幂函数正弦柔性铰链设计与分析

Design and Analysis of Power-function-sine Flexure Hinges

提出了一种新型幂函数正弦柔性铰链,利用卡氏第二定理推导了柔性铰链的柔度与转动精度计算公式,并取不同参数值对柔度和转动精度进行了有限元仿真分析和理论值计算,相对误差在10%以内,验证了计算公式的正确性;分析了柔性铰链的曲线方程参数对铰链性能的影响。结果表明,最小厚度对柔性铰链的性能影响最大。此外,将椭圆、双曲线与新型铰链进行了对比。结果表明,椭圆柔性铰链的柔度最大,但是转动精度最小;双曲线柔性铰链的转动精度最大,但是柔度最小。通过引入柔度精度比β,分析对比得知,在相同L的情况下,改变d,幂函数正弦柔性铰链的β值分别比椭圆和双曲线柔性铰链平均提高了2.68倍和1.237倍;在相同d的情况下,改变L,幂函数正弦柔性铰链的β值分别比椭圆和双曲线柔性铰链平均提高了2.60倍和1.18倍。表明幂函数正弦柔性铰链的综合性能更有优势。

In this study,a new type of power-function-sine flexure hinge is proposed.The calculation for⁃mula of compliance and rotation accuracy of the flexure hinge is derived by using Castigliano's second theorem.The finite element simulation analysis and theoretical value calculation of compliance and rotation accuracy are carried out by taking different parameter values.The relative error is less than 10%,which verifies the correct⁃ness of the calculation formula.The influence of curve equation parameters of the flexure hinge on the perfor⁃mance of the flexure hinge is analyzed.The results show that the minimum thickness has the greatest influence on the performance of the flexure hinge.In addition,the ellipse and hyperbola are compared with the new hinge.The results show that the ellipse flexure hinge has the greatest compliance,but the rotation accuracy is the small⁃est;the hyperbolic flexure hinge has the highest rotation accuracy,but the lowest compliance.By introducing the compliance accuracy ratioβ,through analysis and comparison,it is known that under the same L and the chang⁃ing d,the value of the power function sine flexure hingeβis 2.68 times and 1.237 times higher than those of el⁃liptical and hyperbola flexure hinges respectively.With the same flexure hinge diameter and the changing length,the value of the power function of sinusoidal flexure hingeβis 2.60 times and 1.18 times higher than that of elliptic and hyperbolic flexure hinges respectively.It shows that the power function sinusoidal flexure hinge has more advantages in comprehensive performance.