直齿轮副齿面接触安全条件及安全盆  

Erosion and Bifurcation of Safe Basin Under Tooth Contact Safety Condition for a Spur Gear Pair

作　　者：李正发 苟向锋[1] 朱凌云[1] 石建飞 LI Zhengfa;GOU Xiangfeng;ZHU Lingyun;SHI Jianfei(School of Mechanical Engineering,Tiangong University Tianjin,300387,China)

机构地区：[1]天津工业大学机械工程学院,天津300387

出　　处：《振动．测试与诊断》2022年第3期446-453,613,共9页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51365025);天津市自然科学基金资助项目(18JCYBJC88800)。

摘　　要：为研究齿面接触疲劳对齿轮副安全特性的影响,考虑直齿轮副含单/双齿啮合、脱啮和齿背接触等啮合状态,根据Hertz接触理论建立其齿面接触强度的安全条件。基于胞映射理论,计算考察域内吸引域随参数变化的演变过程。判断共存吸引子在所建安全条件下的安全特性,分析系统安全盆的演变规律,研究安全盆的侵蚀与分岔机理。结果表明:考察域内的共存吸引子在齿面接触安全条件下的安全特性不同;吸引子的出现或消失是安全盆分岔的主要原因;多初值分岔图中的跳跃和分岔导致安全盆分岔。该结果可为齿轮系统的参数选择和故障预测提供参考。To study the influence of the tooth surface contact fatigue on the safety characteristics of gear systems,its safety condition of the spur gear transmission system is established based on the Hertz contact theory. The multi-state meshing including single pair teeth meshing,double pair teeth meshing,tooth disengagement and back-side contacting are considered. Attracting domains of the system and their evolutions with the change of control parameters are numerically calculated by the cell-to-cell method in the investigation region. The safety characteristics of coexistence attracting domains in the region are analyzed under the established safety condition.Safe basins and their evolutions process in the region are analyzed. The erosion and bifurcation mechanism of safe basins for the system are studied according to multi-initial bifurcation diagrams and top Lyapunov exponent diagrams. Results show that the safety characteristics of coexistence attraction domains in the survey area are different under the tooth surface contact safety condition. The disappearance or appearance of attractors is the main cause of the bifurcation for safe basins and their instability. Bifurcation of the safe basin is caused by the periodic jumping or bifurcation. Results can provide references for parameter selection or failure prediction of the gear transmission system.

关 键 词：直齿轮副 多状态啮合 齿面接触强度 安全盆 多初值分岔 

分 类 号：TH132.41[机械工程—机械制造及自动化]