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Considering the elasticity of gear solid bodies, the load applied to gear teeth will force theoretically separated gear teeth to get into engaging state in advance. This phenomenon is named as the extended tooth contact (ETC). Effects of the ETC directly influence the time-varying mesh stiffness of gear pairs and subsequently alter nonlinear dynamic characteristics of gear transmission systems. Time-vary mesh stiffness, considering effects of the ETC, is thus introduced into the dynamic model of the gear transmission system. Periodic motions of a gear transmission system are discussed in detail in this work. The analytical model of time-varying mesh stiffness with effects of the ETC is proposed, and the effectiveness of the analytical model is demonstrated in comparison with finite element (FE) results. The gear transmission system is simplified as a single degree-of-freedom (DOF) model system by employing the lumped mass method. The correctness of the dynamic model is verified in comparison with experimental results. An incremental harmonic balance (IHB) method is modified to obtain periodic responses of the gear transmission system. The improved Floquet theory is employed to determine the stability and bifurcation of the periodic responses of the gear transmission system. Some interesting phenomena exist in the periodic responses consisting of “softening-spring” behaviors, jump phenomena, primary resonances (PRs), and super-harmonic resonances (SP-HRs), and saddle-node bifurcations are observed. Especially, effects of loads on unstable regions, amplitudes, and positions of bifurcation points of frequency response curves are revealed. Analytical results obtained by the IHB method match very well with those from numerical integration.
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This content will become publicly available on December 1, 2026
Mesh Stiffness Calculation and Error Analysis: Hypoid Gear Pair and System
Abstract Accurate mesh stiffness calculation is crucial for developing reliable dynamic models and analyzing vibratory behavior in hypoid gears. Current studies often use a hypoid gear pair, incorporating the misalignment effects of the hypoid gear system model, as a substitute for the full hypoid gear system model to reduce simulation costs. However, this simplification overlooks the boundary problem, particularly the influence of housing on the hypoid gear system. This discrepancy can lead to deviations in mesh stiffness calculation and affect the accuracy of dynamic response predictions. To address this issue, we established a three-dimensional static mesh model to calculate the mesh stiffness under different boundary conditions, i.e., the gear pair model constrained at the base and the gear system model constrained at the housing, based on finite element results. Then, we introduce a 14-degree-of-freedom dynamic model to examine the influence of mesh stiffness differences on system dynamics. Finally, a numerical case study evaluates key factors, including unloaded and loaded transmission error, mesh points, line of action, and static mesh force, to assess their impact on mesh stiffness and the resultant impact on dynamic behavior. The findings provide insights into the selection of an appropriate calculation model for accurate gear design and simulation.
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- Award ID(s):
- 2238269
- PAR ID:
- 10659215
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Vibration and Acoustics
- Volume:
- 147
- Issue:
- 6
- ISSN:
- 1048-9002
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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