Abstract:In order to study the vibration-boundedness and the safety characteristics of gear transmission systems, a single-degree-of-freedom spur gear transmission system was taken as a studied object.The safety basin of the system in the inspection area was analyzed with the variation of the fluctuant coefficient of comprehension-transmission error and the fluctuant amplitude of time-varying stiffness.The erosion and bifurcation process of the safe basin were analyzed.Based on the system phase diagram and Poincaré map, the motion bifurcations process of the system in the investigation area was analyzed, and the top Lyapunov exponent (TLE) and the Floquet multiplier at the bifurcation point were calculated, and the evolution of the system safety basin erosion and bifurcation was further studied by means of the multi-initial bifurcation diagram.The results show that, with the increase of the parameters in a certain range, the evolution of different motions of the system leads to the erosion of safe basin, and the safety of the system becomes worse; in the investigation area, the bifurcation of the safety basin is caused by the bifurcation and periodic jumping of the system, and the periodic jumping will transform a part of the original safe basin into a new safe basin, while the other part of the original safety basin remains unchanged, and the doubling bifurcation and saddle knot bifurcation makes the original whole safety basin become a new safe basin.The results provide a guidance for the design and selection of spur gear system parameters, and provide a theoretical basis for ensuring the safety service of gear transmission systems.
苟向锋1,2,韩林勃1,2,朱凌云1,2,石建飞1,2. 单自由度齿轮传动系统安全盆侵蚀与分岔[J]. 振动与冲击, 2020, 39(2): 123-131.
GOU Xiangfeng1,2,HAN Linbo1,2,ZHU Lingyun1,2,SHI Jianfei1,2. Erosion and bifurcation of the safe basin for a single-degree-of-freedom spur gear system. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(2): 123-131.
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