Torsional Instabilities in a System Incorporating a Hooke’s Joint

Dynamic stability analysis of a driveline which incorporates a Hooke’s joint is presented in this paper. In particular, torsional instabilities due to fluctuating angular velocity ratio across the joint are examined. The method of averaging is used to establish the critical speed ranges by considering the linearized equations which govern the torsional motion of the system. Within these ranges, parametric instability characterized by exponential build up of response amplitudes of the torsional modes occur. Closed form conditions for onset of sub-harmonic as well as sum-type combination resonance have been established. The significance of the sum-type combination resonance in a typical diesel hydraulic locomotive driveline has been demonstrated. Difference-type combination resonance has been shown to be absent. The instability conditions indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke’s joint.