Modeling and vibration analysis of flexible robot arm under fast motion in consideration of nonlinearity

Abstract

This paper deals with a problem of modeling and vibration analysis of a high speed rotating flexible manipulator. Conventional method of modeling does not exactly express the bending mechanism of flexible arm. Then a new description of deformation on the flexible shaft and Hamilton's principle are used to derive the dynamic model of the rigid-flexible manipulator. A nonlinear dynamic model is proposed to describe the dynamic behavior of flexible arm and the dynamic equations of the system are also presented. Derived equations consist of some nonlinear forces and geometrical nonlinear stiffness. The present research considers the effect from those nonlinear forces coupling with angular functions (angular position, velocity, acceleration). An external forced vibration method is applied to evaluate the characteristics of flexible vibration. In this research, numerical calculations based on two strategies are applied to analyze the flexible vibration. In the first strategy (AIM, angle independent method), angles of joints are assumed to be independent of the external forces. In the second strategy (ADM, angle dependent method), the effect on the angular functions of joints due to the external forces is considered. Especially, the gravity force affects significantly on the residual deflection of flexible arm and on the angular functions.