International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) IJMET Volume 4, Issue 5, September - October (2013), pp. 173-181 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) ©IAEME www.jifactor.com A COMPARATIVE STUDY ON MATERIAL REMOVAL RATE BY EXPERIMENTAL METHOD AND FINITE ELEMENT MODELLING IN ELECTRICAL DISCHARGE MACHINING *S. K. Sahu, **Saipad Sahu *Asst. Prof., Department of Mechanical Engineering, Gandhi Institute for Technological Advancement, Bhubaneswar **Asst. Prof., Department of Mechanical Engineering, Gandhi Institute for Technological Advancement, Bhubaneswar ABSTRACT Electrical discharge machining (EDM) is one of the most important non-traditional machining processes. The important process parameters in this technique are discharge pulse on time, discharge pulse off time and gap current. The values of these parameters significantly affect such machining outputs as material removal rate and electrodes wear. In this paper, an axisymmetric thermo-physical finite element model for the simulation of single sparks machining during electrical discharge machining (EDM) process is exhibited. The model has been solved using ANSYS 11.0 software. A transient thermal analysis assuming a Gaussian distribution heat source with temperature-dependent material properties has been used to investigate the temperature distribution. Further, single spark model was extended to simulate the second discharge. For multi-discharge machining material removal was calculated by calculating the number of pulses. Validation of model has been done by comparing the experimental results obtained under the same process parameters with the analytical results. A good agreement was found between the experimental results and the theoretical value. 1. INTRODUCTION EDM is among the earliest and the most popular non-conventional machining process with extensively and effectively used in a wide range of industries such as die and mould-making, aerospace, automotive, medical, micromechanics, etc. The high-density thermal energy discharge creates during machining causes the local temperature in the work piece gets close to the vaporization temperature of the work piece, leads to the thermal erosion. 173 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME EDM is a very complex process involving several disciplines of science and branches of engineering it combines several phenomena, but excluding very tiny discharges, it can be considered with small error that the thermal effect takes over (Hargrove et al 2007, Salah et al 2006). The theories revolving around the formation of plasma channel between the tool and the work piece, thermodynamics of the repetitive spark causing melting and evaporating the electrodes, micro- structural changes, and metallurgical transformations of material, are still not clearly understood. However, it is widely accepted that the mechanism of material erosion is due to intense local heating of the work piece causing melting and evaporation of work piece. The thermal problem to be solved so as to model an EDM discharge is fundamentally a heat transmission problem in which the heat input is representing the electric spark. By solving this thermal problem yields the temperature distribution inside the workpiece, from which the shape of the generated craters can be estimated. For solving these numerical models finite-element method or the finite-differences method are normally used with single spark analysis (Erden et al. (1995)). Yadav et al. (2002) investigated the thermal stress generated in EDM of Cr die steel. The influence of different process variables on temperature distribution and thermal stress distribution has been reported. The thermal stresses exceed the yield strength of the work piece mostly in an extremely thin zone near the spark. Salah and Ghanem (2006) presented temperature distribution in EDM process and from these thermal results, MRR and roughness are inferred and compared with experimental explanation. In this work, a finite-element modelling of the EDM process using ANSYS software is presented. Conduction, convection, thermal properties of material with temperature, the latent heat of melting and evaporation, the percentage of discharge energy transferred to the work piece, the thermal property of D2 tool steel, the plasma channel radius and Gaussian distribution of heat flux based on discharge duration has been used to develop and calculate a numerical model of the EDM process. An attempt has been made to investigate the effect of machining parameters on temperature distribution, which is the deciding factor of MRR. 2. THERMAL MODEL OF EDM a. Description of the model In this process, electrodes are submerged in dielectric and they are physically separated by a gap, called inter-electrode gap. It can be modelled as the heating of the work electrode by the incident plasma channel. Figure shows the idealised case where work piece is being heated by a heat source with Gaussian distribution. Due to axisymmetric nature of the heat transfer in the electrode and the work piece, a two-dimensional physical model is assumed. The various assumptions made to simplify the random and complex nature of EDM and as it simultaneously interact with the thermal, mechanical, chemical, electromagnetism phenomena (Pradhan (2010)). b. Assumptions 1. The work piece domain is considered to be axisymmetric. 2. The composition of work piece material is quasihomogeneous. 3. The heat transfer to the work piece is by conduction. 4. Inertia and body force effects are negligible during stress development. 5. The work piece material is elastic-perfectly plastic and yield stress in tension is same as that in compression. 6. The initial temperature was set to room temperature in single discharge analysis. 7. Analysis is done considering 100% flushing efficiency. 8. The work piece is assumed as stress-free before EDM. 9. The thermal properties of work piece material are considered as a function of temperature. It is assumed that due to thermal expansion, density and element shape are not affected. 174 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME 10. The heat source is assumed to have Gaussian distribution of heat flux on the surface of the work piece. c. Governing Equation The governing heat transfer differential equation without internal heat generation written in a cylindrical coordinates of an axis symmetric thermal model for calculating the heat flux is given by [12 F]. The governing heat transfer differential equation without internal heat generation written in a cylindrical coordinates of an axis symmetric thermal model for calculating the heat flux is given by [12]. ∂T 1 ∂ ∂T ∂ ∂T ρC p = r ∂r K r ∂r + ∂Z K ∂Z ∂t Where ρ is density, Cp is specific heat, K is thermal conductivity of the work piece, T is temperature, t is the time and r& z are coordinates of the work piece. d. Heat Distribution Plasma channel incident on the work piece surface causes the temperature to rise in the work piece. The distribution of plasma channel can be assumed as uniform disk source [13]-[16] or Gaussian heat distribution [17]-[21], for EDM. Gaussian distribution of heat flux is more realistic and accurate than disc heat source. Fig. 1 shows the schematic diagram of thermal model with the applied boundary conditions. R Y hf (T-T0) 1 ∂T =0 ∂T ∂p 4 2 =0 ∂p 3 ∂T X =0 ∂p Figure No: 1 e. Boundary Conditions The work piece domain is considered to be axisymmetric about z axis. Therefore taking this advantage, analysis is done only for one small half (ABCD) of the work piece. The work piece domain considered for analysis is shown in Fig. 1.It is clearly evident from Fig. 1 that the maximum 175 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME heat input will be at point A. On the top surface, the heat transferred to the work piece is shown by Gaussian heat flux distribution. Heat flux is applied on boundary 1 up to spark radius R, beyond R convection takes place due to dielectric fluids. As 2 & 3 are far from the spark location no heat transfer conditions have been assumed for them. For boundary 4, as it is axis of symmetry the heat transfer is zero. In mathematical terms, the applied boundary conditions are given as follows: ∂T K = Q (r ) , when R< r for boundary 1 ∂Z ∂T K = h f (T − T0 ) , when R ≥ r for boundary 1 ∂Z ∂T K = 0 , at boundary 2, 3 & 4 ∂n Where hf is heat transfer coefficient of dielectric fluid, Q(r) is heat flux due to the spark and T0 is the initial temperature. f. Heat Flux A Gaussian distribution for heat flux [21] is assumed in present analysis. 4.45 PVI r 2 Q (r ) = exp− 4.5 πR 2 R where P is the percentage heat input to the workpiece, V is the discharge voltage, I is the current and R is the spark radius. Earlier many researchers have assumed that there is no heat loss between the tool and the workpiece. But Yadav et al. [21] have done experiment on conventional EDM and calculated the value of heat input to the workpiece to be 0.08. Shankar et al. [22] calculated the value of P about 0.4-0.5 using water as dielectric. g. Solution of thermal model For the solution of the model of the EDM process commercial ANSYS 12.0 software was used. An axisymmetric model was created treating the model as semi-infinite and the dimension considered is 6 times the spark radius. A non-uniformly quadrilateral distributed finite element mesh with elements mapped towards the heat-affected regions was meshed, with a total number of 2640 elements and 2734 nodes with the size of the smallest element is of the order of 1.28 × 1.28 cm. The approximate temperature-dependent material properties of AISI D2 tool steel, which are given to ANSYS modeler, are taken from (Pradhan, 2010). The governing equation with boundary conditions mentioned above is solved by finite element method to predict the temperature distribution and thermal stress with the heat flux at the spark location and the discharge duration as the total time step. First, the whole domain is considered to obtain the temperature profile during the heating cycle. The temperature profile just after the heating period is shown in Fig.3, which depicts four distinct regions signifying the state of the workpiece. Figure 4 and 5 shows typical temperature contour for AISI D2 steel under machining conditions: current 1A, and discharge duration 20 µs and 9A, and discharge duration 100 us . 176 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME 3. MATERIAL PROPERTIES FOR FEA Material Property Copper (Cathode) En-19 (anode) Density (g/mm3) 8290 x 10-6 7700 x 10-6 Conductivity (W/mmK) 400 x 10-3 222 x 10-12 Resistivity ( -mm) 1.7 x 10-11 22.2 x 10-11 Specific heat (J/gK) 385 x 10-3 473 x 10-3 4. EXPERIMENTAL RESULT Figure No: 2 (Experimental Setup) Figure No: 3 (Work piece after machining) Experimental Data Table: Gap Pulse on Electrode Current MRR/min Voltage time Diameter In Amp. In m3/min In Volt. In µs In mm 6 6 500 14 0.0145 6 8 1000 16 0.022 6 9 2000 18 0.0845 7 6 1000 18 0.0245 7 8 2000 14 0.044 7 9 500 16 0.03 9 6 2000 16 0.022 9 8 500 18 0.0715 9 9 1000 14 0.0785 177 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME variation of MRR vs current at variation of MRR vs current at different voltages different voltages 0.1 0.1 MRR in gm/min MRR in gm/min 0.08 0.08 0.06 0.06 6V 0.04 14.5 mm 0.04 0.02 7V 0.02 16.5 mm 0 0 9V 18.5 mm 6 8 9 6 8 9 current in ampere current in ampere 5. FINITE ELEMENT SIMULATION Figure No: 4 (Temperature Profile) Figure No: 5 (Profile After Melting of Material) 6. SAMPLE CALCULATION FOR MRR FROM SIMULATION RESULT The morphology of crater is assumed to be spherical dome shape. Where r is the radius of spherical dome and h is depth of dome. And the volume is calculated by given formula of spherical dome volume. From geometry: h = 0.004 m r = 0.008 m 1 C v = πh(3r 2 + h 2 ) = 0.000000435552 m3 6 The NOP can be calculated by dividing the total machining time to pulse duration as given in (6). 178 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME Tmach 20 × 60 NOP = = =1200000 Ton + Toff 1000 × 10 −3 Where Tmach is the machining time, Ton is pulse-on time and Toff is pulse-off time. Knowing the Cv and NOP one can easily derive the MRR for multi-discharge by using. Cv × NOP 0.000000435552 × 1200000 MRR = = = 0.0261 m3/min Tmach 20 Gap Pulse on Electrode MRR/min MRR/min Current Voltage time Diameter (Experimental) (FEM) 6 6 500 14 0.0145 0.0158 6 8 1000 16 0.022 0.0261 * 6 9 2000 18 0.0845 0.0559 7 6 1000 18 0.0245 0.0275 7 8 2000 14 0.044 0.0507 7 9 500 16 0.03 0.0225 9 6 2000 16 0.022 0.0489 9 8 500 18 0.0715 0.0257 9 9 1000 14 0.0785 0.0242 Comparison between Experimental MRR to the FEM Calculated MRR 0.1 0.08 MRR/min 0.06 0.04 Experimental MRR 0.02 FEM MRR 0 1 2 3 4 5 6 7 8 9 Number of Experiment at different levels of factors 179 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME 7. RESULTS AND DISCUSSION Fig. 5 shows the FEA model after material removal, it is evident from the temperature distribution that, during the spark-on time the temperature rises in the work piece and temperature rise is sufficient enough to melt the matrix due to its low melting temperature but the reinforcement remains in solid form due to its very high melting temperature. After the melting of matrix material no binding exists between the matrix and reinforcement, therefore the reinforcement evacuates the crater without getting melted. 8. CONCLUSION In the present investigation, an axisymmetric thermal model is developed to predict the material removal. The important features of this process such as individual material properties, shape and size of heat source (Gaussian heat distribution), percentage of heat input to the work piece, pulse on/off time are taken into account in the development of the model. FEA based model has been developed to analyze the temperature distribution and its effect on material removal rate. To validate the model, the predicted theoretical MRR is compared with the experimentally determined MRR values. A very good agreement between experimental and theoretical results has been obtained. The model developed in present study can be further used to obtain residual stress distributions, thermal stress distribution mechanism of reinforcement particle bursting phenomenon. REFERENCES 1. Ho.K.H and Newman.S.T., “State of the art electrical discharge machining (EDM)” International Journal of Machine Tools & Manufacture, Volume 43, (2003): p. 1287–1300. 2. Narasimhan Jayakumar, Yu Zuyuan and P. Rajurkar Kamlakar, “Tool wear compensation and path generation in micro and macro EDM” Transactions of NAMRI/SME, Volume 32, (2004): p.1-8. 3. 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