Stability of Geared Systems with Linear Suspension in Permanent Contact Regime

Abstract Many experimental, analytical, and numerical works have investigated the dynamic characteristics of geared transmission systems under constant speed and lightly loaded operational conditions. In such a condition, the internal and external excitation terms can easily cause the separation of the gears in mesh, followed by free play mode and impact phases, which introduce strong nonlinearity to the system. This is while, limited works have used analytical approach to investigate the dynamic behavior of the geared systems under constant speed and heavy-load operational condition, where the governing equations of the system reduce to linear periodic time-varying system of equations and the parametric resonance is the main source of Instability. In fact, large oscillations of such a system lead into the separation of the teeth in mesh, where the permanent contact assumption is not valid anymore and the effect of the backlash, free play mode, and impact phases must be considered. Consequently, in this study, lumped parameter analysis method is used to formulate the generalized dynamic model of a one-stage spur gear pair with linear suspension. Poincare-Lindstedt method is used to determine the range of the parameters in which the primary and combined parametric resonance would not happen, where the amplitude of the vibration remains small and the permanent contact condition between the teeth in mesh is satisfied. Afterward, numerical integration along with Floquet theory is used to validate the analytical results.