考虑间隙的刚柔耦合实验平台混沌辨识研究

Research on chaos identification for a rigid–flexible coupling experimental platform considering clearance

运动副间隙和构件柔性是引起机构精度下降的重要因素,其耦合效应会在一定程度导致机构产生混沌现象,严重影响机构的稳定性。为了培养学生对机构运动状态的分析能力,利用相图、庞加莱映射和最大李雅普诺夫指数对六连杆实验平台的混沌现象进行了定性和定量识别;对比分析了含间隙刚性实验平台/刚柔耦合实验平台非线性特性;研究了不同间隙值、驱动速度和摩擦系数对实验平台非线性特性的影响。该研究将为高精度、高性能多连杆机构的非线性动力学研究提供系统、完善的理论依据。

[Objective]Clearance between motion pairs is commonly observed in mechanisms due to manufacturing errors in components,assembly requirements,and wear of the mechanisms.When the mechanism operates at high speeds with large loads and small cross-sectional areas,components are susceptible to elastic deformation.This elastic deformation,combined with the clearance in motion pairs,significantly restricts the motion accuracy of the entire mechanism,leading to chaotic behavior and ultimately reducing its stability and reliability.Therefore,it is essential to investigate the influence of the coupling effect between the clearance of the motion pair and the flexible component on the motion state of the mechanism.[Methods]This paper proposes a chaos identification method for a rigid-flexible coupling experimental teaching platform with revolute clearance joints.First,a revolute clearance joint model was established based on the three-state model of“contact-separation-collision.”In addition,a flexible beam element model was created using the absolute node coordinate method.Following this,a dynamic model of the rigid-flexible coupling six-link experimental platform with revolute clearance joints was established using the Lagrange multiplier method.Finally,both qualitative and quantitative identifications of chaotic phenomena in the six-link experimental platform were conducted using phase diagrams,Poincarémaps,and maximum Lyapunov exponents.The nonlinear characteristics of the rigid experimental platform with clearance and the rigid-flexible coupling experimental platform with clearance were compared and analyzed.Additionally,the effects of different clearance values,driving speeds,and friction coefficients on the nonlinear characteristics of the experimental teaching platform were studied.[Results]The results obtained using methods such as phase diagrams,Poincarémaps,and maximum Lyapunov exponents indicate that compared with the rigid experimental teaching platform mechanism with revolute clearance,the vibration frequency of the rigid-flexible coupling experimental teaching platform mechanism with revolute clearance is higher,leading to reduced stability and more pronounced chaotic phenomena.The chaotic behavior at the clearance of the revolute pair intensifies with an increase in clearance size and driving speed,whereas it weakens as the friction coefficient increases.[Conclusions]The coupling effect between the clearance of the motion pair and the flexibility of the component reduces the stability of the mechanism,leading to the emergence of chaos.The chaos identification method based on the experimental teaching of rigid-flexible coupling with revolute clearance proposed in this article can effectively distinguish the motion states of the mechanism.This method provides a systematic and comprehensive theoretical foundation for the study of nonlinear dynamics in high-precision,high-performance multilink mechanisms.This not only enhances students’ability to analyze and practice the nonlinear characteristics of mechanisms but also increases the diversity,intuitiveness,and engagement of the teaching process,ultimately improving the quality of education.