Chinese Journal of Mechanical Engineering >

2019 , Vol. 32 >Issue 1: 13 - 13

DOI: https://doi.org/10.1186/s10033-019-0332-z

Topological and Shape Optimization of Flexure Hinges for Designing Compliant Mechanisms Using the Level Set Method

  • Benliang Zhu ,
  • Xianmin Zhang ,
  • Min Liu ,
  • Qi Chen ,
  • Hai Li
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  • 1. Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, South China University of Technology, Guangzhou 510640, China;
    2. East China Jiaotong University, Nanchang 330013, China

Received date: 2017-08-30

  Online published: 2019-07-19

Supported by

Supported by National Natural Science Foundation of China (Grant No. 51779107), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20170548), Postdoctoral Science Foundation of China (Grant No. 2017M611724), and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)

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Abstract

A flexure hinge is a major component in designing compliant mechanisms that offers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with different configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.

Key words： Topology optimization; Compliant mechanisms; Flexure hinges; Level set method

Cite this article

Benliang Zhu , Xianmin Zhang , Min Liu , Qi Chen , Hai Li . Topological and Shape Optimization of Flexure Hinges for Designing Compliant Mechanisms Using the Level Set Method[J]. Chinese Journal of Mechanical Engineering, 2019 , 32(1) : 13 -13 . DOI: 10.1186/s10033-019-0332-z

References

[1] S Zimmermann, T Tiemerding, S Fatikow. Automated robotic manipulation of individual colloidal particles using vision-based control. IEEE/ASME Transactions on Mechatronics, 2015, 20(5): 2031-2038.
[2] H Li, G Hao, R C Kavanagh. A new xyz compliant parallel mechanism for micro-/nano-manipulation: Design and analysis. Micromachines, 2016, 7(2): 23.
[3] R Wang, X Zhang. Optimal design of a planar parallel 3-dof nanopositioner with multi-objective. Mechanism and Machine Theory, 2017, 112: 61-83.
[4] H Wu, X Zhang, J Gan, et al. High-quality correspondence imaging based on sorting and compressive sensing technique. Laser Physics Letters, 2016, 13(11): 115205.
[5] H Li, X Zhang, H Wu, et al. Line-based calibration of a micro-vision motion measurement system. Optics and Lasers in Engineering, 2017, 93: 40-46.
[6] N Lobontiu. Compliant mechanisms: design of flexure hinges. CRC Press, 2002.
[7] L L Howell. Compliant Mechanisms. Springer London, 2013.
[8] M Callegari, A Cammarata, A Gabrielli, et al. Analysis and design of a spherical micromechanism with flexure hinges. Journal of Mechanical Design, 2009, 131(5): 051003.
[9] M Verotti, R Crescenzi, M Balucani, et al. Mems-based conjugate surfaces flexure hinge. Journal of Mechanical Design, 2015, 137(1): 012301.
[10] Y Wu, Z Zhou. Design calculations for flexure hinges. Review of Scientific Instruments, 2002, 73(8): 3101-3106.
[11] G Chen, X Liu, Y Du. Elliptical-arc-fillet flexure hinges: Toward a generalized model for commonly used flexure hinges. Journal of Mechanical Design, 2011, 133(8): 081002.
[12] G Chen, X Liu, H Gao, et al. A generalized model for conic flexure hinges. Review of Scientific Instruments, 2009, 80(5): 055106.
[13] S T Smith, V G Badami, J S Dale, et al. Elliptical flexure hinges. Review of Scientific Instruments, 1997, 68(3): 1474-1483.
[14] N Lobontiu. Modeling and design of planar parallel-connection flexible hinges for in- and out-of-plane mechanism applications. Precision Engineering, 2015, 42(1): 113-132.
[15] R Lin, X Zhang, X Long, et al. Hybrid flexure hinges. Review of Scientific Instruments, 2013, 84(8): 394-398.
[16] N Lobontiu, J S Paine, E OMalley, et al. Parabolic and hyperbolic flexure hinges: Flexibility, motion precision and stress characterization based on compliance closed-form equations. Precision Engineering, 2002, 26(2): 183-192.
[17] Y Tian, B Shirinzadeh, D Zhang, et al. Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis. Precision Engineering, 2010, 34(1): 92-100.
[18] J J Yu, X Pei, S S Bi, et al. A unified approach to type synthesis of both rigid and flexure parallel mechanisms. Science in China, 2011, 54(5): 1206-1219.
[19] J B Hopkins, M L Culpepper, Synthesis of multi-degree of freedom, parallel flexure system concepts via Freedom and Constraint Topology (FACT)—Part I: Principles. Precision Engineering, 2010, 34(2): 259-270.
[20] P Xu, J Yu, G Zong, et al. The stiffness model of leaf-type isosceles trapezoidal flexural pivots. Journal of Mechanical Design, 2008, 130(8): 082303.
[21] P Xu. A family of butterfly flexural joints: Q-litf pivots. Journal of Mechanical Design, 2012, 134(12): 121005.
[22] B Zhu, X Zhang, S Fatikow. Design of single-axis flexure hinges using continuum topology optimization method. Science China Technological Sciences, 2014, 57(3): 560-567.
[23] M Liu, X Zhang, S Fatikow. Design of flexure hinges based on stress constrained topology optimization. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 231(24): 4635-4645.
[24] M Liu, X Zhang, S Fatikow. Design and analysis of a multi-notched flexure hinge for compliant mechanisms. Precision Engineering, 2017, 48: 292-304.
[25] L Cao, A T Dolovich, W J Zhang. Hybrid compliant mechanism design using a mixed mesh of flexure hinge elements and beam elements through topology optimization. Journal of Mechanical Design, 2015, 137(9): 092303.
[26] M P Bendsoe, O Sigmund. Topology optimization: theory, methods, and applications. Springer, 2004.
[27] M P Bendsøe, E Kikuchi. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224.
[28] K Maute, A Tkachuk, J Wu, et al. Level set topology optimization of printed active composites. Journal of Mechanical Design, 2015, 137(11): 111402.
[29] B Zhu, X Zhang, Y Zhang, et al. Design of diaphragm structure for piezoresistive pressure sensor using topology optimization. Structural and Multidisciplinary Optimization, 2017, 55(1): 317-329.
[30] B Zhu, X Zhang, S Fatikow. Level set-based topology optimization of hinge-free compliant mechanisms using a two-step elastic modeling method. Journal of Mechanical Design, 2014, 136(3): 031007.
[31] B S Lazarov, F Wang, O Sigmund. Length scale and manufacturability in density-based topology optimization. Archive of Applied Mechanics, 2016, 86(1-2): 189-218.
[32] M P Bendsøe, O Sigmund. Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999, 69(9-10): 635-654.
[33] O Sigmund, P M Clausen. Topology optimization using a mixed formulation: An alternative way to solve pressure load problems. Computer Methods in Applied Mechanics and Engineering, 2007, 196(13-16): 1874-1889.
[34] Y M Xie, X Huang. Recent developments in evolutionary structural optimization (ESO) for continuum structures. IOP Conference Series: Materials Science and Engineering, 2010, 10: 012196.
[35] M Zhou, G I N Rozvany. On the validity of ESO type methods in topology optimization. Structural and Multidisciplinary Optimization, 2001, 21(1): 80-83.
[36] B Zhu, R Wang, H Li, et al. A level set method with a bounded diffusion for structural topology optimization. Journal of Mechanical Design, 2018, 140(7): 071402.
[37] G Allaire, F Jouve, A M Toader. Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics, 2004, 194(1): 363-393.
[38] N P V Dijk, K Maute, M Langelaar, et al. Level-set methods for structural topology optimization: a review. Structural and Multidisciplinary Optimization, 2013, 48(3): 437-472.
[39] M Liu, X Zhang, S Fatikow. Design and analysis of a high-accuracy flexure hinge. Review of Scientific Instruments, 2016, 87(5): 055106.
[40] S Osher, R P Fedkiw. Level set methods: An overview and some recent results. Journal of Computational Physics, 2001, 169(2): 463-502.
[41] B Zhu, X Zhang, S Fatikow. Structural topology and shape optimization using a level set method with distance-suppression scheme. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 1214-1239.
[42] Y K Yong, T F Lu, D C Handley. Review of circular flexure hinge design equations and derivation of empirical formulations. Precision Engineering, 2008, 32(2): 63-70.
[43] B Zhu, X Zhang, N Wang, et al. Topology optimization of hinge-free compliant mechanisms using level set methods. Engineering Optimization, 2014, 46(5): 580-605.
[44] M Zhou, M. Y Wang. A semi-Lagrangian level set method for structural optimization. Structural and Multidisciplinary Optimization, 2012, 46(4): 487-501.
[45] J Sokolowski, J P Zolesio. Introduction to shape optimization. Springer, 1992.
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