Passage through resonance in a universal joint driveline system

Abstract

A driving shaft coupled to a driven shaft by a universal joint is considered. The shafts are taken to be rigid and motion is restricted to one plane. The non-homogeneous differential equation of motion has time-dependent coefficients and both parametric and forced resonances can occur. Here the question of whether one can ‘‘drive’’ through the resonances using a driving angular velocity linear variation is addressed. Also, how long can one ‘‘dwell’’ at a potential resonance before actually encountering it is investigated. Numerical studies led to the following conclusions. For linearly increasing speed profiles no practically feasible sweep rates to avoid resonance build up were found for the forced motion resonances. For certain torque and damping values, parametric resonances are seen for slow angular velocity variations but they are not observed for practically feasible fast variations, thus raising the possibility that one can accelerate through them. For a trapezoidal speed input the dwell time is key in building up instabilities. As the dwell time increases larger response amplification is observed. For the case studied, it was shown that it is possible to drive through the instability if the dwell time is equal to or less than forty times the period of the parametric excitation.