针对精密光学仪器对光学元件柔性支撑的需求, 提出了由带圆角的短直梁复合组成的Cartwheel型双轴柔性铰链, 并利用无量纲设计图研究了设计方法。首先, 基于对Cartwheel双轴柔性铰链的参数化有限元分析进行多项式拟合, 建立了其刚度、应力等力学指标的无量纲设计图。针对光学仪器的工程需要, 利用该无量纲设计图进行了实例设计, 并利用有限元分析对其进行了实验验证。搭建了光学测试平台, 对设计实例的转动刚度进行了测量。结果显示: 有限元分析结果、实验测量数据与设计结果符合得较好, 最大相对误差为10.1%。使用无量纲设计图方法作为设计工具, 设计者可根据对带圆角短直梁复合组成的Cartwheel型双轴柔性铰链的刚度、转角行程、最大应力与结构重量等要求, 确定其几何尺寸, 从而方便、快速、准确地满足设计要求。

To realize the flexural support for optical elements in a precision optical instrument, a Cartwheel bi-axial flexural hinge composed by filleted short beams was proposed. The dimensionless design graph method for the design of the spatial flexural hinge was presented. First, the parametric finite element analysis on the Cartwheel bi-axial flexural hinge was performed, and then a polynomial fitting was carried out according to the analysis results to establish the dimensionless design graph for the mechanical characteristics of the flexural hinge, such as rotational stiffness and maximum stress. A practical design by the dimensionless graph method was performed to satisfy the supporting demand of an optical instrument, and the finite element analysis was used to verify it also. Finally, an optical test platform was established, and the rotational stiffness of the design was measured. Obtained results show that the maximum relative error of the rotational stiffness between analysis result, test result and design result is 10.1%. In conclusion, by using the dimensionless design graph as a design tool, a designer can determine the optimal geometry rapidly and correctly of the Cartwheel bi-axial flexural hinge based upon its demands for the stiffness, rotation angle, maximum stress and the weight. This paper can provide reference for the application of the Cartwheel bi-axial flexural hinge in precision optical instruments.