摘要
建立合理的刚柔耦合系统动力学模型是实现碰撞冲击动态响应分析的基础。利用假设模态法描述了悬臂梁的振动位移响应,在此基础上基于广义坐标建立了系统的运动链。同时考虑悬臂梁的横向振动与纵向振动响应,在计入柔性杆横向弯曲变形引起轴向拉伸变形的2阶耦合量的条件下,分别基于Kane方法和Lagrange方法推导了刚柔耦合悬臂梁系统动力学方程,通过数值仿真揭示了系统广义坐标或速度的时变规律。仿真结果表明:两种方法下具有相同意义广义坐标的时变规律完全吻合。采用3D高速摄像机用于捕获悬臂梁的运动以验证构建模型的有效性。试验测试结果表明:试验测试值与仿真模拟值的误差值均小于5%,试验结果与模拟结果相符,说明动力学模型与计算方法均有效可行。研究结果可为接触面碰撞冲击理论计算及试验验证提供参考。
A reasonable dynamic modeling of the rigid-flexible coupling system serves as the foundation for the dynamicresponse analysis of collision and impact. The vibration displacement response of the cantilever beam is presented with the aid of the assumed mode. The kinematic chain of the system is established based on the generalized coordinates. With the response of transverse and longitudinal vibration, the dynamic equation of the rigid-flexible coupling cantilever beam system is derived by means of Kane method and Lagrange method respectively, while the second-order coupling quantity of the axial longitudinal displacement caused by the transverse bending displacement is taken into consideration. The simulation results manifest the time-variation law of generalized coordinates or speeds. It is concluded that, by means of these two methods, the generalized coordinates with the same meaning share the same law of time variation. A 3D high-speed camera is adopted to capture the motion of the cantilever beam, in order to verify the effectiveness of the established model. The experiment results show that all the errors of experimental value and simulated value are less than 5%. The experiment results are consistent with simulation results, which mean that both the dynamic model and numerical method are effective. This provides reference for theoretical calculation and experimental verification of the collision and impact of contact interface.
作者
王尧
孟文俊
Dan B Marghitu
李淑君
WANG Yao;MENG Wen-jun;Dan B Marghitu;LI Shu-jun(School of Mechanical Engineering,Taiyuan University of Science ＆ Technology,Taiyuan 030024;Department of Mechanical Engineering,Auburn University,Auburn USA 36849)
出处
《机械设计》
CSCD
北大核心
2018年第9期86-92,共7页
Journal of Machine Design
基金
国家自然科学基金面上资助项目(51575370)
山西省回国留学人员科研资助项目(2016-093
2016-094)
山西省研究生优秀创新资助项目(2016BY134)
