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 (Eritenel, T., and Parker, R. G., 2013, “Nonlinear Vibration of Gears With Tooth Surface Modifications,” ASME J. Vib. Acoust., 135(5), p. 051005) where the dynamic force at the mating gear teeth is determined from precalculated static results based on the instantaneous mesh deflection and position in the mesh cycle. The HAC method merges this calculation of the contact force based on an underlying finite element static analysis into a numerical integration of an analytical vibration model. 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 (FDF) that is generated from a series of static finite element analyses performed before the dynamic calculations. Incomplete tooth contact and partial contact loss are captured by the static finite element analyses and included in the FDF, 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. Accelerating gears and transient situations can be analyzed. 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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February 2019
Research-Article
An Efficient Hybrid Analytical-Computational Method for Nonlinear Vibration of Spur Gear Pairs
Xiang Dai,
Xiang Dai
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
Virginia Tech,
Blacksburg, VA 24061
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Christopher G. Cooley,
Christopher G. Cooley
Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
and Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
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Robert G. Parker
Robert G. Parker
Search for other works by this author on:
Xiang Dai
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
Virginia Tech,
Blacksburg, VA 24061
Christopher G. Cooley
Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
and Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
Robert G. Parker
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 6, 2017; final manuscript received June 25, 2018; published online August 13, 2018. Assoc. Editor: Karsten Stahl.
J. Vib. Acoust. Feb 2019, 141(1): 011006 (13 pages)
Published Online: August 13, 2018
Article history
Received:
September 6, 2017
Revised:
June 25, 2018
Citation
Dai, X., Cooley, C. G., and Parker, R. G. (August 13, 2018). "An Efficient Hybrid Analytical-Computational Method for Nonlinear Vibration of Spur Gear Pairs." ASME. J. Vib. Acoust. February 2019; 141(1): 011006. https://doi.org/10.1115/1.4040674
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