Modelling and State Estimation in Pulsed ECM with Variable Electrolyte Conductivity

Abstract:

In Pulsed Electrochemical Machining the control of the size of the process gap is necessaryto achieve process stability. However, the gap size cannot be measured directly during the machiningprocess. Based on an equivalent circuit, a process model has been derived for plane electrodes andconstant conductivity. In a previous study, an approach to controlling and estimating the gap size hasbeen introduced. By input-output-linearisation, a linear system was found, making it easier to controlthe gap size and current flow simultaneously.In this work the existing model is revised for its applicability to the conductivity change duringeach pulse resulting from heat and gas bubble generation. Depending on the particular moment of thecurrent measurement, the value of the conductivity in the electrolyte reservoir cannot be used for thegap size estimation directly. Three different approaches to overcome this problem are reviewed. Themost promising approach was implemented on a real-time platform and optimised for execution time.

• Periodical: Key Engineering Materials (Volumes 554-557)
• Pages: 1910-1915
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.554-557.1910
• Online since: June 2013
• Authors: Markus Boxhammer, Jin Ming Lu
• Keywords: Control, Electrochemical Machining, Gap Estimation, Variable Conductivity

References

[1] Altena, H.S.J.: Precision ECM by Process Characteristic Modelling, Diss., Glasgow Caledonian University, (2000)

[2] Boxhammer, M.; Riedl, G.; Ruhlig D.; Lohmann B.: Simultaneous control of current density and frontal gap in Precise Electrochemical Machining, INSECT, pp.18-24, Vienna, (2011)

[3] Gauthier, J.P.; Bornard, G.: Observability for any u(t) of a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, vol. 26(4), pp.922-926 , (1981)

DOI: 10.1109/tac.1981.1102743

[4] Jain, N.K.; Jain, V.K.: Optimization of Electrochemical Machining Process Parameters using Genetic Algorithms, Machining science and technology, vol. 11(2), pp.235-258, 2007[5] Kozak J., Rajurkar K.P., Wei B.; Modelling and Analysis of Pulse Electrochemical Machining, Journal of Engineering for Industry, vol. 116, pp.316-323, (1994)

DOI: 10.1115/1.2901947

[6] Kozak, J.; Gulbinowicz, D.; Gulbinowicz, Z.: The Mathematical Modeling and Computer Simulation of Pulse Electrochemical Micromachining, Engineering Letters, vol. 16(4), pp.556-561

DOI: 10.1063/1.3146189

[7] Loutrel, S.P.; Cook N.H.: A Theoretical Model for High Rate Electrochemical Machining, Journal Eng. for Industry, vol. 95, pp.1003-1008, (1973)

DOI: 10.1115/1.3438244

[8] Rajurkar, K.P.; Wei, B.; Kozak, J.; McGeough, J. A.: Modelling and Monitoring Interelectrode Gap in Pulse Electrochemical Machining, CIRP Annals-Manufacturing Technology, vol. 44(1), pp.177-180, (1995)

DOI: 10.1016/s0007-8506(07)62301-4

[9] Simon, D.: Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, WileyInterscience, p.405, (2006)

[10] Slotine, J.J.E.; Li, W.: Applied nonlinear control, Prentice-Hall, pp.207-275, (1991)

[11] Thorpe, J.F.; Zerkle, R.D.: Analytic Determination of the Equilibrium Electrode Gap in Electrochemical Machining, International Journal of Machine Tool Design and Research, vol. 9(2), pp.131-144, (1969)

DOI: 10.1016/0020-7357(69)90012-2