外加周期激励控制齿轮传动系统安全-吸引盆侵蚀与分岔

银奎帮; 石咏荷; 郭峰

doi:10.21656/1000-0887.460071

外加周期激励控制齿轮传动系统安全-吸引盆侵蚀与分岔

doi: 10.21656/1000-0887.460071

西安铁路职业技术学院机电工程学院，西安 710026

基金项目:

西安铁路职业技术学院2025年度立项课题（XTZY25K02）

详细信息

作者简介:
银奎帮（1994—），男，硕士(通信作者. E-mail: 18153991602@163.com).

通讯作者:
银奎帮（1994—），男，硕士(通信作者. E-mail: 18153991602@163.com).

中图分类号: O322|TB533^+.1
计量
- 文章访问数: 17
- HTML全文浏览量: 5
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2025-04-10
- 修回日期: 2025-06-17
- 网络出版日期: 2026-04-30

External Periodic Excitation Control of Gear Transmission Systems for Safety-Attraction Basin Erosion and Bifurcation

School of Mechanical and Electrical Engineering, Xi’an Railway Vocational & Technical Institute, Xi’an 710026, P.R.China

摘要

摘要: 针对高速重载齿轮系统因时变啮合刚度与齿侧间隙等强非线性因素耦合引发的失稳问题，本研究引入外加周期激励控制策略，建立单自由度齿轮传动系统动力学模型并进行数值求解.采用胞映射法，定量分析控制参数对系统安全-吸引盆的侵蚀与分岔转迁过程及吸引域占比p演化规律的影响.基于Floquet乘子分析，建立倍频系数、激励幅值与分岔阈值的定量映射关系，结合系统相图和Poincaré映射图，揭示了外加激励通过重构相空间拓扑实现稳定控制的机理，定量阐明了关键控制参数对系统全局稳定性转变的调控机制.研究表明：低频激励易诱发高周期吸引子导致运动越界失稳；高频激励触发安全-吸引盆侵蚀与分岔，其中P3S吸引子稳定，P2S吸引子经逆倍化分岔向P1S单周期安全轨道转迁；反向激励幅值破坏稳定性，而增大正向激励幅值可加速稳定化进程，最终实现P1S吸引域全域覆盖.研究结果为齿轮传动系统的振动抑制、参数优化与安全设计提供了理论支撑.
- 齿轮传动系统 /
- 非线性动力学 /
- 振动控制 /
- 安全-吸引盆
Abstract: In response to the instability problem caused by the coupling of strong nonlinear factors such as time-varying mesh stiffness and backlash in high-speed heavy-duty gear systems, an external periodic excitation control strategy was introduced, to establish and numerically solve a dynamic model for single-degree-of-freedom gear transmission systems. With the cell mapping method, the effects of control parameters on the erosion and bifurcation transition process of the system safety-attraction basin, as well as the evolution law of the attraction domain proportion p, were quantitatively analyzed. Based on the Floquet multiplier analysis, a quantitative mapping relationship between the doubling coefficient, the excitation amplitude, and the bifurcation threshold, was established. Combined with the system phase diagram and the Poincaré mapping diagram, the stable control mechanism realized through reconstruction of the phase space topology under external excitation, was revealed, and the control mechanism of key control parameters on the global stability transition of the system was quantitatively elucidated. The results shows that, the low-frequency excitation can easily induce high period attractors, leading to motion boundary instability; the high frequency excitation can trigger safety-attraction basin erosion and bifurcation, where the P3S attractor is stable and the P2S attractor undergoes inverse doubling bifurcation to transition to the P1S single period safe orbit; and the reverse excitation amplitude will destroy the system stability, while increasing the forward excitation amplitude can accelerate the stabilization process, ultimately achieving full coverage of the P1S attraction domain. The research provides a theoretical support for vibration suppression, parameter optimization, and safety design of gear transmission systems.
- gear transmission system /
- nonlinear dynamics /
- vibration control /
- safety-attraction basin

HTML全文

参考文献(18)

[2]王树国, 张艳波, 刘文亮, 等. 多间隙二级齿轮非线性振动分岔特性研究[J]. 应用数学和力学, 2016,37(2): 173-183.(WANG Shuguo, ZHANG Yanbo, LIU Wenliang, et al. Nonlinear vibration bifurcation characteristics of multi-clearance 2-stage gear systems[J]. Applied Mathematics and Mechanics,2016,37(2): 173-183. (in Chinese))

KAHRAMAN A, SINGH R. Non-linear dynamics of a spur gear pair[J]. Journal of Sound and Vibration,1990,142(1): 49-75.

[3]刘晓宁, 沈允文, 王三民. 3自由度齿轮系统的混沌控制[J]. 机械工程学报, 2006,42(12): 52-58.(LIU Xiaoning, SHEN Yunwen, WANG Sanmin. Chaos control of 3-DOF geared system[J]. Chinese Journal of Mechanical Engineering,2006,42(12): 52-58. (in Chinese))

[4]刘晓宁. 三自由度齿轮传动系统的非线性振动及混沌控制[D]. 西安: 西北工业大学, 2003.(LIU Xiaoning. Nonlinear vibration and chaos control of a three-degree-of-freedom gear transmission system[D]. Xi’an: Northwestern Polytechnical University, 2003. (in Chinese))

[5]HSU C S, GUTTALU R S. An unravelling algorithm for global analysis of dynamical systems: an application of cell-to-cell mappings[J]. Journal of Applied Mechanics,1980,47(4): 940-948.

[6]徐皆苏, 徐健学. 高阶非线性动力系统全局分析: 胞胞映射法应用[J]. 应用数学和力学, 1985,6(11): 953-962. (HSU C S, XU Jianxue. The global analysis of higher order nonlinear dynamical systems and the application of cell-to-cell mapping method[J]. Applied Mathematics and Mechanics,1985,6(11): 953-962. (in Chinese))

[7]THOMPSON J M T. Transient basins: a new tool for designing ships against capsize[C]//IUTAM Symp Dynamics of Marine Vehicles & Structures in Waves. London, 1990.

[8]RAINEY R C T, THOMPSON J M T. The transient capsize diagram: a new method of quantifying stability in waves[J]. Journal of Ship Research,1991,35(1): 58-62.

[9]THOMPSON J M T, MCROBIE F A . Indeterminate bifurcations and the global dynamics of driven oscillators[C]//〖STBX〗1st European Nonlinear Oscillations Conference. Hamburg, 1993.

[10]田亚平, 杨江辉, 王瑞邦. 直齿锥齿轮分岔脱啮特性参数解域界结构[J]. 应用数学和力学, 2023,44(8): 965-976.(TIAN Yaping, YANG Jianghui, WANG Ruibang. Parametric solution domain structures for bifurcation and non-meshing dynamic characteristics of straight bevel gear systems[J]. Applied Mathematics and Mechanics,2023,44(8): 965-976. (in Chinese))

[11]苟向锋, 韩林勃, 朱凌云, 等. 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 Xiangfeng, HAN Linbo, ZHU Lingyun, et al. Erosion and bifurcation of the safe basin for a single-degree-of-freedom spur gear system[J]. Journal of Vibration and Shock,2020,39(2): 123-131. (in Chinese))

[12]李正发, 苟向锋, 朱凌云, 等. 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 Zhengfa, GOU Xiangfeng, ZHU Lingyun, et al. 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. (in Chinese))

[13]李正发, 苟向锋, 朱凌云, 等. 直齿轮副齿面接触安全条件及安全盆[J]. 振动、测试与诊断, 2022,42(3): 446-453.(LI Zhengfa, GOU Xiangfeng, ZHU Lingyun, et al. Erosion and bifurcation of safe basin under tooth contact safety condition for a spur gear pair[J]. Journal of Vibration,Measurement & Diagnosis,2022,42(3): 446-453. (in Chinese))

[14]张莹, 都琳, 岳晓乐. Duffing映射的全局动力学行为分析与研究[J]. 西北工业大学学报, 2017,35(2): 316-320.(ZHANG Ying, DU Lin, YUE Xiaole. Analysis and research on the global dynamical behavior of duffing map[J]. Journal of Northwestern Polytechnical University,2017,35(2): 316-320. (in Chinese))

[15]唐进元, 熊兴波, 陈思雨. 基于图胞映射方法的单自由度非线性齿轮系统全局特性分析[J]. 机械工程学报, 2011,47(5): 59-65.(TANG Jinyuan, XIONG Xingbo, CHEN Siyu. Analysis of global character of single degree of freedom nonlinear gear system based on digraph cell mapping method[J]. Journal of Mechanical Engineering,2011,47(5): 59-65. (in Chinese))

[16]石建飞, 韩闯, 王砚麟, 等. 基于齿面磨损失效的齿轮传动系统动态失稳盆转迁机理研究[J]. 振动与冲击, 2025,44(8): 21-29.(SHI Jianfei, HAN Chuang, WANG Yanlin, et al. Study on dynamic instability basin migration mechanism of gear system based on tooth wear inefficiency[J]. Journal of Vibration and Shock,2025,44(8): 21-29. (in Chinese))

[17]金花, 张子豪, 吕小红. 单级直齿轮副的共存吸引子特性研究[J]. 振动与冲击, 2023,42(23): 1-7.(JIN Hua, ZHANG Zihao, Lü Xiaohong. Coexisting attractors characteristics of single-stage spur gear pair[J]. Journal of Vibration and Shock,2023,42(23): 1-7. (in Chinese))

[18]金花, 吕小红, 张子豪, 等. 齿轮传动系统共存吸引子的不连续分岔[J]. 力学学报, 2023,55(1): 203-212.(JIN Hua, L Xiaohong, ZHANG Zihao, et al. Discontinuous bifurcations of coexisting attractors for a gear transmission system[J]. Chinese Journal of Theoretical and Applied Mechanics,2023,55(1): 203-212. (in Chinese))

施引文献

资源附件(0)

访问统计