Active Magnetic Radial Bearings Applied To Rotor Dynamics

Abstract

This thesis considers the development of a mathematical expression for actively controlled magnetic bearings and their influence on a flexible shaft with two disks supported by two bearings. Active magnetic bearings are a complex mechatronic product incorporating three energy domains as well as a control feature.The control featured in the bearings are based on the lateral displacements of the shaft. The displacement readings are then processed by a PID controller. The controller output generate a voltage and hence current flow in stator pole windings, creating a magnetic flux and hence a force exerted on the rotor. It is difficult to express the loss phenomena in a magnetic circuits based on mathematics, and tests on specimens are virtually always necessary in order to get accurate figures. The mathematical model have two distinct approaches. The first approach make use of approximations on the magnetic circuit, with focus on magnetic flux density and area. These assumptions makes it possible to express the force between the rotor and stator directly from the current flow. The second approach make no use of those simplifications on the magnetic circuit and the force developed is expressed in terms of magnetic flux.The damping factor related to bearings acting on a rotating shaft is a prominent variable to the rotor response. In actively controlled magnetic bearings this feature is thought of as the time rate of the feedback in the controller, the differential parameter. In other words, the velocity of the response how fast do the amplifier induce current, and hence force. Nevertheless, this parameter is difficult to establish in the system, and also here laboratorial tests should be carried out in order to get reliable results. Simulations are done with bond graph models of the bearings. The results indicate that the damping factor plays a vital role, and that the lateral forces exerted on the rotor from the bearings are highly dependable on the initial set up with controller parameters.