考虑多间隙关节和不确定参数机构的非线性动力学分析  

Nonlinear dynamics analysis of mechanism with multi-clearance joints and uncertain parameters

作　　者：王志敏 金国光[1,2] 梁栋 畅博彦[1,2] 周杨 WANG Zhimin;JIN Guoguang;LIANG Dong;CHANG Boyan;ZHOU Yang(School of Mechanical Engineering,Tiangong University,Tianjin 300387,China;Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology,Tianjin 300387,China)

机构地区：[1]天津工业大学机械工程学院,天津300387 [2]天津市现代机电装备技术重点实验室,天津300387

出　　处：《振动与冲击》2023年第12期48-58,共11页Journal of Vibration and Shock

基　　金：国家自然科学基金(51475330,52005368,52175243);天津市高等学校创新团队培养计划(TD13-5037)。

摘　　要：以典型四杆机构为研究对象,利用蒙特卡洛算法模拟不确定几何参数与间隙大小的生成,建立含多间隙关节和不确定参数的四杆机构非线性动力学方程,提出一种考虑多间隙关节和不确定参数机构的非线性动力学分析方法。首先,研究了不同情况下间隙关节和不确定参数对机构运动精度的影响,并量化机构运动误差;然后,重点探究了不确定参数、曲柄转速、间隙尺寸和间隙位置对四杆机构分岔与混沌现象的影响。分析结果表明:由于间隙关节和不确定参数的影响,导致了机构运动精度的降低;同时,利用分岔图证明了系统分岔和混沌行为对曲柄转速、间隙尺寸的依赖和敏感性;曲柄转速与间隙尺寸的变化,是导致机构出现分岔与混沌行为的主要因素,不确定几何参数对机构整体分岔现象的影响有限。Taking four-bar mechanism as the research object,the Monte Carlo algorithm was used to simulate the generation of uncertain geometric parameters and clearance size,the nonlinear dynamic equation of the four-bar mechanism with multi-clearance joints and uncertain parameters was established,and an analysis method for nonlinear dynamics of the mechanism with multi-clearance joints and uncertain parameters was proposed.Firstly,the effects of clearance joints and uncertain parameters on the kinematic accuracy of the mechanism were studied under different conditions,and the kinematic error of the mechanism was quantified.Then,the influence of uncertain parameters,crank speed,clearance size,and clearance position on the bifurcation and chaos of the four-bar mechanism were investigated.Analysis results show that the kinematic accuracy of the mechanism is reduced due to the influence of clearance joints and uncertain parameters.At the same time,the dependence and sensitivity of systems bifurcation and chaos behavior on crank speed and clearance size were proved by using the bifurcation diagram.The changes of crank speed and clearance size are the main factors that cause the bifurcation and chaotic behavior of the mechanism,and the influence of uncertain geometric parameters on the overall bifurcation phenomenon of the mechanism is limited.

关 键 词：分岔 混沌 多间隙关节 不确定参数 非线性动力学 

分 类 号：TH113[机械工程—机械设计及理论]