面向变胞机构动力学建模的变拓扑构型数学描述方法

doi:10.3901/JME.2022.09.049

机械工程学报 ›› 2022, Vol. 58 ›› Issue (9): 49-61.doi: 10.3901/JME.2022.09.049

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面向变胞机构动力学建模的变拓扑构型数学描述方法

周杨^1,2, 畅博彦^1,2, 金国光^1,2, 梁栋^1,2

1. 天津工业大学机械工程学院天津 300387;
2. 天津市现代机电装备技术重点实验室天津 300387

收稿日期:2021-06-29 修回日期:2021-10-08 出版日期:2022-05-05 发布日期:2022-06-23
通讯作者: 金国光(通信作者)，男，1963年出生，博士，教授，博士研究生导师。主要研究方向为机械设计及理论、机械系统动力学与控制。E-mail：jinguoguang@tiangong.edu.cn E-mail:jinguoguang@tiangong.edu.cn
作者简介:周杨，男，1996年出生，博士研究生。主要研究方向为变胞机构结构学、运动学和动力学。E-mail：18740565893@163.com
基金资助:
国家自然科学基金(51475330, 52005368)、天津市高等学校创新团队培养计划(TD13-5037)、天津市自然科学基金(17JCQNJC03900)和天津市教委科研计划(2018KJ205)资助项目

Mathematic Description Method of Variable Topology Configuration for Dynamic Modeling of Metamorphic Mechanism

ZHOU Yang^1,2, CHANG Boyan^1,2, JIN Guoguang^1,2, LIANG Dong^1,2

1. School of Mechanical Engineering, Tiangong University, Tianjin 300387;
2. Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin 300387

Received:2021-06-29 Revised:2021-10-08 Online:2022-05-05 Published:2022-06-23

摘要/Abstract

摘要： 针对变胞机构的变拓扑特性，以拓扑学和多体系统动力学理论为基础，提出一种可由变胞源机构动力学模型自动生成任意子机构动力学模型的建模方法。首先，从变胞机构的拓扑组成和所受约束角度出发，重新定义了变胞源机构的内涵，将变胞源机构向子机构的切换方式简化为构件数减少和构件数不变两种情况。其次，运用关联矩阵描述变胞机构的构态切换过程，提出实现构态切换所需的单位消元矩阵E_{i, j}、关系消去矩阵I_j和关联关系变化矩阵G，将变胞机构的拓扑结构变化转化为一系列的矩阵运算，并给出了统一的数学模型。最后，建立关联矩阵、Huston低序体阵列和通路矩阵三者之间的转换关系，结合R-W方法分析变胞机构子构态动力学模型的自动生成机理，以具有3个构态的闭环五杆变胞机构为例，建立变胞源机构动力学模型，通过编程自动生成所有子构态动力学模型，并对机构的动力学特性进行分析，验证所提方法的有效性和实用性。

关键词: 变胞机构, 关联矩阵, 构态切换, 动力学, 变拓扑

Abstract: According to the variable topology characteristics of metamorphic mechanism, a modeling method is proposed to generate automatically any sub-mechanism dynamic model from metamorphic source dynamic model based on topology and multi-body system dynamics theory. Firstly, from the view of the topological composition and constraints of the metamorphic mechanism, the connotation of metamorphic mechanism is redefined and the configuration transformation mode from the source metamorphic mechanism to the sub-mechanism is simplified into two kinds: Reducing the number of components and keeping the number of components unchanged. Secondly, incidence matrix is used to describe the configuration transformation process of metamorphic mechanism, the elimination E_{i, j}-elementary matrix, the relevance-eliminating matrix I_j and the relevance-change matrix G are proposed to realize the configuration transformation. The topological structure change of the metamorphic mechanism is transformed into a series of matrix operations and a unified mathematical model is given. Finally, the transformation relationship among incidence matrix, Huston lower numbered body array and path matrix is established and the automatic generation mechanism of sub-configuration dynamic model of metamorphic mechanism is analyzed by R-W method. Taking a closed-loop five bar metamorphic mechanism with three configurations as an example, the dynamic model of source metamorphic mechanism is established, and all sub-mechanism dynamic models are generated by programming automatically. The dynamic characteristics of the mechanism are analyzed to verify the effectiveness and practicability of the proposed method.

Key words: metamorphic mechanism, incidence matrix, configuration transformation, dynamics, variable topology

中图分类号:

TH112

周杨, 畅博彦, 金国光, 梁栋. 面向变胞机构动力学建模的变拓扑构型数学描述方法[J]. 机械工程学报, 2022, 58(9): 49-61.

ZHOU Yang, CHANG Boyan, JIN Guoguang, LIANG Dong. Mathematic Description Method of Variable Topology Configuration for Dynamic Modeling of Metamorphic Mechanism[J]. Journal of Mechanical Engineering, 2022, 58(9): 49-61.

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面向变胞机构动力学建模的变拓扑构型数学描述方法

Mathematic Description Method of Variable Topology Configuration for Dynamic Modeling of Metamorphic Mechanism

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