Multi-state meshing dynamics modeling and analysis of an internal meshing spur gear system based on the Johnson contact model

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (18) : 54-62.

MA Xiaojing1，SHI Jianfei1，ZHANG Tianlin2，DANG Xingwu1，ZHANG Li1

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Abstract

The accurate explanation of the tooth deregulation or back meshing induced by the backlash can provide theoretical guidance for the optimal design of the gear structure. Based on the Johnson contact force model, the dynamic meshing force calculation model of involute internal meshing spur gear transmission system is constructed, which takes into account the time-varying backlash and energy dissipation in the meshing process, according to the meshing principle of internal meshing spur gear and the force of gear teeth, the meshing process is decomposed, and the nonlinear dynamic model of involute internal meshing spur gear system with five meshing states under time-varying backlash is established. Five different Poincaré maps are constructed to clarify the characteristics of five-state meshing behavior, and the generation mechanism of multi-state meshing behavior of the system is revealed by phase diagram and dynamic meshing force time history diagram. The results show that with the gradual increase of the meshing frequency, the single-tooth and double-tooth surface meshing occurs in the system, and the sudden change of the dynamic meshing force in the direction leads to the meshing between the gear teeth and the back of the single-tooth and double-tooth, resulting in the impact vibration behavior between the gear teeth. Even if the system shows a stable meshing state, the single and double teeth dismeshing still occurs. The previous dynamic model of internal meshing gear system can not reveal its multi-state meshing characteristics. Aiming at the multi-state meshing behavior, this paper analyzes the nonlinear vibration characteristics of internal meshing gear transmission cycle.

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internal meshing spur gear / multi-state meshing behavior / dynamic meshing force / nonlinear vibration

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MA Xiaojing1，SHI Jianfei1，ZHANG Tianlin2，DANG Xingwu1，ZHANG Li1. Multi-state meshing dynamics modeling and analysis of an internal meshing spur gear system based on the Johnson contact model[J]. Journal of Vibration and Shock, 2023, 42(18): 54-62

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