Design and compliance analysis of large stroke flexible ball hinge with orthogonal reeds

doi:10.3785/j.issn.1006-754X.2023.00.069

Chin J Eng Design

2023, Vol. 30

Issue (5): 626-633 DOI: 10.3785/j.issn.1006-754X.2023.00.069

Product Innovation Design

Design and compliance analysis of large stroke flexible ball hinge with orthogonal reeds

Chao XIE(

),Yunzhuang CHEN,Guangnan SHI,Leijie LAI(

)

School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

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Abstract

The traditional notched flexible ball hinge has smaller working stroke, complex structural configuration and compliance calculation, and high processing requirements, so it can not be applied to the occasions requiring large stroke. Therefore, a large stroke flexible ball hinge with orthogonal reeds was designed, which meant that the reed beam with large deformation capacity could form a Hooke joint through orthogonal combination, enabling it to achieve movement in three functional axis directions. The flexible ball hinge had the advantages of simple structural configuration, easy processing and manufacturing, and large working stroke. Based on the compliance matrix and connection type of a single reed beam of the flexible ball hinge, the global compliance matrix of the flexible ball hinge was modeled and calculated by the compliance matrix method and coordinate transformation method. The established compliance model was verified through finite element simulation and experimental test, and the influence of geometric parameters of the flexible ball hinge on compliance was analyzed. The results showed that the relative error between the theoretical calculating value and the simulated value of compliance was basically within 10%, and the relative error between the calculated value and the test value was within 8%; the influence degree of geometric parameters on compliance was in descending order: thickness, width and length of reed beam 2. The research results can provide reference for the diversified design of large stroke spatial compliant mechanism.

Key words： reed flexible ball hinge large stroke finite element analysis compliance

Received: 08 March 2023 Published: 03 November 2023

CLC:

TH 132

Corresponding Authors: Leijie LAI E-mail: silencexc@126.com;lailj@sues.edu.cn

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Cite this article:

Chao XIE,Yunzhuang CHEN,Guangnan SHI,Leijie LAI. Design and compliance analysis of large stroke flexible ball hinge with orthogonal reeds. Chin J Eng Design, 2023, 30(5): 626-633.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2023.00.069 OR https://www.zjujournals.com/gcsjxb/Y2023/V30/I5/626

正交簧片型大行程柔性球铰设计及柔度分析

传统缺口型柔性球铰的工作行程较小，且存在结构构型及柔度计算复杂、加工工艺要求高等问题，不能应用于需大行程的场合。为此，设计了一种正交簧片型大行程柔性球铰，即将具有较大变形能力的簧片梁通过正交组合形成虎克铰，使其能够实现3个功能轴线方向的运动。该柔性球铰具有结构构型简单、加工制作容易和工作行程较大等优点。根据柔性球铰单个簧片梁的柔度矩阵及连接方式，采用柔度矩阵法和坐标变换方法，对柔性球铰的全局柔度矩阵进行建模和计算，通过有限元仿真和实验测试对所建立的柔度模型进行验证，并分析了柔性球铰几何参数对柔度的影响规律。结果表明：柔度理论计算值与仿真值的相对误差基本在10%以内，与测试值的相对误差在8%以内；几何参数对柔度影响程度从大到小依次是柔性簧片梁2的厚度、宽度、长度。研究结果可以为大行程空间柔顺机构的多样化设计提供参考。

关键词： 簧片, 柔性球铰, 大行程, 有限元分析, 柔度

Fig.1 Structure of large stroke flexible ball hinge

Fig.2 Schematic diagram of deformation principle of large stroke flexible ball hinge

Fig.3 Schematic diagram of reed beam

参数	计算公式
$C δ x - F x$	l/(Etw)
$C δ y - F y$	4l³/(Et³w)
$C δ z - F z$	4l³/(Etw³)
$C θ x - M x$	l/(GJ)
$C θ y - M y$	12l/(Etw³)
$C θ z - M z$	12l/(Et³w)
$C δ y - M z$	6l²/(Et³w)
$C δ z - M y$	6l²/(Etw³)
$C θ y - F z$	6l²/(Etw³)
$C θ z - F y$	6l²/(Et³w)

Table 1 Parameters and their calculation formulas of compliance matrix of reed beam

Fig.4 Section of flexible ball hinge

Fig.5 Spring model of flexible hinge

Table 2 Material and geometric parameters of flexible ball hinge

Fig.6 Mesh generation of flexible ball hinge simulation model

Fig.7 Static simulation analysis results of flexible ball hinge

柔度	计算值	仿真值	相对误差/%
$C δ y - F y$ /(mm/N)	1.013 9	1.112 6	8.87
$C δ z - F z$ /(mm/N)	1.300 0	1.458 3	10.85
$C θ x - M x$ /(rad/(N·m))	1.316 3	1.426 0	7.69
$C δ y - M z$ ， $C θ z - F y$ /(rad/N)	0.029 5	0.031 9	7.52
$C δ z - M y$ ， $C θ y - F z$ /(rad/N)	-0.034 2	-0.033 0	3.64
$C θ y - M y, C θ z - M z$ /(rad/(N·m))	1.061 5	1.032 3	2.83

Table 3 Theoretical calculation and simulation analysis results of compliance of flexible ball hinge

Fig.8 Testing device of compliance of flexible ball hinge

Fig.9 Force-displacement curve of flexible ball hinge in the y and z directions

Fig.10 Torque‒angle curve of flexible ball hinge

Fig.11 Influence of geometric parameters of reed beam 2 on compliance of flexible ball hinge


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