Analytical Rotordynamic Study of a High-Speed Gear Transmission System for Race Applications

In motorsport power transmission systems, high-speed operation can be associated with significant rotordynamic effects. Changes in the natural frequencies of lateral (bending) vibrational modes as a function of spin speed are brought about by gyroscopic action linked to flexible shafts and mounted gear components. In the investigation of high-speed systems, it is important that these effects are included in the analysis in order to accurately predict the critical speeds encountered due to the action of the gear mesh and other sources of excitation. The rotordynamic behaviour of the system can interact with crucial physical parameters of the transmission, such as the stiffnesses of the gear mesh and rolling element-to-raceway contact in the bearings. In addition, the presence of the gear mesh acts to couple the lateral and torsional vibration modes of a dual-shaft transmission through which a torque flows. The relative interactions and effects of bearing and gear components can be captured in the form of modal analysis with parametric studies of key stiffness elements, such as mean value as a linear representation of stiffness. In the presented study, an analytical finite element method is followed in order to construct the mass, stiffness, damping and gyroscopic terms. In this method, the shafts are comprised of flexible elements with distributed mass, the gears are represented by disks of lumped mass and inertia, and the bearings are elements of no mass and multi-directional stiffness. The lateral, torsional and coupled vibrational modes of the system are solved and studied parametrically.