新型单轴柔性铰链拓扑结构设计与柔度分析

Topological structure design and compliance analysis of a new single-axis flexure hinge

采用基于三维连续体拓扑优化理论的变密度法,以柔性铰链柔度比最大为目标,建立了单轴柔性铰链的拓扑优化模型。首先,借助Opti Struct软件设计出一种具有全新三维拓扑结构的单轴柔性铰链;其次,结合卡氏第二定理和能量法对该新型柔性铰链的转动性能进行理论分析,推导出该新型柔性铰链的柔度矩阵,通过16组实例的理论计算和有限元仿真分析,得到其相对误差在6.35%以内,验证了该新型柔性铰链柔度矩阵理论公式的正确性;最后,分析了具有相同切口轮廓的圆弧型柔性铰链和新型柔性铰链的柔度差异。结果表明:新型柔性铰链具有更大的柔度,其柔度性能提升300%。使用三维连续体拓扑优化方法,可为单轴柔性铰链的设计提供一个新思路。

Based on three-dimensional continuum topology optimization theory,aimed at maximizing compliance ratio,solid isotropic material with penalization model was used to establish the topology optimization model of a single-axis flexure hinge. With the help of Opti Struct,this paper designed a kind of single-axis flexure hinge with a new three-dimensional topological structure. Secondly,combining Castigliano＇s second theorem and the method of energy for the compliance of flexure hinge in theory,it deduced the compliance matrix of the new flexure hinge. 16 groups＇ analysis in theory and finite element simulation analysis showed the correctness of the theoretical formula because the relative error of analysis and FEA was within 6. 35%. Finally,it compared the difference of compliance between the new flexure hinge and circular flexure hinge with the same cut profile. The results show that the new flexure hinge has much better performance in compliance.Compared with the circular flexure hinge,its compliance can be improved by 300%. Based on the three-dimensional continuum topology optimization method,this paper presented a new thought for the design of singleaxis flexure hinge.