2PRU-UPR过约束并联机构弹性动力学建模与分析

doi:10.3901/JME.2023.21.209

机械工程学报 ›› 2023, Vol. 59 ›› Issue (21): 209-223.doi: 10.3901/JME.2023.21.209

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2PRU-UPR过约束并联机构弹性动力学建模与分析

杨超¹, 黄风立¹, 叶伟², 陈巧红³

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

收稿日期:2022-12-22 修回日期:2023-06-14 出版日期:2023-11-05 发布日期:2024-01-15
通讯作者: 黄风立(通信作者)，男，1976年出生，博士，教授，硕士研究生导师。主要研究方向为并联机器人。E-mail：hfl@zjxu.edu.cn
作者简介:杨超，男，1982年出生，博士，讲师。主要研究方向为并联机器人。E-mail：cyang@zjxu.edu.cn；陈巧红，女，1978年出生，博士，教授，硕士研究生导师。主要研究方向为并联机器人。E-mail：chen_lisa@zstu.edu.cn
基金资助:
国家自然科学基金(52275036)和嘉兴市科技局重点研发计划(2020BZ10004)资助项目。

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

YANG Chao¹, HUANG Fengli¹, YE Wei², CHEN Qiaohong³

1. College of Mechanical and Electrical Engineering, Jiaxing University, Jiaxing 314001;
2. National and Local Joint Engineering Research Center of Reliability Analysis and Testing for Mechanical and Electrical Products, Zhejiang Sci-Tech University, Hangzhou 310018;
3. School of Computer Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018

Received:2022-12-22 Revised:2023-06-14 Online:2023-11-05 Published:2024-01-15

摘要/Abstract

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。

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

Abstract: 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.

Key words: parallel manipulator, elastodynamic, global independent generalized displacement coordinates, Lagrange’s equation

中图分类号:

TG156

杨超, 黄风立, 叶伟, 陈巧红. 2PRU-UPR过约束并联机构弹性动力学建模与分析[J]. 机械工程学报, 2023, 59(21): 209-223.

YANG Chao, HUANG Fengli, YE Wei, CHEN Qiaohong. Elastodynamic Modeling and Analysis of a 2PRU-UPR Over-constrained Parallel Manipulator[J]. Journal of Mechanical Engineering, 2023, 59(21): 209-223.

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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

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