Characteristic parameters estimation of uncertainties present in an active magnetic bearing integrated flexible rotor system using dynamic reduction technique

Abstract

In this article, an identification algorithm is developed to estimate the characteristic parameters of uncertainties present in rotating machines. A dynamic system consists of two flexible shafts each having a rigid disc and an active magnetic bearing (AMB) at its mid–span, mounted on flexible bearings at ends and connected together with a flexible coupling is considered for numerical simulation. Finite element method (FEM) is used to obtain dynamic equations of motion (EOMs) for coupled flexible rotor system integrated with AMBs. An identification algorithm based on least squares technique is developed to estimate the characteristic parameters of uncertainties/faults (i.e., bearing, coupling and residual unbalance) present in the rotor system. FEM is more accurate and realistic approach to model real rotor test rigs but degrees of freedom (DOFs) of the system increases as the number of nodes increases. Accessibility of these DOFs and accurate displacement measurements are the most challenging problems in the real rotor test rigs. To overcome this difficulty, a dynamic reduction technique is applied in the developed identification algorithm to eliminate some linear and all angular DOFs (that are practically immeasurable and to avoid difficulties of number of sensors). A Proportional Integral Derivative (PID) controller is used to obtain the controlling current for AMBs to stabilize the rotor system. The EOMs derived is solved by fourth order Runge–Kutta method to generate the displacement and current responses. The time domain responses are converted into frequency domain using Fast Fourier Transform (FFT). Full spectrum analysis is performed to estimate the desired characteristic parameters. The effectiveness of the algorithm is checked for measurement error and found to be excellent