Vibration analysis of hypoid transmissions applying an exact geometry-based gear mesh theory

A new kinetic model based on exact gear geometry that is derivable from a set of manufacturing parameters is developed for analyzing the hypoid gear-mesh-coupling mechanism. The approach involves a discretization of the contact lines in the plane of action assuming an unperturbed quasi-static gear meshing state to obtain the effective mesh excitation and position vectors. This mesh formulation forms the basis for a three-dimensional multiple-degrees-of-freedom (d.o.f.s) dynamic model of the hypoid gear pair, which is used to simulate the rotation and translation response spectra due to the harmonically driven transmission error excitation. From the free and forced vibration results, the unique elastic modes that contribute to the generation of gear-mesh-induced vibrations are identified. The mesh force response function is also analyzed to examine the sensitivity of dynamic coupling and vibratory response to critical design parameters. This study demonstrates the superiority of the proposed theory compared to the simpler gear-mesh representations utilized in previous studies, and leads to the conclusion that all 6 d.o.f.s of each gear body must be modelled explicitly. Numerous parametric studies are performed to quantify the dependence of vibration modes and response trends to selected design values and operating conditions.