Pitchfork and Hopf bifurcations of geared systems with nonlinear suspension in permanent contact regime

Abstract

Noname manuscript No.

Nonlinear Dynamics of a Multi-shaft Gear System in Parameter-state Space

“…Sheng [7] used the Runge-kutta numerical integration method to solve the differential equation of planetary gear train motion, analyzed the influence of meshing frequency, meshing clearance, bearing clearance and other nonlinear parameters on the bifurcation and chaotic characteristics, and discussed the coupling effect of clearance on the nonlinear behavior of the system. Azimi [8] used the Poincare-Lindstedt method to study the dynamical parametric response of a one-stage spur gear pair with nonlinear suspension. It was found that pitchfork bifurcation and hopf bifurcation occurred around the primary and combination parametrically unstable tongues as the control parameters and meshing frequency varied and suggested that the selection of suitable suspension parameters could effectively prevent gear mesh-apart.…”

Vibro-impact dynamics of large-scale geared systems

“…Most nonlinear gear dynamics studies in the literature resort to using lumped parameter, torsional models of the gear pair without considering the flexibility of other components [25,17,20,7], although some consider the bearings [33,3] and the shafts with a lumped torsional stiffness [19,22]. Such models are limited to a single, up to a dozen of degrees of freedom (DoF) and are quite restrictive in their assumptions.…”