Modeling, Analysis, and Identification of Parallel and Angular Misalignments in a Coupled Rotor-Bearing-Active Magnetic Bearing System

Abstract

The standard techniques used to detect misalignment in rotor systems are loopy orbits, multiple harmonics with predominant 2X component, and high axial vibration. This paper develops a new approach for the identification of misalignment in coupled rotor systems modeled using two-node Timoshenko beam finite elements. The coupling connecting the turbine and generator rotor systems is modeled by a stiffness matrix, which has both static and additive components. While the magnitude of static stiffness component is fixed during operation, the time-varying additive stiffness component displays a multiharmonic behavior and exists only in the presence of misalignment. To numerically simulate the multiharmonic nature coupling force/moment as observed in experiments, a pulse wave is used as the steering function in the mathematical model of the additive coupling stiffness (ACS). The representative turbogenerator (TG) system has two rotor systems, each having two disks and supported on two flexible bearings—connected by coupling. An active magnetic bearing (AMB) is used as an auxiliary bearing on each rotor for the purposes of vibration suppression and fault identification. The formulation of mathematical model is followed by the development of an identification algorithm based on the model developed, which is an inverse problem. Least-squares linear regression technique is used to identify the unbalances, bearing dynamic parameters, AMB constants, and importantly the coupling static and additive stiffness coefficients. The sensitivity of the identification algorithm to signal noise and bias errors in modeling parameters has been tested. The novelty of paper is the representation and identification of misalignment using the ACS matrix coefficients, which are direct indicators of both type and severity of the misalignment.