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工程设计学报
Chinese Journal of Engineering Design  2025, Vol. 32 Issue (2): 252-261    DOI: 10.3785/j.issn.1006-754X.2025.04.158
Optimization Design     
Design and analysis of nested cosine function type multi-axis flexure hinge
Meijuan XU(),Qiliang WANG(),Yongfeng HONG,Yiping LONG,Tong LIU,Bin GUO
School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
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Abstract  

The notch shapes of existing flexure hinges are primarily limited to conic sections and their combinations, which tend to fail due to excessive stress under complex loads and large angular movements. Therefore, a novel nested cosine function type multi-axis flexure hinge is designed. Firstly, based on the finite beam compliance matrix modeling (FBMM) method, the compliance and precision models of the novel flexure hinge were established. Compared with the finite element simulation results of ANSYS Workbench software, the relative errors of compliance and precision were less than 4.89% and 4.97% respectively, which verified the validity of theoretical models. Then, the effects of structural parameters on the compliance, precision and compliance-precision ratio of the novel flexure hinge were discussed, and compared with elliptic type, arc type and sinusoidal type multi-axis flexure hinges. The results indicated that the designed flexure hinge had the characteristics of high flexibility and low stress. Finally, an experimental platform for flexure hinge was built to test the deformation. The relative error between the measured results and the theoretical results was less than 8%, which further verified the validity of the compliance model. The nested cosine function type multi-axis flexure hinge can provide reference for the design of large-stroke compliant precision positioning stages.

Key words： multi-axis flexure hinge      finite beam compliance matrix modeling      compliance      stress      finite element simulation     
Received: 15 July 2024      Published: 06 May 2025
CLC:  TH 112  
Corresponding Authors: Qiliang WANG     E-mail: 2517608138@qq.com;wangqiliang@jxust.edu.cn
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Meijuan XU
Qiliang WANG
Yongfeng HONG
Yiping LONG
Tong LIU
Bin GUO
Cite this article:

Meijuan XU,Qiliang WANG,Yongfeng HONG,Yiping LONG,Tong LIU,Bin GUO. Design and analysis of nested cosine function type multi-axis flexure hinge. Chinese Journal of Engineering Design, 2025, 32(2): 252-261.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.04.158     OR     https://www.zjujournals.com/gcsjxb/Y2025/V32/I2/252


嵌套余弦函数型多轴柔性铰链的设计与分析

现有柔性铰链的缺口形状主要局限于圆锥曲线及其组合，且在应对复杂载荷和大角度运动时容易因应力过大而失效。为此，设计了一种新型的嵌套余弦函数型多轴柔性铰链。首先，基于有限梁柔度矩阵建模（finite beam compliance matrix modeling, FBMM）法构建了新型柔性铰链的柔度和精度模型，并与ANSYS Workbench软件的有限元仿真结果对比，发现柔度和精度的相对误差分别小于4.89%和4.97%，验证了理论模型的有效性。然后，讨论了结构参数对新型柔性铰链柔度、精度和柔度精度比的影响，并与椭圆型、圆弧型、正弦型多轴柔性铰链进行了比较。结果表明，所设计的柔性铰链具有柔度大、应力低的特点。最后，通过搭建柔性铰链实验平台来测试其变形情况，实测结果与理论结果的相对误差小于8%，进一步验证了柔度模型的有效性。嵌套余弦函数型多轴柔性铰链可为大行程柔顺精密定位平台的设计提供参考。


关键词： 多轴柔性铰链,  有限梁柔度矩阵建模,  柔度,  应力,  有限元仿真 
Fig.1 Structure diagram of nested cosine function type multi-axis flexure hinge
Fig.2 Force diagram of nested cosine function type multi-axis flexure hinge
Fig.3 Deformation diagram of rotation center of nested cosine function type multi-axis flexure hinge
Fig.4 Finite element model of nested cosine function type multi-axis flexure hinge
组别lat
1102.01.0
2102.51.0
3122.01.0
4102.00.8
Table 1 Four groups of flexure hinge dimension parameters
组别对比项

Cx1, Fx /

(m·N-1)

Cy1, Mz /N-1Cθz, Mz /(N-1·m-1)

Cy1, Fy /

(m·N-1)

Cθz, Fy /N-1

Cx2, Fx /

(m·N-1)

Cy2, Mz /N-1

Cy2, Fy /

(m·N-1)

1理论值8.065×10-85.013×10-31.0022.671×10-55.013×10-34.037×10-84.894×10-43.259×10-6
仿真值8.326×10-85.116×10-31.0232.730×10-55.117×10-34.192×10-85.083×10-43.403×10-6
相对误差/%3.132.012.052.162.033.703.724.23
2理论值7.567×10-84.720×10-30.9432.499×10-54.720×10-33.788×10-84.326×10-42.846×10-6
仿真值7.904×10-84.832×10-30.9672.561×10-54.833×10-33.986×10-84.510×10-42.983×10-6
相对误差/%4.262.322.482.422.344.974.084.59
3理论值9.678×10-87.219×10-31.2024.604×10-57.219×10-34.844×10-87.048×10-45.575×10-6
仿真值9.912×10-87.322×10-31.2204.674×10-57.322×10-34.982×10-87.237×10-45.749×10-6
相对误差/%2.361.411.481.501.412.772.613.03
4理论值1.182×10-71.152×10-22.3026.082×10-51.152×10-25.918×10-81.056×10-36.859×10-6
仿真值1.222×10-71.170×10-22.3396.178×10-51.170×10-26.133×10-81.085×10-37.080×10-6
相对误差/%4.891.541.581.551.543.512.673.12
Table 2 Comparison of theoretical and simulated values of compliance and precision of flexure hinges
Fig.5 Influence of structural parameters of flexure hinge on compliance
Fig.6 Influence of structural parameters of flexure hinge on precision
Fig.7 Influence of structural parameters of flexure hinge on compliance-precision ratio
Fig.8 Comparison of compliance, precision and compliance-precision ratio of different flexure hinges
Fig.9 Comparison of compliance-stress ratio of different flexure hinges
Fig.10 Structural dimension of nested cosine function type multi-axis flexure hinge sample
Fig.11 Experimental platform for flexure hinge
Fig.12 Comparison of theoretical and measured values of displacement at point 1' and rotation angle at point 2'
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