Stability Analysis of Planetary Rotor with Variable Speed Self Rotation and Uniform Eccentric Revolution in the Rubber Tapping Machinery

Abstract

Natural rubber is a critical material that is essential to industry and transportation. In order to reduce the cost of rubber tapping and improve the efficiency and profitability of rubber production, the 4GXJ-2 portable electric rubber cutter and automatic rubber tapping robot have been developed. In their vibration tool holder, the planetary rotor with variable speed self rotation and uniform eccentric revolution is the most important transmission component, and its instability will cause irregular vibration of the tapping tool, thereby reducing the accuracy of vibration cutting and increasing noise. Base on the ANCF (Absolute Nodal Coordinate Formulation) 3D-beam element and 3D REF (3D Ring on Elastic Foundation), a novel eccentric 3D REF model of a planetary rotor is proposed. By introducing multiple coordinate systems, the coupled motion of uniform eccentric revolution, variable speed self rotation and flexible deformation is decomposed and the influences of these motions on the centrifugal force and Coriolis force are more clearly derived. The model is degraded and validated by comparing with other examples of a rotating circular ring model and uniformly eccentrically revolving annular plate. According to the Floquet theory and Runge−Kutta method, the unstable region of revolution speed of a planetary rotor in rubber tapping machinery is predicted as [817 rad/s, 909 rad/s], [1017 rad/s, 1095 rad/s] and [1263 rad/s,1312 rad/s]. Compared with the rubber-tapping experiment of rubber tapping machinery, the validity of the proposed model is further verified. This model provides important design references for the speed settings of those rubber tapping machines.