新型直圆椭圆复合型多轴柔性铰链的柔度计算及其性能分析
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摘要
多轴柔性铰链应用于空间柔性机构。提出一种新型多轴柔性铰链——直圆椭圆复合型多轴柔性铰链,以卡氏第二定理为理论基础,推导直圆椭圆复合型多轴柔性铰链的柔度计算式。采用所得计算式对一组实例进行柔度计算,同时对其进行有限元分析。通过对比分析,二者误差在14%以内,验证了计算式的正确性。借助于推导的计算式,分析直圆椭圆复合型多轴柔性铰链的结构参数对其柔度的影响。定义相对柔度比,得出直圆椭圆复合型多轴柔性铰链的转动能力、对载荷的敏感性均优于直圆型多轴柔性铰链。综上,直圆椭圆复合型多轴柔性铰链的提出,为柔性铰链在空间柔性机构的工程应用提供了新的思路。
The multiple-axis flexure hinges with multiple degrees of freedom are used in the three-dimensional motion. A novel multiple-axis flexure hinge right circular elliptical hybrid multiple-axis flexure hinge was introduced. Based on the Castigliano's second theorem, the compliance formulations of the novel multiple-axis flexure hinge were formulated. The compliance calculations and the finite element simulation were performed simultaneously for a set of examples. By contrast to the above results, the error between them is within 14%, so the correctness of the compliance formulations is indicated. By means of the compliance formulations, the effects of the geometric parameters on the compliance were analyzed. The relative compliance ratio was defined, the novel multiple-axis flexure hinge had better compliance and sensitivity to the loads than the right circular multiple-axis flexure hinge. All of the above provides a new idea for the analysis and design of the multiple-axis flexure hinges in the spatial compliant mechanisms.
The multiple-axis flexure hinges with multiple degrees of freedom are used in the three-dimensional motion. A novel multiple-axis flexure hinge right circular elliptical hybrid multiple-axis flexure hinge was introduced. Based on the Castigliano's second theorem, the compliance formulations of the novel multiple-axis flexure hinge were formulated. The compliance calculations and the finite element simulation were performed simultaneously for a set of examples. By contrast to the above results, the error between them is within 14%, so the correctness of the compliance formulations is indicated. By means of the compliance formulations, the effects of the geometric parameters on the compliance were analyzed. The relative compliance ratio was defined, the novel multiple-axis flexure hinge had better compliance and sensitivity to the loads than the right circular multiple-axis flexure hinge. All of the above provides a new idea for the analysis and design of the multiple-axis flexure hinges in the spatial compliant mechanisms.
引文
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[10] 刘庆玲,翁海珊,邱丽芳.新型单边直圆椭圆混合柔性铰链的柔度计算及其性能分析[J].工程力学,2010,27(10):52-56.LIU Q L,WENG H S,QIU L F.Compliances Calculation and Behavior Analysis of the Half Right Circular Elliptical Hybrid Flexure Hinge[J].Engineering Mechanics,2010,27(10):52-56.
[2] PAROS J M,WEISBORO L.How to Design Flexure Hinges[J].Machine Design,1965,37(27):151-157.
[3] HOWELL L L.Compliant Mechanisms[M].New York:John Wiley & SonsInc,2001.
[4] LOBONTIU N.Compliant Mechanisms:Design of the Flexure Hinges[M].New Work:CRC Press LLC,2003.
[5] 曹锋,焦宗夏.双轴椭圆柔性铰链的设计计算[J].工程力学,2007,24(4):178-182.CAO F,JIAO Z X.Design of Double-axis Elliptical Flexure Hinges[J].Engineering Mechanics,2007,24(4):178-182.
[6] 李玉和,李庆祥,陈璐云,等.单轴柔性铰链设计方法的研究[J].清华大学学报(自然科学版),2002,42(2):172-174.LI Y H,LI Q X,CHEN L Y,et al.Study on Design Method of One-axis Flexure Hinge[J].Journal of Tsinghua University(Science and Technology),2002,42(2):172-174.
[7] 赵磊,巩岩,华洋洋.直梁圆角型柔性铰链的回转精度分析[J].中国机械工程,2013,24(6):715-720.ZHAO L,GONG Y,HUA Y Y.Rotation Analysis of Corner-filled Flexure Hinge[J].China Mechanical Engineering,2013,24(6):715-720.
[8] 刘庆玲,翁海珊,邱丽芳.微位移机构中变截面柔性铰链等效刚度的求解方法研究[J].中国机械工程,2010,21(8):917-919.LIU Q L,WENG H S,QIU L F.Study on Equivalent Stiffness of a Flexure Hinge and Its Application in Micro-displacement Compliant Mechanism[J].China Mechanical Engineering,2010,21(8):917-919.
[9] 刘庆玲,翁海珊,邱丽芳.新型单边复和型柔性铰链的柔度计算及其性能分析[J].工程设计学报,2009,16(4):276-280.LIU Q L,WENG H S,QIU L F.Compliances Calculation and Performance Analysis of Half Hybrid Flexure Hinge[J].Journal of Engineering Design,2009,16(4):276-280.
[10] 刘庆玲,翁海珊,邱丽芳.新型单边直圆椭圆混合柔性铰链的柔度计算及其性能分析[J].工程力学,2010,27(10):52-56.LIU Q L,WENG H S,QIU L F.Compliances Calculation and Behavior Analysis of the Half Right Circular Elliptical Hybrid Flexure Hinge[J].Engineering Mechanics,2010,27(10):52-56.