Influence of gyroscopic effect on hypoid and bevel geared system dynamics

The noise and vibration response of hypoid or bevel geared rotor system, primarily excited by transmission error (TE), and mesh vector and stiffness variations, can be affected significantly by the coupling between the driveline rotor dynamics and gear vibratory response. This is because of the inherent design comprising of non-parallel rotational axes and time-varying as well as spatial-varying gear mesh characteristics. One of the important factors of the driveline system dynamics is the rotor gyroscopic effect that has not been studied extensively in traditional gear dynamics. To address this gap in the literature, this paper attempts to examine the influence of incorporating gyroscopic terms in the hypoid gear dynamic simulation. A multi-degrees-of-freedom, multi-body dynamic model is used as a generalized representation of a hypoid geared rotor system. The gyroscopic matrices are introduced to formulate both the linear time-invariant (LTI) and nonlinear time-varying (NLTV) dynamic equations. The system vibratory responses are solved in the frequency domain for LTI model and through time domain numerical integration for NLTV model. The results are compared to those calculations obtained from the traditional models without including the gyroscopic effect. The influence of gyroscopic behavior on the typical hypoid gear dynamic response is analyzed and the condition where the gyroscopic effect needs concern or can be neglected is revealed.