A Reduced Model of Higher Order Viscoelastic Rotor Using Modified SEREP

Abstract

Damping is present in most of the materials and it plays a crucial role in its dynamics. Modelling of rotors by incorporating material damping through frequency dependent viscous or frequency independent hysteretic damping is not sufficient to predict the exact dynamic behaviour of the system. The use of general viscoelastic material captures the influence of both type of damping and predicts the exact dynamic characteristics. The finite element model of a general viscoelastic rotor shaft supported by journal bearings becomes bulky and complicated. Higher order model is derived after incorporating operator based constitutive relationship for the damped shaft. The EulerBernoulli beam theory is used to form the finite element model of the general viscoelastic rotor. Due to consideration of internal damping, gyroscopic effect, and journal bearing, asymmetry is also present in the higher order system. Hence, the system becomes computationally stiff, especially for eigen analysis. Thus it becomes necessary to reduce the size of the model with important coordinates for better computational efficiency and to make the eigenvalue analysis easy. The interest of the paper is to investigate the effectiveness of a Modified System Equivalent Reduction Expansion Process (SEREP) as a tool to reduce higher order system equations of motion. The reduction process is done on equations of motion written in state-space form. The conventional SEREP process uses only the right eigenvectors whereas the modified SEREP uses both the right and left eigenvectors to form the transformation matrix. A multi-disc rotor–shaft bearing system is considered for numerical illustration to show the effectiveness of the process. The effectiveness of the reduced model is examined using various dynamic parameters like Campbell diagram and modal damping factor.