Parametric stability of geared systems with linear suspension in permanent contact regime

Abstract

The prediction and control of excessive vibration are one of the most important concerns in the design and development of geared systems. For any gear set, parametric resonance is the main source of instability, resulting in the separation of gears in mesh and chaotic behavior. In many works, gears are modeled with rigid mountings, and various analytical and numerical approaches have been used to investigate the dynamic characteristics of the system in different regimes: permanent contact (no impact), free play, single-sided impact, and double-sided impact. Alternatively, in other works, the effect of the deformation of the mountings is included in the dynamic modeling; in almost all these studies, the dynamic characteristic of the system is investigated through direct numerical integration of the governing differential equations, and there is no analytical work to determine the effect of suspension on the parametric resonance of the system. Consequently, in this work, both analytical and numerical approaches, including the Poincare–Lindstedt method and Floquet theory, are used to investigate the dynamic characteristics of a one-stage spur gear pair with linear suspension in the permanent contact regime. It has been shown that, unlike systems with rigid mounting that have one set of unstable tongues, systems with suspension have three sets of unstable tongues. The results show that the additional sets of unstable tongues appear at higher parametric frequencies. Therefore, the rigid mounting assumption is accurate only for systems operating at low speeds; for systems operating at high speeds, the deformation of the suspension must be included in the dynamic modeling, as it significantly contributes to the parametric instability of the system.