Multi-objective optimization of machining variables for wire-EDM of LM6/fly ash composite materials using grey relational analysis

Research Article Charles Sarala Rubi, Jayavelu Udaya Prakash, Sunder Jebarose Juliyana, Robert Čep, Sachin Salunkhe*, Sharad Ramdas Gawade, and Emad S. Abouel Nasr Multi-objective optimization of machining variables for wire-EDM of LM6/fly ash composite materials using grey relational analysis https://doi.org/10.1515/secm-2024-0008 received November 01, 2023; accepted April 16, 2024 Abstract: With the enhancement in science and technology, necessity of complex shapes in manufacturing industries have become essential for more versatile applications. This leads to the demand for lightweight and durable materials for applications in aerospace, defense, automotive, as well as sports and thermal management. Wire electric discharge machining (WEDM) is an extensively utilized process that is used for the exact and indented shaped components of all materials that are electrically conductive. This technique is suitable in practically all industrial sectors owing to its widespread application. The present investigation explores WEDM for LM6/flyashcomposites to optimize different process variables for attaining performance measures in terms of maximum material removal rate (MRR) and minimum surface roughness (SR). Taguchi’s L 27 OA design of experiments, grey relational analysis, and analysis of variance (ANOVA) were employed to optimize SR and MRR. It has been noted from ANOVA that reinforcement (R)percentageandpulseontimearethemostinfluential aspects for Grey Relational Grade (GRG) with their contributions of 28.22 and 18.18%, respectively. It is found that the best process variables for achieving the highest MRR and lowest SR simultaneously during the machining of the composite are gapvoltageof30V,pulseontimeof10µs,pulseofftime of 2 µs, wire feed of 8 m/min, and R of 9%. The predicted GRG is 0.84, and the experimental GRG value is 0.86. The validation experiments at the optimized setting show close agreement between predicted and experimental values. The morphological study by optical microscopy revealed a homogenous distribution of reinforcement in the matrix which enhances the composite’s hardness and decreases the density. Keywords: AMCs, ANOVA, DoE, grey relational analysis, wire EDM 1 Introduction Although composites have been available since the earliest days, it was only in World War II that they were commercially viable. In order to create new materials and improve the properties of the base materials, a composite material combines multiple physical elements [1]. Aluminum matrix composites (AMCs) are growing in demand for use in automobiles, airplanes, and other applications in engineering. AMCs consistently meet the demand for robust, lightweight, and outstanding performance components. Exceptional durability, resistance to wear, and low thermal expansion and conductivity in electricity are all the characteristics of AMCs. It facilitates replacing traditional Al alloys [2]. Al alloy is a viable substitute for brake rotors due to the cast iron recyclable qualities issue and improved efficiency, and it has a wide variety of automotive uses. To Charles Sarala Rubi: Department of Physics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India, e-mail: [email protected] Jayavelu Udaya Prakash: Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India, e-mail: [email protected] Sunder Jebarose Juliyana: Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India, e-mail: [email protected] Robert Čep: Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 708 00, Ostrava, Czech Republic  * Corresponding author: Sachin Salunkhe, Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India; Department of Mechanical Engineering, Faculty of Engineering, Gazi University, Maltepe, Ankara, Turkey, e-mail: [email protected] Sharad Ramdas Gawade: Department of Mechanical Engineering, Sharadchandra Pawar College of Engineering and Technology, Someshwar, Baramati, 412306, India, e-mail: [email protected] Emad S. Abouel Nasr: Department of Industrial Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh, 11421, Saudi Arabia Science and Engineering of Composite Materials 2024; 31: 20240008 Open Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. improve the structural durability and maintain proper coefficient of friction regardless of repeated braking, abrasive particles, like silicon carbide and alumina, are utilized [3–5]. Over 80% of metal matrix composites (MMCs), according to the investigation, are utilized for ground-based transportation. For certain applications, appropriate inclusion of the matrix, reinforcement (R), and manufacturing techniques results in better physical and corrosive characteristics [6]. The size of a reinforcement particle used in a typical MMC ranges from 2 to 200 µm and the volume fraction varies between 5 and 40%. Also, matrices are generally based on light metal alloys like aluminum, copper, zinc, steel, and magnesium. Reinforcements used are generally of abrasive nature with high hardness [7]. The goal of the sector is to make things that are both affordable and high-quality in a short amount of time. To achieve effective cutting efficiency, the industry must operate near the optimum cutting factors [8]. Because of this, it is important to choose machining variables like gap voltage (GV), pulse on time (T on ), pulse offtime (T off ), wire feed (WF), and Rcarefully. Digitally controlled cutting machines must run effectively in order to produce the required product since they are more expensive than their conventional counterparts [9]. The fabrication of hybrid MMC materials, which have recently proven to have more desirable properties, involves embedding the matrix phase with two or more secondphase materials [10]. Hybrid AMCs are designed for various uses, including drive shafts, brake rotors, airframe structures, vehicle parts, aviation, and airplane components. These materials can be manufactured by a variety of techniques [11]. The manufacturing sector first encountered wire electric discharge machining (WEDM) in the latter half of the 1960s. The unconventional material removal technique WEDM is commonly utilized to create parts with complex forms and shapes. The WEDM technology minimizes stresses that happen while machining. It additionally reduces the changes in geometry that take place during the machining of heat-treated steel and can work with exotic materials [12]. Nonconventional machining techniques, including electrical discharge machining (EDM), electro chemical machining, abrasive water jet machining, and laser beam machining, are alternatives that get beyond the restrictions of conventional machining methods, like machining a complicated shape, low precision, energy consumption, recycling, etc.[13 ,14]. Complex dimensions, such as hydraulic andinjectionmoldparts,canbe machined using WEDM. In WEDM, the component being machined and the wire material interact thermoelectrically to carry out the machining so that the hardest materials can be easily machined [15]. The parameters such as GV, T on ,T off , WF, and Rall influence how well the WEDM performs. EDM and WEDM have similar material removal methods; however, they have different functional properties. WEDM uses an extremely fine wire continually fed through the work piece by a microprocessor controller, allowing for the incredibly high accuracy needed to make components with intricate shapes [16]. For the roughing and finishing processes in EDM, WEDM does not require the complex pre-shaped electrodes that are frequently needed. Materials are removed by repeated electrical pulses with duration of 10 −4 to 10 −6 s across the specimen and the tool electrode [17]. The machine generator produces these electrical impulses and removes material through evaporation in addition to electrical discharge. A stream of dielectric liquid that has elevated resistance to electricity always washes the eroded material away from the cutting point [18,19]. The component being machined does not get stressed by traditional forces, as is typical when using traditional machining techniques because there is always a gap between the wire electrode and the specimen. Because of this, even very fragile materials can be machined, and thinwalled profiles can be made [20]. Another benefitisthat irrespective of their toughness or hardness, all materials thatarepreferablysomewhatconductivetoelectricity can be machined, which can also hinder the conventional machining of certain materials. The procedure’s increased energy usage and comparatively slow material removal are drawbacks [21,22]. Ti-6Al-4V was employed as the work material by Basak et al. [23], and a brass wire with 0.25 mm diameter served as the electrode. The surface roughness (SR) was predicted and modeled using a two-level factorial approach. The machining variables were input voltage, T on , dielectric fluid pressure, and T off . The findings demonstrated that with shorter pulse-on and at a lower dielectric fluid pressure, a superior surface quality could be achieved. Ti-6Al-4V has been investigated as a potential work material by Alis et al. [24]. A titanium alloy was machined using brass wire and a steady 4 A current. The wire tension, wire speed, and discharge current were chosen as the machining variables. Based on their research, they concluded that increasing the current produced a higher rate of material removal and that increasing the wire tension produced a smooth surface. Furthermore, it was seen that as wire tension increased, the vibrations of the wire decreased. A Ti-6Al-4V alloy was machined using the WEDM technique by Gupta et al. [25] using a steady 6 A current and variable machining speeds between 2 and 6 mm/min. The machining variables included the pulse duration, wire speed, servo voltage, feed rate, and wire tension. The responses were the material removal rate (MRR) and SR. At a reduced machining feed rate and a greater wire tension, the surface circumstances were satisfactory. 2Charles Sarala Rubi et al. Some process variables, such as wire speed and pulse length, were found to be less beneficial for MRR. Ni 55.8 Ti shape memory alloy has been machined by WEDM process. The effects of input parameters such as spark GV, pulse on-time, pulse off-time, and WF on metal removal rate (MRR) and surface quality have been investigated. Empirical modeling and analysis of variance (ANOVA) study have been done after conducting 16 experiments based on Taguchi’sL 16 design of experiments (DoE) technique. Ranking andcrowdingdistance-basednon-dominated sorting algorithmII (NSGA-II) is used for process optimization. The error percentage varies within ±6% between experimental results and the predicted results developed by NSGA-II [26]. Several researchers attempted to improve the performance characteristics such as MRR, SR, surface and subsurface properties in WEDM. But full potential utilization of this process is still not completely solved due to its complexity, stochastic nature, and in addition, involvement of more number of process variables in this process [27]. The prior works on WEDM indicate that most of the studies concentrated on the influence of process parameters on SR and MRR during machining of different composites. Hence, the aim of the present study is to develop the mathematical models using Minitab software for the WEDM characteristics and then to simultaneously optimize the proposed WEDM characteristics of LM6/fly ash composites. Al-Matrix composites are considered as one of those classes of advanced engineering materials. Hence, it is obligatory to investigate the impact of different machining conditions for the selection of optimum parameter settings for aluminum-based hybrid MMC material. The present investigation demonstrates the significance of cutting variables on Grey Relational Grade (GRG) of LM6/ fly-ash composites. ANOVA is used to confirm the model’s validity. The findings demonstrate that the given model can precisely predict the MRR and SR in WEDM LM6/fly-ash composite material within the reported parameters. The present work provides optimum process variables for the researchers engaged in the WEDM of different kinds of MMCs. The trend is the same even when the material is different. This investigation reveals how process variables affect various responses. This article will be useful to the budding researchers to know about the WEDM process parameters, and their effect on MRR, SR, and GRG. 2 Materials and methods 2.1 Al alloy LM6 Due to its tendency to drag and fast tool wear, Al alloy (LM6) is hard to machine. It exhibits good corrosion resistance in both ambient and marine environments. Unlike any other casting alloy, it is capable of being cast into thin, complex components. It provides outstanding pressure tightness, hence is a good choice for hydraulic systems and pressure vessels. The casting properties make it very efficient for complex parts. Optical emission spectrometry (ASTM E 125107) was used to determine the elemental Composition of the LM6 alloy, which is displayed in Table 1. 2.2 Fly ash Fly ash particulates with a particle size of 12 μm have been used in this study as reinforcement. The presence of reinforcement in the LM6 alloy enhances their resistance to wear, damping abilities, hardness, and stiffness and decreases the weight. Fly ash particulates are thermal power plant wastes that are present in high amounts and are a form of intermittent reinforcement. The unique properties associated with flyash, such as low electrical and thermal conductivity and lightweight, makes it useful in fabricating composite material that are less in weight and insulating. Al-fly ash composite materials have potential applications in the automobile and electrochemical sectors [28].Table2andFigure1showtheelementalconstitution and surface morphology of fly ash particles, respectively. 2.3 Fabrication of LM6/fly ash composites The simple and economical technique for producing the composites is stir casting. In this method, the reinforcement is embedded uniformly in the molten LM6 alloy by mechanical stirring [29,30]. Figure 2 shows the fabrication setup utilized in composite preparation. Blocks of Al alloy LM6 have been heated in an electric furnace to melt them. Slowly, the furnace’s temperature Table 1: Elemental composition of the LM6 alloy Constituent Si Cu Fe Mg Mn Ti Ni Zn Al Weight (%) 11.48 0.013 0.52 0.02 0.01 0.02 0.01 0.01 Remainder Optimization of machining variables for WEDM of LM6/fly ash composite materials 3 was increased to 850°C, and the melt was degassed using hexachloroethane in order to get rid of the dissolved gases. The melted metal was then mixed with the flyashparticles that had been heated to 250°C. For 10 min, a mechanical stirrer was used to continually agitate the slurry at 600 rpm in order to create a slurry. A tiny amount of Mg was mixed with the slurry to increase the wettability of the particles as they interacted with the metal. The slurry was then transferred into 650°C preheated molds, where it was allowed to cool to ambient temperature. Fly ash was incorporated into the continuous phase with the concentration of 3, 6, and 9 wt%. 2.4 Selection of parameters and orthogonal array (OA)-DoE The DoE is a technique used to define what data, and in what quantity and settings must be collected during an experimentation, to satisfy two foremost goals: the statistical accuracy of the response parameters accompanied by lesser cost [31]. In the present investigation, five different process parameters at three levels were selected, viz. GV, pulse on time (T on ), pulse offtime (T off ), WF, and R%. The responses are MRR and SR. Based on the selected parameters, L 27 array is selected for the present investigation. L 27 array has an exceptional property that the two-way interactions between several factors are partially confounded with various columns and hence their effect on the estimation of the main effects of the various parameters is minimized. The number of parameters is five and their levels are three. Therefore, 3 5 = 243 experiments using full factorial design should be conducted, but 27 experiments were conducted using DoE. So, 216 experiments were reduced. 1/9 experiments were conducted and saved 88% time and resources. Experiments have been repeated three times at each experimental condition. The machining variables and their levels are depicted in Table 3. 2.5 Grey relational analysis (GRA) While dealing with machining optimization problems, there are usually more than one quality characteristics (and often conflicting), due to high process complexity. The overall goal is to find solutions that are acceptable by the decision maker. Although in single-objective optimization problems, it is Table 2: Elemental constitution of fly ash Constituent Al Si O Fe Ti K Ca LOI Weight (%) 16.73 26.43 38.88 3.82 1.42 0.99 0.5 Remainder Figure 1: Surface morphology of fly ash particles. Figure 2: Stir casting set up. Table 3: Machining variables and their levels Levels Pulse on time (µs) Pulse off time (µs) WF (m/min) GV (V) R% 1 2 2 4 30 3 2 6 6 6 50 6 3 10 10 8 70 9 4Charles Sarala Rubi et al. straight forward to find an optimal solution, multi-objective ones provide users with sets of solutions, out of which one should be chosen so as to be applied in physical systems [32]. GRA can be used to determine the relation among sequences. For the optimization of machining variables, the below-mentioned steps are followed: 1) Normalize the MRR and SR for WEDM experimental data; 2) Identify the sequence of deviation. 3) Find the grey relational coefficient (GRC). 4) By averaging the GRC, determine the GRG. 5) Utilize statistical examination of variance and GRG to analyze the experimental outcomes. 6) Choose the optimum machining variable. 7) Conduct confirmation experiments to validate the optimization method. 2.5.1 Data pre-processing The preparation of data in GRA is the process of first normalizing the results of the experiment of the MRR and SR to be in the range of 0–1. For the GRA, different data preliminary processing approaches are available depending on the features of a data sequence. “Higher-the-better”property is used if the target value is infinite. The normalization of the original sequence is given in Equation (1). () () () () () () () () () =− − x kxk xk xk xk min max min . iii ii ⁎00 00 (1) For “lower-the-better”property, the normalization of the sequence is given in Equation (2), () () () () () () () () () =− − x kxk xk xk xk max max min , iii ii ⁎00 00 (2) where () x k i⁎ is the normalized value, () () x k i0is the desired sequence, min () () x k i0is the minimum value of the sequence, and max () () x k i0is the maximum value of the sequence. 2.5.2 GRC The term “GRC”refers to the measure of significance among two distinct processes or sequences in GRA. The purpose of the GRA is to demonstrate the degree of relationship between the x o (k)andx i (k) sequences. The GRC is given in Equation (3). () () =+ + γx k x ΔζΔ Δk ζΔ ,, i 0⁎min max 0i max (3) where Δ 0i (k) denotes the deviation sequence. () () ()= Δ kxk xk–, ii 00⁎ where Δ min and Δ max are the smallest and largest value of Δ 0i (k), respectively, and ζ is the distinguishing coefficient. 2.5.3 GRG The GRG is the foundation for the evaluation of the multiresponse feature. It is given in Equation (4). ((() ()) ∑ == τ nγx k x k 1,, ii n i 10⁎(4) where τ i is the GRG, and nis the number of process responses. The closer the experimental finding is to the optimum normalized value, the greater the GRG. 2.5.4 Predicting the optimum responses The optimal condition is chosen based on the experiment’sgoal, which is either maximization or reduction of the response. If there are three variables, say A,B,andCand three levels, 1, 2, and 3 and the first levels are the optimum conditions, then the predicted optimum response µ pred isgiveninEquation(5). ()=++−μABCY   2, pred 111 (5) where =Y Overall mean response and =ABC ,1,  11 Average response at level 1 of these factors. 2.6 ANOVA ANOVA is used to analyze investigational findings concerning the investigation’s parameters. The % contribution shows how much each interaction contributed to the overall variance. The percentage of error-related responses shows the experiment’s efficiency before pooling. Generally speaking, if the proportion contribution attributable to error is 15% or less, no significant variables have been left out of the experiment. If it is higher (at least 50%), either there was a significant measurement error, or certain factors were not taken into account. 3 Machining and measurement 3.1 WEDM The WEDM process is chosen for studying the machinability of the composites and the LM6 Al alloys. The image of CNC WEDM is presented in Figure 3. Optimization of machining variables for WEDM of LM6/fly ash composite materials 5 3.2 Machining performance variables MRR and SR were taken as the output responses in this study. 3.2.1 MRR MRR is obtained by the ratio of the volume of the material removed from the specimen (mm 3 ) to the time taken (min). 3.2.2 SR Figure 4 shows the SR of the machined component as determined using a Surfcorder SE 3500 surface roughness tester. This measurement plays an important role in several fundamental issues, including friction, surface distortion, heat transmission, electrical current, joint stiffness, and spatial accuracy. The information was collected at three different locations on the machined surface, and the SR was calculated using the mean of the three measurements. An SR calculation’s orientation was perpendicular to the surface that was being machined [33]. 4 Results and discussion 4.1 Microstructure Microstructure is the term used to describe the materials’ appearance from the scale of micrometer to nanometer length. Microstructure helps analyze the presence of various phases in a composition. By modifying the microstructure, the desired properties can be obtained. It also affects the physical properties and mechanical behavior of materials. Theultimategoalofthemicrographistoobservethenature of the dispersion of reinforcement in the continuous phase. An optical microscope was used for this analysis, and the images show the uniform dispersion of the second phase material in the matrix and are depicted in Figure 5. The physical properties of reinforcement particles and the physical properties of Al alloy decide the outcome of the composites. Figure 5(b) shows the distribution of 3% reinforcement in LM6 alloy matrix composites. The distribution is uniform, and the particles are closer to neighboring particles. This is due to the very low viscosity of LM6 Al alloy. Figure 5(c) and (d) shows the presence of 6 and 9% fly ash in LM6 alloy matrix composites, respectively. The Al-Si eutectic remains unchanged with a script-like shape in the composite materials (Figure 5a). 4.2 Density The density of the composites and Al alloy (LM6) was found using the Archimedes principle and it is given in Equation (6). = D ensity Mass Volume . (6) Figure 6 displays the impact of fly ash particle weight percentages on the density of composites. The specimen’s density reduces with a rise in the amount of second-phase material. The key reason is that fly ash has a lower density (2.09 g/cm 3 ) than LM6 alloys (2.70 g/cm 3 ). A linear reduction Figure 3: Photograph of ECOCUT –CNC wire EDM. Figure 4: Surface roughness tester. 6Charles Sarala Rubi et al. is seen in the composite materials with rising dispersoid content [34,35]. The findings indicate that when the wt% of R increased, the specimen’s density decreased [36]. 4.3 Hardness The hardness of the composite materials and LM6 were determined using a Rockwell hardness tester. It is observed from Figure 7 that the hardness of the specimen was larger than that of the LM6 alloy. The composite material LM6/9% fly ash has the highest hardness value among the LM6 matrix composites. The result of high hardness is due to the inclusion of fly ash particles like cenospheres and precipitators [37,38]. By adding the reinforcement particles to the composites, surface area of the reinforcement increases and the grain Figure 5: (a–d) Micrographs of LM6 and LM6/Fly ash composites. (a) Al alloy (LM6). (b) LM6 + 3% fly ash. (c) LM6 + 6% fly ash. (d) LM6 + 9% fly ash. Figure 6: Effect of fly ash on the density of AMCs. Figure 7: Influence of fly ash on the hardness of AMCs. Optimization of machining variables for WEDM of LM6/fly ash composite materials 7 sizes of the matrix decrease. The presence of such hard reinforcement particles on the surface resists the plastic deformation of the material. The strength of the grain boundaries increases to maximum level and dislocation of atoms are decreased by increasing the wt% of the reinforcement, which gives strength to the matrix and thereby hardness of the composite gets increased [39,40]. 4.4 Optimization of WEDM LM6/fly ash AMCs The experimental findings on WEDM of LM6/fly ash are presented in this section. GRA was used to optimize the responses to obtain the highest MRR and the lowest SR values concurrently. The value of GRG was used to identify the best machining variables. 4.4.1 Experimental results The goal of the WEDM studies is to investigate how cutting variables influenced the features of the output response. The 27 rows of the L 27 OA, which has 13 columns and 3 levels, correspond to the number of experiments. Table 4 displays the experimental outcomes together with associated GRG and Ranks. 4.4.2 Analysis and discussion This section discusses the influence of various cutting variables on the MRR and SR quality characteristics that were chosen. Using the findings of the experiment, GRA has been employed to generate a GRG of the output parameters for each factor at multiple levels. Plots illustrating the GRG data’s major effects on process variables were drawn. Examining how parametric variables influence the response features is done using the response graphs. ANOVA is used to determine the important factors and analyze how much of an impact they have on the response features. Figure 8 demonstrates that the GRG rises with the increase in the “WF”and “R” during the pulse on time and diminishes with the increase in the “GV”and “T off .”This is because a higher rate of MRR results from an increase in the discharge energy as “T on ” Table 4: Experimental results of MRR and SR Ex. no. GV (V) T on (µs) T off (µs) WF (m/min) R(wt%) MRR (mm 3 /min) SR (µm) GRG Rank 1 30 2 2 4 3 27.118 4.74 0.507 24 2 30 2 6 6 6 23.874 4.07 0.542 20 3 30 2 10 8 9 21.586 3.76 0.566 17 4 30 6 2 6 9 41.493 3.1 0.975 1 5 30 6 6 8 3 27.609 4.74 0.511 23 6 30 6 10 4 6 28.728 3.35 0.692 6 7 30 10 2 8 6 41.038 3.51 0.871 3 8 30 10 6 4 9 37.248 3.02 0.891 2 9 30 10 10 6 3 27.339 5.36 0.471 25 10 50 2 2 4 3 24.092 4.3 0.520 22 11 50 2 6 6 6 17.96 3.5 0.587 15 12 50 2 10 8 9 17.408 3.11 0.669 8 13 50 6 2 6 9 33.224 3.8 0.667 9 14 50 6 6 8 3 23.82 4.03 0.546 19 15 50 6 10 4 6 21.173 3.24 0.658 11 16 50 10 2 8 6 33.982 3.24 0.778 4 17 50 10 6 4 9 28.083 3.31 0.694 5 18 50 10 10 6 3 25.27 6.34 0.413 27 19 70 2 2 4 3 18.109 4.82 0.441 26 20 70 2 6 6 6 10.688 3.54 0.549 18 21 70 2 10 8 9 10.003 3.67 0.525 21 22 70 6 2 6 9 18.068 3.56 0.577 16 23 70 6 6 8 3 15.014 3.01 0.687 7 24 70 6 10 4 6 13.127 3.38 0.588 14 25 70 10 2 8 6 20.521 3.4 0.620 13 26 70 10 6 4 9 16.292 3.1 0.667 10 27 70 10 10 6 3 15.481 3.15 0.650 12 8Charles Sarala Rubi et al. increases. The amount of discharges during a given period decreases as “T off ”increases, which provides a good surface finish. The average discharge gap widens with an increase in “GV,”resulting in a minimum SR value. Because greater WF values result in larger MRR, the MRR increases with the “WF”. 4.4.3 Selection of optimal levels The ranks and the delta values reveal that “R,”followed in that order by “T on ,”“T off ,”“GV,”and “WF,”has the major impact on achieving the larger GRG. It is observed from Figure 8 that the first level of “GV,”third level of “T on ,”first level of “T off ,”third level of “WF,”and third level of “R” provide optimal values. ANOVA is utilized in this investigation to optimize the cutting factors by examining the relative importance of each variable in terms of how significantly they contribute to the MRR and SR. The analysis strategy was examined with a 95% confidence level. Table 5 provides the findings of ANOVA for GRG. The value of R 2 for GRG is 89.08%. The p-value is lesser than 0.05 for “T on ,”“R,”and interaction between “GV”and “R,”which depicts that the factors are influencing the GRG. In contrast, the value of “p”is greater than 0.05 for GV, T off , and interaction between GV and T off , which indicates that the factors are insignificant on GRG. The Fisher’sF-test was utilized in addition to the p-value to analyze the process factors, and it proved that they had a significant effect on the response. According to Fisher’sF-test, its impact is determined to be significant if the computed value of the F-ratio is more than the tabulated F-value. At a 5% level of significance, the F-values from the table are F 0.05,2,10 =4.10 and F 0.05,4,10 =3.48. It is clear from Table 5 that the percentages of the “T on ,”“R,”and interaction between “GV”and “R”are significant. In contrast, GV, T off , and the interaction between GV and T off are insignificant. As a result, it is observed from ANOVA Table 5 that the variables “WF”and the interaction between “GV” and “WF”were combined into the error term. From the experiments conducted, “R”has the greatest impact on GRG (28.22%), followed by T on (18.18%), the interaction between “GV”and “R”(17.96%), the interaction between GV and T off (12.13%), GV (6.37%), and T off (6.22%). The contribution of “WF”and interaction between “GV”and “WF” is very less, so it is pooled up with the error term. 4.4.4 Confirmation experiments The confirmation experiments and prediction of GRG are carried out using the optimum variables. The optimal variables are found by analyzing the experimental data. The Figure 8: Response graphs for GRG. Table 6: Response table for GRG Level GV T on T off WF R 10.670 0.545 0.662 0.629 0.527 2 0.615 0.656 0.630 0.603 0.654 3 0.589 0.673 0.581 0.641 0.692 Delta 0.081 0.128 0.081 0.038 0.165 Rank 4 2 3 5 1 The bold values show the optimum levels. Optimization of machining variables for WEDM of LM6/fly ash composite materials 9