Modeling of the Dynamics of Rotors of an Energy Gas Turbine Installation Using an Analytical Method for Analyzing Active Magnetic Bearing Circuits

Abstract

The paper discusses an approach to the analysis of the dynamic behavior of turbine rotors and a generator of an energy gas turbine unit with active magnetic bearings as supports. This unit is a part of the gas turbine cogeneration plant (GT CP). The problem of modeling the phenomena of rotor dynamics is solved with full consideration of controlled electromagnetic processes in active magnetic bearing (AMB) circuits. In order to analyze them, the method of contour flows similar to the method of contour currents for the analysis of electrical circuits is used. To describe the electromagnetic circuits of the AMB, detailed substitution schemes are introduced which take into account almost all the elements of the magnetic circuit (air gaps, sections of magnetic cores, grooves with windings, coils and other parts). Description of the considered mechatronic system requires constructing a mathematical model on the basis of application of the magnetomechanical Lagrange-Maxwell equations. The resulting system of differential equations relates to the generalized mechanical coordinates and flux linkages of the electric circuits of the AMB coils. The calculation results have the form of Cambell diagrams and amplitude-frequency characteristics of rotating rotors. Verification of the proposed approach to the modeling of dynamic phenomena in a rotary mechatronic system involves comparison with known calculation data. A comparative analysis reveals the advantages of the proposed approach for numerical simulation of the dynamics of rotors of controlled mechatronic systems and industrial electromechanical machines.