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Derivation of empirical compliance equations for circular flexure hinge considering the effect of stress concentration

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Abstract

This paper presents the compliance modeling of circular flexure hinge. The calculation accuracies of several compliance equations are firstly compared with the finite element analysis (FEA) results. Then the influences of the stress concentration on the compliance calculations of the flexure hinge are analyzed systematically. It shows that the stress concentration has great influence on the axial compliance calculation. Utilizing the exponential model, empirical compliance equations of circular flexure hinge are derived, and the influences of the stress concentration on the axial compliance are considered. These empirical compliance equations are verified to be with high calculation accuracy for a wide range of t/R ratios. Finally, the empirical compliance equations are utilized to analyze the compliance and displacement amplification ratio of a bridge-type compliant amplifier. The results are compared with FEA software, and it proves the accuracy and effectiveness of these empirical equations once again. In addition, the modeling method presented in this paper is general and can also be applied to the compliance equations derivation of other types of flexure hinges.

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Authors and Affiliations

  1. Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Tie-Min Li, Jing-Lei Zhang & Yao Jiang

  2. Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing, 100084, China

    Tie-Min Li

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  1. Tie-Min Li
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  2. Jing-Lei Zhang
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  3. Yao Jiang
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Correspondence to Yao Jiang.

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Li, TM., Zhang, JL. & Jiang, Y. Derivation of empirical compliance equations for circular flexure hinge considering the effect of stress concentration. Int. J. Precis. Eng. Manuf. 16, 1735–1743 (2015). https://doi.org/10.1007/s12541-015-0228-5

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  • DOI: https://doi.org/10.1007/s12541-015-0228-5

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