An Efficient Hybrid Analytical-Computational Method for Nonlinear Vibration of Spur Gear Pairs

[+] Author and Article Information
Xiang Dai

Virginia Tech, Blacksburg, VA, USA

Christopher G. Cooley

Southern Illinois University Carbondale, Carbondale, IL, USA

Robert Parker

Virginia Tech, Blacksburg, VA, USA

1Corresponding author.

ASME doi:10.1115/1.4040674 History: Received September 06, 2017; Revised June 25, 2018


This work develops a hybrid analytical-computational (HAC) method for nonlinear dynamic response in spur gear pairs. The formulation adopts a contact model developed in [1] whereby the dynamic force at the mating gear teeth is determined from pre-calculated static results based on the instantaneous mesh deflection and position in the mesh cycle. The HAC method merges this analytical contact force model with an underlying finite element code. The gear translational and rotational vibrations are calculated from a lumped-parameter analytical model where the crucial dynamic mesh force is calculated using a force-deflection function that is generated from a series of static finite element analyses before the dynamic calculations. Incomplete tooth contact and partial contact loss are captured by the static finite element analyses and included in the force-deflection function, as are tooth modifications. In contrast to typical lumped-parameter models elastic deformations of the gear teeth, including the tooth root strains and contact stresses, are calculated. Comparisons with finite element calculations and available experiments validate the HAC model in predicting the dynamic response of spur gear pairs, including for resonant gear speeds when high amplitude vibrations are excited and contact loss occurs. The HAC model is five orders of magnitude faster than the underlying finite element code with almost no loss of accuracy.

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