Tripod and Ball Joint Automotive Transmission Kinetostatic Model Including Friction

Abstract

This paper deals with a mechanical model of an automotive transmissionconsisting of a plunging tripod joint close to the gearbox and a balljoint close to the wheel. Both joints are connected by an intermediateshaft. The ball joint is modelled as a constant velocity (CVJ) andfrictionless joint. Due to the plunging movement, the tripod joint isnot a true CVJ but may be modelled as a perturbed CVJ. To avoidnumerical solutions, approximated analytic kinematical equations arederived. Then, it is shown that for a constant input velocity, dynamicaleffects due to the tripod joint are negligible versus static effects.Accordingly, an inverse kinetostatic model with a constant inputvelocity and a constant output torque is introduced. Friction betweenthe rollers and the tulip ramps and between the rollers and thetrunnions is modelled using a viscous or a Coulomb approach. For viscousfriction, analytic expressions of forces and torque's are provided andnumerical simulations are presented to validate these results. ForCoulomb friction only numerical results are available. In particular, itis shown that viscous friction alone cannot generate shudder vibrations.