考虑多间隙关节和不确定参数机构的非线性动力学分析

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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。

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	王志敏1
	2
	金国光1
	2
	梁栋1
	2
	畅博彦1
	2
	周杨1
	2

关键词 ：分岔, 混沌, 多间隙关节, 不确定参数, 非线性动力学

Abstract：Taking the four-bar mechanism as the research object, the Monte Carlo algorithm is 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 is established, and an analysis method for nonlinear dynamics of mechanisms with multi-clearance joints and uncertain parameters is proposed. Firstly, the effects of clearance joints and uncertain parameters on the kinematic accuracy of the mechanism are studied under different conditions, and the kinematic error of the mechanism is quantified. Then, the influence of uncertain parameters, crank speed, clearance size and clearance position on the bifurcation and chaos of the four-bar mechanism are investigated. The 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 are proved by using 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.

Key words： Bifurcation Chaos Multi-clearance joints Uncertain parameters Nonlinear dynamics

收稿日期: 2022-03-30 出版日期: 2023-06-28

引用本文:

王志敏1,2，金国光1,2，梁栋1,2，畅博彦1,2，周杨1,2. 考虑多间隙关节和不确定参数机构的非线性动力学分析[J]. 振动与冲击, 2023, 42(12): 48-58.
WANG Zhimin1,2，JIN Guoguang1,2，LIANG Dong1,2，CHANG Boyan1,2，ZHOU Yang1,2. Nonlinear dynamics analysis of mechanism with multi-clearance joints and uncertain parameters. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(12): 48-58.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I12/48

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