Dynamics of an automotive transmission consisting of a tripod joint and a ball joint. A symbolic approach

Abstract

The present paper deals with the zero friction dynamics of an automotive transmission consisting of an inboard ball joint close to the wheel and an outboard tripod joint close to the gearbox, connected by an intermediate shaft. The ball joint is a constant-velocity joint (CVJ) whereas the tripod joint is not. In the idealized case of an intermediate shaft of infinite length, the tripod joint behaves like a CVJ and has the following properties: the input and output torque are equal, the transverse forces generating the output torque are equal and there are no shudder vibrations or inertial shaft effects. For a real transmission with a finite-length shaft, deviations from constant-velocity (CV) properties are due to tripod joint angle variation which causes static and dynamic perturbations; these perturbations are expressed symbolically using first-order approximations in terms of tripod joint angle and ratio of shaft length to tulip radius. For most of the front drive cars equipped, the angle of the tripod joint remains close to 0.1 rad; considering a constant input torque at a 100rad/s input velocity, the perturbations are found to be less than 3 per cent for the driving forces when compared with the CVJ.