Topological structure design and compliance analysis of a new single-axis flexure hinge
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摘要:
采用基于三维连续体拓扑优化理论的变密度法,以柔性铰链柔度比最大为目标,建立了单轴柔性铰链的拓扑优化模型。首先,借助OptiStruct软件设计出一种具有全新三维拓扑结构的单轴柔性铰链;其次,结合卡氏第二定理和能量法对该新型柔性铰链的转动性能进行理论分析,推导出该新型柔性铰链的柔度矩阵,通过16组实例的理论计算和有限元仿真分析,得到其相对误差在6.35%以内,验证了该新型柔性铰链柔度矩阵理论公式的正确性;最后,分析了具有相同切口轮廓的圆弧型柔性铰链和新型柔性铰链的柔度差异。结果表明:新型柔性铰链具有更大的柔度,其柔度性能提升300%。使用三维连续体拓扑优化方法,可为单轴柔性铰链的设计提供一个新思路。
Abstract:Based on three-dimensional continuum topology optimization theory, aimed at maximizing compliance ratio, solid isotropic material with penalization model was used to establish the topology optimization model of a single-axis flexure hinge. With the help of OptiStruct, this paper designed a kind of single-axis flexure hinge with a new three-dimensional topological structure. Secondly, combining Castigliano's second theorem and the method of energy for the compliance of flexure hinge in theory, it deduced the compliance matrix of the new flexure hinge. 16 groups' analysis in theory and finite element simulation analysis showed the correctness of the theoretical formula because the relative error of analysis and FEA was within 6.35%. Finally, it compared the difference of compliance between the new flexure hinge and circular flexure hinge with the same cut profile. The results show that the new flexure hinge has much better performance in compliance. Compared with the circular flexure hinge, its compliance can be improved by 300%. Based on the three-dimensional continuum topology optimization method, this paper presented a new thought for the design of single-axis flexure hinge.
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表 1 新型柔性铰链柔度理论值与仿真值对比
Table 1. Comparison of theoretical and simulation compliance values of new flexure hinge
R/mm t/mm Cθy-My Cz-Fz Cx-Fx 理论值/(10-4rad·(N·mm)-1) 仿真值/(10-4rad·(N·mm)-1) 相对误差/% 理论值/(10-2N-1·mm) 仿真值/ (10-2N-1· mm) 相对误差/% 理论值/ (10-6N-1· mm) 仿真值/ (10-6N-1· mm) 相对误差/% 4 0.2 64.442 66.383 3.01 10.420 10.770 3.36 37.143 38.302 3.12 4 0.3 23.106 23.298 0.83 3.775 3.805 0.79 28.384 28.538 0.54 4 0.4 11.298 11.005 2.59 1.858 1.810 2.58 23.641 22.985 2.77 4 0.5 6.202 6.123 1.27 1.026 1.014 1.17 19.700 19.352 1.77 6 0.2 77.907 78.843 1.20 28.263 28.695 1.53 42.968 43.792 1.92 6 0.3 28.290 27.365 3.27 10.316 10.023 2.84 33.563 32.419 3.41 6 0.4 13.458 12.810 4.81 4.927 4.724 4.12 27.114 26.029 4.00 6 0.5 7.401 7.073 4.43 2.720 2.626 3.46 22.915 21.882 4.51 8 0.2 86.393 88.427 2.35 55.480 57.161 3.03 46.336 47.892 3.36 8 0.3 31.454 30.408 3.33 20.309 19.784 2.59 36.874 35.342 4.15 8 0.4 14.781 14.133 4.38 9.571 9.259 3.26 29.199 28.345 2.92 8 0.5 8.288 7.761 6.36 5.282 5.012 5.11 25.165 23.827 5.32 10 0.2 95.256 96.204 1.00 95.177 97.148 2.07 50.632 51.210 1.14 10 0.3 34.478 32.827 4.79 34.696 33.372 3.82 38.963 37.730 3.16 10 0.4 16.066 15.174 5.55 16.209 15.534 4.16 31.940 30.258 5.27 10 0.5 8.849 8.299 6.22 8.997 8.557 4.89 26.450 25.449 3.78 -
[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. http://www.cnki.com.cn/Article/CJFDTotal-JXXB201513006.htmYU J J, HAO G B, CHEN G M, et al.State-of-art of compliant mechanisms and their applications[J].Chinese Journal of Mechanical Engineering, 2015, 51(13):53-68(in Chinese). http://www.cnki.com.cn/Article/CJFDTotal-JXXB201513006.htm [2] 余跃庆, 李清清.Y型柔性铰链的设计与实验[J].光学精密工程, 2017, 25(2):394-400. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201702015YU Y Q, LI Q Q.Design and experiment of Y-type flexure hinge[J].Optics and Precision Engineering, 2017, 25(2):394-400(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201702015 [3] 陈贵敏, 贾建援, 刘小院, 等.柔性铰链精度特性研究[J].仪器仪表学报, 2004, 25(4):107-109. http://www.cnki.com.cn/Article/CJFDTOTAL-YQXB2004S2035.htmCHEN G M, JIA J Y, LIU X Y, et al.Study on the accuracy of flexible hinges[J].Chinese Journal of Scientific Instrument, 2004, 25(4):107-109(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YQXB2004S2035.htm [4] LOBONTIU N, GARCIA E.Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms[J].Computers and Structures, 2003, 81(32):2797-2810. doi: 10.1016/j.compstruc.2003.07.003 [5] SMITH S T, BADAMI V G, Dale J S, et al.Elliptical flexure hinges[J].Review of Scientific Instruments, 1997, 68(3):1474-1483. doi: 10.1063/1.1147635 [6] CHEN G M, LIU X Y, GAO H W, et al.A generalized model for conic flexure hinges[J].Review of Scientific Instruments, 2009, 80(5):106-116. doi: 10.1063/1.3137074 [7] 邱丽芳, 南铁玲, 柳林.微柔性铰链转动能力和精度特性研究[J].微纳电子技术, 2007, 44(12):1068-1072. doi: 10.3969/j.issn.1671-4776.2007.12.008QIU L F, NAN T L, LIU L.Study on the rotation capacity and the precision of micro flexible hinges[J].Micronanoelectronic Technology, 2007, 44(12):1068-1072(in Chinese). doi: 10.3969/j.issn.1671-4776.2007.12.008 [8] 卢倩, 黄卫清, 王寅, 等.深切口椭圆柔性铰链优化设计[J].光学精密工程, 2015, 23(1):206-215. http://industry.wanfangdata.com.cn/yj/Detail/Periodical?id=Periodical_gxjmgc201501027LU Q, HUANG W Q, WANG Y, et al.Optimization design of deep-notch elliptical flexure hinges[J].Optics and Precision Engineering, 2015, 23(1):206-215(in Chinese). http://industry.wanfangdata.com.cn/yj/Detail/Periodical?id=Periodical_gxjmgc201501027 [9] 卢倩, 黄卫清, 孙梦馨.基于柔度比优化设计杠杆式柔性铰链放大机构[J].光学精密工程, 2016, 24(1):102-111. http://www.cqvip.com/QK/92835A/201601/667923024.htmlLU Q, HUANG W Q, SUN M X.Optimization design of amplification mechanism for level flexure hinge based on compliance ratio[J].Optics and Precision Engineering, 2016, 24(1):102-111(in Chinese). http://www.cqvip.com/QK/92835A/201601/667923024.html [10] 于靖军, 裴旭, 毕树生, 等.柔性铰链机构设计方法的研究进展[J].机械工程学报, 2010, 45(13):2-13. http://mall.cnki.net/magazine/Article/JXXB201013003.htmYU J J, PEI X, BI S S, et al.State-of-arts of design method for flexure mechanisms[J].Journal of Mechanical Engineering, 2010, 45(13):2-13(in Chinese). http://mall.cnki.net/magazine/Article/JXXB201013003.htm [11] ZHU B L, ZHANG X M, FATIKOW S.Design of single-flexure hinges using continuum topology optimization method[J].Science China:Technological Sciences, 2014, 57(3):560-567. doi: 10.1007/s11431-013-5446-4 [12] LIU M, ZHANG X M, FATIKOW S.Design and analysis of a high-accuracy flexure hinge[J].Review of Scientific Instruments, 2016, 87(5):055106. doi: 10.1063/1.4948924 [13] 刘敏, 张宪民.基于类V型柔性铰链的微位移放大机构[J].光学精密工程, 2017, 25(4):467-476. http://www.eope.net/gxjmgc/CN/abstract/abstract17002.shtmlLIU M, ZHANG X M.Mico-displacement amplifier based on quasi-V-shaped flexure hinge[J].Optics and Precision Engineering, 2017, 25(4):467-476(in Chinese). http://www.eope.net/gxjmgc/CN/abstract/abstract17002.shtml [14] LIU M, ZHANG X M, FATIKOW S.Design and analysis of a multi-notched flexure hinge for compliant mechanisms[J].Precision Engineering, 2017, 48:292-304. doi: 10.1016/j.precisioneng.2016.12.012 [15] PAROS J M, WEISBORO L.How to design flexure hinges[J].Machine Design, 1965, 37(27):151-156. doi: 10.1007%2Fs00170-009-2478-9