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Due to the design of lightweight, high speed driveline system, the coupled bending and torsional vibration and rotordynamics must be considered to predict vibratory responses more realistically. In the current analysis, a lumped parameter model of the propeller shaft is developed with Timoshenko beam elements, which includes the effect of rotary inertia and shear deformation. The propeller shaft model is then coupled with a hypoid gear pair representation using the component mode synthesis approach. In the proposed formulation, the gyroscopic effect of both the gear and propeller shaft is considered. The simulation results show that the interaction between gear gyroscopic effect and propeller shaft bending flexibility has considerable influence on the gear dynamic mesh responses around bending resonances, whereas the torsional modes still dominate in the overall frequency spectrum.

A multi-point hypoid gear mesh model based on 3-dimensional loaded tooth contact analysis is incorporated into a coupled multi-body dynamic and vibration hypoid gear model to predict more detailed dynamic behavior of each tooth pair. To validate the accuracy of the proposed model, the time-averaged mesh parameters are applied to linear time-invariant (LTI) analysis and the dynamic responses, such as dynamic mesh force, dynamic transmission error, are computed, which demonstrates good agreement with that predicted by single-point mesh model. Furthermore, a nonlinear time-varying (NLTV) dynamic analysis is performed considering the effect of backlash nonlinearity and time-varying mesh parameters, such as mesh stiffness, transmission error, mesh point and line-of-action. Simulation results show that the time history of the mesh parameters and dynamic mesh force for each pair of teeth within a full engagement cycle can be simulated.