Multiple Fault Parameters Estimation of an Active Magnetic Bearing Integrated Coupled–Rotor–Bearing System

Abstract

Condition monitoring techniques have an important role in continuously running high-speed machines including jet engines, ship propellers, compressors, steam turbines and generators. Early detection and diagnosis of faults such as inherent unbalance, shaft bow/bent, misalignment, bearing, gear, rotor cracks and motor faults associated with these machines are the primary concern of researchers in the field. The excessive vibration generated at higher operating speeds due to these faults can be suppressed and controlled with the help of Active Magnetic Bearings (AMBs). AMB is a mechatronic product used in industries due to its excellent features such as no wear and tear, lubrication-free and frictionless operation due to the absence of mechanical loading. The present work mainly concentrates on the development of an identification algorithm to estimate fault parameters (inherent unbalance and misalignment) along with AMB parameters in an AMB integrated rotor-bearing-coupling system. First, an identification methodology is proposed to quantify fault parameters along with AMB characteristic parameters of a coupled turbine generator system. A simplest possible turbo-generator system is modelled to analyze coupling misalignment and inherent unbalance. Conventional methodology to estimate dynamic system parameters based on forced response information is not enough for an AMB-integrated rotor system because it requires additional current information along with displacement information. The controlling current of AMB is tuned and controlled with the help of a proportional–integral–derivative (PID) type controller. Lagrange’s equation is used to obtain equations of motion (EOMs). Accordingly, a SIMULINKTM model is developed and solved using Runge–Kutta technique to acquire the time domain responses (current and displacement). The fast Fourier transformation (FFT) is applied on obtained responses to acquire responses in frequency domain. A methodology based on the least-squares regression approach is proposed to evaluate the multi-fault parameters of AMB integrated rotor system. The robustness of the algorithm is checked against various levels of noise and modelling error and observed efficient. An appreciable reduction in misalignment forces and moments is observed by using AMBs. Next, a finite element method (FEM) is implemented on the proposed model to overcome the limitations of the numerical model. The purpose of the FEM model is to represent the complex physical system more accurately. A quantification technique is suggested to evaluate the tuned AMB characteristics along with imbalance and coupling misalignment dynamic parameters. A FEM modelling with a high-frequency reduction scheme is utilized to acquire reduced system equations of motion. The advantage of employing a condensation scheme is twofold; first, it reduces the number of sensors required and second, only linear (practically measurable) degrees of freedom present in equations of motion. A SIMULINKTM code is prepared to solve a reduced linear differential equation. The time series signals (current and displacement) obtained are transformed into a frequency series utilizing Fast Fourier Transformation (FFT) and utilized in proposed algorithm. To establish the accuracy and effectiveness of the methodology, the estimated parameters are evaluated under two different frequency bands against measurement noise and modelling error (5% variation in mass of the disc and bearing characteristic parameters). The proposed FEM model is then extended to estimate the speed-dependent fault and AMB characteristic parameters along with speed independent unbalance parameters. Here, a novel gyroscopic high-frequency condensation (GHFC) scheme is proposed to obtain reduced EOMs for the system. The transformation matrix obtained in standard high-frequency condensation (SHFC) is modified by adding a gyroscopic effect into the transformation matrix to achieve the novel GHFC. The estimated parameters are compared for SHFC and GHFC. The GHFC is found effective over SHFC techniques. The effect of noisy response and modelling error on the estimation algorithm is analyzed and found competent. The work carried out in this thesis mainly focuses on the modelling, analysis and estimation of fault parameters of an AMB integrated coupled rotor-bearing system. AMB is used as an agent to suppress the excessive vibration generated due to various faults present in the system. The faults considered in this analysis are coupling misalignment and inherent unbalance. The identification methodology developed has scope in the online condition monitoring of rotating machines.