Resonant Oscillations of Non-Symmetrical Rotor with Mass Imbalance and Disk Skew

Abstract

The non-symmetrical rotor with mass imbalance and disk skew has been considered. For full description of the rotor motion dynamic and mathematical models of the machine have been developed. Expressions for Lagrangian functions and Rayleigh dissipative function are formed. The motion equations are written as the Lagrangian equations of the second kind. By separation of variables the expressions of amplitude and phase of vibrations have been determined. The special emphasis is placed to the joint effect of mass imbalance and disk skew on the rotor dynamics which is observed over the whole range of shaft speed. The amplitudes of the vibrations near the critical speeds and residual phase angle depending on the generalized imbalance and the relative distance to the disk are studied. Detection of the residual phase angle at low rotation speeds is of practical importance, it is extremely important at balancing the rotor, since for determination of the mass eccentricity line the results of measurements at low speeds are used. The main working expressions are presented in a compact and non-dimensional form.