齿根安全条件下多状态啮合齿轮传动系统安全-吸引盆侵蚀与分岔

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (5) : 63-74.

论文

李正发1,2，苟向锋1,2，朱凌云1,2，石建飞1,2，尹桩1,2

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Erosion and bifurcation of safety-attraction basin for multi-state meshing gear transmission system under tooth root safety condition

LI Zhengfa1,2, GOU Xiangfeng1,2, ZHU Lingyun1,2, SHI Jianfei1,2, YIN Zhuang1,2

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摘要

轮齿折断是齿轮主要失效形式之一。以包含单双齿交替啮合、轮齿脱啮和齿背接触等的多状态啮合直齿圆柱齿轮传动系统为研究对象，计算齿根危险截面上的弯曲应力，以齿根许用弯曲应力为边界条件，建立防止轮齿折断的齿根安全条件。基于胞映射方法，用四阶Runge-Kutta法数值计算考察区域内随负载和齿侧间隙变化时系统的吸引盆及其演变过程。判断齿根安全条件下吸引盆中不同运动类型吸引域的安全特性得到系统的安全-吸引盆。借助吸引子、多初值分岔图和最大Lyapunov指数图（TLE）分析安全-吸引盆的侵蚀与分岔机理。研究发现：吸引盆中不同运动类型吸引域在齿根安全条件下的安全特性不同；吸引子的出现和消失直接导致安全-吸引盆的分岔；多初值分岔图中出现周期跳跃和分岔是引发安全-吸引盆分岔的主要原因。研究结果可为直齿轮传动系统安全运行提供参考。

Abstract

The break of tooth is one of the main failure modes of the gear. The spur gear transmission system with multiple meshing states, such as the alternating mesh of single and double teeth, disengagement and back-side contacting, is taken as the research object. The tooth root safety condition for preventing tooth fracture is established by calculating the bending stress of the tooth root in the dangerous section of the tooth during the gear meshing process and the allowable bending stress of the tooth root is chosen as a boundary condition. Based on the cell mapping method, system's attraction basins and its evolutions with the change of the load or the flank clearance are calculated numerically by 4-order Runge-Kutta method in the area of investigation. Safety-attraction basins of the system are obtained by judging the safety characteristics of the attraction domains of different motion types in attraction basins under the safety condition of tooth root. Attractors, multiple initial values bifurcation diagrams and top Lyapunov exponents (TLE) are used to analyze erosions and bifurcations process of safety-attraction basins. The results show that different motion types of attraction basins have different safety characteristics under the condition of tooth root safety. The appearances and disappearances of attractors directly lead to the bifurcations of safety-attraction basins. The occurrence of cycle jumps and bifurcations in multiple initial value bifurcation diagrams is the main cause of bifurcations of safety-attraction basins. The research can provide references for the safety operation of the spur gear transmission system.

导出引用

李正发1,2，苟向锋1,2，朱凌云1,2，石建飞1,2，尹桩1,2. 齿根安全条件下多状态啮合齿轮传动系统安全-吸引盆侵蚀与分岔[J]. 振动与冲击, 2021, 40(5): 63-74

LI Zhengfa1,2, GOU Xiangfeng1,2, ZHU Lingyun1,2, SHI Jianfei1,2, YIN Zhuang1,2. Erosion and bifurcation of safety-attraction basin for multi-state meshing gear transmission system under tooth root safety condition[J]. Journal of Vibration and Shock, 2021, 40(5): 63-74

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