Analysis of gyroscopic effects in rotor disc systems

Abstract

This work deals with study of dynamics of a viscoelastic rotor shaft system, where Stability Limit of Spin Speed (SLS) and Unbalance Response amplitude (UBR) are two indices. The Rotor Internal Damping in the system introduces rotary dissipative forces which are tangential to the rotor orbit, well known to cause instability after certain spin speed. There are two major problems in rotor operation, namely high transverse vibration response at resonance and instability due to internal damping. The gyroscopic stiffening effect has some influence on the stability. The gyroscopic effect on the disc depends on the disc dimensions and disc positions on the rotor. The dynamic performance of the rotor shaft system is enhanced with the help of gyroscopic stiffening effect by optimizing the various disc parameters (viz. disc position and disc dimension). This optimization problem can be formulated using Linear Matrix Inequalities (LMI) technique. The LMI defines a convex constraint on a variable which makes an optimization problem involving the minimization or maximization of a performance function belong to the class of convex optimization problems and these can incorporate design parameter constraints efficiently. The unbalance response of the system can be treated with H¡Þ norm together with parameterization of system matrices. The system matrices in the equation of motion here are obtained after discretizing the continuum by beam finite element. The constitutive relationship for the damped beam element is written by assuming a Kelvin ¨C Voigt model and is used to obtain the equation of motion. A numerical example of a viscoelastic rotor is shown to demonstrate the effectiveness of the proposed technique.