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

Abstract

Gears are important mechanical parts with various industrial applications. Many researchers have investigated the complex nonlinear behavior of geared systems by studying the effect of time-varying mesh stiffness, clearance between the gears in mesh, radial clearance in the bearings, and bending of the supporting shafts. Most of these studies assume that the gear set operates under lightly loaded operational conditions, where the separation of the teeth in mesh occurs and the nonlinearity caused by the clearance between the gears in mesh has the major influence on the dynamic response of the system. Alternatively, in this work it is assumed that the transmitting load is great enough that gears in mesh do not separate, and consequently the clearance between the teeth does not participate in the dynamic response of the system. Then analytical and numerical techniques are used specifically to investigate the effect of the nonlinearity of the shafts on the dynamic behavior of the system. The results show that the nonlinear suspension has a significant influence on the creation of nontrivial equilibria and limit cycle within the parametrically unstable tongues which, for the right range of the parameters, can affect the rate of amplitude detonation and stabilization of the system.