Analysis and Mathematical Modeling of Wire EDM Process Parameters for Commercial Graphite by Using Response Surface Methodology

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1 Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM Analysis and Mathematical Modeling of Wire EDM Process Parameters for Commercial Graphite by Using Response Surface Methodology N.G. Roy, A. Pramanick, P.P. Dey and P.K. Das Abstract--- The CNC Wire cut electrical discharge machining is found to have tremendous potential in the present day metal cutting process, for achieving improved geometric features of work pieces, dimensional accuracy, surface roughness, kerfs width and material removal rate for stable and controlled machining with least wire breakage. The experimental results will show that the Wire-Cut EDM process is a viable material processing method for the machining of graphite, still some work have to be carried out to further study the ways and means of improving the productivity in WEDM depends solely on analysis of various process parameters viz. Pulse on time (T on ), Pulse off time (T off ), pulse peak current, Wire feed. The schematic diagram of WEDM is shown in Fig.1. Keywords--- ANOVA, Central Composite Design, Mathematical Modeling, Wire EDM I. INTRODUCTION HE present work is aimed at experimental evaluation of Tthose machining parameters for pure Graphite which is a prominent and well established mould material for ceramic sintering process at high temperature > C conductivity, highly refractory and chemically inert. Graphite is generally greyish-black, opaque and has a lustrous black sheen. It has unique properties of both a metal and a non-metal. It is flexible but not elastic, having high thermal and electrical conductivity, highly refractory and chemically inert. Graphite has a low adsorption of X-rays and neutrons making it a particular material in nuclear applications. The unusual combination of properties is due its crystal structure Fig. 2. The carbon atoms are arranged hexagonally in a planar condensed ring system. The layers are stacked parallel to each other. The atoms within the rings are bonded covalently, whilst the layers are loosely bonded together by Vander Waals forces. Nani.Gopal Roy, Technical Assistant, Gr.II,, Mechanical Engg. Dept. Bengal Engg. & Science University, Shibpur, Howrah, India ngroywedm@gmail.com Ayan Pramanick, M.E. Student, Mechanical Engg. Dept, Bengal Engg. & Science University, Shibpur, Howrah, India. ayan_mech07@yahoo.co.in Dr. Partha Pratim Dey, Associate Prof., Mechanical Engg. Department Bengal Engg. & Science University, Shibpur, Howrah. ppdey2000@yahoo.com Dr. Prabal Kr. Das, Head of N.O.C.C Department, Central Glass & Ceramic Research Institute, Jadavpur, Kolkata, India. Table 1: Key Properties (Source: Ceram Research Ltd., Staffordshire, ST 7LQ, United Kingdom) Property Commercial graphite Bulk Density (g/cm 3 ) Porosity (%) Modulus of Elasticity (GPa) -15 Compressive strength(mpa) Flexural strength (MPa) Coefficient of Thermal Expansion (x10 6 C) Thermal conductivity (W/m.K) Sp. heat capacity (J/kg.K) Electrical resistivity (W.m) 5x x10-6 Fig.1: Crystal Structure of Graphite A. Literature Survey More advanced approaches have been used like experimental design and robust experiments, response surface methodology [15], [16], analysis of variance (ANOVA) [13]. The RSM is an empirical modeling approach for determining the relationship between various process parameters and responses with the various desired criteria and searching to signify these process parameters on the coupled responses [2]. It is a sequential experimentation strategy for building and optimizing the empirical model. Therefore, RSM is a collection of mathematical and statistical procedures that are useful for the modeling and analysis of problems in which response of demand is affected by several variables and the objective is to optimize this response [3-6]. The necessary data for building the response models are generally collected by the design of experiments. In this study, the collection of experimental data adopts the centered central composite design (CCD) in order to fit the quadratic model of f [7]. B. Experiment The pure, dense graphite material was applied as experimental work piece. The experiments were carried out

2 Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM using CNC WEDM machine. Brass wire of 0.25 mm diameter was used as tool electrode in the experimental set up. The small pieces of rectangular shaped graphite material of dimensions 10mm in length 5mm in width and 16 mm thick machined out from a rectangular large block. Based on the experimental results, empirical correlations will establish and validate to evaluate the best suited process parameter set analytically under various cutting conditions of Graphite [], [1]. Four factors, five level, central composite rotatable design matrix is used to optimize the number of experiments. The mathematical models have to be developed by response surface method with 95% confidence level. The adequacy of the models is checked by ANOVA technique. Fig. 2: Wire EDM Machine Setup C. Methodology In this work, experimental results were used for modeling using Response surface methodology, is a practical, accurate and easy for implementation. The experimental data was used to build first order and second order mathematical models by using regression analysis method. This developed mathematical models were optimized by using the RSM optimization procedure for the output responses by imposing lower and upper limit for the input machining parameters namely Pulse on time T on in (µsec), pulse off time (µsec), pulse peak current (IP) (Ampere), Wire feed (WF) in m/min. Input parameters are used in this study are shown in table 2. These have been chosen through preliminary investigations. The most important performance measures in WEDM are metal removal rate (MRR) [1], work materials surface finish and kerf width. The surface finish value (in µm) has been obtained by measuring the mean absolute deviation R a (surface roughness) by using Talysurf (Taylor Hobson, contour measurement system). The Kerf value has been measured using Tool Maker s microscope (100X) which can be expressed as sum of the wire diameter and twice of wirework piece gap, the equation of kerf width = (2w g +d), where, w g =wire gap of each side and d=diameter of brass wire in mm. MRR is calculated as MRR=ktV c ρ [1], here k is th kerf, t is the thickness of work piece, V c is the cutting speed and ρ is the density of the Graphite block. II. Wire guide STATISTICAL ANALYSIS A. Design of Experiments (DOE) The study of most important variables affecting quality characteristics and a plan for conducting such experiments is called the Design of Experiments. Experiments might be changed one or more in numbers. These advanced Design of Experiments (DOE) capabilities helps to improve the processes. In an experiment, it should be deliberately change one or more process variables (or factors) in order to observe the effect the changes have on one or more response variables. The (statistical) design of experiments (DOE) is an efficient procedure for planning experiments so that the data obtained can be analyzed to yield valid and objective conclusions. By screening the factors to determine which are important for explaining process variation. After screening the factors, helps to understand how factors interact and drive the process. Thus the factor settings that produce optimal process performance can find out. The method is advantageous of being highly flexible and readily enable allocation of different levels of factors, even when these levels are not the same in number for all the factors studied [5]. B. Response Surface Methodology (RSM) In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The main idea of RSM is to use a set of designed experiments to obtain an optimal response. In this work, RSM is utilized for establishing the relations between the different WEDM process parameters with a variety of machining criteria and exploring their effects on MRR and surface finish [11]. To perform this task second order polynomial response surface mathematical models can be developed. In the general case, the response surface is described as: Y= C 0 + i*x i + + ii*x ii + ij* X ij (1) Where, Y is the corresponding response of MRR yield by the various EDM process variables and the x i (1, 2,., n) are coded levels of n quantitative process variables, the terms C 0, C i, C ii and C ij are the second order regression coefficients. The second term under the summation sign of this polynomial equation is attributable to linear effect, whereas the third term corresponds to the higher-order effects; the fourth term of the equation includes the interactive effects of the process parameters. Equation [1] can be rewritten according to the four variables (X 1, X 2, X 3, X ) used as in following equation [2]: Y = C 0 + C 1 * X 1 + C 2 * X 2 + C 3 * X 3 + C * X + C 11 * X 11 + C 22 * X 22 + C 33 * X 33 + C * X +X C 12 * X 1 * X 2 + C 13 * X 1 * X 3 + C 1 * X 1 * X + C 23 * X 2 * X 3 + C 2 * X 2 * X + C 3 * X 3 * X (2) The coefficients of the linear regression model have been evaluated by Minitab 16 (statistical software package). The level of significance of the factor coefficients have been checked by ANOVA (analysis of variance) at 95% confidence level. The final reduced models for three objectives are given below. The trends have been found consistent to interpret the correlation among process parameters as well as responses physically are tabulated in Table 3 and. The table shows the variance analysis results of the RSM models for MRR, R a and kerf width separately. The associated P value for the three response model is lower than 0.05 (i.e. α = 0.05 or 95% confidence) indicating that the model is statistically significant.

3 Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM C. Central Composite Design The CCD contains Factors, 1 Replicates, 31 numbers of Base runs and total runs, 1 Base and total blocks, full factorial design. The design developed by 16 Cube points, 7 Center points in cube, axial points, no center points in axial and the Alpha factor is 2. This value indicates the distance of the axial points from the design centre in a central composite design and is expressed in coded units. A value less than one places the axial points inside the cube; a value equal to one places them on the faces of the cube; and a value greater than one places them outside the cube. Table 2: Design of Experiment Run Block A B C D Table 3: Input Factors Level Control Unit Factor T on µs T off µs IP Amp. Wf m/min. Table : Response Factors SL. Predicted NO. MRR (g/cc) Kerf (mm) Ra (µm) MRR (g/cc) Kerf (mm) Ra (µm) III. MATHEMATICAL MODELING MRR = Ton* Toff* E-0- IP* WF* Ton*Ton*3.3571E-05 +IP*IP* E-06-WF*WF* E-0 +Ton*Toff* E-05+Ton*IP* E-06- Ton*WF* E-05-Toff*IP*5.1667E-06- Toff*WF*.5333E-05+IP*WF* E-06 (3) Kerf Width = T on * T off * IP*3.3393E-0-WF* T on *T on *1.7202E-05 + T off *T off * IP*IP*7.9E-06 - T on *WF* E-0-T off *IP*7.3953E-05 +T off *WF* IP*WF* () Surface Roughness (R a ) = T on * T off * IP* WF* T on *T on *5.6173E-06 - T off *T off * E-05 - IP*IP*1.0560E-06 -WF*WF*1.1060E-0 - T on *T off * E-06 - T on *WF* E-06 +T off *IP* E-06+ T off *WF*1.2500E-05 (5)

4 Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM Trend Analysis Plot for Kerf Width Yt = *t *t**2 MRR (g/cc) Kerf Width (mm) MAPE MAD MSD Predicted MRR (g/cc) Fig.3: Comparison of Predicted and Experimental Results of Material Removal Rate Kerf Width (mm) Predicted Kerf Width (mm) Fig.: Comparison of Predicted and Experimental Results of Kerf Width Surface Roughness (µm) Predicted Surface Roughness (µm) Fig. 5: Comparison of Predicted and Experimental Results of Surface Roughness MRR (g/cc) Trend Analysis Plot for MRR Yt = *t *t** Fig.6: Trend Analysis for MRR MAPE MAD MSD Surface Roughness (µm) Fig.7: Trend Analysis for Kerf Width Trend Analysis Plot for Surface Roughness Yt = *t *t** MAPE.293 MAD MSD Fig.: Trend Analysis for Surface Roughness IV. RESULT AND DISCUSSION The influence of different process parameters such as Wire EDM pulse on time, pulse off time, discharge current, wire feed, on material removal rate, kerf width, surface roughness is analyzed and the same is represented in terms of mean response curve. The percentage contribution of the individual and interacting process parameters on response parameters obtained from ANOVA analysis of variance, and in this study the linear and quadratic effects of individual and interacting parameters are considered for developing the orthogonal polynomial models for MRR, Kerf Width and Surface Roughness. The proposed strategy is employed for generating optimum set of process parameters and validating using confirmation experiments. Statistical analysis has been done by MINITAB-16 software. The result (Fig.3) show that the predicted value R 2 of 93.61% is in reasonable agreement with the adjusted R 2 of 97.07% in case of MRR. Fig. shows that the predicted value R 2 of 93.67% is in reasonable agreement with the Adjusted R 2 of 97.7% in case of Surface Roughness (R a ). Fig. 5 shows that the predicted value R 2 of 9.26% is in close agreement with the Adjusted R 2 of 97.72% in case of Kerf width. In trend analysis Graphs (fig.6-) black symbols are data collected over time (i.e. number of experiments), red symbols are the predicted values and green symbols are the probable forecast and this is extrapolation of the trend model fit. The trend analysis procedure also displays, along with the graph, three measures to help us determine the accuracy of the fitted

5 Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM values MAPE mean absolute percentage error, MAD-mean absolute deviation, MSD -mean squared deviation. The three measures are not very informative by themselves, but they are used to compare the fits obtained by using different trend models. Fig. 7: Kerf Width of Graphite Material (Average Data Taken) V. CONCLUSION 1) The samples were machined with Wire EDM with different range of machine parameters. 2) To improve the machining performance as well as product quality, statistical models were employed to develop the relationship between the input parameters (i.e. machine parameters) and output responses (e.g. material removal rate, surface roughness and Kerf width). 3) Mathematical regression models generated by design of experiment, response surface method and central composite design shows good fit with the experimental response factors with the predicted response factors. The models created were highly significant as P-value (probability factor) is less than 0.05 (i.e. confidence level is 95%) and high determination coefficient (R 2 ) which indicates the goodness of fit for the model. Also, the experimental and predicted values are very close to each other. ) Trends of the equations are in good fit with the Quadratic model. 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ACKNOWLEDGEMENT I would like to thank Head of CG&CRI, Kolkata for giving me the opportunity to do the collaborative research works with BESU, Howrah I am thankful to and fortunate enough to get constant support and guidance from all the team members of CG&CRI and also the staffs of Mechanical Engineering & Metallurgy Engineering Department, BESU which helped in successfully completing the project work. REFERENCES [1]. B. Lauwers et. al. Investigation of Material Removal Mechanism in EDM of Composite Ceramic Materials Journal of Materials Processing Technology 19, (200) [2]. R.H. Myers, D.H. Montgomery, Response Surface Methodology, John Wiley & Sons, USA, [3]. J. Grum, J.M. Slab, The use of factorial design and response surface methodology for fast determination of optimal heat treatment conditions of different Ni Co Mo surface layers, J. Mater. Process. Technol , , (200). []. B. Ozcelik, T. 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