,192 北京科技大学学报 第30卷 3.0 型柔性铰链优化为设计实例,进行了多目标优化 一优化前曲线 设计. 2.5 年优化后曲线 (2)对直圆型柔性铰链优化结果进行了分析 20 结果表明,当施加一确定力时,优化后柔性铰链的运 动性能比优化前的性能有了明显提高,达到了改善 柔性铰链的运动性能的目的:绕z轴的转动能力增 1.0 大,沿z轴方向的运动能力减小,沿轴方向的运动 0.5 能力只略有增大 10 2030 40 50 参考文献 EF/N [1]Huang J Y.Wei Y D.Zhang W.Optimal design of the flexure 图3∑F,与u,的关系 hinge parameter based on space micro-displacement worktable. Mech Electr Eng Mag.2006.23(1):55 Fig.3 Relationship between >Fy and uy (黄金永,魏燕定,张炜.空间微动平台的柔性铰链参数优化设 计.机电工程,2006,23(1):55) 3.5 [2]Lobontiu N.Design of symmetric conic-section flexure hinges 3.0 一优化前曲线 based on closed form compliance equations.Mech Mach Theory. +优化后曲线 2002,37(5):477 日2.5 [3]Lobontiu N.Paine JS N.O'Malley E.et al.Parabolie and hyper 2.0 bolic flexure hinges:flexibility.motion precision and stress char- 15 acterization based on compliance closed form equations.Precis Eng,2002,26(2):183 1.0- [4]Zhou WW.He G P.Optimizing flexure hinges of a planar full 0.5 compliant parallel mechanism.J North China Univ Technol Bei- jing,2007,19(1).20 0.2 0.4 0.6 0.8 1.0 (周文闻,何广平,平面全柔性并联机构柔性铰链的优化分析 F/N 北方工业大学学报,2007,19(1):20) [5]Chen S J.Yang Y H.Shun X Z.et al.Optimal design and capa- 图4F,与u:的关系 bility analysis of micro-displacement worktable base on flexure Fig.4 Relationship between F,and us hinge.JMach Des.2004.21(7):46 (陈时锦,杨元华,孙西艺,等.基于柔性铰链的微位移工作台 12 性能分析与优化设计.机械设计,2004,21(7):46) [6]Yu JJ.Zhou Q.BiSS.et al.Optimal design of a fully compliant 1.0 一优化前曲线 mechanism based on its dynamic characteristics.Chin J Mech 0.8 +优化后曲线 Eng,2003,39(8):32 (于靖军,周强,毕树生,等.基于动力学性能的全柔性机构优 0.6 化设计,机械工程学报,2003,39(8):32) [7]Lobontiu N.Analytical model of displacement amplification and 0.4 stiffness optimization for a class of flexure-based compliant mecha 02 nisms.Comput Struct.2003.81(32):2797 [8]Lobontiu N.Compliant Mechanisms:Design of Flexure Hinges.USA:CRC Press LLC.2003:60 10 EF/N [9]MinlK S.Choi W C.Song S H.et al.Static and dynamic analysis of a nanopositioning flexure-hinge stage with a flexible lever mech- 图5F.与u的关系 anism.Proc Inst Mech Eng Part B J Eng Manuf.2005.219. Fig.5 Relationship between >F:and u 447 [10]Zuo K T.Zhao Y D.Zhong Y F,et al.Computer-aided design 因此达到了优化的目的, of compliant micro"mechanism with multi-objective topology op- timization.J Comput Aid Des Comput Graphics.2006,18 4结论 (6):854 (左孔天,赵雨东,钟毅芳,等.微型柔性机构的多目标计算机 (1)以提高柔性铰链的转动性能为目标,建立 辅助拓扑优化设计,计算机辅助设计与图形学学报,2006, 了柔性铰链多目标优化设计的数学模型,并以直圆 18(6):854)图3 ∑Fy 与 uy 的关系 Fig.3 Relationship between ∑Fy and uy 图4 Fx 与 ux 的关系 Fig.4 Relationship between Fx and ux 图5 ∑Fz 与 uz 的关系 Fig.5 Relationship between ∑Fz and uz 因此达到了优化的目的. 4 结论 (1) 以提高柔性铰链的转动性能为目标建立 了柔性铰链多目标优化设计的数学模型并以直圆 型柔性铰链优化为设计实例进行了多目标优化 设计. (2) 对直圆型柔性铰链优化结果进行了分析. 结果表明当施加一确定力时优化后柔性铰链的运 动性能比优化前的性能有了明显提高达到了改善 柔性铰链的运动性能的目的:绕 z 轴的转动能力增 大沿 z 轴方向的运动能力减小沿轴方向的运动 能力只略有增大. 参 考 文 献 [1] Huang J YWei Y DZhang W.Optimal design of the flexure hinge parameter based on space micro-displacement worktable. Mech Electr Eng Mag200623(1):55 (黄金永魏燕定张炜.空间微动平台的柔性铰链参数优化设 计.机电工程200623(1):55) [2] Lobontiu N.Design of symmetric conic-section flexure hinges based on closed-form compliance equations.Mech Mach Theory 200237(5):477 [3] Lobontiu NPaine J S NO’Malley Eet al.Parabolic and hyperbolic flexure hinges:flexibilitymotion precision and stress characterization based on compliance closed-form equations. Precis Eng200226(2):183 [4] Zhou W WHe G P.Optimizing flexure hinges of a planar full compliant parallel mechanism.J North China Univ Technol Beijing200719(1):20 (周文闻何广平.平面全柔性并联机构柔性铰链的优化分析. 北方工业大学学报200719(1):20) [5] Chen S JYang Y HShun X Zet al.Optimal design and capability analysis of micro-displacement worktable base on flexure hinge.J Mach Des200421(7):46 (陈时锦杨元华孙西芝等.基于柔性铰链的微位移工作台 性能分析与优化设计.机械设计200421(7):46) [6] Yu J JZhou QBi S Set al.Optimal design of a fully compliant mechanism based on its dynamic characteristics. Chin J Mech Eng200339(8):32 (于靖军周强毕树生等.基于动力学性能的全柔性机构优 化设计.机械工程学报200339(8):32) [7] Lobontiu N.Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms.Comput Struct200381(32):2797 [8] Lobontiu N. Compliant Mechanisms: Design of Flexure Hinges.USA:CRC Press LLC2003:60 [9] Min1K SChoi W CSong S Het al.Static and dynamic analysis of a nanopositioning flexure-hinge stage with a flexible lever mechanism.Proc Inst Mech Eng Part B J Eng Manuf2005219: 447 [10] Zuo K TZhao Y DZhong Y Fet al.Computer-aided design of compliant micro-mechanism with mult-i objective topology optimization. J Comput Aid Des Comput Graphics200618 (6):854 (左孔天赵雨东钟毅芳等.微型柔性机构的多目标计算机 辅助拓扑优化设计.计算机辅助设计与图形学学报2006 18(6):854) ·192· 北 京 科 技 大 学 学 报 第30卷