直梁圆角形柔性铰链的柔度矩阵分析

对直梁圆角形柔性铰链的柔度矩阵进行了研究。首先,基于悬臂梁理论推导了直梁圆角形柔性铰链平面内变形的解析计算方法,建立了柔性铰链平面内柔度矩阵的闭环解析模型,并给出了rt(r为铰链圆角半径,t为铰链厚度)时柔度矩阵的简化计算公式。然后,建立了直梁圆角形柔性铰链的有限元模型,得到了柔性铰链结构参数r/t和l/t(l为铰链长度）变化时柔度矩阵解析值和有限元仿真值的相对误差,以及r/t变化时柔度矩阵简化解析值和仿真值的相对误差。结果表明:采用悬臂梁理论建立的柔性铰链柔度矩阵模型,当l/t≥4时,柔度矩阵各项参数的理论解析值与有限元仿真值相对误差在5.5%以内,当0.1≤r/t≤0.5时,两者的相对误差能够控制在9%以内,当0.2≤r/t≤0.3时,两者的相对误差能够控制在6.5%以内;当r/t≤0.3时,简化解析值与仿真值的相对误差控制在9%以内, 当r/t≤0.2时,简化解析值与仿真值的相对误差控制在7%以内,从而验证了柔度矩阵闭环解析模型的正确性。建立的直梁圆角形柔性铰链柔度矩阵闭环解析模型可为柔性铰链以及柔性体机构的设计和优化提供理论依据。

Compliance Matrix Analysis of Corner-filleted Flexure Hinge

This paper focused on the corner-filleted flexure hinge to investigate its compliance matrix.First,based on the beam theory,an analytical equation of corner-filleted flexure hinge's planar deformations  were obtained,and the closed-form  planar compliance matrix equation was obtained,the simple calculation equation of compliance matrix was also reduced when rt r is the radio of the hinge,t is the thickness of the hinge.Then,finite element model of the corner-filleted flexure hinge was established,the analytical results and finite element results of the compliant matrix were obtained when changing the radio of r/t and l/t(l is the length of the hinge),and the relative errors between the analytical and finite element data were calculated.The results indicate that when the ratio of l/t≥4,the analytical data error will be less than 5.5%,and when the ratio of 0.1≤r/t≤0.5,the analytical data error will be less than 9%,especially when 0.2≤r/t≤0.3,the error will less than 6.5%;when r/t≤0.3 and r/t≤0.2 the simple analytical data error will be  less than 9% and 7% separately.Finite element simulation results confirm the theoretical formulation data.The above closed-form compliance matrix equation will be useful for the design and optimization of flexure hinges and compliant mechanisms.