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

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