直梁圆角型柔性铰链的回转精度分析

Rotation Precision Analysis of Corner-filleted Flexure Hinge

首先,基于悬臂梁理论推导了直梁圆角型柔性铰链回转精度的解析计算方法,建立了柔性铰链回转精度的闭环解析模型,并给出了rt时的回转精度简化计算公式。然后,采用与有限元分析结果相比较的方式对解析模型进行了验证,结果表明两者的相对误差小于5%,从而验证了回转精度矩阵闭环解析模型的正确性。最后,分析了柔性铰链的材料参数和几何参数对其回转精度的影响,结果表明:直梁圆角型柔性铰链材料的弹性模量E越大、泊松比ν越小,其回转精度越高;直梁圆角型柔性铰链的高度h越大,其回转精度越高;当量纲一参数0≤s≤1,3≤q≤10时,随着s的增大、q的减小,回转精度越来越高;柔性铰链的厚度t一定时,圆角半径r越大,铰链长度l越小,其回转精度就越高;当0.5mm≤t≤4mm,几何参数h、r、l一定时,随着t的增大,其回转精度越高,且其变化速率越来越小。建立的直梁圆角型柔性铰链回转精度矩阵闭环解析模型,可为柔性铰链以及柔性机构的设计优化提供理论依据。

First, based on the beam theory, an analytical equation of corner-- filleted flexure hinge＇ s pla- nar rotation precision was obtained, and the closed--form planar rotation precision matrix equation was also obtained, and the simple calculation equation was reduced when r〈〈t. Then, using the finite element method to check the analytical equation, results show the relative errors between the analytical and finite element data are less than 5 ~, finite element simulation results confirm the theoretical formulation data. Finally, influence of the material parameters and structural parameters on the rotation precision were analyzed, the results are as follows.when Young＇s modulus E increases or Passion ratio v decreases, then the rotation precision will be better;when the height of flexure hinge h increases,its rotation precision will be better; when 0≤s≤l, 3≤q≤10,if s increases or q decreases,then the rotation precision will be better;when thickness of flexure hinge t is fixed,if the corner radio r increases or the hinge＇s length l decreases,then the rotation precision will be better; when 0. 5mm≤t≤4mm and the parameters h, r, l are fixed respectively, if the thickness of flexure hinge t increases, the rotation precision will be better, and the changing radio will decrease. The above closed--form rotation precision matrix equation will be useful for the design and optimization of flexure hinges and compliant mechanisms.