精密柔性角度调节机构的几何非线性建模分析  

Geometric nonlinear modeling and analysis of precise mechanism with flexible angle adjustment

作　　者：赵高峰[1,2,3] 祝万钱 金利民 薛松 ZHAO Gaofeng;ZHU Wanqian;JIN Limin;XUE Song(Shanghai Institute of Applied Physics,Chinese Academy of Sciences,Shanghai 201800;Shanghai Advanced Research Institute,Chinese Academy of Sciences,Shanghai 201204;University of Chinese Academy of Sciences,Beijing 100049)

机构地区：[1]中国科学院上海应用物理研究所,上海201800 [2]中国科学院上海高等研究院,上海201204 [3]中国科学院大学,北京100049

出　　处：《机械设计》2024年第9期119-125,共7页Journal of Machine Design

基　　金：国家自然科学基金项目资助(11805262);中国科学院青年创新促进会资助项目(2020288)。

摘　　要：为同步辐射关键光学设备,文中优化设计了一种精密圆盘式柔性角度调节机构,柔性铰链采用直梁圆角形,既可以实现微纳弧度级的高精度,又能有较大的转角范围。对该角度调节机构在较大转角时产生几何非线性的因素进行分析,建立分段式边界约束模型,采用数值分析方法求解。同时,建立了增量型更新拉格朗日法的非线性平衡方程,采用牛顿-拉普森方法对平衡方程进行迭代求解。采用两种方法分析了机构的输出角度与输入载荷的非线性关系,以及考虑非线性时柔性铰链中心的漂移,并通过有限元的非线性与线性分析对比,研究了非线性对机构输出角度和最大应力的影响。结果表明:建立两种模型分析吻合度较好,该角度调节机构呈强非线性,可实现的最大安全调节角度为1.6°,分析证明了为机构设计建立的非线性模型的准确性和有效性。In this article,in order to ensure synchrotron radiation of the key optical equipment,efforts are made to design and optimize a precise disc mechanism with flexible angle adjustment.The corner-filleted flexible hinge achieves high precision at the micro nano arc level and has a large angle range.The analysis is conducted on the factors that cause the mechanism’s geo-metric nonlinearity at large turning angles;a model of segmented boundary constraint is set up,and then the numerical analysis is used to solve this model.At the same time,a nonlinear equilibrium equation of the incremental updating Lagrangian method is constructed,and the Newton-Raphson method is used to iteratively solve this equation.The two methods are used to analyze the nonlinear relationship between the mechanism’s output angle and input load;in terms of nonlinearity,the drift at the center of the flexible hinge is taken into consideration.The finite-element analysis is carried out to compare nonlinearity and linearity;then,the influence of nonlinearity on the mechanism’s output angle and maximum stress is explored.The results indicate that the two models have good agreement,and the mechanism exhibits strong nonlinearity,with the secure adjusted angle of 1.6°to the largest extent.This study has proved that the nonlinear model used for mechanism design is accuracy and effective.

关 键 词：直梁圆角形柔性铰链 角度调节 几何非线性 边界约束 有限元分析 

分 类 号：TH122[机械工程—机械设计及理论]