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

A new kinematic 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 con tact 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-de grees-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 h armonically driven transmission error excitation. From the free and forced vibration results, the unique elastic modes that contribute to the generati on of gear-mesh-induced vibrations are identified. The mesh force response function is also analyzed to examine the sensitivity of dynamic coupling an d vibratory response to critical design parameters. This study demonstrates the superiority of the proposed theory compared to the simpler gear-mesh r epresentations utilized in previous studies, and leads to the conclusion th at all 6 d.o.f.s of each gear body must be modelled explicitly. Numerous pa rametric studies are performed to quantify the dependence of vibration mode s and response trends to selected design values and operating conditions. ( C) 2001 Academic Press.