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The flexibility of gear teeth under cyclic varying loads can induce meshing impact and nonlinear vibration of gear pairs. Revealing the multi-state meshing characteristics and nonlinear dynamic characteristics of spur gear systems considering teeth flexibility lays the foundation for the safe and reliable operation of transmission systems. Based on the cantilever beam theory and gear meshing principles, the flexible deformation of meshing teeth is calculated, and the calculation method for flexible time-varying meshing parameters of gear pairs is derived； based on the contact states and loading conditions of the gear pairs, extract the characteristics of multi-state flexible meshing, and a nonlinear dynamic model of the spur gear system with multi-status flexible meshing is established； study the evolution laws of flexible time-varying meshing parameters and the distribution characteristics of flexible deformation of gear teeth under multi-parameters correlation, and uncover the global bifurcation and chaos characteristics of the system when the teeth flank clearance changes. The results indicate that the flexibility of the gear teeth reduces the double teeth meshing area, affects the meshing parameters and multi-status meshing characteristics of the gear system, and induces out-of-line meshing of the gear pair； the variation of teeth flank clearance causes the coexistence of periodic motions and chaotic motions, and incomplete bifurcation under multiple initial conditions is the fundamental cause for such dynamic behavior coexistence.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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