DYNAMIC STABILITY OF A ROTATING SHAFT DRIVEN THROUGH A UNIVERSAL JOINT

Abstract

The dynamic stability of a system composed of driving and driven shafts connected by a universal joint is investigated. Due to the characteristics of the joint, even if the driving shaft experiences constant torque and rotational speed, the driven shaft experiences fluctuating rotational speed, bending moments and torque. These are sources of potential parametric, forced and flutter type instabilities. The focus of this work is on the lateral instabilities of the driven shaft. Two distinct models are developed, namely, a rigid body model (linear and non-linear) and a flexible model (linear). The driven shaft is taken to be pinned at the joint end and to be resting on a compliant damped bearing at the other end. Both models lead to sets of differential equations with time dependent coefficients. For both rigid (linear and non-linear) and flexible models, flutter instabilities were found but occurred outside the practical range of operation (rotational speed and torque) for lightly damped systems. Parametric instability charts were obtained by using the monodromy matrix technique for both rigid and flexible linear models. The transmitted bending moments were found to cause strong parametric instabilities in the system. By comparing the results from the two linear models, it is shown that the inclusion of flexibility leads to new zones of instability, not predicted by previous models. These zones, depending on the physical parameters of the system, can occur for practical conditions of operation. Using direct numerical integration for a few sets of specific parameter values, forced resonances were found when the rotational speed reached a value equal to a natural frequency of the system divided by two.