Near-Critical Behavior of an Elastic Rotating Shaft Stabilized by Electromagnetic Actuators

Abstract

The paper is concerned with the problem of dynamic stability of a rotating elastic shaft supported on rolling bearing at both ends. The material of the shaft is characterized by some dissipative properties which leads to dynamic loss of stability at a certain angular velocity called the critical rotation speed. The shaft is equipped with a system of two perpendicularly arranged pairs of electromagnets which exerts some attractive force upon the shaft in two transverse direction. Presence of such forces, phenomenon of magnetic induction as well as resistance in the electric circuits substantially affect dynamics of the entire system. Application of a semi- and fully active control strategies has proved that the proposed structural solution considerably increases the critical speed and thus enlarges the range of safe operation of the shaft. A growth in the critical threshold by half and even more has occurred to be achievable for quite moderate values of the supply voltage. It has been also shown that the electromagnetic actuators favorably influence near-critical response of the system right after the stability is lost. It has been found that the nonlinear behavior of the system is orbitally stable and the observed self-excited vibration exhibits smooth supercritical nature. Electromagnetic actuation additionally decreases amplitude of the arisen limit cycle.