so are of little practical use. Ramakrishnan et al. [11] also lack the way to convert multiple objectives into a single objective format though the method is relatively simple. Through the grey relational analysis (GRA), a grey relational grade is obtained to evaluate the multiple performance characteristics. For example, Hsiao et al. [12] used the TM with GRA to optimize the plasma arc welding process. Prabhu et al. [13] analyzed surface characteristics like surface roughness and micro cracks of Inconel 825 and found out that an excellent machined nano finish can be obtained by setting the machining parameters at optimum level. The Taguchi design of experimental technique is used to optimize the machining parameters and an L9 orthogonal array is selected [13]. Grey relational analysis can be recommended as a method for optimizing the complicated interrelationships among multiple performance characteristics [14–17]. Moreover, Lin et al. showed that grey relational analysis is more straightforward than the fuzzy-based Taguchi method for optimizing the EDM process with multiple process responses [18]. Khan [19] presented his analysis on material removal rate during EDM of aluminum and mild steel using copper and brass electrodes. The highest material removal rate was observed during machining of aluminum due to high thermal conductivity and low melting point when compared to steel at low thermal conductivity and high melting point. As a result, highest material removal rates were obtained during machining of aluminum alloy. Inconel 825 is a nickel-based high-temperature strength alloy which is useful for applications in aerospace, missile, nuclear power, chemical and petrochemical, heat treatment, marine, and space shuttle components. The characteristics such as higher strain hardening tendency, high dynamic shear strength, and poor thermal diffusivity are the major causes of difficulty in machining of this alloy. These, in turn, produce higher cutting forces, highly strain hardened and toughened chips, and excessive tool wear and cause surface damages extending to subsurface levels. Besides, various processes, cutting tool, and work material-related parameters have complex interactions during machining. All these effects, in general, hamper the machinability of this alloy. There is a complex interrelation between processing conditions and output variables in Fig. 2.

Thus, selecting the best machining conditions during machining, which introduces high material removal rate and surface quality, is really a tough task. It is found, though, from the machining literature that a very few authors conducted parameter optimization in machining of Inconel 825. No study has been available on Inconel 825 machining with multi-objective optimization. This paper presents the optimization of wire electrical discharge machining of Inconel 825 process so as to optimize the responses using Taguchi-based grey relational analysis (TGRA). Eighteen experimental runs based on Taguchi orthogonal array were conducted to determine the best factor level combination. The factor levels were assessed according to the three response variables, namely material removal rate (MRR), surface roughness (SR), and spark gap (SG). The influence of the control factors on these response variables was studied by assessing the single grey relational grade for all performance characteristics. Huang et al. [20] investigated experimentally the effect of machining parameters on the gap width, the surface roughness, and the depth of white layer on the machined workpiece surface. The outline of the paper is as follows. The paper begins with the experimental plan and procedure followed by the Taguchi analysis of the observed data. Then, TGRA of the multiple responses is discussed in detail. Analysis of variance (ANOVA) of the grey relational grade has been performed to predict the optimum parameters. In the last section of the paper, experimental validation of the results is carried out.

2 Materials and methods 2.1 Work material Due to their high-temperature mechanical strength and highcorrosion resistance properties, super alloys are nowadays used in marine, space, and other applications. Their ability to maintain their mechanical properties at high temperatures severely hinders the machinability of these alloys [21, 22]. Its poor thermal diffusivity generates high temperature at the tool tip as well as high thermal gradients in the cutting tool, affecting the tool life adversely. Inconel 825 is very chemically reactive and therefore has a tendency to weld to the cutting tool during machining, thus leading to premature tool failure. Owing to all these problems, it is very difficult to machine Inconel 825 by conventional machining processes and moreover by conventionally used tool materials. Of late, modern machining techniques such as WEDM are increasingly being used for machining such hard materials. Hence, this study focused on machining of Inconel 825 using WEDM in order to satisfy production and quality requirement.

Int J Adv Manuf Technol Fig. 2 Interaction between processing conditions and output variables

PULSE ON TIME PULSE OFF TIME CORNER SERVO VOLTAGE

FLUSHING PRESSURE

WIRE FEED WIRE TENSION SPARK GAP VOLTAGE

MATERIAL REMOVAL Inconel825 Wire EDM machining

RATE

SURFACE ROUGHNESS

SPARK GAP

SERVO FEED RATE

The compositional range for Inconel 825 is provided in Table 1 and typical properties are covered in Table 2. 2.2 Experimental setup and experimental procedure 2.2.1 Schematic of machining The experiments were carried out on Ultra Cut 843/ULTRA CUT f2 CNC WEDM machine. In this machine, all the axes are servo controlled and can be programmed to follow a CNC code which is fed through the control panel. All three axes have an accuracy of 1 μm. The electrode material used was a 0.25-mm diameter brass wire. A small gap of 0.025 to 0.05 mm is maintained in between the wire and workpiece. The high-energy density erodes material from both the wire and workpiece by local melting and vaporizing. The dielectric fluid (deionized water) is continuously flushed through the gap along the wire and to the sparking area to remove the debris produced during the erosion. A collection tank is located at the bottom to collect the used wire erosions and then discarded. The wires once used cannot be reused again, due to the variation in dimensional accuracy. Through an NC code, machining can be programmed. Wire cut electrical discharge machining of Inconel 825 alloy has been considered in the present set of research work. The size of the workpiece considered for experimentation on the wire cut EDM is 10 mm width, 10 mm length, and 15 mm depth of cut. According to the Taguchi method based on robust design, a L36 (21×37) mixed orthogonal array is employed for the experimentation. Each experiment was repeated two times and an average of two readings is taken for analysis. Totally, 72 workpieces are cut for this analysis.

Table 1 Chemical composition of Inconel 825

Element

Content (%)

Ni Fe Cr Mo Cu Ti

38–46 22 19.5–23.5 2.5–3.5 1.5–3 0.6–1.2

In setting the machining parameters, particularly in rough cutting operation, the goal is threefold—the maximization of MRR, minimization of SR, and minimization of gap width. Generally, the machine tool builder provides machining parameter table to be used for setting machining parameter. This process relies heavily on the experience of the operators. In practice, it is very difficult to utilize the optimal functions of a machine owing to there being too many adjustable machining parameters. With a view to alleviate this difficulty, a simple but reliable method based on statistically designed experiments is suggested for investigating the effects of various process parameters on MRR, SR, and gap width and determines optimal process settings. In the present work, data have been collected from few experimental runs with randomly chosen factor combinations. A quadratic model has been fitted for identification of the process to establish approximate interrelation among various process parameters as well as response variables. These mathematical models have been utilized to generate data as per Taguchi design. Finally, grey-based Taguchi technique has been adopted to evaluate the optimal process environment. Among the eight WEDM parameters, two levels for one control factor (pulse on time) and three levels for remaining seven control factors are considered for optimality analysis during machining of Inconel 825 alloy. Figure 3 shows the workpiece after WED machining. 2.3 Machining parameter selection and performance evaluation The selection of optimum machining parameters in WEDM is an important step. Improperly selected parameters may result in serious problems like short circuiting of wire, wire breakage, and work surface damage which is imposing certain limits on the production schedule and also reducing productivity. As MRR, SR, and SG are most important responses in WEDM; various investigations have been carried out by several researchers for improving the MRR, surface finish, and kerf width [3–7]. However, the problem of selection of machining parameters is not fully depending on machine controls rather on material dependence. To perform the experimental design, the levels of machining parameters are selected as in Table 3.

Int J Adv Manuf Technol Table 2 Properties of Inconel 825

Property

Metric

Imperial

Density Melting point Coefficient of expansion Modulus of rigidity Modulus of elasticity

8.14 g/cm3 1,400 °C 14.0 m/m/°C (20–100 °C) 75.9 N/mm2 196 kN/mm2

0.294 lb/in.3 2,550 °F 7.8×10−6 in./in./°F (70–212 °F) 11,009 ksi 28,428 ksi

3 Experimental results and discussions

3.1 Statistical results based on Taguchi analysis

The multiple responses from the experiment were calculated as follows: Material removal rate is calculated as:

Statistical analysis of the individual performance characteristics was carried out to determine the influence of the control factors on the response variables. Table 5 shows the ANOVA results for the chosen performance characteristics—spark gap, material removal rate, and surface roughness.

MRR ¼ V c  b  h mm3 = min Where: V b h

Cutting speed in millimeters per minute Width of cut in millimeter Height of the workpiece in millimeter and surface roughness is measured with SurfcorderSE3500 in micrometer and spark gap is measured with micrometer in millimeter

Statistical analysis was carried out on the experimental data obtained through Taguchi experimental design using statistical software Minitab 14. ANOVA was performed to determine the influence of input parameters on the output response variables. Since the major focus of this study is on grey relational analysis, the results of Taguchi experiments have not been elaborated here. This section therefore has two subsections. The first subsection discusses the results of Taguchi method experiments briefly. The second subsection on the results discusses the application of grey relational analysis in detail (Table 4).

3.2 Optimization steps using Taguchi grey method In our case, the problem has eight performance characteristics that need to be minimized by choosing appropriate processing conditions. They are material removal rate, spark gap, and surface roughness. In such cases, the problem is converted into a single objective problem using grey relational analysis (see Fig. 4). The grey relational analysis deals with the ranks and not with the real value of the grey relational grade [23]. 3.2.1 Approach of the present investigation The wire electrical discharge machining process to be investigated corresponds to 36 different experiments. For the GRA, these 36 experiments become 36 subsystems. The influence of these subsystems on the response variable is to be analyzed using the GRA technique [24]. Hence, the process (system) is assessed by conducting 36 experiments (subsystems) where each experiment is termed as comparability sequences were obtained. The parametric conditions corresponding to the highest grey relational grade give minimum values of the spark gap and the surface roughness and maximum value of the material removal rate. In this manner, the multi-objective problem has been converted into single objective optimization using the GRA technique. 3.2.2 Formulation of the problem

Fig. 3 Workpiece after wire cut electrical discharge machining

Thus, the multi-objective optimization problem under investigation can be stated as “minimize: f (SG, SR)” and maximize: f (MRR), subject to independent decision variables as: pulse on time T ON (in microsecond), pulse off time T OFF (in microsecond), corner servo voltage (volts), flushing pressure WP (in kilograms per centimeter), wire feed rate WF (in meters per minute), wire tension WT (in kilogram-force),

Int J Adv Manuf Technol Table 3 Experimental factors and their levels for wire electrical discharge machining process Sample no.

Factor

Parameter

Symbol

Level 1

Level 2

Level 3

Range of process parameters

1 2 3 4 5 6 7 8

A B C D E F G H

Pulse on time Pulse off time Corner servo Flushing pressure of dielectric fluid Wire feed rate Wire tension N Spark gap voltage Servo Feed

T on (μs) T off (μs) CS (volts) WP (kg/cm2) WF (m/min) WT (kg-f) SV (volts) SF (mm/min)

105 50 50 8 2 9 20 1,050

115 55 60 10 5 10 25 1,100

– 60 70 15 6 11 30 1,150

105–115 50–60 50–70 8–15 2–6 9–11 20–30 1,050–1,150

spark gap voltage SV (volts), and servo feed rate SF (in millimeters per minute). The range of the independent decision variables should be: 105≤T ON≤115; T OFF, 50≤55≤60; CS, 50≤ 60≤70; WP, 8≤10≤15; WF, 2≤5≤6; WT, 9≤10≤11; SV, 20≤ 25≤30; and SF, 1,050≤1,100≤1,150. Furthermore, the above multi-objective problem can be converted into a single optimization problem using grey relational grade as “maximize grey relational grade (GRG); 0≤GRG≤1,” subjected to independent decision variables in the range mentioned above. 3.2.3 Methodology The stepwise procedure of GRA optimization shown in the flowchart (see Fig. 5) is used to solve the above formulation. The absolute value of data difference between comparability sequences could be used to measure approximate correlation between these sequences in terms of grey relational grade. Step 1 Normalization of S/N ratio It is the first step in the grey relational analysis; a normalization of the S/N ratio is performed to prepare raw data for the analysis where the original sequence is transferred to a comparable sequence. Linear normalization is usually required since the range and unit in one data sequence may differ from the others. A linear normalization of the S/N ratio in the range between zero and unity is also called as the grey relational generation [5]. Further analysis is carried out based on these S/N ratio values. The material removal rate is a higher-thebetter performance characteristic, since the maximization of the quality characteristic of interest is sought and can be expressed as: n
X 1 S=N ratio ¼ −log10 1=n y2 i ¼ 1 ij

Where n yij

Number of replications and Observed response value

ð1Þ

Where i=1, 2 …n; j=1, 2 …k. The surface roughness and spark gap are the lower-the-better performance characteristic and the loss function for the same can be expressed as: n
X y2ij S=N ratio ¼ −log10 1=n

ð2Þ

i ¼ 1

Step 2 Determination of deviation sequences, Δ0i(k) The deviation sequence Δ0i(k) is the absolute the reference sequence x 0*(k) and the comparability sequence x i*(k) after normalization. It is determined using Eq. 3:   Δ0i ðk Þ ¼ x0 ðk Þ−xi ðk Þ: ð3Þ Step 3 Calculation of grey relational coefficient (GRC) GRC for all the sequences expresses the relationship between the ideal (best) and actual normalized S/N ratio. If the two sequences agree at all points, then their grey relational coefficient is 1; + (x0(k), xi(k)) can be expressed by Eq. 4 [15]. g ðx0 ðk Þ; xi ðk ÞÞ ¼

Δmin þ ξΔmax Δ0i ðk Þ þ ξΔmax

ð4Þ

where Δmin is the smallest value of Δ0i(k)= min i min k|x 0*(k)−x 0*(k)| and Δmax is the larg  est value of Δ0i ðk Þ ¼ maxi maxk x0 ðk Þ−xi ðk Þ, x 0*(k) is the ideal normalized S/N ratio, x i*(k) is the normalized comparability sequence, and ζ is the distinguishing coefficient. The value of ζ can be adjusted with the systematic actual need and defined in the range between 0 and 1, ζ∈[0, 1]. It will be 0.5 generally [15]. Step 4 Determination of GRG The overall evaluation of the multiple performance characteristics is based on the grey relational grade. The grey relational grade [5] is an

Int J Adv Manuf Technol Table 4 Experimental layout using an L36 orthogonal array and experimental results Experiment no.

T on

T off

CS

WP

WF

WT

SV

SF

MRR (mm3/min)

SR (μm)

SG (mm)

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

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

1 2 3 1 2 3 1 2 3 1 2 3 2 3 1 2 3

1 2 3 1 2 3 2 3 1 3 1 2 3 1 2 3 1

1 2 3 1 2 3 3 1 2 2 3 1 1 2 3 2 3

1 2 3 2 3 1 1 2 3 1 2 3 3 1 2 1 2

1 2 3 2 3 1 2 3 1 3 1 2 2 3 1 1 2

1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1

120.375 143.250 182.250 119.625 139.500 183.750 112.875 142.500 195.750 114.750 147.750 202.125 115.875 127.125 144.375 123.375 131.625

1.54 1.86 1.41 1.68 1.66 1.75 1.47 1.17 1.99 1.86 1.54 1.94 1.86 1.85 1.61 1.94 1.38

0.0250 0.0350 0.0375 0.0150 0.0450 0.0150 0.0450 0.0500 0.0450 0.0400 0.0450 0.0450 0.0350 0.0150 0.0400 0.0450 0.0400

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2 3 1 2

2 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 1 2 3

1 3 1 2 3 1 2 1 2 3 2 3 1 3 1 2 2 3 1

3 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1 3 1 2

3 3 1 2 1 2 3 3 1 2 1 2 3 3 1 2 2 3 1

2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2

187.125 371.250 315.375 325.500 277.875 294.375 309.375 267.375 329.250 325.875 264.750 247.875 352.250 401.250 348.750 360.000 322.500 352.500 274.875

1.47 1.91 1.88 2.58 2.03 2.30 1.91 1.94 1.95 2.25 2.23 2.04 2.44 2.05 2.94 2.32 1.90 1.82 2.30

0.0400 0.0500 0.0100 0.0400 0.0400 0.0150 0.0350 0.0100 0.0300 0.0350 0.0500 0.0400 0.0150 0.0100 0.0300 0.0350 0.0450 0.0350 0.0450

average sum of the grey relational coefficients which is defined as follows: g ð x0 ; xi Þ ¼

1 m

m

∑ g ðx0 ðk Þ; xi ðk ÞÞ

i ¼ 1

ð5Þ

where + (x0, xi) is the grey relational grade for the jth experiment and m is the number of performance characteristics If the two sequences agree at all points, then their grey relational coefficient is 1 everywhere,

and therefore, their grey relational grade is equal to 1. In view of this, the relational grade of two comparing sequences can be quantified by the mean value of their grey relational coefficients and the grey relational grade. The grey relational grade also indicates the degree of influence that a 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 sequence, then the grey relational grade for

Int J Adv Manuf Technol Table 5 Analysis of variance (ANOVA) for response variables

ANOVA for MRR Source df A 1 B 2 C 2 D 2 E 2 F 2 G 2 H 2 Error 20 Total 35 ANOVA for SG Source df A 1 B 2 C 2 D 2 E 2 F 2 G 2 H 2 Error 20 Total 35 ANOVA for SR Source df A 1 B 2 C 2 D 2 E 2 F 2 G 2 H 2 Error 20 Total 35

Sum of squares 268,151 8,398 1,326 853 968 2,570 3,051 1,089 26,788 313,194

Mean sum of squares 268,151 4,199 663 427 484 1,285 1,526 545 1,339.42

F ratio 200.202 3.1341 0.4949 0.31879 0.36315 .9593 1.139 .4069

% contribution 81.618 2.68 0.423 0.272 0.309 0.821 0.974 0.347

Sum of squares 0.000213 0.000059 0.000792

Mean sum of squares 0.000213 0.000029 0.000396

F ratio 1.695 0.232 3.168

% contribution 3.76 1.043 14.012

0.000057 0.000719 0.000973 0.000090 0.000236 0.002513 0.005652

0.000028 0.000360 0.000487 0.000045 0.000118 0.000125

0.224 2.88 3.896 0.36 0.944

1.008 12.72 17.21 1.592 4.175

Sum of squares 2.1560 0.137 0.019 0.061 0.360 0.061 0.257 0.173 1.3093 4.5333

Mean sum of squares 2.1560 0.068 0.009 0.030 0.180 0.030 0.129 0.086 0.065465

F ratio 32.93 1.038 0.4526 0.4583 2.749 0.4583 1.97 1.313

% contribution 47.56 3.02 0.419 1.345 7.942 1.345 5.669 3.82

that comparability sequence and reference sequence will be higher than other grey relational grades [15]. Step 5 Determination of optimum parameters The grey relational grade calculated for each sequence is taken as a response for the further analysis. The larger-the-better quality characteristic was used for analyzing the GRG, since a larger value indicates the better performance of the Fig. 4 Purpose of grey relational analysis

Multi objective optimization

process. The quality characteristics used is given by Eq. 1 [4]. The number of repeated test is one, since only one relational grade was acquired in each group for this particular calculation of S/N. The grey relational grade obtained using Eq. 5 is analyzed using analysis of variance (ANOVA). ANOVA is used to reveal the level of significance of influence of factor(s) on a particular response.

Grey Relational Analysis

Single objective optimization

Int J Adv Manuf Technol

Comparability Sequences Single processing condition

Experimental runs 1-36 TGRA

Wire electrical discharge R machining Grey system

Response variables

MRR, SG, SR

S/N ratio

Input parameters

S/N ratio of 136 experiments

normalization, 1-18

Step 1

Step2

Step5

Single grey relational grade Step4 Grey relational coefficient 1-36

Step3

Fig. 5 Stepwise procedure of GRA optimization

This is accomplished by separating the total variability of the grey relational grades, which is measured by the sum of the squared deviations from the total mean of the grey relational grade, into contributions by each process parameter and the error. The response table of Taguchi method was employed here to calculate the average grey relational grade for each factor level. In this, the grouping of the grey relational grades was done initially by the factor level for each column in the orthogonal array and then by averaging them.

4 Application of grey relational analysis We know from the analysis of machining process that the higher the material removal rate and lower spark gap as well as lower value of surface roughness provide better quality of the machined surface. Thus, the data sequences of material removal rate, spark gap, and surface roughness have “larger-the-better” and “smallerthe-better” characteristics, respectively. The smaller-the-better methodology as expressed in Eqs. 1 and 2 was used for determining the S/N ratio. The S/N ratio values of the response variables are shown in Table 6. The S/N ratio values were normalized using Eq. 3. All the sequences after normalization are denoted as x0*(k) and xi*(k) for reference sequence and comparability sequence, respectively. The larger value of normalized results can indicate the better performance characteristic, and the bestnormalized results will be equal to 1. Then, the deviation sequences Δ0i(k)=|x0*(k)−xi*(k)| are determined using Eq. 3. Next,

the grey relational coefficient is calculated. In this study, all the machining parameters influence the material removal rate, spark gap, and surface roughness, moreover, equally. Considering that all the process parameters are of equal weighting, the distinguishing coefficient ζ=0.5 was substituted in Eq. 4. Then, the grey relational grade was determined by Eq. 5. Table 7 shows the grey relational grade for each experiment using the L36 orthogonal array. A higher grey relational grade indicates that the corresponding S/N ratio is closer to the ideally normalized S/N ratio. It is observed that experiment 3 has the highest grey relational grade (see Table 7); it therefore can be considered as a best experimental sequence for multiple performance of the process. Furthermore, the order of the experiments according to the values of grey relational grade is depicted in Table 7. Taguchi method is used to analyze the grey relational grades obtained. The calculated grey relational grade was taken as the response value in the Taguchi method. The mean response table for the overall grey relational grade is shown in Table 8 and is represented graphically in Fig. 8. The ordinate of Fig. 7 represents the means of grey relational grade calculated using larger-the-better criteria using Eq. 1. The steep slope of grey relational grade graph indicates more influence of machining parameters in the performance characteristics. Basically, the larger the grey relational grade, the better are the multiple performance characteristics. From the grey relational grade graph, the optimal parametric combination was determined. The optimal factor setting is A1, B1, C1, D1, E1, F2, G2, and H2, Similar results were observed by the others during machining of this alloy at higher cutting speeds [25, 26]. At a higher cutting speed, the surface flaws and discontinuities get wiped out due to higher thermal influence in

Int J Adv Manuf Technol Table 6 The S/N ratio values for the experimental results Experiment number

A

B

C

D

E

F

G

H

S/N ratio, MRR

S/N ratio, surface roughness

S/N ratio, spark gap

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

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

1 2 3 1 2 3 1 2 3 1 2 3 2 3 1 2 3

1 2 3 1 2 3 2 3 1 3 1 2 3 1 2 3 1

1 2 3 1 2 3 3 1 2 2 3 1 1 2 3 2 3

1 2 3 2 3 1 1 2 3 1 2 3 3 1 2 1 2

1 2 3 2 3 1 2 3 1 3 1 2 2 3 1 1 2

1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1

41.6107 43.1219 45.2134 41.5564 42.8915 45.2845 41.052 43.0763 45.834 41.1951 43.3905 46.1124 41.2798 42.0846 43.1898 41.8245 42.3868

−3.75041 −5.39026 −2.98438 −4.50619 −4.40216 −4.86076 −3.34635 −1.36372 −5.97706 −5.39026 −3.75041 −5.75603 −5.39026 −5.34343 −4.13652 −5.75603 −2.79758

32.0412 29.1186 28.5194 36.4782 26.9357 36.4782 26.9357 26.0206 26.9357 27.9588 26.9357 26.9357 29.1186 36.4782 27.9588 26.9357 27.9588

18 19 20 21 22 23 24 25 26 27 28

1 2 2 2 2 2 2 2 2 2 2

3 1 2 3 1 2 3 1 2 3 1

1 2 3 1 2 3 1 3 1 2 3

2 1 2 3 2 3 1 2 3 1 2

1 3 1 2 3 1 2 1 2 3 2

3 3 1 2 3 1 2 2 3 1 2

3 3 1 2 1 2 3 3 1 2 1

2 1 2 3 2 3 1 3 1 2 1

45.4426 51.3933 49.9765 50.251 48.877 49.378 49.8097 48.5424 50.3505 50.261 48.4567

−3.34635 −5.62067 −5.48316 −8.23239 −6.14992 −7.23456 −5.62067 −5.75603 −5.80069 −7.04365

27.9588 26.0206 40 27.9588 27.9588 36.4782 29.1186 40 30.4576 29.1186

29 30 31 32 33 34 35 36

2 2 2 2 2 2 2 2

2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2

3 1 3 1 2 1 2 3

3 1 3 1 2 2 3 1

3 1 2 3 1 3 1 2

2 3 3 1 2 2 3 1

2 3 2 3 1 3 1 2

47.8847 50.937 52.0683 50.8503 51.1261 50.1706 50.9432 48.7827

−6.9661 −6.1926 −7.7478 −6.23508 −9.36695 −7.30976 −5.57507 −5.20143 −7.23456

26.0206 27.9588 36.4782 40 30.4576 29.1186 26.9357 29.1186 26.9357

the machining region. Therefore, significant reduction in the surface roughness is observed [27, 28]. Furthermore, it facilitates the easy removal of the work material due to reduced dynamic shear strength of Inconel 825 in the presence of higher thermal influence in the machining region. Therefore, lower forces are produced during machining [27, 28]. Thus, the overall machining performance is higher and reflects in the higher value of the grey-related grade. A similar increase in the surface roughness was mentioned by Pawade et al. [26]. This trend could be due to complex deformation pattern of

this material, which involves excessive strain hardening; therefore, the overall machining performance is better at a higher value of GRG (Figs. 6, 7, and 8).

5 ANOVA The results obtained from the experiments were analyzed using analysis of variance to find the significance of each input factor on the measures of process performances, material removal rate, surface roughness, and spark gap. Using

Int J Adv Manuf Technol Table 7 Grey relational coefficients and grey grade Experiment number

GRC material removal rate

GRC surface roughness

GRC spark gap

Grey relational grade

Rank

1

0.9079

0.6264

0.4675

0.6672

6

2

0.7269

0.4984

0.3911

0.5388

18

3

0.5696

0.71174

0.3784

0.5532

17

4

0.9162

0.562

0.6649

0.7144

1

5

0.7497

0.5684

0.3485

0.5555

16

6

0.5654

0.5336

0.6649

0.5879

13

7

1

0.6686

0.3485

0.6724

4

8

0.7313

1

0.3333

0.6882

3

9

0.5353

0.46449

0.3485

0.5097

20

10

0.9748

0.4985

0.3672

0.6135

11

11

0.7019

0.6264

0.3485

0.5589

14

12

0.5212

0.4767

0.3485

0.4488

23

13

0.9604

0.4984

0.3911

0.6166

10

14

0.8421

0.5014

0.6649

0.6695

5

15

0.7169

0.5906

0.3672

0.5582

15

16

0.877

0.8795

0.3485

0.7077

2

17

0.8049

0.7362

0.3672

0.6361

7

18

0.5564

0.6686

0.3672

0.5307

19

19

0.3475

0.4845

0.3333

0.3884

33

20

0.3816

0.4927

1

0.6248

9

21

0.3506

0.3681

0.3672

0.3622

36

22

0.4131

0.4553

0.3672

0.4119

28

23

0.39818

0.4053

0.6649

0.4894

21

24

0.3861

0.4845

0.3911

0.4206

26

25

0.4237

0.4767

1

0.6335

8

26

0.3726

0.4742

0.4299

0.4232

24

27

0.3742

0.4133

0.3911

0.3929

30

28

0.42658

0.4166

0.3333

0.3921

31

29

0.4463

0.4531

0.3672

0.4222

25

30

0.3529

0.3853

0.6649

0.4677

22

31

0.3333

0.451

1

0.5948

12

32

0.3598

0.3333

0.42279

0.3719

35

33

0.3535

0.4622

0.3911

0.3823

34

34

0.3765

0.4872

0.3485

0.4041

29

35

0.3527

0.5104

0.3911

0.4197

27

36

0.416

0.4053

0.3485

0.3899

32

Table 8 Response table for grey relational grade

the grey grade value, ANOVA is formulated for identifying the significant factors. The results of ANOVA are presented in Tables 9 and 10. The results of the ANOVA are represented in the table above, and from the table, it is clear that pulse on time is the major influencing factor (contributing 50.18 % to performance measures), followed by pulse off time (contributing 14.19 %), wire tension (contributing 11.79 %), wire feed (contributing 4.29 %), corner servo voltage (contributing 2.14 %), spark gap voltage (contributing 2.06 %), servo voltage (contributing 1.19 %), and flushing pressure (contributing 0.87 %).

Factor

Level 1

Level 2

Level 3

Min–max

A

0.601517

0.443978

B

0.568050

0.533183

0.467008

0.101042

C D

0.514683

0.508233

0.545325

0.037092

0.516783

0.514058

0.537400

0.023342

E

0.553592

0.498267

0.516383

0.055325

F

0.557917

0.540642

0.469683

0.088233

G

0.516950

0.506683

0.544608

0.037925

H

0.505925

0.534425

0.527892

0.028500

0.157539

Boldface presentation of data indicates the optimal parameters

Int J Adv Manuf Technol

Fig. 8 Response graph of average grey relational grade Fig. 6 Grey relational grade for maximum MRR, minimum Ra, minimum spark gap

7 Development of mathematical models

6 Confirmation tests The experimental results are used to obtain the mathematical relationship between process parameters and machining outputs. The coefficients of mathematical models are computed using method of multiple regressions. In this study, Minitab 14 (Software Package for Statistical Solutions) was used for the regression analysis. This software is used to test linear models (user defined). The regression equation is

The confirmation test for the optimal parameter setting with its selected levels was conducted to evaluate the quality characteristics for WEDM of Inconel 825. Experiment 4 (Table 7) shows the highest grey relational grade, indicating that the optimal process parameter set of A1B1C3D3E1F1G3H2 has the best multiple performance characteristics among the 36 experiments, which can be compared with the results of confirmation experiment for validation of results. Tables 9 and 10 show the comparison of the experimental results using the orthogonal array (A1B1C1D1E1F2G2H2) and optimal grey theory design (A1B1C3D3E1F1G3H2) WEDM parameters on Inconel 825. The response values obtained from the confirmation experiment are MRR= 126.85 mm3/min, SR=1.44 μm, and SG=0.012 mm. The material removal rate shows an increased value of 119.625 to 126.85 mm3/min, the surface roughness shows a reduced value of 1.68 to 1.44 μm, and the spark gap shows a reduced value of 0.015 to 0.012 mm. The corresponding improvement in material removal rate is 7.22 % and surface roughness and spark gap were 16.66 and 13.3 %, respectively.

Fig. 7 The main effects of the factors on the grey relational grade

MRR ¼ −96:7 þ 173 A þ 18:0 B þ 7:33 C−5:69 D þ 5:78 E þ 5:73 F þ 9:21 G–5:10 H S ¼ 33:87 R−Sq ¼ 90:1% R−SqðadjÞ ¼ 87:2% The regression equation is SR ¼ 1:31 þ 0:489 A þ 0:0650 B−0:0104 C−0:0050 D−0:0917 E−0:0133 F−0:0921 G þ 0:0812 H S ¼ 0:2513 R−Sq ¼ 62:4% R−SqðadjÞ ¼ 51:3%

Main Effects Plot for Means B

A

C

D

E

F

H

G

0.60

O.56 MEAN O.52

0.48

0.44 1

2

1

2

3

1

2

3 1

2

3

1

2

3 1

2

3 1

2

3

1

2

3

Int J Adv Manuf Technol Table 9 ANOVA for Grey relational Grade

Factor

Degrees of freedom

Sum of squares

Mean sum of squares

F value

% contribution

A B C D E

1 2 2 2 2

0.22337 0.0632 0.0094 0.0039 0.0191

0.22337 0.0316 0.0047 0.0020 0.0095

75.552 10.688 1.5852 0.676 2.3132

50.18 14.19 2.14 0.87 4.29

F G H Error Total

2 2 2 20 35

0.0525 0.0092 0.0053 0.05913 0.4451

0.0262 0.0046 0.0027 0.0029565

8.8618 1.5558 0.91324

11.79 2.066 1.19

The regression equation is SG ¼ 0:0308−0:00486 A þ 0:00073 B−0:00323 C þ 0:00031 D þ 0:00406 E þ 0:00635 F−0:00156 G−0:00135 H

S ¼ 0:01172 R−Sq ¼ 34:4 % R−SqðadjÞ ¼ 15:0 %

8 Conclusions In this work, an attempt was made to determine the important machining parameters for performance measures like MRR, SF, and SG separately in the WEDM process. Factors like pulse on time, pulse off time, corner servo voltage, wire feed rate, wire tension, servo feed, spark gap voltage, and dielectric flow rate have been found to play a significant role in rough cutting operations for maximizations of MRR, minimization of surface roughness, and minimization of spark gap. Taguchi’s experimental design method is used to obtain optimum parameter combination for maximization of MRR and minimization of surface roughness as well as spark gap. Interestingly, the optimal levels of the factors for all the objectives differ widely. In order to optimize for all the three objectives, grey relational analysis was recommended as a method for optimizing Table 10 Optimization results of OA (L36) vs grey theory design Optimal process parameters

Level MRR (mm3/min) SG (mm) SR (μm)

Orthogonal array

Grey theory design

A1B1C1D1E1F2G2H2 119.625 0.0150 1.68

A1B1C3D3E1F1G3H2 126.85 0.013 1.44

the complicated interrelationships among multiple performance characteristics. As a result, this method greatly simplifies the optimization of complicated multiple performance characteristics, and since it does not involve complicated mathematical computations, this can be easily utilized by the stakeholders of the manufacturing world. 1. The optimal “process parameters” based on grey relational analysis for the wire cut EDM of Inconel 825 include 105 μs pulse on time, 50 μs pulse off time, 70 V corner servo voltage, 15 kg/cm2 flushing pressure, 2 m/min wire feed rate, 9 kg-f wire tension, 30 V spark gap voltage, and 1,100 mm/min servo feed rate. 2. While applying the grey–Taguchi method, the material removal rate shows an increased value of 119.625 to 126.85 mm3/min, the surface roughness shows a reduced value of 1.68 to 1.44 μm, and the spark gap shows a reduced value of 0.015 to 0.013 mm, which are positive indicators of efficiency in the machining process. Thus, it can be concluded that the grey– Taguchi Method is most ideal and suitable for the parametric optimization of the wire cut EDM process, when using the multiple performance characteristics such as MRR, surface roughness, and spark gap, for machining the Inconel 825. 3. Mathematical relations between the machining parameters, namely pulse on time, pulse off time, flushing pressure, corner servo voltage, wire tension, spark gap voltage, servo feed, and wire feed and performance characteristics such as MRR, SR, and SG are established by the regression analysis method. The established mathematical models can be used in estimating the material removal rate, surface roughness, and spark gap without conducting experiments.

Acknowledgments The authors are thankful to the reviewers for their suggestions that significantly improved our paper.

Int J Adv Manuf Technol

References 1. Tarng YS, Ma SC, Chung LK (1995) Determination of optimal cutting parameters in wire electrical discharge machining. Int J Mach Tool Manuf 35(12):1693–1701 2. Mahapatra SS, Patnaik A (2006) Optimization of wire electrical discharge machining (WEDM) process parameters using Taguchi method. Int J Adv Manuf Technol 34:911–925 3. Lin JL, Tarng YS (1998) Optimization of the multi-response process by the Taguchi method with grey relational analysis. J Grey Syst 10(4):355–370 4. Deng JL (1989) Introduction to grey system. J Grey Syst 1:1–24 5. Lin JL, Wang KS, Yan BH, Tarng YS (2000) Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics. J Mater Process Technol 102:48–55 6. Feng C, Jeffrey K, Su T-L (2006) Optimization of multiple quality characteristics for polyether ether ketone injection molding process. Fibers Polymers 7(4):404–413 7. Tosun N (2006) Determination of optimum parameters for multi performance characteristics in drilling by using grey relational analysis. Int J Adv Manuf Technol 28:450–455 8. Lin CL, Lin JL, Ko TC (2002) Optimization of the EDM process based on the orthogonal array with fuzzy logic and grey relational analysis method. Int J Adv Manuf Technol 19:271–277 9. Jeyapaul R, Shahabudeen P, Krishnaiah K (2005) Quality management research by considering multi-response problems in the Taguchi method—a review. Int J Adv Manuf Technol 26:1331–1337 10. Haq AN, Marimuthu P, Jeyapaul R (2008) Multi response optimization of machining parameters of drilling Al/SiC metal matrix composite using grey relational analysis in the Taguchi method. Int J Adv Manuf Technol 37:250–255 11. Ramakrishnan R, Karunamoorthy L (2006) Multi response optimization of wire EDM operations using robust design of experiments. Int J Adv Manuf Technol 29:105–112 12. Hsiao YF, Tarng YS, Huang WJ (2008) Optimization of plasma arc welding parameters by using the Taguchi method with the grey relational analysis. J Mater Manuf Process 23:51–58 13. Prabhu S, Vinayagam BK (2011) AFM surface investigation of Inconel 825 with multi wall carbon nano tube in electrical discharge machining process using Taguchi analysis. Archives of Civil and Mechanical Engineering, vol. XI, no. 1 14. Kung LM, Yu SW (2008) Prediction of index futures returns and the analysis of financial spillovers—a comparison between GARCH and the grey theorem. Eur J Oper Res 186(3):1184–1200

15. Ng David KW (1994) Grey system and grey relational model. ACM SIGICE Bulletin 20(2):1–9 16. Chang SH, Hwang JR, Doong JL (2000) Optimization of the injection molding process of short glass fiber reinforced polycarbonate composites using grey relational analysis. J Mater Process Technol 97:186–193 17. Lin JL, Lin CL (2002) The use of the orthogonal array with grey relational analysis to optimize the electrical discharge machining process with multiple performance characteristics. Inter J Mach Tools Manuf 42(2):237–244 18. Fung CP (2003) Manufacturing process optimization for wear property of fiber-reinforced poly butylene terephthalate composites with grey relational analysis. Wear 254:298–306 19. Khan AA (2008) Electrode wear and material removal rate during EDM of aluminum and mild steel using copper and brass electrodes. Int J Adv Manuf Technol 39(5–6):482–487 20. Huang JT, Liao YS, Hsue WJ (1999) Determination of finish cutting operation number and machining parameters setting in wire electrical discharge machining. J Mater Process Technol 87:69–81 21. Ezugwu EO (2005) Key improvements in the machining of difficult-to-cut aerospace superalloys. Int J Mach Tool Manu 45:1353–1367 22. Choudhury IA, El-Baradie MA (1998) Machinability of nickelbase super alloys: a general review. Journal of Materials Processing Tech 77:278–284, ISSN: 0975–5462 1546 23. Chiang KT, Chang FP (2006) Optimization of the WEDM process of particle-reinforced material with multiple performance characteristics using grey relational analysis. J Mater Process Technol 180:96–101 24. Lin CL, Lin JL, Ko TC (2002) Optimisation of the EDM process based on the orthogonal array with fuzzy logic and grey relational analysis method. Inter J Adv Manuf Technol 19:271–277 25. Arunachalam RM, Mannan MA, Spowage AC (2004) Residual stress and surface roughness when facing age hardened Inconel 718 with CBN and ceramic cutting tools. Int J Mach Tools Manuf 44(9):879–887 26. Pawade RS, Joshi SS, Brahmankar PK, Rahman M (2004) In: Raja VS, Kuppan (eds) Some investigations of high-speed turned Inconel 718. In Proc. of 21st AIMTDR Conference. VIT, Vellore, pp 41–47 27. Pawade RS, Joshi SS, Brahmankar PK (2008) Effect of cutting edge geometry and machining parameters on surface integrity of highspeed turned Inconel 718. Int J Mach Tools Manuf 48(1):15–28 28. Pawade RS, Joshi SS (2011) Multi-objective optimization of surface roughness and cutting forces in high-speed turning of Inconel 718 using Taguchi grey relational analysis (TGRA). Int J Adv Manuf Technol 56:47–62