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Correlation dimension and bifurcation analysis for the planar slider-crank mechanism with multiple clearance joints
Multibody System Dynamics ( IF 3.4 ) Pub Date : 2021-01-19 , DOI: 10.1007/s11044-020-09769-3
Xuze Wu , Yu Sun , Yu Wang , Yu Chen

Joint clearance serves as a crucial element of nonlinearity in multibody systems. The quantization of the system chaos is conducive to not only the understanding of the nonlinear nature but the rationalization of system controlled parameters. In the present work, the system dynamics for the planar slider-crank mechanism with multiple clearance joints is depicted by the correlation dimension and bifurcation actions. Considering the obliqueness of the slider, the general configuration of the planar joint is proposed. Generalized coordinates and the Lagrangian approach are adopted to derive the dynamic motion equations. The effects of clearance size and driving speed on the bifurcations of the dynamic response are investigated. Furthermore, the fractal dimension of the strange attractor is identified by the correlation dimension from time series. Based on the Cao method, the Mutual Information (MI) function, and the Grassberger-Procaccia (G-P) algorithm, the controlled factors in the evaluation of correlation dimension are cautiously determined. Ultimately, the compound effect of translational and revolute clearance joints on the mechanism dynamics is featured. The numerical results testify that the correlation dimension of the slider displacement approximately saturates beyond a specific translational clearance value. Moreover, with the parameters used in this work, the complexity of system response seems to be more sensitive to the variation of translational clearance size than with the revolute joint.



中文翻译:

多间隙关节平面滑块曲柄机构的相关尺寸和分叉分析

关节间隙是多体系统中非线性的关键因素。系统混沌的量化不仅有利于理解非线性性质,而且有利于系统控制参数的合理化。在当前的工作中,具有相关联的尺寸和分叉作用描绘了具有多个间隙接头的平面滑块曲柄机构的系统动力学。考虑到滑块的倾斜,提出了平面接头的一般构造。采用广义坐标和拉格朗日方法推导动态运动方程。研究了间隙尺寸和驱动速度对动力响应分叉的影响。此外,陌生吸引子的分形维数由时间序列中的相关维数确定。基于Cao方法,互信息(MI)函数和Grassberger-Procaccia(GP)算法,谨慎确定相关维数评估中的受控因素。最终,具有平移和旋转间隙关节对机构动力学的复合作用。数值结果证明,滑块位移的相关尺寸大约超出特定的平移游隙值饱和。此外,在这项工作中使用的参数,系统响应的复杂性似乎比平移关节对平移间隙大小的变化更敏感。谨慎确定相关维数评估中的受控因素。最终,具有平移和旋转间隙关节对机构动力学的复合作用。数值结果证明,滑块位移的相关尺寸大约超出特定的平移游隙值饱和。此外,在这项工作中使用的参数,系统响应的复杂性似乎比平移关节对平移间隙大小的变化更敏感。谨慎确定相关维数评估中的受控因素。最终,提出了平移和旋转间隙关节对机构动力学的复合作用。数值结果证明,滑块位移的相关尺寸大约超出特定的平移游隙值饱和。此外,在这项工作中使用的参数,系统响应的复杂性似乎比平移关节对平移间隙大小的变化更敏感。

更新日期:2021-01-19
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