Abstract
A mathematical model is developed which couples the torsional oscillation of the driveline, the vertical and longitudinal vibration of a vehicle. It is used in analysing the stability of self-excited torsional oscillation of the driveline. This mathematical model is represented as a matrix equation with nonlinear characteristics. By means of a linearisation method in the vicinity of the static equilibrium positions of the lumped masses, the nonlinear equation is changed into a linear matrix equation. Complex eigenvalues and eigenvectors of the equation in state space are calculated under the state of the damped free vibration. Results indicate that two complex eigenvalues that correspond to two torsional oscillation modes of the driveline are of positive real parts, which makes the torsional oscillation modes of the driveline unsteady and leads to the occurrence of the self-excited oscillation of the driveline. Effects of the structural parameters on the torsional oscillation stability are discussed. It is deduced, further, that critical steady curve plane (CSCP for short) can be used to determine the stability of the vehicle system when the external parameters are assigned the different values. The above research provides a basis for refinement and optimisation of vehicle design.
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