直齿锥齿轮分岔脱啮特性参数解域界结构  

Parametric Solution Domain Structures for Bifurcation and Non-Meshing Dynamic Characteristics of Straight Bevel Gear Systems

作　　者：田亚平[1] 杨江辉 王瑞邦 TIAN Yaping;YANG Jianghui;WANG Ruibang(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,P.R.China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《应用数学和力学》2023年第8期965-976,共12页Applied Mathematics and Mechanics

基　　金：甘肃省科技厅计划项目(21JR7RA316;20YF8WA043);国家自然科学基金项目(12062008;11962011)。

摘　　要：为研究含间隙直齿锥齿轮系统周期运动与齿面冲击、脱啮、动载间的耦合转迁关系,基于胞映射原理构建了时变啮合刚度和频率比双参平面,采用改进的CPNF(continuous-Poincaré-Newton-Floquet)法求解了系统胞元的周期、冲击、脱啮、动载特性解域界结构.仿真结果表明,在双参解域界内系统存在鞍结、Hopf、倍化、激变及周期3等分岔方式和3种齿面冲击共存现象,随时变啮合刚度系数递增其冲击和混沌现象加剧.齿面脱啮、齿背接触及动载系数受齿面冲击和周期分岔的影响而发生突变,在同一界域内随频率比增加而降低,随刚度系数增加而加剧.Aimed at the coupling transition relationship between the periodic motion,the tooth surface impact,the non-meshing state and the dynamic load of straight bevel gear systems with backlash,the 2-parameter plane with respect to the time-varying meshing stiffness and the frequency ratio was built based on the cell mapping principle.Besides,the improved CPNF(continuous-Poincaré-Newton-Floquet)method was applied to solve the solution domain structure of the periodicity,impact,non-meshing and dynamic load characteristics of the system cells.The simulation results show that,there are plentiful bifurcation modes with 3 kinds of tooth surface impacts coexisting in the 2-parameter solution domain structure,including the saddle node bifurcation,the Hopf bifurcation,the period-doubling bifurcation,the catastrophe bifurcation and the period-3 bifurcation.The tooth surface impact and chaos will intensify due to increase of the time-varying meshing stiffness coefficient.The tooth surface non-meshing,the tooth back meshing and the dynamic load coefficient will exhibit mutations under the influences of the tooth impact and the periodic motion.Meanwhile,in the same domain,the tooth surface non-meshing and the tooth back meshing will weaken with the frequency ratio but heighten with the stiffness coefficient.

关 键 词：直齿锥齿轮传动系统 分岔 CPNF法 解域界结构 齿面脱啮 

分 类 号：O322[理学—一般力学与力学基础] TH132.422[理学—力学]