Modelling and Dynamic Analysis of the Spiral Bevel Gear-Shaft-Bearing-Gearbox Coupling System

To accurately study the dynamic characteristics of the spiral bevel gear transmission system in a helicopter tail transmission system, the finite element model of the gear shaft was established by a Timoshenko beam element, and the mechanical model of the spiral bevel gear was created by the lumped mass method. The substructure method is employed to extract the dynamic parameters from the gearbox's finite element model, and the dynamic model of the spiral bevel gear-shaft-bearing-gearbox coupling system was built according to the interface coordination conditions. In the model, the influences of time-varying stiffness, a time-varying transmission error, gearbox flexibility, unbalance excitation, and a flexible shaft and bearing support on the system vibration were taken into account simultaneously. On this basis, the dynamic differential equations of the full coupling system of the spiral bevel gear were derived, and the effects of the gearbox flexibility, the shaft angle, and the unbalance on the dynamic properties of the system were analysed. The results show that the gearbox flexibility can reduce the gear meshing force and bearing force, in which there is a more significant impact on the bearing force. The shaft angle affects the position, size, and direction of the system's axis trajectory. Meanwhile, the meshing force and the bearing force of the system are also varied because of the various pitch angles of the driving and driven gears under different shaft angles. The unbalance of the gear shaft has an effect on the vibration of the spiral bevel gear transmission system in all directions, wherein the influence on the torsional vibration is the most significant, and the influence increases as the unbalance rises. The unbalance of the gear shaft also affects the meshing force and bearing force, which increases as the rotational speed rises. This research provides a theoretical basis to optimize dynamic performance and reduce the vibration and noise of a spiral bevel gear full coupling system.