Almost sure asymptotic stability of rotor systems subjected to stochastical axial loads

Abstract

The stochastical axial loads, to which the rotor system of the turbomachine is usually subjected, are due to the aerodynamic forces, hydrodynamic forces, preload and so on. The modeling of rotor systems subjected to stochastical axial loads is presented as stochastically excited and dissipated Hamiltonian systems. The stochastic averaging method for quasi-integrable-Hamiltonian systems is applied to obtain the averaged equations and the expression for the largest Lyapunov exponent is formulated. The necessary and sufficient conditions for the almost sure asymptotic stability of the rotor system are presented approximately. The largest Lyapunov exponent is evaluated and employed to determine the region of almost sure asymptotic stability of rotor systems with random axial loads. It is found that the angular motion plays a key role in almost sure asymptotic stability of rotor systems. The effects of the spectral density of random axial load and the polar mass moments of inertia on stochastic stability of the rotor system are significant.