柔顺桥式位移放大机构的非线性建模与优化
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摘要
柔顺桥式位移放大机构因结构紧凑、位移放大倍数大等优点已成为精密工程领域的研究热点。针对以往研究仅在线性范围内讨论桥式位移放大机构的设计与分析的问题,本文对典型集中柔度桥式位移放大机构进行了非线性建模与优化。考虑剪切作用与几何非线性,通过能量法、有限单元法与数值拟合,对机构的输入输出关系进行半解析建模,以实现非线性结果的快速预测。为实现输出位移最大化与抑制几何非线性作用,提出机构平面内尺寸与厚度的综合优化策略。ANSYS Workbench有限元仿真显示,机构非线性建模误差均在5%以内且优化结果具备有效性。本文提出的两步法半解析非线性建模方法以及平面内尺寸和厚度的综合非线性优化策略对其它复杂柔顺机构的非线性结果快速预测与优化设计具有参考意义。
Due to the advantages of compact structure and large displacement amplification ratio,compliant bridge-type displacement amplification mechanism(DAM)has increasingly gained attention in the field of precision engineering.In previous reports,the design and analysis of bridge-type DAM have been limited to the linear range.In this work,nonlinear modeling and optimization of a typical lumped bridge-type DAM were investigated.Considering the shearing effect and geometrical nonlinearity,the output-input relation of the mechanism was modeled half-analytically using the energy method,finite element method,and numerical fitting,and rapid prediction of nonlinear results was realized.For maximizing the output displacement and restricting the geometrical nonlinearity,comprehensive optimization strategies of planar dimensions and thickness were proposed.ANSYS Workbench finite element simulation reveals that the error of nonlinear modeling for the mechanism is limited to 5%,and the optimal results are effective.The two-step half-analytical nonlinear modeling method and comprehensive nonlinear optimization strategies of planar dimensions and thickness proposed in this paper can be applied for the rapid prediction of nonlinear results and optimal design of other complicated compliant mechanisms.
Due to the advantages of compact structure and large displacement amplification ratio,compliant bridge-type displacement amplification mechanism(DAM)has increasingly gained attention in the field of precision engineering.In previous reports,the design and analysis of bridge-type DAM have been limited to the linear range.In this work,nonlinear modeling and optimization of a typical lumped bridge-type DAM were investigated.Considering the shearing effect and geometrical nonlinearity,the output-input relation of the mechanism was modeled half-analytically using the energy method,finite element method,and numerical fitting,and rapid prediction of nonlinear results was realized.For maximizing the output displacement and restricting the geometrical nonlinearity,comprehensive optimization strategies of planar dimensions and thickness were proposed.ANSYS Workbench finite element simulation reveals that the error of nonlinear modeling for the mechanism is limited to 5%,and the optimal results are effective.The two-step half-analytical nonlinear modeling method and comprehensive nonlinear optimization strategies of planar dimensions and thickness proposed in this paper can be applied for the rapid prediction of nonlinear results and optimal design of other complicated compliant mechanisms.
引文
[1]GAN J Q,ZHANG X M,LI H,et al..Full closed-loop controls of micro/nano positioning system with nonlinear hysteresis using micro-vision system[J].Sensors&Actuators A Physical,2017,257:125-133.
[2]LIU Y L,ZHANG Y L,XU Q S.Design and control of a novel compliant constant-force gripper based on buckled fixed-guided beams[J].IEEE/ASME Transactions on Mechatronics,2017,22(1):476-486.
[3]DONG W,CHEN F X,YANG M,et al..Development of a high-efficient bridge-type mechanism based on negative stiffness[J].Smart Materials&Structures,2017,26:95053.
[4]CHEN W L,ZHANG X M,FATIKOW S.Design,modeling and test of a novel compliant orthogonal displacement amplification mechanism for the compact micro-grasping system[J].Microsystem Technologies,2017,23(7):2485-2498.
[5]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.LU Q,HUANG W Q,SUN M X.Optimization design of amplification mechanism for level flexure hinge based on compliance ratio[J].Opt.Precision Eng.,2016,24(1):102-111.(in Chinese)
[6]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):999-1008.LIU M,ZHANG X M.Micro-displacement amplifier based on quasi-V-shaped flexure hinge[J].Opt.Precision Eng.,2017,25(4):999-1008.(in Chinese)
[7]LOBONTIU N,GARCIA E.Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms[J].Computers&Structures,2003,81(32):2797-2810.
[8]MA H W,YAO S M,WANG L Q,et al..Analysis of the displacement amplification ratio of bridgetype flexure hinge[J].Sensors&Actuators APhysical,2006,132(2):730-736.
[9]QI K Q,XIANG Y,FANG C,et al..Analysis of the displacement amplification ratio of bridge-type mechanism[J].Mechanism&Machine Theory,2015,87:45-56.
[10]凌明祥,刘谦,曹军义,等.压电位移放大机构的力学解析模型及有限元分析[J].光学精密工程,2016,24(4):812-818.LING M X,LIU Q,CAO J Y,et al..Analytical model and finite element analysis of piezoelectric displacement amplification mechanism[J].Opt.Precision Eng.,.2016,24(4):812-818.(in Chinese)
[11]LIU P,YAN P.A new model analysis approach for bridge-type amplifiers supporting nano-stage design[J].Mechanism&Machine Theory,2016,99:176-188.
[12]WEI H X,SHIRINZADEH B,LI W,et al..Development of piezo-driven compliant bridge mechanisms:general analytical equations and optimization of displacement amplification[J].Micromachines,2017,8(8):238.
[13]KIM J H,KIM S H,KWAK Y K.Development of a piezoelectric actuator using a three-dimensional bridge-type hinge mechanism[J].Review of Scientific Instruments,2003,74(5):2918-2924.
[14]XU Q,LI Y.Analytical modeling,optimization and testing of a compound bridge-type compliant displacement amplifier[J].Mechanism and Machine Theory,2011,46(2):183-200.
[15]LING M X.A general two-port dynamic stiffness model and static-dynamic comparison for three bridge-type flexure displacement amplifiers[J].Mechanical Systems and Signal Processing,2019,119:486-500.
[16]赖磊捷,梅峻华,朱姿娜.分布柔度桥式位移放大机构静动力学性能研究[J].压电与声光,2018(2):251-256.LAI L J,MEI J H,ZHU Z N.Study on static and dynamic performances of distributed-compliance bridge-type displacement amplification mechanism[J].Piezoelectrics and Acoustooptics,2018(2):251-256.(in Chinese)
[17]陈方鑫,高福天,杜志江,等.基于混合铰链的三维桥式放大机构的建模、分析与试验[J].机械工程学报,2018,54(13):110-116.CHEN F X,GAO F T,DU ZH J,et al..Modeling,analysis and experiment of the hybrid flexure hinge-based three-dimensional bridge-type amplification mechanism[J].Journal of Mechanical Engineering,2018,54(13):110-116.(in Chinese)
[18]LOBONTIU N.Compliant Mechanism-Design of Flexure Hinges[M].Boca Raton,Florida:CRC Press,2003.
[19]HAO G.Extended nonlinear analytical models of compliant parallelogram mechanisms:Third-order models[J].Transactions-Canadian Society for Mechanical Engineering,2015,39(1):71-83.
[20]胡俊峰,陈星星.具有零刚度特性的微动平台优化设计[J].光学精密工程,2018,26(6):1430-1440.HU J F,CHEN X X.Optimized design of a micromotion stage with zero stiffness[J].Opt.Precision Eng.,2018,26(6):1430-1440.(in Chinese)
[21]CHEN W L,ZHANG X M,LI H,et al..Nonlinear analysis and optimal design of a novel piezoelectric-driven compliant microgripper[J].Mechanism and Machine Theory,2017,118:32-52.
[22]ZHU B,CHEN Q,WANG R,et al..Structural topology optimization using a moving morphable component-based method considering geometrical nonlinearity[J].Journal of Mechanical Design,2018,140(8):081403.
[23]张爱梅,陈贵敏,贾建援.基于完备椭圆积分解的交叉簧片式柔性铰链大挠度建模[J].机械工程学报,2014,50(11):80-85.ZHANG A M,CHEN G M,JIA J Y.Large deflection modeling of cross-spring pivots based on comprehensive elliptic integral solution[J].Journal of Mechanical Engineering,2014,50(11):80-85.(in Chinese)
[24]CHEN G M,MA F L.Kinetostatic modeling of fully compliant bistable mechanisms using timoshenko beam constraint model[J].Journal of Mechanical Design,2015,137(2):22301.
[2]LIU Y L,ZHANG Y L,XU Q S.Design and control of a novel compliant constant-force gripper based on buckled fixed-guided beams[J].IEEE/ASME Transactions on Mechatronics,2017,22(1):476-486.
[3]DONG W,CHEN F X,YANG M,et al..Development of a high-efficient bridge-type mechanism based on negative stiffness[J].Smart Materials&Structures,2017,26:95053.
[4]CHEN W L,ZHANG X M,FATIKOW S.Design,modeling and test of a novel compliant orthogonal displacement amplification mechanism for the compact micro-grasping system[J].Microsystem Technologies,2017,23(7):2485-2498.
[5]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.LU Q,HUANG W Q,SUN M X.Optimization design of amplification mechanism for level flexure hinge based on compliance ratio[J].Opt.Precision Eng.,2016,24(1):102-111.(in Chinese)
[6]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):999-1008.LIU M,ZHANG X M.Micro-displacement amplifier based on quasi-V-shaped flexure hinge[J].Opt.Precision Eng.,2017,25(4):999-1008.(in Chinese)
[7]LOBONTIU N,GARCIA E.Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms[J].Computers&Structures,2003,81(32):2797-2810.
[8]MA H W,YAO S M,WANG L Q,et al..Analysis of the displacement amplification ratio of bridgetype flexure hinge[J].Sensors&Actuators APhysical,2006,132(2):730-736.
[9]QI K Q,XIANG Y,FANG C,et al..Analysis of the displacement amplification ratio of bridge-type mechanism[J].Mechanism&Machine Theory,2015,87:45-56.
[10]凌明祥,刘谦,曹军义,等.压电位移放大机构的力学解析模型及有限元分析[J].光学精密工程,2016,24(4):812-818.LING M X,LIU Q,CAO J Y,et al..Analytical model and finite element analysis of piezoelectric displacement amplification mechanism[J].Opt.Precision Eng.,.2016,24(4):812-818.(in Chinese)
[11]LIU P,YAN P.A new model analysis approach for bridge-type amplifiers supporting nano-stage design[J].Mechanism&Machine Theory,2016,99:176-188.
[12]WEI H X,SHIRINZADEH B,LI W,et al..Development of piezo-driven compliant bridge mechanisms:general analytical equations and optimization of displacement amplification[J].Micromachines,2017,8(8):238.
[13]KIM J H,KIM S H,KWAK Y K.Development of a piezoelectric actuator using a three-dimensional bridge-type hinge mechanism[J].Review of Scientific Instruments,2003,74(5):2918-2924.
[14]XU Q,LI Y.Analytical modeling,optimization and testing of a compound bridge-type compliant displacement amplifier[J].Mechanism and Machine Theory,2011,46(2):183-200.
[15]LING M X.A general two-port dynamic stiffness model and static-dynamic comparison for three bridge-type flexure displacement amplifiers[J].Mechanical Systems and Signal Processing,2019,119:486-500.
[16]赖磊捷,梅峻华,朱姿娜.分布柔度桥式位移放大机构静动力学性能研究[J].压电与声光,2018(2):251-256.LAI L J,MEI J H,ZHU Z N.Study on static and dynamic performances of distributed-compliance bridge-type displacement amplification mechanism[J].Piezoelectrics and Acoustooptics,2018(2):251-256.(in Chinese)
[17]陈方鑫,高福天,杜志江,等.基于混合铰链的三维桥式放大机构的建模、分析与试验[J].机械工程学报,2018,54(13):110-116.CHEN F X,GAO F T,DU ZH J,et al..Modeling,analysis and experiment of the hybrid flexure hinge-based three-dimensional bridge-type amplification mechanism[J].Journal of Mechanical Engineering,2018,54(13):110-116.(in Chinese)
[18]LOBONTIU N.Compliant Mechanism-Design of Flexure Hinges[M].Boca Raton,Florida:CRC Press,2003.
[19]HAO G.Extended nonlinear analytical models of compliant parallelogram mechanisms:Third-order models[J].Transactions-Canadian Society for Mechanical Engineering,2015,39(1):71-83.
[20]胡俊峰,陈星星.具有零刚度特性的微动平台优化设计[J].光学精密工程,2018,26(6):1430-1440.HU J F,CHEN X X.Optimized design of a micromotion stage with zero stiffness[J].Opt.Precision Eng.,2018,26(6):1430-1440.(in Chinese)
[21]CHEN W L,ZHANG X M,LI H,et al..Nonlinear analysis and optimal design of a novel piezoelectric-driven compliant microgripper[J].Mechanism and Machine Theory,2017,118:32-52.
[22]ZHU B,CHEN Q,WANG R,et al..Structural topology optimization using a moving morphable component-based method considering geometrical nonlinearity[J].Journal of Mechanical Design,2018,140(8):081403.
[23]张爱梅,陈贵敏,贾建援.基于完备椭圆积分解的交叉簧片式柔性铰链大挠度建模[J].机械工程学报,2014,50(11):80-85.ZHANG A M,CHEN G M,JIA J Y.Large deflection modeling of cross-spring pivots based on comprehensive elliptic integral solution[J].Journal of Mechanical Engineering,2014,50(11):80-85.(in Chinese)
[24]CHEN G M,MA F L.Kinetostatic modeling of fully compliant bistable mechanisms using timoshenko beam constraint model[J].Journal of Mechanical Design,2015,137(2):22301.