椭圆形多轴柔性铰链的柔度计算及性能分析
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摘要
多轴柔性铰链具有多个自由度,适用于三维空间运动。文中基于线弹性小变形假设,以卡氏第二定理为理论基础,得出椭圆形多轴柔性铰链的柔度计算式。选择一组椭圆形多轴柔性铰链进行柔度实例计算,同时对其进行有限元分析,验证椭圆形多轴柔性铰链柔度计算式的正确性,同时进行误差分析。引入比例系数ζ,当ζ<0.5时,所有柔度项的误差基本在11%以内,当ζ≥0.5时,除C1,x-Fx之外的各柔度项误差明显增大,最大误差达到28%。利用所得的柔度计算式分析了铰链半短轴n、最小截面直径t对柔度的影响,同时对比分析了柱形、椭圆形、直圆形多轴柔性铰链柔度的差异。综上所述,为椭圆形多轴柔性铰链在空间柔性机构应用中的性能分析与选型设计提供了理论基础与思路。
The multiple-axis flexure hinges with multiple degrees of freedom are applied in the three-dimensional motion. In this paper, based on the hypothesis of linear elasticity and small deformation as well as the Castigliano's Second Theorem, the compliance formula of elliptical multiple-axis flexure hinges is worked out. A set of elliptical multi-axis flexure hinges are selected for the calculation; the finite element analysis is carried out to verify whether the calculation is correct and whether there are any errors. Besides, the coefficient ζ is introduced. When ζ is < 0.5, the error between the theoretical calculation and the simulation is less than 11%; when ζ is ≥0.5, except C1,x-Fx, the error of other compliance increases with the maximum of 28%. With the aid of the compliance formula, the analysis is conducted on the effects of such structural parameters as the hinge semi-short axis n and the minimum cross-sectional diameter t on the compliance as well as the compliance difference among the cylinder,elliptical and right-circle multiple-axis flexure hinges. The results provide new ideas and theoretical basis for the analysis and design of elliptical multiple-axis flexure hinges in the spatial compliant mechanism.
The multiple-axis flexure hinges with multiple degrees of freedom are applied in the three-dimensional motion. In this paper, based on the hypothesis of linear elasticity and small deformation as well as the Castigliano's Second Theorem, the compliance formula of elliptical multiple-axis flexure hinges is worked out. A set of elliptical multi-axis flexure hinges are selected for the calculation; the finite element analysis is carried out to verify whether the calculation is correct and whether there are any errors. Besides, the coefficient ζ is introduced. When ζ is < 0.5, the error between the theoretical calculation and the simulation is less than 11%; when ζ is ≥0.5, except C1,x-Fx, the error of other compliance increases with the maximum of 28%. With the aid of the compliance formula, the analysis is conducted on the effects of such structural parameters as the hinge semi-short axis n and the minimum cross-sectional diameter t on the compliance as well as the compliance difference among the cylinder,elliptical and right-circle multiple-axis flexure hinges. The results provide new ideas and theoretical basis for the analysis and design of elliptical multiple-axis flexure hinges in the spatial compliant mechanism.
引文
[1]于靖军,郝广波,陈贵敏,等.柔性机构及其应用研究进展[J].机械工程学报, 2015,51(13):53-68.
[2]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.
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[9]杜云松,李铁民,姜峣,等.平面柔性铰链机构的柔度计算方法[J].清华大学学报:自然科学版, 2016,56(6):633-639.
[10]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.
[11]沈健,谢祖强,朱仁胜.双轴柔性铰链转动柔度的计算与分析[J].上海交通大学学报, 2007,41(9):1514-1517.
[12]姚建涛,李立建,杨维,等.直圆柔性球铰柔度矩阵的解析计算[J].光学精密工程,2014,22(7):1857-1863.
[13]杨春辉,刘平安.圆弧型柔性球铰柔度设计计算[J].工程设计学报,2014,21(4):389-392.
[14]刘庆玲,翁海珊,邱丽芳.新型单边复合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.
[2]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.
[3] Howell L L. Compliant mechanisms[M]. New York:JohnWiley&SonsInc, 2001.
[4] Nicolae Lobontiu. Compliant mechanisms:design of the flex-ure hinges[M]. New York:CRC PressLLC, 2003.
[5] Paros J M,Weisboro L. How to design flexure hinges[J].Machine Design,1965,37(27):151-157.
[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.
[7]赵磊,巩岩.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):715-719.
[8]赵磊,巩岩,华洋洋.直梁圆角形柔性铰链的柔度矩阵分析[J].中国机械工程, 2013,24(18):2462-2468.
[9]杜云松,李铁民,姜峣,等.平面柔性铰链机构的柔度计算方法[J].清华大学学报:自然科学版, 2016,56(6):633-639.
[10]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.
[11]沈健,谢祖强,朱仁胜.双轴柔性铰链转动柔度的计算与分析[J].上海交通大学学报, 2007,41(9):1514-1517.
[12]姚建涛,李立建,杨维,等.直圆柔性球铰柔度矩阵的解析计算[J].光学精密工程,2014,22(7):1857-1863.
[13]杨春辉,刘平安.圆弧型柔性球铰柔度设计计算[J].工程设计学报,2014,21(4):389-392.
[14]刘庆玲,翁海珊,邱丽芳.新型单边复合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.