Volume 15, no. 2Pages 43 - 55

# Calculation of the Three-Dimensional Magnetic Field of a System of Permanent Magnets and Ferromagnets Based on the Integral Magnetization Equation and the Jills-Atterton Model

R.V. Harutyunyann
The article considers the calculation of the three-dimensional magnetic field of a system of permanent magnets and ferromagnets based on the integral magnetization equation and the Jills-Atterton model. It is assumed that the magnetic system consists of permanent magnets and structural parts made of ferromagnetic materials with known characteristics. One of the problems is to take into account the influence of the magnetic hysteresis of the frame material on the accuracy of calculating the magnetic field. The cell method and iterative relaxation method are used to solve the integral magnetization equation. The main magnetization curve is calculated using the Langevin formula. As a model problem, we consider the calculation of the magnetic field created by a rectangular permanent magnet located on a ferromagnetic base in the form of a parallelepiped. The results obtained can also be used in solving direct and inverse problems for a system of ferromagnetic bodies and in test problems for comparison with other methods.
Full text
Keywords
ferromagnetic; permanent magnet; magnetic field; integral equation; hysteresis; cell method; relaxation method.
References
1. Denisov P A. Solution of Direct and Inverse Problems of Magnetic Field Analysis of Electrical Devices with Permanent Magnets at Their Local Demagnetization. PhD thesis, Novocherkassk, 2016. (in Russian)
2. Bloch Yu.I. Teoreticheskie osnovy kompleksnoj magnitorazvedki [Theoretical Foundations of Complex Magnetic Exploration]. Moscow, MGGA, 2012. (in Russian)
3. Jiles D.C., Atherton D.L. Theory of Ferromagnetic Hysteresis. Journal of Magnetism and Magnetic Materials, 1986, no. 61, pp. 48-60.
4. Denisov P. A. [Description of the Hysteresis Loop Using Explicit Expressions for the Jills-Atherton Model of the Second Level]. Izvestiya Vuzov. Elektromekhanika, 2018, vol. 61, no. 1, рp. 6-12. (in Russian)
5. Cherkasova O.A. [Investigation of the Magnetic Field of a Permanent Magnet Using Computer Modeling]. Geteromagnitnaya Mikroelektronika, Saratov, Saratov Publishing House, 2014, no. 17, pp. 112-120. (in Russian)
6. Matyuk V.F., Churilo V.R., Strelyukhin A.B. [Numerical Simulation of the Magnetic State of a Ferromagnet in an Inhomogeneous Constant Field by the Method of Spatial Integral Equations]. Defektoskopiya, 2003, no. 8, pp. 71-84. (in Russian)
7. Ignat'ev V.K., Orlov A.A. [Inverse Magneto-Static Problem for a Ferromagnetic]. Nauka i obrazovanie, 2014, no. 1, pp. 300-324. (in Russian)
8. Pechenkov A.N. Algorithms of Calculations and Modeling of Direct and Inverse Problems of Magnetostatic Flaw Detection and Devices of Technical Magnetostatics. PhD thesis, Novocherkassk, 2007. (in Russian)
9. Dyakin V.V., Kudryashova O.V., Raevskii V.Y. On the Solution of the Magnetostatic Field Problem in the Case of Magnetic Permeability That is Dependent on Coordinates. Russian Journal of Nondestructive Testing, 2015, vol. 51, no. 9, pp. 554-562.
10. Akishin P.G., Sapozhnikov A.A. The Method of Volumetric Integral Equations in Problems of Magnetostatics. Vestnik RUDN. Mathematics, Computer Science, Physics, 2014, no. 2, pp. 310-315. (in Russian)
11. Arutyunyan R.V., Nekrasov S.A., Seredina P.B. Identification of Permanent Magnet Magnetization Based on the Scalar Magnetic Potential Method. Izvestia Vuzov. Electromechanics, 2018, vol. 61, no. 6, pp. 19-25. (in Russian)
12. Petukhov I.S. [Model of Vector Hysteresis in a Periodic Electromagnetic Field]. Tekhnik elektrodinamika, 2014, no. 1, pp. 28-34. (in Russian)
13. Vector Magnetic Hysteresis [Electronic Resource]. Available at: https://cae-club.ru/forum/vektornyymagnitnyy-gisterezis
14. Podgorny D.E. Modeling of Electromagnetic Fields and Processes in Current Transformers and Their Circuits. PhD thesis, Novocherkassk, 1998. (in Russian)