Design, Analysis and Experimental Test of the Bridge-type Displacement Amplification Mechanism Based on the Topology Optimization of Flexure Hinge

doi:10.3901/JME.2022.11.057

Abstract

Abstract: Bridge-type compliant displacement amplification mechanisms (CDAMs) have been widely used as transmission mechanisms for precision positioning and micro-nano-manipulation equipments. In the field of precision engineering, the design and modeling of bridge-type CDAMs are key issues. Traditional researches have not solved the problem that which kind of topological structure for the flexure hinges makes the output performances of bridge-type CDAMs the best. Existing researches on the topology optimization of flexure hinges generally do not consider the distribution property of internal forces for an actual compliant mechanism, which affects the application effect of topology optimization results in the actual compliant mechanism. In this paper, a bridge-type CDAM based on the topology optimization of flexure hinge is designed, analyzed and tested experimentally. Firstly, in the condition that the topological structure of flexure hinges is unknown, the distribution property of internal forces for a bridge-type CDAM is carried out. With a combination of the distribution property of internal forces and the variable density method, taking the maximum compliance as the objective function, the topology optimization of flexure hinge was conducted, which improves the output property of CDAM from the perspective of optimizing the topological structure of flexure hinge. Under different volume constraints, the topology optimization results of flexure hinge in a bridge-type CDAM are all V-shaped structures. Then, using the matrix displacement method, the distribution property of internal forces for the bridge-type CDAM and the relationship among the compliance matrixes of a parallel mechanism, the static model of V-shaped flexure hinge was established. With a combination of the compliance matrix of a V-shaped flexure hinge, the distribution property of internal forces and the relationship among the compliance matrixes of a serial mechanism, the analytical relation between the output displacement and the input force of bridge-type CDAM based on the topology optimization of flexure hinge was derived. The parametric optimization of CDAM was carried out to further improve the output property of CDAM. Finite element simulation and experimental tests verified the effectiveness of topology optimization results for the flexure hinge in a bridge-type CDAM, static modelling of V-shaped flexure hinge and parametric optimization of CDAM.

Key words: flexure hinge, topology optimization, bridge-type displacement amplification mechanism, parametric optimization

CLC Number:

TH112

LU Qinghua, KANG Shidi, CHEN Weilin, WEI Huiling, ZHANG Yunzhi, LUO Lufeng. Design, Analysis and Experimental Test of the Bridge-type Displacement Amplification Mechanism Based on the Topology Optimization of Flexure Hinge[J]. Journal of Mechanical Engineering, 2022, 58(11): 57-71.

References

[1] LAI Leijie, ZHU Zina. Design, modeling and testing of a novel flexure-based displacement amplification mechanism[J]. Sensors & Actuators:A. Physical, 2017, 266:122-129.
[2] QI Keqi, XIANG Yang, FANG Chao, et al. Analysis of the displacement amplification ratio of bridge-type mechanism[J]. Mechanism and Machine Theory, 2015, 87:45-56.
[3] XU De, LI Fudong, ZHANG Zhengtao, et al. Characteristic of monocular microscope vision and its application on assembly of micro-pipe and micro-sphere[C]//Proceedings of the 32nd Chinese Control Conference. Xi'an:32nd Chinese Control Conference, 2013:5758-5763.
[4] DONG Wei, CHEN Fangxin, YANG Miao, et al. Development of a highly efficient bridge-type mechanism based on negative stiffness[J]. Smart Materials and Structures, 2017, 26(9):095053.
[5] CHEN Weilin, ZHANG Xianmin, FATIKOW Sergej. 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.
[6] LU Qian, HUANG Weiqing, SUN Mengxin. The optimization design of lever type flexible hinge amplification mechanism based on compliance ratio[J]. Optical Precision Engineering, 2016, 24(1):102-111. 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.
[7] LIU Min, ZHANG Xianmin. Micro displacement amplification mechanism based on type V flexure hinge[J]. Optical Precision Engineering, 2017, 25(4):467-476. 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.
[8] 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.
[9] MA Hongwen, YAO Shaoming, WANG Liquan, et al. Analysis of the displacement amplification ratio of bridge-type flexure hinge[J]. Sensors & Actuators:A-Physical, 2005, 132(2):730-736.
[10] QI Keqi, XIANG Yang, FANG Chao, et al. Analysis of the displacement amplification ratio of bridge-type mechanism[J]. Mechanism and Machine Theory, 2015, 87:45-56.
[11] LING Mingxiang, LIU Qian, CAO Junyi, et al. Mechanical analytical model and finite element analysis of piezoelectric displacement amplification mechanism[J]. Optical Precision Engineering, 2016, 24(4):812-818. 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.
[12] LIU Pengbo, YAN Peng. A new model analysis approach for bridge-type amplifiers supporting nano-stage design[J]. Mechanism and Machine Theory, 2016, 99:176-188.
[13] WEI Huaxian, SHIRINZADEH Bijan, LI Wei, et al. Development of piezo-driven compliant bridge mechanisms:General analytical equations and optimization of displacement amplification[J]. Micromachines, 2017, 8(8):238.
[14] KIM J, KIM S, KWAK Y. Development and optimization of 3-D bridge-type hinge mechanisms[J]. Sensors and Actuators, A. Physical, 2004, 116(3):530-538.
[15] XU Qingsong, LI Yangmin. Analytical modeling, optimization and testing of a compound bridge-type compliant displacement amplifier[J]. Mechanism and Machine Theory, 2011, 46(2):183-200.
[16] LING Mingxiang. 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(15):486-500.
[17] LAI Leijie, MEI Junhua, ZHU Zina. Study on static and dynamic performance of bridge displacement amplification mechanism with distributed compliance[J]. Piezoelectricity And Sound And Light, 2018, 40(2):251-256. 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, 40(2):251-256.
[18] CHEN Weilin, LU Qinghua, QIAO Jian, et al. Nonlinear modeling and optimization of compliant bridge displacement amplification mechanism[J]. Optical Precision Engineering, 2019, 27(4):849-859. 陈为林, 卢清华, 乔健, 等. 柔顺桥式位移放大机构的非线性建模与优化[J]. 光学精密工程, 2019, 27(4):849-859.
[19] LOBONTIU N. Compliant mechanisms:Design of flexure hinges[M]. CRC Press, 2020.
[20] CHEN Fangxin, GAO Futian, DU Zhijiang, et al. Modeling, analysis and test of 3d bridge amplification mechanism based on hybrid hinge[J]. Journal of Mechanical Engineering, 2018, 54(13):110-116. 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.
[21] CHEN Weilin, LU Qinghua, KONG Chuiwang, et al. Design, analysis and validation of the bridge-type displacement amplification mechanism with circular-axis leaf-type flexure hinges for micro-grasping system[J]. Microsystem Technologies, 2019, 25(3):1121-1128.
[22] YANG Chunhui, LIU Pingan. Design and calculation of flexibility of circular arc flexible ball joints[J]. Journal of Engineering Design, 2014, 21(4):389-392. 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.
[23] LOBONTIU N, PAINE J S N, GARCIA E, et al. Corner-filleted flexure hinges[J]. Journal of Mechanical Design, 2001, 123(3):346-352.
[24] SMITH S T, BADAMI V G, DALE J S, et al. Elliptical flexure hinges[J]. Review of Scientific Instruments, 1997, 68(3):1474-1483.
[25] LOBONTIU N, PAINE J S N, O'MALLEY E, et al. Parabolic and hyperbolic flexure hinges:Flexibility, motion precision and stress characterization based on compliance closed-form equations[J]. Precision Engineering, 2002, 26(2):183-192.
[26] WANG Nianfeng, LIANG Xiaohe, ZHANG Xianmin. Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms[J]. Chinese Journal of Mechanical Engineering, 2014, 27(1):122-129.
[27] YANG Miao, DU Zhijiang, CHEN Yi, et al. Mechanical modeling and deformation characteristics analysis of cross spring flexure hinge with variable section[J]. Journal of Mechanical Engineering, 2018, 54(13):73-78. 杨淼, 杜志江, 陈依, 等. 变截面交叉簧片柔性铰链的力学建模与变形特性分析[J]. 机械工程学报, 2018, 54(13):73-78.
[28] LIU Min, ZHANG Xianmin, FATIKOW Sergej. Design and analysis of a high-accuracy flexure hinge[J]. Review of Scientific Instruments, 2016, 87(5):55101-55106.
[29] QIU Lifang, CHEN Haixiang, WU Youwei. Topology design and compliance analysis of a novel uniaxial flexure hinge[J]. Journal of Beijing University Of Aeronautics And Astronsutics, 2018, 44(6):1133-1140. 邱丽芳, 陈海翔, 吴友炜. 新型单轴柔性铰链拓扑结构设计与柔度分析[J]. 北京航空航天大学学报, 2018, 44(6):1133-1140.
[30] ZHOU M, ROZVANY G I N. DCOC:An optimality criteria method for large systems part Ⅰ:theory[J]. Structural Optimization, 1992, 5(1-2):12-25.
[31] WU Heng, ZHANG Xianmin, WANG Ruizhou, et al. Displacement measurement of the compliant positioning stage based on a computer micro-vision method[J]. Aip Advances, 2016, 6(2):25009.
[32] LI Hai, ZHU Benliang, ZHANG Xianmin, et al. Pose sensing and servo control of the compliant nanopositioners based on microscopic vision[J]. IEEE Transactions on Industrial Electronics, 2021, 68(4):3324-3335.
[33] GUELPA V, LAURENT G, SANDOZ P, et al. Vision-based microforce measurement with a large range-to-resolution ratio using a twin-scale pattern[J]. IEEE/ASME Transactions on Mechatronics, 2015, 20(6):1-9.