Abstract
Teeth disengagement or back-side teeth engagement induced by backlash reduces the transmission quality and dynamic performance of gear systems, and the accurate interpretation of multi-state meshing behavior can provide guidance for structural optimization and performance evaluation. Therefore, the multi-state meshing behavior of the gear system is elaborated. A new nonlinear dynamic model of a spur gear system with five-state meshing behavior is established based on the time-varying backlash and contact ratio. The time-varying meshing stiffness and time-varying backlash considering the elastic contact of gear teeth, gear temperature rise and lubrication are included in the model. The five-state meshing behavior is clearly characterized by constructing five Poincaré maps, and its generation mechanism is revealed using dynamic meshing force time history, teeth relative displacement time history and phase portrait. The bifurcation and evolution of five-state meshing behavior are analyzed under the effects of load factor, meshing frequency and error coefficient. The results show that the mutation in the direction of dynamic meshing force leads to teeth disengaging and back-side single- or double-tooth contact, forming multi-state meshing behavior. Bifurcation caused by parameter changes greatly affects the evolution of five-state meshing behavior, particularly grazing bifurcation can decrease the number of teeth disengagement. Chaotic behavior or trajectory expansion inspires multi-state meshing vibration of the system. Previous gear system models could not reveal these phenomena due to ignoring the multi-state meshing behavior.
Highlights
Gear transmission is a basic key component for transmitting motion and power in mechanical equipment, and is commonly used in critical fields such as aviation, ships, vehicles, wind power generation, and manufacturing
Accurate elaboration of gear-tooth contact characteristics is the basis of dynamic modeling and analysis of gear systems [5,6,7]
Based on the time-varying backlash model, this paper proposes a new nonlinear dynamic model of the involute spur gear system including five-state meshing behavior, such as single-tooth drive-side meshing, double-teeth drive-side meshing, teeth disengaging, single-tooth back-side meshing and double-teeth back-side meshing
Summary
Time-varying backlash can identify multi-state meshing behavior of spur gear system. The elastic deformation of gear tooth and the deformation of the oil film thickness increase backlash, and the thermal deformation of tooth reduces backlash. D(t) is a time variable caused by the elastic deformation and thermal deformation of gear teeth as well as the oil film thickness deformation at the meshing point. The time-varying backlash in the single-tooth area is greater than the one in the double-teeth areas. Half of the dimensionless time-varying backlash is Ds=0.89 in the single-tooth area and Dd=0.79 in the double-teeth areas. This helps to identify and analyze the single-tooth and double-teeth meshing behavior of the gear pair
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