Mathematical model of the axial electromagnetic bearing taking into account eddy currents
Yu.A. Makarichev, Doctor of Technical Sciences, Associate professor, Samara State Technical University. E-mail: firstname.lastname@example.org
A.V. Starikov, Doctor of Technical Sciences, Associate professor, Samara State Technical University. E-mail: email@example.com
I.S. Belyaeva, Post-graduate student, Samara State Technical University.
The mathematical model of the axial electromagnetic bearing considering influence of eddy currents is viewed in article. The system of rotor movement equations in the electromagnetic bearing field assuming the differential law of pressure management on windings by means of the pulse-width modulator has been made. The structural diagram of the rotor moving process as a control target has been developed. It is shown that the axial electromagnetic bearing represents a nonlinear and non-stationary control target. The linearization of the equations of control target movement around some working point has been made. The linearized structural diagram of the axial electromagnetic bearing, differentiated by a considerable quantity of cross communications has been presented. By the method of consecutive substitution of intermediate variables the transfer function of the rotor moving process in a magnetic field of the axial bearing has been found. The received transfer function allows analyzing influence of eddy currents, the initial position of a rotor and size of control action on dynamic properties of the axial electromagnetic bearing.
axial electromagnetic bearing, eddy currents, control target, mathematical model, transfer function
1. Vereshchagin V.P., Klabukov V.A. Matematicheskaya model' osevogo magnitnogo podshipnika s uchetom vikhrevykh tokov.[ Mathematical model of the axle magnetic bearing based on eddy currents ]. Trudy NPP VNIIEM. [Proc. NPP VNIIEM]. Moscow, 2011, vol. 123, pp. 4 – 8.
2. Evdokimov Yu.K., Toguzov S.A. Matematicheskaya model' osevogo magnitnogo podshipnika. [Mathematical model of the axle magnetic bearing ]. Available at: http: //fetmag.mrsu.ru/20092/pdf/axial_active_magnetic_bearing.pdf.
3. Makarichev Yu.A. Metody analiza i sinteza aktivnykh elektromagnitnykh podshipnikov: avtoref. dis. … d-ra tekhn. nauk. [Methods of analysis and synthesis of active electromagnetic bearings: author’s abstract, thesis of doctor of technical sciences]. Samara Samarskiy gosudarstvennyy tekhnicheskiy universitet, 2013, 41 p.
4. Makarichev Yu.A. Metod modelirovaniya protsessov, vyzvannykh vikhrevymi tokami, v nestatsionarnykh rezhimakh osevykh elektromagnitnykh podshipnikov. [Method of processes’ modeling caused by eddy currents in the transients conditions of axle electromagnetic bearings]. Vestn. SamGTU. Tekhnicheskie nauki, 2013, no. 2 (38), pp. 164 – 170. [In Russ.]