# A REFINED MATHEMATICAL MODEL OF MULTIPHYSICS PROCESSES FOR MAGNETIC PULSE TREATMENT OF MATERIALS

## Authors

• E. I. Baida National Technical University "Kharkiv Polytechnic Institute", Ukraine

## Keywords:

magnetic pulse treatment, electromagnetic field, mathematical model

## Abstract

Introduction. The complexity of the theoretical description of the magnetic pulse treatment of the material is in the mutual coupled processes of electromagnetic and thermal fields with plastic deformation of the material and processes in an electrical circuit. The paper deals with the combined transient mathematical model of the system of equations of the electromagnetic field, theory of elasticity, thermal conductivity and electrical circuit. Purpose. Research and testing of the developed mathematical model and assess the impact of various parameters on the process of deformation of the work piece. Methodology. Investigation of nonlinear mathematical model is carried out by the finite element method using a special software package. Results. The resulting solution of the transient mathematical model allows studying the influence of parameters of the circuit, the speed and the characteristics of the material to plastic deformation and heating of the work piece, which allows to select the optimum process parameters. Originality. This is an integrated approach to the development of a mathematical model, which includes the electromagnetic field equations, the theory of elasticity, thermal conductivity and electrical circuit equations with a storage capacitor. Conclusions. A comprehensive mathematical model and its solution are obtained. It is established a small effect of heating temperature on the amount of strain. Currents caused by movement of the work piece must be taken into account in the calculations. Inertial forces significantly affect the nature of the deformation. During the deformation it is necessary to consider the nonlinearity of elasticity modulus. Thermal deformation of the work piece is much less mechanical strain and opposite in sign to them, but the surface temperature stresses due to the high temperature gradient equal to 20 % of the yield strength of the work piece.

## Author Biography

### E. I. Baida, National Technical University "Kharkiv Polytechnic Institute"

кафедра "Электрические аппараты"

## References

Belyj I.V., Fertik S.M., Himenko L.T. Spravochnik po magnitno-impulsnoj obrabotke metallov [Directory of magnetic-pulse treatment of metals]. Kharkiv, Vishcha shkola Publ., 1977, 189 p. (Rus).

Turenko A.N., Batygin Yu.V., Gnatov A.V. Impulsnyie magnitnyie polya dlya progressivnyih tehnologiy. Tom 3. Teoriia i eksperiment pritiazheniia tonkostennykh metallov impul'snymi magnitnymi poliami [The pulse magnetic fields for advanced technologies. Vol.3. Theory and experiment of thin-walled metals attraction by the pulse magnetic fields]. Kharkov, KhNAHU Publ., 2009. 240 p. (Rus).

Shneerson G.A. Polya i perehodnye processy v apparature sverhsilnyh tokov [Fields and transients in equipment ultra strong currents]. Leningrad, Energoizdat Publ., 1981. 200 p. (Rus).

Bondarenko A.Yu. Electromagnetic processes in a flat inductor system with two coils under uniform surface currents distribution in the coils. Elektrotekhnika i elektromekhanika – Electrical engineering & electromechanics, 2012, no.3, pp. 61-65. (Rus).

Batygin Yu.V., Gnatov A.V., Chaplygin E.A., Smirnov D.O. Electromagnetic processes in an inductor induction inductive circular-turn system with a cut between two thin-walled metal sheets. Elektrotekhnika i elektromekhanika – Electrical engineering & electromechanics, 2012, no.3, pp. 51-55. (Rus).

Batygin Yu.V., Gnatov A.V., Serikov G.S. Calculation of forces in a rectangular-geometry induction inductor system with a non-ferromagnetic massive screen and a work-piece. Elektrotekhnika i elektromekhanika – Electrical engineering & electromechanics, 2009, no.3, pp. 61-64. (Rus).

Batygin Yu.V., Gnatov A.V. Calculation of electrodynamic forces in an induction inductor system with a non-ferromagnetic massive screen and a sheet work-piece. Elektrotekhnika i elektromekhanika – Electrical engineering & electromechanics, 2009, no.4, pp. 56-59. (Rus).

Ramo S., Uineri D. Polia i volny v sovremennoi radiotekhnike [Fields and waves in modern radio engineering]. Moscow-Leningrad, State publishing scientific and technical literature, 1948. 631 p. (Rus).

Frenkel' Ya.I. Kurs teoreticheskoi mekhaniki [Course of Theoretical Mechanics]. Leningrad, Krasniy pechatnik Publ., 1939. 386 p. (Rus).

Timoshenko S.P., Gudier Dzh. Teoriya uprugosti [Theory of elasticity]. Moscow, Nauka Publ., 1979. 560 p. (Rus).

2015-04-28

## How to Cite

Baida, E. I. (2015). A REFINED MATHEMATICAL MODEL OF MULTIPHYSICS PROCESSES FOR MAGNETIC PULSE TREATMENT OF MATERIALS. Electrical Engineering & Electromechanics, (2), 41–47. https://doi.org/10.20998/2074-272X.2015.2.08

## Section

Engineering Electrophysics. High Electric and Magnetic Field Engineering