Non-linear compliance effect on the stability of drivelines including universal joints

摘要

Due to the presence of universal joints in drivelines, the driven shaft experiences time dependent moments and support reactions even when the driving shaft rotates at constant angular velocity. As a consequence of these time dependent loads, the driven shaft can experience instabilities. In previous analyses the compliant bearings were linearly modeled. Here an initial exploration of some effects of non-linear bearing compliance is presented. The bearing springs are taken to be weakly non-linear. The shafts are taken to be rigid with the driving shaft moving at constant angular velocity and the motion is restricted to one plane. The resulting differential equations are weakly non-linear and the method of multiple scales is used to obtain a set of "perturbation equations". Using these equations the stability of stationary solutions is investigated. Stability predictions from the linear model are compared with those given by direct numerical integration of the equations of motion of the non-linear model. It is found that unbounded response given by the linear model is bounded in the non-linear model predictions. Also, a new feature, not found in the linear model, is that there are multiple stable stationary solutions.