Vibration of Flexible Rotor Driven by Limited Torque through Its Critical Speed

Abstract

Analysis of vibration of a flexible rotor driven by limited torque through its critical speed is an important subject as rotating machines speed up. But a method of this analysis has not been established. In this study the method of the vibration analysis on a linear asymmetrical flexible rotor having an arbitrary distributed mass is presented. Equations of motion are written in the form of partial integro-differential equations. They are transformed to nonlinear simultaneous ordinary differential equations by the method of series expansion by eigenfunctions. These equations are solved by application of the asymptotic method and the averaging method assuming that asymmetry of the rotor, internal and external resistance coefficients, eccentricity and angular acceleration are small. The results of numerical calculation show that the amplitude through the critical speed increases as (1) the moment of inertia of the rotor is larger, (2) the incline of the torque-angular velocity curve is smaller.