Stability and Nonstationary Vibrations of Rotor in Elastoviscous Field

Abstract

The efforts directed toward ensuring long trouble-free operation of rotating machinery are in the focus of many scientific investigations. Electric power rotors and turbines, aircraft engines, automotive drive trains, kinetic energy storage systems are only few examples of machines that are to operate efficiently and safely. Very often they are imposed on external excitations, which are characterized by time-dependent characteristics and causing nonstationary random oscillations. In this paper, the dynamics of high-speed rotating rotor is analytically and numerically analyzed. The analytical investigations studied the steady-state vibrations in the neighborhood of resonance conditions of a rotor with 6 degrees of freedom in linear homogeneous elastoviscous field. Unstable frequencies zones are determined by “limited” power of an electric motor with linear characteristic and only one time constant. The analytical solution of the differential equations is implemented applying Bogoliubov–Mitropolski's asymptotical method in neighborhood of resonances. The analytical solution verifies the numerical dynamic model derived using a general purpose program system for computer code generation of the dynamic equation and simulation of motion of multibody systems of rigid and flexible bodies. It is regarded an unbalanced rotor attached to a flexible shaft and operating in elastoviscous field. Examples of the rotor in elastoviscous field with clearances in the bearings are presented.