Development of a Dynamic Model for Calculating the Kinematic Error and Evaluating Its Effect on the Efficiency of Planetary Mechanisms With Rolling Bodies

Abstract

When studying the characteristics of the mechanisms of small-sized drives, an important task is to develop ways to increase the efficiency of the mechanism. The article discusses theoretical issues related to the influence assessment of kinematic error on the efficiency of gears with rolling bodies. As a result of the research, a generalized dynamic model of planetary ball and roller mechanisms is obtained, taking into account kinematic errors, linking manufacturing errors or elastic deformations and kinematic transmission error. Mathematical dependences of the dynamic model of mechanisms with rolling bodies are derived. The model was tested on the example of calculating the kinematic error of a single-stage planetary ball transmission. Polynomial equations with constant coefficients are obtained for determining kinematic errors from the influence of manufacturing errors of transmission links. It is established that for different kinematic schemes, gear ratios and angular velocities of planetary mechanisms with rolling bodies, the transmission efficiency can vary significantly depending on its kinematic error. For gear ratios from 1.5 to 5, drive shaft rotation speeds from 1,500 to 3,000 rpm, depending on the highest values of the kinematic error from 0.00175 to 0.0349 radians, the transmission efficiency within the driven shaft rotation can decrease from 0.93 to 11 %. At the same time, transmissions constructed according to the sixth kinematic scheme have the highest efficiency values. The average efficiency value per revolution of the driven shaft from the influence of kinematic errors can decrease up to 5 %. Graphs of the dependences of transmission efficiency on their kinematic errors are given.