Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 04, April-2016 Improved Electrical Discharge (EDM) Servomechanism Controller for Machining Micro Pits

M. Olubiwe, L. O Uzoechi, V. C. Uchegbu, Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri, Nigeria.

Abstract - This research work is aimed at designing a better principle of EDM process is based on the thermoelectric and more suitable servo control system to maintain an energy created between a workpiece and an electrode accurate spark gap between the electrode and the workpiece. submerged in a dielectric fluid with the passage of electric A poor performance of EDM servo controller results in longer current [2]. The workpiece and the electrode are separated Ignition Delay Time, and inadequate speed of EDM by a specific small gap called spark gap. In the EDM in the micromachining process. Also, harmful arcing and short circuit as a result of inaccurate position control of the process, there is no mechanical contact between the machine electrode in relation to the work piece are electrodes and workpiece, and spark erosion is produced by undesirable machining cases experienced in poorly controlled electrical discharge. This process has as its basic EDM process. The objective of this paper is to design a good requirement the electrical conductivity of electrode and servo system with a very good precision to obtain a better work-piece. A resistivity ranging from 100Ω/cm to settling time. A PID controller is designed and fine-tuned with 300Ω/cm is also required for the electrodes. The dielectric SIMULINK and MATLAB PID tuner to obtain suitable gains must have low viscosity, high dielectric strength, and quick for faster and accurate response of the EDM process. Verified recovery after breakdown, effective quenching/cooling and results obtained from the step response and Bode plot of the flushing ability [4]. servo control system include: a settling time of 3.52 seconds, the rise time of 1.05 seconds, the percentage overshoot of The electrical discharge in the EDM process causes strong 7.68%, the phase gain of 62 degrees at a frequency of heating of the workpiece material and electrode material 1.27rad/s, and a steady-state error less than 2%. The research tool, rapidly creating a small molten metal pool at the work produced a better design and simulated results proved surface of the workpiece. The molten metal pool at the the accuracy and precision of the servo controller. workpiece surface is flushed with dielectric in the form of debris. The material removal rate is determined by the Key Words: Micromachining, Servo-control, Electrical crater size and the frequency of crater generation (i.e. discharge, Delay- Time, Ignition. discharge energy and the frequency of discharges). Also, the cavity produced in the work piece is approximately the I INTRODUCTION replica of the tool [4]. A better explanation of EDM The Electrical Discharge Machining (EDM) is a controlled principle is provided by the EDM process. EDM is process where pulsed of electrical discharge is used to employed in industrial micromachining processes that erode metal in a work-piece. In other words, Electrical require high precision to produce best quality products Discharge Machining is the machining method in which involving micro pits with complex geometry. The voltage is applied through a dielectric medium between the electrode-to-workpiece spark gap is controlled by a servo tool electrode and work-piece [1]. EDM can also be defined control system. A poor performance of this EDM servo as the process of machining electrically conductive controller results in longer Ignition Delay Time, and materials by using precisely controlled sparks that occur inadequate speed of EDM machines in the micromachining between an electrode and a work-piece in the presence of a process. Also, harmful arcing and short circuit as a result of dielectric fluid [2]. In typical industrial terms, EDM is a inaccurate position control of the machine electrode in controlled metal removal process that is used to remove relation to the work-piece are undesirable machining cases metal by means of electric spark erosion [3]. Electric experienced in poorly controlled EDM process. discharge machining provides an effective manufacturing A good number of previous researches have been done in technique that enables the production of parts made of the field of Electrical Discharge Machining (EDM). [5] special materials with complicated geometry which is applied an intelligent approach for process modeling and difficult to produce by conventional machining processes optimization of electric discharge machining (EDM), Micro [2]. Electrical Discharge Machine machining (Micro-EDM) as a Modern day EDM (also known as spark machining or powerful bulk micromachining technique that is applicable Spark Erosion) process has been given a significant amount to any type of electrical conductor was described in [6], of research focus in manufacturing micro components and including all kinds of metals and alloys as well as doped highly advanced electrical discharge machines which are semiconductors, in a research by [7] an experiment to available for most machine applications. The working

IJERTV5IS040486 316 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 04, April-2016 analyze the effect of machining parameters such as A DC servo motor is an that converts electrical discharge current (Ip), pulse on time (Ton), voltage (v) over energy to mechanical rotation using the principles of the responses of Material Removal Rate (MRR) and electromagnetism. DC are one of the main Surface Roughness (SR) was performed. In the experiment, components of automatic systems. Any automatic system various techniques were applied to improve the material should have an actuator module that makes the system to removal rate (MRR), surface roughness (SR) and tool wear actually perform its function [8]. rate (TWR) with different electrode combination, [3] Figure 2 shows that a DC has two main carried out a research on how servo control system can be components, the electrical and the mechanical components. used to maintain the gap between Electrode and workpiece The electrical components consists of resistance, in Electrical Discharge Machining (EDM), improving the inductance, input voltage and the back electromotive force. performance of the machine. The mechanical component determines the mechanical In this paper, the modelling and simulation of the Electrical rotational movement at the servomotor shaft. The Discharge Machining (EDM) and a servo system controller mechanical component consist of the motor’s shaft, inertia will be carried out in order to have a better performance of of the motor or load inertia and damping. micro-machining positioning. Most DC Servomotors have good torque and speed characteristics and are controlled by changing the voltage II EDM DC SERVO MOTOR signal connected to the input. The parameters considered in MATHEMATICAL MODEL figure 2 are denoted as follows: A servomechanism (or simply Servo) is an automatic 푅푚 = resistance, 퐿푚 = inductance, 푉푎 = applied or input device that uses error-sensing to correct the voltage, 푉푏 = the back electromotive force (emf), 퐽푚 = load performance of a control system. Figure 1 shows the block or shaft inertia, 푏푚 = damping, 휃푚 = angular position of the diagram of an EDM servo control system. output shaft, 휔푚 = the angular speed of the shaft, 푇푚 = the motor torque, 푖푚 = the current, 퐾푚 = the torque constant. Electronic From figure 2, the transfer function of the DC servomotor Discharge can be derived using Kirchhoff’s voltage law and Laplace SERVO Gap transforms as follows: Input CONTROLLER + Applying Kirchhoff’s voltage law, SYSTEM 푑푖 푉 = 푅 푖 + 퐿 푚 + 푉 (1) - 푎 푚 푚 푚 푑푡 푏

The angular speed of the shaft, 휔푚 and the angular

position of the output shaft 휃푚 are connected by equation SYSTEM (1) Ignition Delay 푑휃 휔 = 푚 = 휃̇ (2) Time 푚 푑푡 The Back-electromotive force (emf), Vb can be expressed in Nois terms of 휃푚 or 휔푚 as shown in equation (2) e 푑휃 Figure 1: Block diagram of an EDM Servo Control System. 푉 (푠) = 퐾 푚 = 퐾 휔 (3) 푏 푚 푑푡 푚 푚 A servo is mostly employed in systems where the feedback Putting equation (3) into (1), 푑푖 or error-correction signals are applied to controlling 푉 = 푅 푖 + 퐿 푚 + 퐾 휔 (4) 푎 푚 푚 푚 푑푡 푚 푚 mechanical position or other parameters. Servomechanisms Taking the Laplace transform of equation (4), are primarily driven by servo motors, especially DC servo 푉푎(푠) − 푅푚(푠)퐼푚(푠) − 퐿푚(푠)퐼푚(푠)푠 + 푉푏(푠) (5) motors. Figure 1 shows the block diagram of an EDM servo Expressing the current 퐼푚(푠) in terms of the other control system.The circuit diagram of a servo motor is parameters in equation (5), shown in figure 2. 푉푎(푠)− 퐾푚(푠)휔푚(푠) 퐼푚(푠) = (6) 퐿푚(푠)푠 + 푅푚(푠) The mechanical component of the servomotor can be represented by equation (7) 푑2휃 푑휃 퐽 푚 + 푏 푚 − 푇 = 0 (7) 푚 푑푡2 푚 푑푡 푚 But the motor torque 푇푚 can be written as in equation (8) 푇푚 = 퐾푚푖푚 (8) Substituting equation (8) into (7) gives 푑2휃 푑휃 퐽 푚 + 푏 푚 − 퐾 푖 = 0 (9) 푚 푑푡2 푚 푑푡 푚 푚 푑휃 푚 in equation (9) can be replaced with equation (2) to 푑푡 obtain equation (10). 푑휔푚 퐽푚 + 퐵푚휔푚 − 퐾푚푖푚 = 0 (10) Figure 2: A servomotor circuit Diagram. 푑푡 Taking the Laplace transform of equation (10), 퐽푚(푠)휔푚(푠)푠 + 퐵푚(푠)휔푚(푠) − 퐾푚(푠)퐼푚(푠) = 0 (11)

IJERTV5IS040486 317 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 04, April-2016

Expressing the current in equation (11) 퐼푚(푠) in terms of stability. Figure 3 shows the control system model with other parameters, general PID controller. 퐽 (푠)휔 (푠)푠+ 퐵 (푠)휔 (푠) 퐼 (푠) = 푚 푚 푚 푚 (12) 푚 퐾 (푠) 푚 P 푲풑풆(풕) Combining equations (6) and (12) gives the Transfer Function of the servo motor, G(s) as shown in equations 풚(풕) 풓(풕) 풆(풕) 풖(풕) Plant (13). 풕 푲 풆(풕)풅풕 퐽 (푠)휔 (푠)푠+ 퐵 (푠)휔 (푠) 푉 (푠)− 퐾 (푠)휔 (푠) I 풊 ∫ퟎ 푚 푚 푚 푚 = 푎 푚 푚 (13) 퐾 (푠) 퐿 (푠)푠 + 푅 (푠) 푚 푚 푚 휔푚(퐽푚(푠)푠 + 퐵푚(푠))(퐿푚(푠)푠 + 푅푚(푠)) = 풅풆(풕) D 푲풅 퐾 (푠)(푉 (푠) − 퐾 (푠)휔 (푠)) (14) 풅풕 푚 푎 푚 푚 휔푚(퐽푚(푠)푠 + 퐵푚(푠))(퐿푚(푠)푠 + 푅푚(푠)) = 2 퐾푚(푠)푉푎(푠) − 퐾푚(푠) 휔푚(푠) (15) 휔 (퐽 (푠)푠 + 퐵 (푠))(퐿 (푠)푠 + 푅 (푠)) + 퐾 (푠)2 = Figure 3: The Model of a PID Controller Configuration. 푚 푚 푚 푚 푚 푚 퐾푚(푠)푉푎(푠) (16) 2 From Figure 3, the mathematical expression for the three 휔푚[(퐽푚(푠)푠 + 퐵푚(푠))(퐿푚(푠)푠 + 푅푚(푠)) + 퐾푚(푠) ] = controller gains can be written as follows: 퐾푚(푠)푉푎(푠) (17) . The proportional controller is an with 휔푚(푠) 퐾푚(푠) = 2 (18) adjustable proportional gain, Kp. The action of this 푉푎(푠) [퐽푚(푠)푠+ 퐵푚(푠)].[퐿푚(푠)푠+ 푅푚(푠)]+ 퐾푚(푠) 휔푚(푠) controller depends on the error present . The equation is: 퐺(푠) = (19) 푉푎(푠) m(t) = Kpe(t) (23) 퐾푚(푠) Where m(t) = controller output, Kp = Proportional 퐺(푠) = 2 (20) [퐽푚(푠)푠+ 퐵푚(푠)].[퐿푚(푠)푠+ 푅푚(푠)]+ 퐾푚(푠) gain/sensitivity, and e(t) = actuating error signal Equations (22) shows that the Transfer Function of the . In the integral gain K or integral controller action (also servo motor is the ratio of the angular speed of the shaft and i known as Reset Control), the output of the controller the angular position. The standard parameter values of a changes at a rate proportional to the actuating typical Die-Sinking EDM servomechanism obtained accumulation of past error signal e(t). experimentally from a previous research (Ananya et al., -6 integral gain, as shown in equation (24). 2011) are given as: 푅푚 = 4.0 Ω, 퐿푚 = 2.75 x 10 H, 퐽푚 = 푡 -6 2 -6 m(t) = Ki∫ 푒(푡) + 푚(0) (24) 3.22 x 10 Kgm , 퐵푚 = 3.508 x 10 Nm/(rad/s), 퐾푚 = 0 0.027 V/(rad/s) Where Ki = Integral gain, m(0) = Control output. Substituting the above parameter values into eqation (20) . In the derivative control action or derivative gain Kd, the gives the actual Transfer Function of the servo motor as output of the controller depends on the rate of change of shown in equation (4). the actuating prediction of future error signal e(t). The 0.027 퐺(푠) = equation for D is written as [3.22 x 10−6 푠+ 3.508 x 10−6].[2.75 x 10−6푠+ 4.0]+ 0.0272 푑 m(t) = Kd 푒(푡) (25) (21) 푑푡 The three separate controller gains parameters involved in 휔푚(푠) 0.027 PID controller algorithm can be combined as in equation 퐺(푠) = = 2 (22) 푉푎(푠) 푠 + 1.086푠 + 0.000779 (26). 푑푒(푡) 푢(푡) = 퐾 푒(푡) + 퐾 ∫ 푒(푡)푑푡 + 퐾 (26) III DESIGN SPECIFICATIONS 푝 푖 푑 푑푡 a) Percentage overshoots less than 10% to a unit Ti = integral time and Td = derivative time. step input. Applying the PID controller to any control system involves b) Settling time less than 5 seconds to a unit step adjusting the values of gain Kp, Ki and Kd in order to get the input. best response of the system. The selection of PID controller c) Rise time of less than 2 seconds to a unit step gain values causes the variation of observed response with input. respect to desired response. d) Steady-state error less than 0.2%. e) IV RESULT AND DISCUSSION A EDM Controller (PID) Design The analysis and discussion of the results obtained from the A Proportional Integral Derivative (PID) controller is a design of the Electrical Discharge Machining (EDM), generic control loop feedback mechanism widely used in process mathematical model, servo control system industrial control systems and is regarded as the standard modelling, and controller design and simulation is control structures. A PID controller, sometimes called presented below. The results include the step responses of three-term control, calculates an error value as the the EDM servomechanism, mathematical model transfer difference between a measured process variable and a function as well as the improving effects of the controller desired setpoint. The controller attempts to minimize the on the overall system. error by adjusting the process through the use of a A PID Controller Tuning Using Mathlab/Simulink manipulated variable. The PID controller has the optimum The actual PID controller gains from tuning Using control dynamics including zero steady state error, fast MATLAB/SIMULINK are: 퐾푝 = 59.3, 퐾푖 = 0.655 and response (short rise time), no oscillations and higher 퐾푑 = 28.1. Putting these controller gains obtained from the

IJERTV5IS040486 318 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 04, April-2016 tuning into a standard controller equation, this gives The control parameters obtained in figure 5 are: a settling equation (27). time of 3.52 seconds, the rise time of 1.05 seconds, the 1 percentage overshoot of 7.68%, the phase gain of 62 퐺푐(푠) = 59.3 + 0.655 + 28.1s (27) 푠 degrees at a frequency of 1.27rad/s, and a steady-state error B Initial Step Response of EDM Servo Control less than 2%. These servo control parameter values indicate System Model significant improvements in the performance of the system. The initial performance of the EDM servo control system Such improvements include a shorter and constant ignition without a well tuned PID Controller was investigated by delay time corresponding to the reduced rise time, and a simulating equation 14 using MATLAB/SIMULINK. The higher speed and accuracy of the EDM tool electrode step response plot of the result are shown in figure 4. From positioning to achieve the appropriate spark gap. the plot, the open-loop response of the EDM servo control system does not satisfy the design criteria at all. The V CONCLUSION settling time of 520 seconds, the rise time of 355 seconds, the percentage overshoot of 0%, the phase gain of -120 In this research the servomechanism have been successfully degrees at a frequency of 113.5rad/s, and a steady-state developed and simulated based on the initial, ignition and error less than 5%. This describes a very poor stability of discharge phase of current and voltage gap. Also, the design the system. It can be inferred from the plot that with the of a classical servo controller that optimizes the open-loop response the system is partially unstable. It can performance of the EDM process is presented. The ultimate also be interpreted that the response of the EDM) servo goal of the research is to improve the servomechanism of control system without a well tuned PID is practically very an EDM process for a better efficiency of the EDM slow and a longer ignition delay time. This can lead to micromachining process. The PID controller has been uncontrolled performance of the EDM process as a result of successfully designed and fine-tuned with non-linearities. MATLAB/SIMULINK and MATLAB PID tuner to obtain suitable gains for faster and accurate response of the EDM process. The PID controller gains obtained were integrated with a servo control system to achieve a better result. Moreover, the overall control system was improved to establish a more intelligent and robust response of the EDM process especially in our modern industries.

VI REFERENCES

[1] Chung, C., Chao, S., and Lu, M. F. (2009). Modeling and Control of Die-sinking EDM, 8(6), 713–722 Figure 4: Initial Step response the Servo Transfer Function, G(s). [2] Chandra, B., and Singh, H. (2015). Machining of aluminium metal matrix composites with Electrical discharge machining C EDM Servo Control System Model with Tuned PID - A Review. Materials Today: Proceedings, 2(4-5), 1665– Controller 1671. http://doi.org/10.1016/j.matpr.2015.07.094. The step response and Bode plot of the EDM servo control [3] Andromeda, T., and Samion, S. (2013). PID Controller system with a well tuned PID controller as shown in figure Tuning by Differential Evolution Algorithm on EDM Servo 1 was simulated using MATLAB/SIMULINK. The PID Control System, 287, 2266–2270. http://doi.org/10.4028/www.scientific.net/AMM.2 84- controller was tuned with a Matlab/Simulink PID tuner 287.2266. application. The results of the simulation for the system [4] M. M. Pawade and S. S. Banwait (2013). An Exhaustive with transfer function and state equation are shown in Review of Die Sinking Electrical Discharge Machining figure 5. From the step response plot for the EDM servo Process and Scope for Future Research. International control system with the transfer function, G(s) is shown in Scholarly and Scientific Research & Innovation 7(6) 2013 figure 5 1104. [5] Joshi, S. N., and Pande, S. S. (2010). Intelligent process modeling and optimization of die-sinking electric discharge machining. Applied Soft Computing Journal, 11(2), 2743– 2755. http://doi.org/10.1016/j.asoc.2010.11.005 [6] Takahata, K. (2009). Micro-Electro-Discharge Machining Technologies for MEMS, (December). [7] Patel, N. K. (2014). Parametric Optimization of Process Parameters For EDM of Stainless Steel 304 Narendra Kumar Patel National Institute of Technology Rourkela, (May). [8] Makableh, Y. (2011). Efficient Control of DC Servomotor Systems Using Backpropagation Neural Networks. [9] Chandra, B., and Singh, H. (2015). Machining of aluminium metal matrix composites with Electrical discharge machining Figure 5: Step Response of the Overall EDM Servo Control System. - A Review. Materials Today: Proceedings, 2(4-5), 1665–

1671. http://doi.org/10.1016/j.matpr.2015.07.094

IJERTV5IS040486 319 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 04, April-2016

[10] Chung, C., Chao, S., and Lu, M. F. (2009). Modeling and Control of Die-sinking EDM, 8(6), 713–722. [11] Datta, S., and Mahapatra, S. S. (2010). Modeling , simulation and parametric optimization of wire EDM process using response surface methodology coupled with grey- Taguchi technique, 2(5), 162–183. [12] Daud, M. R., Samion, S., Yahya, A., Mahmud, N., Hasyim, N. L. S., and Nugroho, K. (2013). Micro-Pits on Biomaterial in Electrical Discharge Machining By Using Taguchi Method. Latest Trends in Circuits, Control and Signal Processing, 172–177.

IJERTV5IS040486 320 (This work is licensed under a Creative Commons Attribution 4.0 International License.)