Analysis of the dynamic characteristics of the model of an energy cumulation system with composite flywheel. 4. Forced vibrations

Abstract

1. We conclude the examination of the dynamic properties of the model of an energy cumulation system [1-3] by an analysis of its forced vibrations. The main source of such vibration are linear and angular eccentricities of the flywheel shaft and rim. As before we will regard the rim as absolutely rigid. This is based, in addition to its being massive, on the circumstance that on account of eccentricity it is impossible to excite in the rim vibrations other than the first form (as a rigid whole) since they all are symmetric [4] and yield a zero resultant of interaction with the shaft through a symmetric joint. Therefore, like in [1-3], we deal with a system of two masses consisting of a vertically arranged rigid rim and shaft in which the rim is connected with the shaft by an elastic joint, and the shaft runs in elastic damping bearings. A special trait of the system is that for technical considerations external damping can be effected solely in relation to the shaft. The effectiveness of its influence on the vibrations of the rim is determined by the parameters of the system which to some extent can be controlled, in particular: the mass and moment of inertia of the shaft and of the rigid supports. An analysis of the influence of these parameters on the amplitudes of the damped resonance vibrations, the forces in the supports, and the loads in the joint of rim and shaft is the aim of the present work. 2. When we complement the system of equations from [3] with the load induced by the radial and angular eccentricity of the rim and shaft, we obtain the system of dimensionless equations in complex form z~ + (C:l~ - io~a~) ~ +/~ (1 + K) Z~ -/2 Z2 = ~2 (1 - a,) r~ e ~' ; }, - i a2 ~ Z2 + Z2 - Zl = ~2 (1 - a2) r2 e' (~' + e)