杆件与倾斜平面弹塑性接触冲击动力学建模与分析

Dynamics Modelling and Analysis of Elasto-plastic Contact-impact of a Rod-like Structure with a Oblique Flat Surface

针对垂直杆件冲击倾斜固体平面的弹塑性接触冲击问题,建立了杆件动力学方程和接触冲击各阶段瞬时接触力计算模型,系统地探讨和研究了运动参数和接触力变化规律;采用ODE45函数分析了杆件动能、接触点位置和速度、杆件角度和角速度等时变规律,恢复系数和永久变形与初始冲击速度关系,接触力与接触变形关系。研究结果表明:初始坠落高度越大,接触冲击时间越短且恢复反弹现象越明显;随初始坠落高度的增大,接触力与接触变形曲线呈相同变化趋势,但永久变形更接近于最大变形。开展了末端圆形杆件以不同初始坠落高度垂直冲击45°倾斜固体平面的试验研究,再结合已公开文献中恢复系数和永久变形的正冲击试验数据进行对比分析,结果表明,仿真与试验结果基本吻合,验证了所建模型的正确性。

For the elasto-plastic contact-impact problems of a vertical rod-like structure impacting the fixed oblique flat surface,the dynamics equations of the rod-like structure and the formulations of instantaneous contact forces in each phase during contact-impact events were established,and the various laws of the motion parameters and the contact forces were systematically studied in detail.Using ODE45 function,the time-variation laws such as the kinetic energy of the rod-like structure,position and velocity of the contact point,angle and angular velocity of the rod-like structure were analyzed.Besides,the relationships between the coefficient of restitution and the initial impact velocity,and the permanent deformations depending on initial impact velocity,as well as the contact forces with the contact deflection,were also achieved by the numerical analyses.The results show that the higher the initial drop height,the shorter the contact-impact time and the more obvious the rebounding phenomenon.And the contact force vs.contact deflection curves show similar trends with increasing initial drop height,but the permanent deformations are closer to the maximum deformation.Contact-impact tests were performed by dropping the vertical rounded ended rod-like structure from different initial drop heights on the fixed oblique flat surface with the inclination angle of 45°,and then,combined with testing data for the coefficient of restitution and permanent deformation in normal impact events reported in literatures,the comparative analysis results show that the simulation results are basically match with the testing results,which is verified the accuracy of the established model.