椭圆弧柔性铰链刚度简化计算及优化设计

Stiffness calculation and optimal design of elliptical flexure hinges

本文主要研究了椭圆弧柔性铰链刚度的优化设计方法。首无,针对椭圆弧柔性铰链刚度计算公式过于复杂的问题,采用幂函数非线性曲线拟合的方法,推导了椭圆弧柔性铰链刚度的近似理论计算公式。然后,基于近似理论计算公式,分析了柔性铰链的精度特性及工作时的最大应力;采用GlobalSearch全域优化指令和Fmincon局域优化指令对椭圆弧柔性铰链工作方向的最大刚度进行了优化设计。最后,采用有限元仿真和实验验证的方法证实近似理论计算公式的适用性和优化结果的可靠性。验证显示:实验结果与近似理论计算结果的相对误差小于5%,表明提出的方法不仅省去了繁杂的有限元模型建立以及计算和修改的过程,大大提高了设计效率;而且通过优化计算可以得到椭圆弧柔性铰链的最大刚度。

An optimization design method for elliptical flexure hinges is researched.As the traditional calculation formula for the stiffness of elliptical flexure hinges is more complex,this paper deduces a approximate theoretical formula by nonlinear fitting method with power function.Based on the approximate theoretical formula,it analyzes the precision characteristics of the flexure hinges and their maximum stresses at working.Then,the global optimization solver GlobalSearch and local optimization solver Fmincon are used to design optimally the maximum stiffness of an elliptical flexure hinge at a working direction.Finally,the applicability of the approximate theoretical calculation equation and the accuracy of the optimization results are assessed by comparison with the results from finite element analysis and experimental data.The results show that the relative errors between the finite element simulation,experimental data and the approximate theoretical calculation for the stiffness of elliptic hinge are within 5%.It concludes that the method avoids establishing the complex finite element mode and the processes of calculation and modification,and greatly improves the design efficiency.Moreover,it can obtain the maximum stiffness of the elliptical flexure hinges by optimizationcalculation.