直齿锥齿轮分岔脱啮特性参数解域界结构

田亚平; 杨江辉; 王瑞邦

doi:10.21656/1000-0887.430330

直齿锥齿轮分岔脱啮特性参数解域界结构

doi: 10.21656/1000-0887.430330

兰州交通大学机电工程学院，兰州 730070

基金项目:

甘肃省科技厅计划项目 21JR7RA316

甘肃省科技厅计划项目 20YF8WA043

国家自然科学基金项目 12062008

国家自然科学基金项目 11962011

详细信息

通讯作者:
田亚平(1977—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: tianyp@lzjtu.edu.cn)

中图分类号: O322;TH132.422
计量
- 文章访问数: 277
- HTML全文浏览量: 106
- PDF下载量: 45
- 被引次数: 0
出版历程
- 收稿日期: 2022-10-20
- 修回日期: 2022-12-27
- 刊出日期: 2023-08-01

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

School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, P.R.China

摘要

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.
- 直齿锥齿轮传动系统 /
- 分岔 /
- CPNF法 /
- 解域界结构 /
- 齿面脱啮
Abstract: 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.
- straight bevel gear system /
- bifurcation /
- CPNF method /
- solution domain structure /
- tooth surface no-meshing

HTML全文

图 1 齿轮箱

Figure 1. The bevel gearbox

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图 2 动力学模型

Figure 2. The nonlinear dynamic model for a spiral bevel gear set

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图 3 Ω×α平面动态特性解域界结构

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. Dynamic properties solution domain boundary structures in the Ω×α 2-parameter plane

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图 4 Ω×α双参分岔图

Figure 4. The bifurcation diagram in the Ω×α 2-parameter plane

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图 5 分岔图

Figure 5. The bifurcation diagram via α

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图 6 Poincaré映射图和相图

Figure 6. Poincaré and phase maps

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图 7 Poincaré映射图和相图

Figure 7. Poincaré and phase maps

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图 8 脱啮比、动载系数分布图

Figure 8. The δ_NMDC, δ_BMDC and δ_DLC distribution diagrams

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