A static and dynamic model of a three-dimensional (3-D) helical gear pair is presented and extended to multi-mesh gear systems. The gear bodies are assumed to be rigid cylinders mounted on linear stiffnesses representing the bearings/housing. The mesh model is formulated by dividing each theoretical contact line into multiple contact segments. A deflection function that incorporates tooth modifications and six degree of freedom (DOF) gear motion is defined for each contact segment. This deflection function determines whether individual contact segments are in contact or not, and, if so, what mesh force exists at that segment. The net forces and moments of these contact segments provide a multi-dimensional mesh force vector that draws gear tilting into the six DOF vibration. These contact segments form a network of springs that eliminates the need to solve a detailed contact problem, albeit at the cost of some accuracy as compared to more complex 3-D gear models. Stiffness values of these springs are obtained from a commercial finite element (FE) program specifically designed for gears. Misalignments and lead/profile modifications can be modeled included in the analytical model without further reference to the FE software. This approach is expected to be more accurate than transmission error (TE) excited 3-D dynamic models that use the static load distribution and pre-specified variable mesh stiffness. The model is validated against FE software for static analysis of a helical gear pair. The model is used to compare the 3-D vibration modes of a helical and a spur idler gear system. The dynamic behavior near resonance and occurrence of nonlinear contact loss is investigated.
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