Subscribe Now Subscribe Today
Research Article

Modeling and Analysis of Material Removal Rate During Electro Discharge Machining of Inconel 718 under Orbital Tool Movement

Harshit K. Dave, Keyur P. Desai and Harit K. Raval
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail

In electro discharge machining, it is possible to decouple the size of tool electrode from the desired size of cavity by actuating the tool electrode on orbital trajectory. In present study, experimental investigation based on Taguchi experimental design is carried out to study the effect of orbital parameters along with machine parameters during orbital EDM process. Copper is used as tool electrode for machining of a nickel based superalloy material viz., Inconel 718. The empirical model has been developed using linear regression analysis by applying logarithmic data transformation of non linear equation. The prediction based on the above developed model has been verified with another set of experiments and are found to be in good agreement with the experimental results. Further, analysis of the results has been carried out using signal-noise ratio formulae and ANOVA to identify the significant parameters and their degree of contribution in the process output.

Related Articles in ASCI
Similar Articles in this Journal
Search in Google Scholar
View Citation
Report Citation

  How to cite this article:

Harshit K. Dave, Keyur P. Desai and Harit K. Raval, 2012. Modeling and Analysis of Material Removal Rate During Electro Discharge Machining of Inconel 718 under Orbital Tool Movement. International Journal of Manufacturing Systems, 2: 12-20.

DOI: 10.3923/ijmsaj.2012.12.20

Received: November 03, 2011; Accepted: February 11, 2012; Published: May 29, 2012


In recent times, nickel based alloys like Inconel 718 are gaining importance in making of gas turbines, space crafts, rocket motors, nuclear reactors etc. These classes of materials, being strong, light weight and aesthetic in appearance represent an excellent choice specifically for construction of aerospace components (Habeeb et al., 2008). However, nickel based super alloys are among the work materials with the lowest machinability properties. They are specifically designed to retain high strength at elevated temperatures due to which higher cutting forces are encountered as compared to steel. The low thermal conductivity of nickel alloys give rise to high temperatures as compared to steel material is another issue. These lead to difficulty in machining of these alloys using conventional techniques (Shaw, 1997). As a result, EDM process becomes a natural choice for machining of nickel based super alloys. Electro Discharge Machining (EDM) is one of the most successful, profitable and extensively used non conventional machining processes for high degree of dimensional accuracy and economical cost of production of any conductive material irrespective of its hardness. It is particularly advantageous in manufacturing of moulds, dies, automotive, aerospace and surgical components owing to its unique feature of using thermal energy to machine electrically conductive parts regardless of its hardness (Ho and Newman, 2003).

In EDM process, Material removal and its mechanism has been one of the main concerns for several years. Since the development of this process, researchers have explained the material removal mechanism by developing different thermal models by considering relationship between pulse conditions and material removal by solving time dependent heat transfer equations based on various assumptions based on different heat source models (Snoeys and van Dijck, 1971; Snoeys et al., 1972; Erden and Kaftanoglou, 1981; Patel et al., 1989). All of these and most of the many other theoretical models are concerned with die sinking EDM process which shows large discrepancy between the predictions and the experimental results due to simplified and unavoidable assumptions. Many attempts have been made in recent past to develop empirical models for EDM process (Pei-Jen and Kuo-Ming, 2001; Dhar et al., 2007; Doniavi et al., 2008; Sarkar et al., 2008; Chattopadhyay et al., 2009).

However, literature related to the study of EDM process under orbital tool actuation is limited. Most of the reported literature is based on the study of process capabilities of orbital EDM as compared to cavity sinking EDM (Rajurkar and Royo, 1989a, b; Yu et al., 2002; Bamberg et al., 2005; El-Taweel and Hewidy, 2009). These researchers and many others (Rahman et al., 2011) have attempted to work on various grades of steel and very few have attempted to work on superalloy metal. No attempt to develop theoretical and/or empirical model considering orbital tool movement has been reported to the best of the authors’ knowledge. The present study is an attempt to bridge this gap. In this paper, a systematic and simplified approach is used for model development and analysis of MRR with various machining parameters and orbital parameters. Taguchi based experimental approach has been employed to design the experimental plan.


Orbital tool actuation in EDM process helps to decouple the size of the electrode from the size of the feature to be machined. An electrode that is significantly smaller than the cavity to be generated can be actuated on a tool path that will articulate its outer surface on a trajectory equal to the shape of the hole. Hence, a standard electrode can be used to drill a wide range of holes while the increased clearance between the hole and the electrode helps getting the dielectric fluid to the bottom of the hole. The use of a small size of standard electrodes instead of matched electrodes for every single hole size drastically reduces tooling efforts. The improved flushing will reduce recasting of removed material which tends to diminish surface quality (Guitrau, 1997).

Joemars make ZNC EDM with orbit cut mechanism is used in present study. The machine has the capability to control Z-axis movement with precision upto 1 μm. The orbital cut mechanism can control X and Y axis movement independently with same precision.

In present study, orbital movement is actuated along helical path as shown in Fig. 1. Over and above this, the mechanism has a capability to initiate the movement on orbital path at 10 different speeds ranging between 0.04 to 0.36 mm sec-1 at the central point of electrode.


Workpiece and tool electrode: Inconel 718 is taken as work piece materials and electrolyte copper is taken as electrode material. The properties and compositions of Inconel 718 are summarized in Table 1.

The work piece is cut into the size of 13x13x10 mm. Two work pieces are clamped together as shown in Fig. 2 and hole is drilled at the interface of two polished surfaces of the work piece.

Table 1: Chemical composition of Inconel 718

Fig. 1: Helical path traced during orbital tool actuation

Fig. 2(a-b): Work piece design and method of application

The split work piece enables easy separation after machining and hence opens the internal surface for further study.

Copper electrode is fabricated to a length of 20 mm with varying diameter of 5, 6, 7, 8 and 9 mm. Each tool with a specific diameter is given orbital movement at a orbital radius so as to split generate a circular hole of 10 mm diameter upto a depth of 10 mm.

Table 2: Parameters and their level

Commercially available dielectric fluid is used during the experiments.

Parameter selection: The process parameters chosen for the present experiment are: (A) Orbital Radius Ro, (B) Orbital Speed So, (C) Current I, (D) Gap Voltage Vg, (E) Pulse ON time ton and (F) Duty Factor DF. These parameters were selected because they can potentially affect Material Removal Rate during EDM operation. The machining conditions and number of levels of the parameters are selected as given in Table 2.

Response selection: MRR (mm3/min) is calculated by weight difference of the work piece before and after machining using a precision weighing machine (maximum capacity = 300 g, least count = 1 mg).

The Equation used for calculating MRR is as under:


where, Wwi and Wwf are initial and final weights of work piece, respectively; ñw is density (g mm-3) of work piece and t is the machining time (min).

The objective of this experimental study is to determine the machining conditions required to achieve maximum Material Removal Rate (MRR) under orbital tool motion in EDM process. Therefore, quality characteristic of larger the better (LB) for MRR is implemented in this study. The S/N ratio (η) is calculated using the Eq. 2 given as under:

For LB characteristics:


where, yij is the response of ith quality characteristics at jth experimental run and n is the total number of repetition of a run.

The experimental plan is designed as per L 25 orthogonal array which considers 6 parameters each at 5 levels. The experimental plan is shown in Table 3. All experimental runs have been conducted twice for effective S/N ratio calculation. The mean and S/N ratio of MRR are also shown in Table 3.

Table 3: L 25 table and observed values


Empirical expressions have been developed for evaluating the relationship between input and output parameters. The mean output values for MRR are used to construct the empirical expressions.

The functional relationship between a dependent output parameter viz., MRR with the input independent parameters viz., orbital radius, orbital speed, current, gap voltage, pulse ON time and duty factor can be postulated using the following Eq. 3:


where, Y is a dependent parameter viz., MRR; X1, X2, X3, X4, X5 and X6 are independent parameters viz., orbital radius, orbital speed, current, gap voltage, pulse ON time and duty factor; a,b,c,d,e and f are power indices of the respective terms and A is a constant.

The above non linear Eq. 3 can be converted into linear form by logarithmic transformation of Eq. 4 as under:


The above Eq. 4 can be rewritten as under:


where, is the true value of the dependent machining output on a logarithmic scale; x1, x2, x3, x4, x5 and x6 are the logarithmic transformations of the different input parameters; β0, β1, β2, β3, β4, β5 and β6 are the corresponding parameters to be estimated.

Gauss Newton algorithm has been used to estimate the parameters of the above first order model using the data shown in Table 3. The developed empirical model for MRR is given below:


The predicted MRR for each experiment have been calculated and verified for the closeness between actual and predicted values. The adequacy of the empirical model presented in Eq. 6 is checked and validated by the mean error (Emean), Standard deviation (σdev) or Root mean square error and average percentage error (Eavg) which, are given as under:






where, Xi is the ith result obtained from the model and X is the corresponding experimental result, n is the total number of observations considered in present case i.e., 25.

The value of Emean is found to be -0.042 and the value of Eavg (%) is found as 0.46%. These values show that the model is very well suited for predicting MRR in EDM during orbital tool actuation.

Further, the observations of M.R.R. for Inconel 718 are checked for existence of any objectionable data points which may be rejected using Chauvenet’s criterion (Taylor, 1997) which, states that “An observation may be rejected if the probability of obtaining the particular deviation from the mean is less than 1/2n”.

Based on Chauvenet’s criterion, it is found that there is no observation in AISI 304 required to be rejected. However, one observation in Inconel 718 is rejected. Hence, the revised standard deviation comes out to be 9.41 which, are better than the standard deviation shown in Table 4.

Table 4: Adequacy check of empirical model

Table 5: ANOVA for MRR of Inconel 718

Thus, it can be noted that the proposed empirical model also fits well with the observations recorded during Taguchi approach based experiments. This is evident from very less average error found in the models.


The basic idea behind analysis of variance is to breakdown total variability of the experimental results into components of variance and then to assess their significance by comparing them with the residuals. The F-test is carried out to compare the variance attributed to a particular factor effect with the variance attributed to the residual (Montgomery, 1997). Standard values of F can be obtained from standard tables of statisticians depending on the desired confidence level. If the calculated F ratio values exceed the standard values, then the contribution of the respective input parameter is considered to be significant. In present case, analysis of variance has been carried out based on the theory proposed by Phadke (1989).

The main effect plot for MRR of Inconel 718 is shown in Fig. 3 and the ANOVA table for MRR of Inconel 718 is given in Table 5.

From Fig. 3, it is found that best MRR is obtained at minimum orbital radius of 0.5 mm. In present study, variation in orbital radius is taken in such a way that final dimension of the generated cavity remains same. Thus, when orbital radius increases, there is reduction in tool diameter. It is observed that as the orbital radius increases (i.e., tool electrode diameter reduces), there is sharp reduction in MRR. When orbital radius is more, there is relatively more open space available between the circumference of tool and cavity being generated. Thus, the side gap across periphery is not uniform which results in to reduction in effective sparks occurring around the electrode cylindrical surface. Further, there is improvement in flushing due to large space available between tool and workpiece surfaces. This results in faster removal of eroded particles. This reduces the occurrence of secondary sparks which generally contribute in high MRR during cavity sinking EDM.

Fig. 3: Main effect plot for MRR of Inconel 718

From the Table 5, it is found that current is the single most significant parameter that affects MRR followed by orbital radius. Thus, it can be seen that just as cavity sinking EDM, current remains the most significant parameter in orbital EDM. Orbital radius proves to be more significant parameter than any other machining parameters which lead to the fact that orbital radius can greatly affect MRR.


Attempt has been to study the effect of orbital parameters viz., radius and speed during EDM process by carrying out experiments based on Taguchi approach. Empirical model has been developed for predicting MRR which matches well with the experimental results. Thus, it can be used for MRR prediction in selected range of process parameters.

The significance of parameters involved has been checked through ANOVA technique. It is found that current along with orbital radius have significant effect on MRR.


The authors are thankful to Department of Science and Technology, Government of India for financial support for this work through the research grant vide grant permission SR/S3/MERC-0044/2010(G).

1:  Bamberg, E., S. Heamawatanachai and J.D. Jorgensen, 2005. Flexural micro-EDM head for increased productivity of micro-holes. Proceedings of the 2005 ASPE Conference, October 10-14, 2005, Norfolk, VA, pp: 82-85.

2:  Chattopadhyay, K.D., S. Verma, P.S. Satsangi and P.C. Sharma, 2009. Development of empirical model for different process parameters during rotary electrical discharge machining of copper-steel (EN-8) system. J. Mater. Process. Technol., 209: 1454-1465.
Direct Link  |  

3:  Dhar, S., R. Purohit, N. Saini, A. Sharma and G.H. Kumar, 2007. Mathematical modelling of electric discharge machining of cast Al-4Cu-6Si alloy-10 wt% SiCp composites. J. Mater. Process. Technol., 194: 24-29.

4:  Doniavi, A., M. Eskandarzade, A. Abdi and A. Totonchi, 2008. Empirical modeling of EDM parameters using Grey relational analysis. Asian J. Scientific Res., 1: 502-509.
CrossRef  |  Direct Link  |  

5:  El-Taweel, T.A. and M.S. Hewidy, 2009. Enhancing the performance of electro discharge machining via various planetary modes. Int. J. Mach. Mach. Mater., 5: 308-320.
Direct Link  |  

6:  Erden, A. and B. Kaftanoglou, 1981. Thermo-mathematical modelling and optimization of energy pulse forms in Electric Discharge Machining (EDM). Int. J. Mach. Tool Des. Res., 21: 11-22.
Direct Link  |  

7:  Guitrau, E.B., 1997. The EDM handbook.. Hanser Gardner Publications, Cincinnati, pp: 306.

8:  Habeeb, H.H., K.A. Abou-El-Hossein, B. Mohamad, J.A. Ghani and K. Kadirgama, 2008. Investigating of tool wear, tool life and surface roughness when machining of nickel alloy 242 with using of different cutting tools. Asian J. Scientific Res., 1: 222-230.
CrossRef  |  Direct Link  |  

9:  Ho, K.H. and S.T. Newman, 2003. State of the art Electro Discharge Machining (EDM). Int. J. Mach. Tools Manuf., 43: 1287-1300.
Direct Link  |  

10:  Montgomery, D.C., 1991. Design and Analysis of Experiments. 3rd Edn., John Wiley & Sons Inc., New York, Pages: 500.

11:  Patel, M.R., M.A. Barrufet, P.T. Eubank and D.D. Dibitonto, 1989. Theoretical models of the electrical discharge machining process-II: The anode erosion model. J. Applied Phys., 66: 4104-4111.
CrossRef  |  Direct Link  |  

12:  Phadke, M.S., 1989. Quality Engineering Using Robust Design. Prentice Hall, Englewood Cliff, New Jersey, pp: 30-112.

13:  Rahman, M.M., M.A.R. Khan, K. Kadirgama, M.M. Noor and R.A. Bakar, 2011. Experimental investigation into electrical discharge machining of stainless steel 304. J. Applied Sci., 11: 549-554.
CrossRef  |  Direct Link  |  

14:  Rajurkar, K.P. and G.F. Royo, 1989. Improvement in EDM performance by R.F. control and orbital motion. Am. Soc. Mech. Eng., 34: 51-62.

15:  Rajurkar, K.P. and G.F. Royo, 1989. Effect of R. F. Control and orbital motion on Surface integrity of EDM Components. J. Mech. Working Technol., 20: 341-352.
Direct Link  |  

16:  Sarkar, S., M. Sekh, S. Mitra and B. Bhattacharyya, 2008. Modeling and optimization of wire electro discharge machining of γ-TiAl in trim cutting operation. J. Mater. Process. Technol., 205: 376-387.
Direct Link  |  

17:  Snoeys, R. and F.S. van Dijck, 1971. Investigation of electro discharge machining operations by means of thermo-mathematical model. CIRP Ann., 20: 35-37.

18:  Snoeys, R., F.S. van Dijck and J. Peters, 1972. Plasma channel diameter growth affects stock removal in EDM. CIRP. Ann., 21: 39-40.

19:  Shaw, M.C., 1997. Metal cutting principles. 3rd Edn., Oxford ISBN-10: 0-262-69021-7, Clarendon, pp: 478.

20:  Taylor, J.R., 1997. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. 2nd Edn., University Science Books, USA., ISBN-13: 9780935702750, pp: 128-129.

21:  Pei-Jen, W. and T. Kuo-Ming, 2001. Semi empirical model on work removal and tool wear in electrical discharge machining. J. Mater. Process. Technol., 114: 1-17.
Direct Link  |  

22:  Yu, Z.Y., K.P. Rajurkar and H. Shen, 2002. High aspect ratio and complex shaped blind micro holes by micro EDM. CIRP Ann.-Manuf. Technol., 51: 359-362.
Direct Link  |  

©  2021 Science Alert. All Rights Reserved