Accounting for an Interconnection of Electrical, Magnetic and Mechanical Processes in Modeling the Dynamics of Turbomachines Rotors in Passive and Controlled Active Magnetic Bearings

Abstract

The work is devoted to the way of describing and modeling dynamic phenomena in rotor systems, in particular turbomachines, with magnetic bearings (MBs) of different types – the passive and active ones. The feature of such systems is an essential interconnection of processes having a different physical nature–mechanical, electrical and magnetic ones. To adequately reflect this relationship, the Lagrange-Maxwell equations are used, taking into account the laws governing the active magnetic bearings in them. A critical analysis of simplified methods for modeling rotor dynamics is given. For a correct consideration of electromagnetic processes, the method of analyzing electromagnetic circuits of active magnetic bearings (AMBs) is used, based on a consideration of substitution schemes. Magnetic resistances of magnetic circuits, grooves and air gaps are determined by schematizing the paths of magnetic fluxes. The power characteristics of passive magnetic bearings (PMBs) are determined on a basis of a series of magnetostatics analyzes. The refined analytical expressions for a magnetic energy of active magnetic bearings and the dependences of magnetic forces of passive magnetic bearings, found using the proposed approach, are used in the coupled Lagrange-Maxwell equations. A laboratory model is considered as an example of rotary systems with passive and active magnetic bearings, which is a prototype of a complete magnetic suspension of a rotor of an expander- compressor unit. Based on a comparison of the results of experimental studies and a numerical analysis of the rotor dynamics of this model, a substantiation and proof of a necessity of applying the proposed approaches are given.