Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system

Abstract Frequency response characteristics of a non-linear geared rotor-bearing system with time-varying mesh stiffness k h ( t ) are examined in this paper. First, the single-degree-of-freedom spur gear pair model with backlash is extended to include sinusoidal or periodic mesh stiffness k h ( t ) . Second, a three-degree-of-freedom model with k h ( t ) and clearance non-lineariries associated with gear backlash and rolling element bearings, as excited by the static transmission error e ( t ) under a mean torque load, is developed. The governing equations are solved using digital simulation technique and only the primary resonances are studied. Resonances of the corresponding linear time-varying system associated with parametric and external excitations are identified using the method of multiple scales and digital simulation. Interactions between the mesh stiffness variation and clearance non-linearities have been investigated; a strong interaction between time-varying mesh stiffness k h ( t ) and gear backlash is found, whereas the coupling between k h ( t ) and bearing non-linearities is weak. Finally, our time-varying non-linear formulations yield reasonably good predictions when compared with the benchmark experimental results available in the literature.