Shi, Z. and Lim, T., "Nonlinear Time-Varying Dynamic Interactions of Hypoid Gear-Shaft-Bearing Systems," SAE Int. J. Veh. Dyn., Stab., and NVH 1(2):372-383, 2017.
Nonlinear interaction between time-varying hypoid gear mesh and bearing support is investigated in this study. Mesh parameters are time-varying due to complex tooth profile of hypoid gear. Bearing stiffness is formulated based on real geometry and instantaneous orbital position of rolling elements. Linear model is firstly analyzed to study the modal frequency and mode shape variations under different stiffness ratio between gear mesh and bearing support. Then, nonlinear analysis is conducted to compare the differences between linear and nonlinear dynamic response based on specific nonlinear conditions of geared rotor system. It is found that the coupling between hypoid gear mesh and bearing support can be either strong or weak depending on the ratio between mesh stiffness along line-of-action (LOA) and bearing stiffness in radial direction. Parametric studies indicate that dynamic mesh force is sensitive to bearing clearance for certain stiffness ratio. Spectrum analysis further reveals complex nonlinear behavior due to loss of contact between meshing gear teeth. Dynamic force changes on actual bearing locations due to bearing clearance are evaluated. It is found that bearing radial clearance has influence on structure-borne noise transmission for a complete hypoid gear transmission system due to its effect on gear dynamic response and actual bearing loads.