The mathematical model for analysis of attenuation of nonlinear vibration of rigid rotors influenced by electromagnetic effects

Abstract

The vibration of rotors supported by rolling element bearings mounted in controllable squeeze film magnetorheological dampers depends of a complex interaction between mutually coupled mechanical, hydraulic, magnetic and electric phenomena. In the developed mathematical model of the magnetorheological damper the magnetorheological oil is represented by a bilinear material, the yielding shear stress of which is a function of magnetic induction, and the damper body by a set of meridian segments. Each segment is considered to be a divided core of an electromagnet with the gap filled with magnetorheological oil. The pressure distribution in the lubricating film is governed by the Reynolds equation, adapted to bilinear material. The dependence of the yielding shear stress of magnetic induction is approximated by a power function. The current in the electric circuit is determined from the equation of the voltage equilibrium. The presented mathematical model of the magnetorheological squeeze film damper was implemented in the computational procedures for transient dynamical analysis of rotor systems. The goal of the investigations was to learn more about the nonlinear effects, time delays, and complex influences of the electromagnetic phenomena occurring in magnetorheological damping devices used in the vibration attenuation of rotors. The development of the enhanced mathematical model of a magnetorheological squeeze film damper and extending knowledge upon the influence of electromagnetic phenomena in reducing lateral vibration of rigid rotors are the main contributions of this article.