Nonlinear vibration mechanism of elastic beam in large overall rotation with rotor eccentricity effect

Abstract

The eccentric effect of rotor has seriously affected on the stability and precision of the mechanism at high speed for light and flexible mechanism in industrial application. The analysis of nonlinear vibration mechanism must be completed to realize precision and stable control of elastic beam in a large overall rotation. Firstly, the slender flexible rod is assumed as Euler-Bernoulli beam. We apply the deformation theory of elastic beam to establish its kinematic constraint relationship. Its dynamic model is built with Galerkin method and Hamilton principle. Then the Lagrange method is used to establish the rotor dynamics model based on the Jeffcott rotor. The coupling part between the motor and the elastic beam is assumed to be rigidly connected, and the dynamic model of the motor-elastic beam system can be obtained. Lastly, we analyze the nonlinear vibration mechanism of the elastic beam with rotor eccentricity effect through applying the fourth-order Runge-Kutta method and the superposition principle of traveling wave. It provides an important theoretical basis for making an effective vibration suppression strategy for elastic beam.