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Design and analysis of porous flexure hinge based on dual-objective topology optimization of three-dimensional continuum

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Abstract

This paper properly presents a dual-objective topology optimization mathematical model for compliance and precision performance of flexure hinges based on the three-dimensional continuum topology optimization. The OptiStruct module is applied to solving the problem. And through the post-processing design and parameterization of the results, a single-axis quasi-leaf porous flexure hinge (QLPFH) is generated. The dimensionless empirical equations of the stiffness and rotational center of the hinge are derived by finite element analysis, and the performance of the flexure hinge under different dimensionless parameters is analyzed. Comparing the QLPFH and the leaf flexure hinge (LFH) with the same external space dimensions, the results show that the translational stiffness of the LFH in the desired working direction and the rotational stiffness are much larger than those of the QLPFH. In addition, in the case of the stiffness of the QLPFH is greatly reduced, its precision performance has also been improved to a certain extent. The feasibility of dual-objective design method based on three-dimensional continuum topology optimization is further confirmed.

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References

  1. Howell LL (2001) Compliant mechanisms. Wiley, New York

    Google Scholar 

  2. Chen GM, Ma FL, Hao GB, Zhu WD (2018) Modeling large deflections of initially curved beams in compliant mechanisms using chained beam constraint model. J Mech Robot 11:011002. https://doi.org/10.1115/1.4041585

    Article  Google Scholar 

  3. Wang NF, Zhang ZY, Zhang XM, Cui CY (2018) Optimization of a 2-DOF micro-positioning stage using corrugated flexure units. Mech Mach Theory 121:683–696. https://doi.org/10.1016/j.mechmachtheory.2017.11.021

    Article  Google Scholar 

  4. Huang JM, Liu A, Deng Z, Zhang Q (2006) A modeling and analysis of spring-shaped torsion micromirrors for low-voltage applications. Int J Mech Sci 48:650–661. https://doi.org/10.1016/j.ijmecsci.2005.12.011

    Article  Google Scholar 

  5. Bakhtiari-Shahri M, Moeenfard H (2018) Topology optimization of fundamental compliant mechanisms using a novel asymmetric beam flexure. Int J Mech Sci 135:383–397. https://doi.org/10.1016/j.ijmecsci.2017.11.023

    Article  Google Scholar 

  6. Zeng W, Gao F, Jiang H, Huang C, Liu JX, Li HF (2018) Design and analysis of a compliant variable-diameter mechanism used in variable-diameter wheels for lunar rover. Mech Mach Theory 125:240–258. https://doi.org/10.1016/j.mechmachtheory.2018.03.003

    Article  Google Scholar 

  7. Bashir M, Rajendran P, Sharma C et al (2018) Investigation of smart material actuators & aerodynamic optimization of morphing wing. Mater Today Proc 5:21068–21075. https://doi.org/10.1016/j.matpr.2018.06.501

    Article  Google Scholar 

  8. Chen WH, Qu JL, Chen WJ et al (2017) A compliant dual-axis gripper with integrated position and force sensing. Mechatronics 47:105–115. https://doi.org/10.1016/j.mechatronics.2017.09.005

    Article  Google Scholar 

  9. Chen GM, Aten QT, Zirbel S et al (2010) A tristable mechanism configuration employing orthogonal compliant mechanisms. J Mech Robot 2:014501. https://doi.org/10.1115/1.4000529

    Article  Google Scholar 

  10. Hao GB, Yu JJ (2016) Design, modelling and analysis of a completely-decoupled XY compliant parallel manipulator. Mech Mach Theory 102:179–195. https://doi.org/10.1016/j.mechmachtheory.2016.04.006

    Article  Google Scholar 

  11. Khasawneh QA, Jaradat MAK, Naji MI, Al-Azzeh MY (2018) Enhancement of hard disk drive manipulator using piezoelectric actuator mechanisms. J Braz Soc Mech Sci Eng 40:517. https://doi.org/10.1007/s40430-018-14432-x

    Article  Google Scholar 

  12. Gao Y, Chen K, Gao H, Xiao P, Wang L (2019) Small-angle perturbation method for moving platform orientation to avoid singularity of asymmetrical 3-RRR planner parallel manipulator. J Braz Soc Mech Sci Eng 41:538. https://doi.org/10.1007/s40430-019-2012-4

    Article  Google Scholar 

  13. Zhan ZH, Zhang XM, Jian ZC, Zhang HD (2018) Error modelling and motion reliability analysis of a planar parallel manipulator with multiple uncertainties. Mech Mach Theory 124:55–72. https://doi.org/10.1016/j.mechmachtheory.2018.02.005

    Article  Google Scholar 

  14. Paros JM, Weisbord L (1965) How to design flexure hinges. Mach Des 37:151–156

    Google Scholar 

  15. Smith ST, Badami VG, Dale JS, Xu Y (1997) Elliptical flexure hinges. Rev Sci Instrum 68:1474–1483. https://doi.org/10.1063/1.1147635

    Article  Google Scholar 

  16. Lobontiu N, Paine JSN, Malley EO, Samuelson M (2002) Parabolic and hyperbolic flexure hinges: flexibility, motion precision and stress characterization based on compliance closed-form equations. Precis Eng 26:183–192. https://doi.org/10.1016/S0141-6359(01)00108-8

    Article  Google Scholar 

  17. Zhang ZJ, Yuan YB (2006) Research on a novel flexure hinge. J Phys: Conf Ser 48:287–291. https://doi.org/10.1088/1742-6596/48/1/053

    Article  Google Scholar 

  18. Chen GM, Liu XY, Gao HW, Jia JY (2009) A generalized model for conic flexure hinges. Rev Sci Instrum 80:055106. https://doi.org/10.1063/1.3137074

    Article  Google Scholar 

  19. Du WT (2011) Fatigue analysis and life prediction for straight beam flexure hinge. Mech Electr Eng Technol 40:52–56. https://doi.org/10.3969/j.issn.1009-9492.2011.06.016

    Article  Google Scholar 

  20. Chen GM, Liu XY, Du YL (2011) Elliptical-Arc-Fillet Flexure Hinges: toward a generalized model for commonly used flexure hinges. J Mech Des 133:081002. https://doi.org/10.1115/1.4004441

    Article  Google Scholar 

  21. Chen GM, Jia JY, Liu XY (2005) On right-circular elliptical flexure hinge. Mach Des Res 21:37–39. https://doi.org/10.3969/j.issn.1006-2343.2005.04.010

    Article  Google Scholar 

  22. Li LJ, Zhang D, Guo S, Qu HB (2019) Design, modeling, and analysis of hybrid flexure hinges. Mech Mach Theory 131:300–316. https://doi.org/10.1016/j.mechmachtheory.2018.10.005

    Article  Google Scholar 

  23. Zhang ZJ, Yuan YB, Yu W et al (2007) Design calculation and analysis of half elliptical flexure hinge. Mach Des Res 23:50–53. https://doi.org/10.3969/j.issn.1006-2343.2007.01.013

    Article  Google Scholar 

  24. Lobontiu N, Crask JW, Kawagley C (2019) Straight-axis folded flexure hinges: in-plane elastic response. Precis Eng 57:54–63. https://doi.org/10.1016/j.precisioneng.2019.03.006

    Article  Google Scholar 

  25. Xie Y, Yu JJ, Zhao HZ (2018) Deterministic design for a compliant parallel universal joint with constant rotational stiffness. J Mech Robot 10:031006–1–031006–12. https://doi.org/10.1115/1.4039065

    Article  Google Scholar 

  26. Xie ZT, Qiu LF, Yang DB (2018) Design and analysis of a variable stiffness Inside-Deployed Lamina Emergent Joint. Mech Mach Theory 120:166–177. https://doi.org/10.1016/j.mechmachtheory.2017.09.023

    Article  Google Scholar 

  27. Xie ZT, Qiu LF, Yang DB (2020) Analysis of a novel variable stiffness filleted leaf hinge. Mech Mach Theory 144:103673. https://doi.org/10.1016/j.mechmachtheory.2019.103673

    Article  Google Scholar 

  28. Zelenika S, Munteanu MG, Bona FD (2009) Optimized flexural hinge shapes for microsystems and high-precision applications. Mech Mach Theory 44:1826–1839. https://doi.org/10.1016/j.mechmachtheory.2009.03.007

    Article  MATH  Google Scholar 

  29. Bona FD, Munteanu MG (2005) Optimized flexural hinges for compliant micromechanisms. Analog Integr Circ Sig Process 44:163–174. https://doi.org/10.1007/s10470-005-2597-7

    Article  Google Scholar 

  30. Kim K, Ahn D, Gweon D (2012) Optimal design of a 1-rotational DOF flexure joint for a 3-DOF H-type stage. Mechatronics 22:24–32. https://doi.org/10.1016/j.mechatronics.2011.10.002

    Article  Google Scholar 

  31. Lu Q, Huang WQ, Wang Y et al (2015) Optimization design of deep-notch elliptical flexure hinges. Opt Precis Eng 23:206–215. https://doi.org/10.3788/OPE.20152301.0206

    Article  Google Scholar 

  32. Freire G, Booker JD, Mellor PH (2015) 2D shape optimization of leaf-type crossed flexure pivot springs for minimum stress. Precis Eng 42:6–21. https://doi.org/10.1016/j.precisioneng.2015.03.003

    Article  Google Scholar 

  33. Aarts RGKM, Wiersma DH, Boer SE et al (2014) Design and performance optimization of large stroke spatial flexures. J Comput Nonlinear Dyn 9:011016. https://doi.org/10.1115/1.4025669

    Article  Google Scholar 

  34. Venkiteswaran VK, Turkkan OA, Su HJ (2017) Speeding up topology optimization of compliant mechanisms with a pseudorigid-body model. J Mech Robot 9:041007. https://doi.org/10.1115/1.4035992

    Article  Google Scholar 

  35. Zhu BL, Chen Q, Jin MH, Zhang XM (2018) Design of fully decoupled compliant mechanisms with multiple degrees of freedom using topology optimization. Mech Mach Theory 126:413–428. https://doi.org/10.1016/j.mechmachtheory.2018.04.028

    Article  Google Scholar 

  36. Cao L, Dolovich AT, Zhang WJ (2015) Hybrid compliant mechanism design using a mixed mesh of flexure hinge elements and beam elements through topology optimization. J Mech Des 137:092303. https://doi.org/10.1115/1.4030990

    Article  Google Scholar 

  37. Zhu BL, Zhang XM, Fatikow S (2014) Design of single-axis flexure hinges using continuum topology optimization method. Sci China Technol Sci 57:560–567. https://doi.org/10.1007/s11431-013-5446-4

    Article  Google Scholar 

  38. Liu M, Zhang XM, Fatikow S (2016) Design and analysis of a high-accuracy flexure hinge. Rev Sci Instrum 87:770. https://doi.org/10.1063/1.4948924

    Article  Google Scholar 

  39. Liu M, Zhang XM, Fatikow S (2017) Design and analysis of a multi-notched flexure hinge for compliant mechanisms. Precis Eng 48:292–304. https://doi.org/10.1016/j.precisioneng.2016.12.012

    Article  Google Scholar 

  40. Qiu LF, Chen HX, Wu YW (2018) Topological structure design and compliance analysis of a new single-axis flexure hinge. J Beijing Univ Aeronaut Astronaut 44:1133–1140. https://doi.org/10.13700/j.bh.1001-5965.2017.0388

    Article  Google Scholar 

  41. Qiu LF, Yue X, Xie ZT (2019) Design and analysis of multicavity flexure hinge (MCFH) based on three-dimensional continuum topology optimization. Mech Mach Theory 139:21–33. https://doi.org/10.1016/j.mechmachtheory.2019.04.004

    Article  Google Scholar 

  42. Liu M (2017) Research on topology optimization theory and method of flexure hinges. South China University of Technology, GuangDong, pp 1–132

    Google Scholar 

  43. Tian Y, Shirinzadeh B, Zhang D, Zhong Y (2010) Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis. Precis Eng 34:92–100. https://doi.org/10.1016/j.precisioneng.2009.03.004

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the support provided by National Natural Science Foundation of China No. 51475037.

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Authors and Affiliations

  1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Lifang Qiu, Xin Yue, Lin Zheng & Yanlin Li

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  1. Lifang Qiu
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  2. Xin Yue
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Correspondence to Lifang Qiu.

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Technical Editor: Paulo de Tarso Rocha de Mendonça, Ph.D.

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Qiu, L., Yue, X., Zheng, L. et al. Design and analysis of porous flexure hinge based on dual-objective topology optimization of three-dimensional continuum. J Braz. Soc. Mech. Sci. Eng. 42, 225 (2020). https://doi.org/10.1007/s40430-020-02312-7

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  • DOI: https://doi.org/10.1007/s40430-020-02312-7

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