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| Mechanical model and performance analysis of a flexure hinge based on the finite element method |
| HU Jun-feng， HAO Ya-zhou， XU Gui-yang |
| School of Mechanical & Electrical Engineering， Jiangxi University of Science and Technology， Ganzhou 341000， China |
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Abstract In order to accurately describe the mechanical properties of a flexure hinge, a general mechanical model based on finite element method is proposed, and the static and dynamic performance analysis is carried out according to the propose model. Euler-Bernoulli beam was adopted to simulate the mechanical behavior of the flexure hinge, and it was divided into three nodes with three degrees of freedom and two elements with variable crosssection. A closed stiffness matrix related to the structural parameters of the flexure hinge was established by using the principle of minimizing potential energy, and the mass matrix and dynamics equations were built by employing Lagrange equation. In order to validate the precision of the proposed mechanical model, the analysis results by ANSYS was compared and got the difference range from 1.1% to 5.6%, which showed that the theoretical model was close to ANSYS and the proposed model could accurately illustrate the static and dynamic properties. The finite element model of the flexure hinge can be applied accurately to analyze the relationship between its accuracy and natural frequency and structural parameters, stress distributions and frequency response. Therefore, a precise mechanical model of the circular flexure hinge is provided for the design of compliant mechanisms.
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Received: 19 May 2014
Published: 28 October 2014
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基于有限元法的柔性铰链力学模型和性能分析
为了精确描述柔性铰链力学性能，提出一种通用的基于有限元法的力学模型，并基于该模型分析其静态和动态性能.柔性铰链采用欧拉伯努利梁模拟其力学行为，将其划分为3个三自由度的结点、2个变截面单元.采用最小势能原理建立与柔性铰链结构参数相关的封闭形式刚度矩阵，采用拉格郎日方程建立铰链的质量矩阵和动力学方程.为了验证所推导的力学模型的精确性，与ANSYS分析结果进行比较分析，两者的结果差值在1.1%～5.6%范围之内，说明理论模型与ANSYS分析结果吻合，所建立的模型能精确反映其静态和动态性能.基于柔性铰链有限元模型，可精确分析铰链参数与其精度和固有频率的关系、应力分布和频率响应，为正圆型柔性铰链应用于柔顺机构设计提供了一种精确的力学模型.
关键词：
柔性铰链,
有限元法,
力学性能,
欧拉-伯努利梁
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