Electromagnetic Part of the Mathematical Model for Simulating Processes in the Mechatronic System “Rotor in Active Magnetic Bearings”

The paper considers an approach to the formation of an analytical mathematical model for simulating dynamic processes in a mechatronic system of a rotor in active magnetic bearings. Many industrial rotary machines can be reduced to such an electromechanical system, in which radial and axial controlled electromagnetic bearings are used as rotor supports. Traditionally, the processes in such active magnetic bearings are described in a simplified way as the dependence of the electromagnetic force on the current in the coil circuit and the rotor displacement, which does not take into account the dynamics of electromagnetic processes. The paper proposes a method for joint mathematical description of the dynamic behavior of a given mechatronic system. For this, the interrelated magnetomechanical equations of Lagrange-Maxwell are applied. Two forms of writing the electromagnetic part of this system of equations are considered using independent alternating currents and flux linkages in the coils of electromagnets with an analysis of the advantages of each of them. Based on the proposed method of the mathematical description, a simulation of the dynamic behavior of the rotor was performed, taking into account the dynamics of controlled electromagnetic processes in the circuits of active magnetic bearings for a large-scale laboratory model of a turbocompressor of a gas-pumping unit with two radial and one axial active magnetic bearings. The results of numerical analyzes are presented in the form of time dependences for rotor displacements and currents in circuits. Their comparison with experimental data allowed verifying the proposed method of the mathematical simulation. This method of the mathematical description of the electromagnetic part of the rotor system can be used for active magnetic bearings of various types and with different configurations of rotor and especially stator parts.