Non-linear model of energy consumption for in-process control in electrical discharge machining
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ORIGINAL ARTICLE
Non-linear model of energy consumption for in-process control in electrical discharge machining Kanka Goswami 1
&
G. L. Samuel 2
Received: 19 September 2019 / Accepted: 17 August 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The stochastic nature in the electrical discharge machining (EDM) is inherent to the process. The process instabilities like shortcircuiting and arcing instances damage the workpiece and reduce machining efficiency. Pseudo-empirical or empirical relationships are presently in use for in-process control of parameters like discharge efficiency, energy consumption, and surface roughness. In this paper, a field-programmable gate array (FPGA)–based control strategy for discharge stabilisation is proposed, and a non-linear model for energy consumption is formulated to predict the in-process energy consumption. The model captures the dynamic behaviour of the EDM process. A novel method of pulse discrimination based on the pulse train gradient is used to determine the pulse duration, classify the pulses and finally calculate the discharge energy for building the model. A lumped control parameter named as gap condition number or “Gc number” is proposed to quantify the amount of debris and contaminants like soot and suspended particles in the electrode gap. Numerical simulations at various gap conditions and analysis for stability and sensitivity at different operating scenarios are studied. The simulation shows that the model converges to a single root for Gc number up to 1.93, undergoes periodic oscillations between two roots for the values between 1.93 and 2.42 and exhibits chaos for greater Gc numbers. Stability analysis of the model finds that the values of the non-dimensionalised discharge energy for which the energy oscillations during the discharge avoids arcing or short-circuiting are 60% of the maximum discharge energy. The present model has an increased monostability of 20% in comparison to a similar model and has a correlation of 63.48% with the experimental data. The proposed control strategy can be implemented to achieve stability control over the process, eventually improving the quality of machining. Keywords Micro-EDM . Pulse classification . Energy model . Non-linear EDM model . EDM process control
Nomenclature Symbol Description E Non-dimensional energy Ei Energy at present instant of time (J) Ei + 1 Energy at the immediate future time step (J) Ei − 1 Energy at the immediate past time step (J)
* G. L. Samuel [email protected] Kanka Goswami [email protected] 1
Manufacturing Engineering Section Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
2
Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
Emax Edis Ecorr Eexp Gc V I T t ton toff δ ρ μEcorr μEexp σcorr σexp
Maximum energy (J) Discharge energy (J) Combined signal vector Experimental data vector Lumped control parameter (Gc number) represent
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