2PRU-UPR过约束并联机构弹性动力学建模与分析  

Elastodynamic Modeling and Analysis of a 2PRU-UPR Over-constrained Parallel Manipulator

作　　者：杨超 黄风立[1] 叶伟[2] 陈巧红[3] YANG Chao;HUANG Fengli;YE Wei;CHEN Qiaohong(College of Mechanical and Electrical Engineering,Jiaxing University,Jiaxing 314001;National and Local Joint Engineering Research Center of Reliability Analysis and Testing for Mechanical and Electrical Products,Zhejiang Sci-Tech University,Hangzhou 310018;School of Computer Science and Technology,Zhejiang Sci-Tech University,Hangzhou 310018)

机构地区：[1]嘉兴学院机电工程学院,嘉兴314001 [2]浙江理工大学机电产品可靠性分析与测试国家地方联合工程研究中心,杭州310018 [3]浙江理工大学计算机科学与技术学院,杭州310018

出　　处：《机械工程学报》2023年第21期209-223,共15页Journal of Mechanical Engineering

基　　金：国家自然科学基金(52275036);嘉兴市科技局重点研发计划(2020BZ10004)资助项目。

摘　　要：运用全局独立广义位移坐标和拉格朗日方程研究了具有2R1T三自由度的2PRU-UPR过约束并联机构的动力学性能。首先,将连杆划分为一定数量的梁单元,建立每一个单元的动力学控制方程,基于拉格朗日方程建立连杆的动力学控制方程;其次,基于多点约束单元理论与映射矩阵的奇异性分析建立物体与物体以及物体与基座连接点的一组独立位移坐标,结合关节连接点的独立位移坐标与内部节点位移坐标得到机构的全局独立广义位移坐标;再次,结合拉格朗日方程和全局独立广义位移坐标得到机构的总体动力学控制方程;与ANSYS Workbench软件建立的有限元模型结果对比发现自然频率最大误差在3.6%之内。最后对比分析了自然频率求解子空间迭代方法、静态缩聚法和动态缩聚法的计算精度和计算成本。该方法同样适用于其他并联和串联机构。The elastodynamic modeling of a 2PRU-UPR parallel manipulator with 2R1T 3-DOF(degrees of freedom)is studied based on the global independent generalized displacement coordinates and Lagrange’s equation.First,the links are divided into a number of elements using the Euler-Bernoulli beam element,the dynamic control equation of each element is obtained,and the dynamic control equation of each link can be obtained using the Lagrange’s equation.Second,one set of nonsingular independent displacement coordinates of the joint connection points is established using a multipoint constraint element and singularity assessment of the mapping matrix in the workspace,and the global independent generalized displacement coordinates(IGDC)of the mechanism is obtained by combining the internal node displacement coordinates and independent displacement coordinates of the joint connection points.Finally,the dynamic control equation of the mechanism is established using the Lagrange’s equation and global IGDC.Numerical results of natural frequencies show that the relative error between the finite element model established by the ANSYS Workbench software and the theoretical model is within 3.6%,which verify the correctness of the proposed model.The comparison of computational accuracy and cost of subspace iteration method,static condensation method,and dynamic condensation method for the natural frequency analysis is also presented.The proposed method is also applicable to other parallel and serial mechanisms.

关 键 词：并联机构 弹性动力学 全局独立广义位移坐标 拉格朗日方程 

分 类 号：TG156[金属学及工艺—热处理]