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Advances in Acoustics and Vibration
Volume 2011 (2011), Article ID 583678, 13 pages
Research Article

On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

1Advanced Components Systems Division, Caterpillar Inc., Peoria, IL 61630, USA
2Mechanical Engineering Program, School of Dynamic Systems, University of Cincinnati, 598 Rhodes Hall, P.O. Box 210072, Cincinnati, OH 45221, USA

Received 27 October 2010; Revised 10 March 2011; Accepted 17 March 2011

Academic Editor: Mohammad Tawfik

Copyright © 2011 Jun Wang and Teik C. Lim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A nonlinear time-varying (NLTV) dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.