Optimal determination of stability domains of vibrations in gear drives

Abstract

The article deals with the optimization of stable vibration zones of a two-stage gearbox with parametric excitation as a consequence of periodically variable tooth stiffness during meshing. In order to ensure a calm running of the gearbox and to reduce noise, we want to minimize the vibration instability zone in the gearbox design process. The reduction of individual instability zone is largely influenced by the contact ratio of each gear pair and their phase shift. Unfortunately, as one unstable area decreases, other unstable areas can increase. This raises the need to find the optimal solution that can be provided by solving the multi-criteria optimization problem. The article presents the multi-criteria optimization of gear vibration stability zones by using the Weighted Sum Method and the ε-Constraint Method, respectively. The results of multicriteria optimization of stability zones in the article are analytically explained. Both multi-criteria optimization methods are presented in the article for a two-stage, three-gear gearbox with the same meshing frequencies.