摘要
针对人字齿轮系统运行中普遍存在的非线性振动与分岔问题,首先,笔者基于集中参数法,构建融合拓扑修形效应、时变啮合刚度与齿侧间隙影响的24自由度弯-扭-轴-摆耦合动力学模型;其次,基于势能法精确建立含拓扑修形的人字齿轮时变啮合刚度模型,揭示修形对啮合刚度演化规律的深层机制;最后,采用龙格库塔法求解方程,结合分岔图、时域响应、频域特性、相平面轨迹及庞加莱截面,深入分析拓扑修形对系统分岔演化与混沌特性的影响。结果表明:拓扑修形后,系统振动与分岔特性的基本演化规律保持一致,局部分岔行为和振动响应得到有效改善;随着齿侧间隙增大,系统分岔特性呈现单周期、倍周期至混沌的演变趋势,在拓扑修形作用下,部分混沌解转变为周期解,整体混沌区域明显减少。理论结果与试验数据一致性较好,研究成果为高性能人字齿轮系统的动力学优化与振动控制提供了重要参考。
To address the prevalent nonlinear vibration and bifurcation issues in herringbone gear systems during operation,firstly,a 24-degree-of-freedom bending torsion axis pendulum coupled dynamic model is constructed based on the lumped parameter method.This model integrates the effects of topological modification,time-varying mesh stiffness,and backlash.Secondly,a time-varying mesh stiffness model for herringbone gear with topological modification is accurately established based on the potential energy method,revealing the underlying mechanism of how modification influences the evolution of mesh stiffness.Finally,the equations are solved using the Runge-Kutta method.The influences of topological modification on the bifurcation evolution and chaotic characteristics of the system are analyzed in depth by combining bifurcation diagrams,time-domain responses,frequency-domain characteristics,phase-plane trajectories,and Poincare surface of section.The results show that after topological modification,the fundamental evolution laws of system vibration and bifurcation characteristics remain consistent,local bifurcation behavior and vibration response are effectively improved.As backlash increases,the bifurcation characteristics of the system exhibit an evolution trend from single period to double period and then to chaos.Under the effect of topological modification,some chaotic solutions trans-form into periodic solutions,and the overall chaotic region is significantly reduced.The theoretical results are consistent with the experimental data.The results provide important references for the dynamic optimization and vibration control of high-performance herringbone gear systems.
作者
董皓
毕越
刘升升
吕鑫龙
韩灏
侯祥颖
靳广虎
DONG Hao;BI Yue;LIU Shengsheng;LÜXinlong;HAN Hao;HOU Xiangying;JIN Guanghu(School of Mechatronic Engineering,Xi'an Technological University Xi'an,710021,China;Engineering Research Center of Digital Intelligent Technology of High Performance Gear Transmission,University of Shaanxi Province,Xi'an Technological University Xi'an,710021,China;College of Mechanical and Electrical Engineering,Nanjing University of Aeronautics and Astronautics Nanjing,210016,China;National Key Laboratory of Helicopter Aeromechanics,Nanjing University of Aeronautics and Astronautics Nanjing,210016,China)
出处
《振动.测试与诊断》
北大核心
2025年第4期797-804,849,850,共10页
Journal of Vibration,Measurement & Diagnosis
基金
国家自然科学基金资助项目(52375062)
直升机动力学全国重点实验室开放基金资助项目(2024-ZSJ-LB-03-01)
陕西省教育厅科研计划资助项目(23JC038)
西安市科技计划资助项目(23GXFW0037)。
关键词
人字齿
拓扑修形
时变啮合刚度
非线性
分岔特性
herringbone gear
topological modification
time-varying mesh stiffness
nonlinear
bifurcation characteristics
作者简介
第一作者:董皓,男,1985年2月生,博士、教授。主要研究方向为齿轮传动与齿轮系统动力学。曾发表《Establish-ment of a multi-clearance coupled 3D floating nonlinear model and vibration analysis for a coaxial reverse closed dif-ferential herringbone gear transmission system》(《Nonlinear Dynamics》2024,Vol.113)等论文。E-mail:donghao@xatu.edu.cn。
