International Journal of Mechanical Engineering and Applications

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Analytical Solution of Stiffness for a Corner-Fillet Leaf-Spring Type Flexure Hinge with a Long Fatigue Life

Received: May 17, 2018    Accepted: Jun. 05, 2018    Published: Jun. 29, 2018
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Abstract

Flexure hinges as the displacement guiding and amplifying mechanism or sensing component are widely used for micro-actuators and sensors. However, the existing flexure hinges, leaf-spring or notch type, cause serious stress concentration which severely weaken the fatigue life of compliance mechanism. Therefore, developing long fatigue life flexure hinges is very important for high working frequency actuators and sensors, such as fast-tool-servo. Corner-fillet leaf-spring type flexure hinge could provide large displacement with lower stress. Stiffness expressions of it with both fixed-fixed and fixed-guided boundary conditions are derived by using Castigliano’s theorem. The main influence factors for stress concentration are investigated and the formulas of stress concentration factor are obtained in terms of ratio of fillet radius to the minimum thickness. These analytical formulas have been verified by comparing with finite element analysis (FEA) results. Stress-life method is chosen to research the influence of fillet radius on fatigue life and the results indicate fillet radius can improve fatigue life of flexure hinge effectively. The proposed analytical solution is the fundamental of optimal design of a leaf-spring type flexure hinge based mechanism with fatigue life constraints.

DOI 10.11648/j.ijmea.20180603.14
Published in International Journal of Mechanical Engineering and Applications ( Volume 6, Issue 3, June 2018 )
Page(s) 64-72
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Stiffness, Stress Concentration, Corner-Fillet, Flexure Hinge, Long Fatigue Life

References
[1] Chen X, Su C Y, Li Z, et al., Design of Implementable Adaptive Control for Micro/Nano Positioning System Driven by Piezoelectric Actuator. IEEE Transactions on Industrial Electronics, 2016, 63(10):6471-6481.
[2] S. B. Choi, S. S. Han, Y. M. Han, et al., A magnification device for precision mechanisms featuring piezoactuators and flexure hinges: Design and experimental validation. Mechanism and Machine Theory, 2007. 42(9): p. 1184-1198.
[3] W. Dong, J. Tang, and Y. ElDeeb, Design of a linear-motion dual-stage actuation system for precision control. Smart Materials & Structures, 2009. 18(9).
[4] Akbari S and Pirbodaghi T, Precision positioning using a novel six axes compliant nano-manipulator. Microsystem Technologies, 2016, 23(7):1-9.
[5] Sun X and Yang B, A new methodology for developing flexure-hinged displacement amplifiers with micro-vibration suppression for a giant magnetostrictive micro drive system, Sensors & Actuators A Physical, 2017, 263.
[6] Zhang X and Xu Q, Design and testing of a new 3-DOF spatial flexure parallel micropositioning stage. International Journal of Precision Engineering & Manufacturing, 2018, 19(1):109-118.
[7] Qu J, Chen W, Zhang J, et al., A piezo-driven 2-DOF compliant micropositioning stage with remote center of motion. Sensors & Actuators A Physical, 2016, 239:114-126.
[8] Wang F, Liang C, Tian Y, et al., A Flexure-Based Kinematically Decoupled Micropositioning Stage With a Centimeter Range Dedicated to Micro/Nano Manufacturing. IEEE/ASME Transactions on Mechatronics, 2016, 21(2):1055-1062.
[9] Q. Xu, Design and Development of a Flexure-Based Dual-Stage Nanopositioning System With Minimum Interference Behavior. IEEE Transactions on Automation Science and Engineering, 2012. 9(3): p. 554-563.
[10] Zhang Y, Zhang W, Zhang Y, et al., 2-D Medium–High Frequency Fiber Bragg Gratings Accelerometer. IEEE Sensors Journal, 2017, 17(3):614-618.
[11] S. Desrochers, D. Pasini, and J. Angeles, Optimum Design of a Compliant Uniaxial Accelerometer. Journal of Mechanical Design, 2010. 132(4).
[12] S. Kavitha, R. J. Daniel, and K. Sumangala, A simple analytical design approach based on computer aided analysis of bulk micromachined piezoresistive MEMS accelerometer for concrete SHM applications. Measurement, 2013. 46(9): p. 3372-3388.
[13] Chen D, Wu Z, Shi X, Wang J, Liu L, Design and modelling of an electromagnetically excited silicon nitride beam resonant pressure sensor, In: Proceedings 4th IEEE international conference nano/micro engineered and molecular systems, 2009, pp.754–757
[14] M. J. Lachut and J. E. Sader, Effect of surface stress on the stiffness of thin elastic plates and beams. Physical Review B, 2012. 85(8).
[15] D. Kang, et al., Optimal design of high precision XY-scanner with nanometer-level resolution and millimeter-level working range. Mechatronics, 2009. 19(4): p. 562-570. DOI: 10.1016/j.mechatronics.2009.01.002
[16] Q. Xu, Design, testing and precision control of a novel long-stroke flexure micropositioning system. Mechanism and Machine Theory, 2013. 70: p. 209-224.
[17] G. Chen, X. Y. Liu, H. Gao, A generalized model for conic flexure hinges. Review of Scientific Instruments, 2009. 80(5).
[18] N. Lobontiu, J. S. N. Paine and E. Garcia, et al., Design of symmetric conic-section flexure hinges based on closed-form compliance equations. Mechanism and Machine Theory, 2002. 37(5): p. 477-498.
[19] G. M. Chen, X. Shao, and X. Huang, A new generalized model for elliptical arc flexure hinges. Review of Scientific Instruments, 2008. 79(9).
[20] Y. Tian, B. Shirinzadeh, and D. Zhang, Closed-form compliance equations of filleted V-shaped flexure hinges for compliant mechanism design. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2010. 34(3): p. 408-418.
[21] F. Dirksen, M. Anselmann and TI. Zohdi, Incorporation of flexural hinge fatigue-life cycle criteria into the topological design of compliant small-scale devices. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2013. 37(3): p. 531-541.
[22] Q. Wang, and X. M. Zhang, Fatigue reliability based optimal design of planar compliant micropositioning stages. Review of Scientific Instruments, 2015. 86(10):p.105-117.
[23] Y. M. Tseytlin, Notch flexure hinges: An effective theory. Review of Scientific Instruments, 2002. 73(9): p. 3363-3368.
[24] Y. F. Wu, and Z. Y. Zhou, Design calculations for flexure hinges. Review of Scientific Instruments, 2002. 73(8): p. 3101-3106.
[25] Y. K. Yong, T. F. Lu, and D. C. Handley, Review of circular flexure hinge design equations and derivation of empirical formulations. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2008. 32(2): p. 63-70.
[26] Y. K. Yong, T. F. Lu, Comparison of circular flexure hinge design equations and the derivation of empirical stiffness formulations, in 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2009. p. 510-515.
[27] G. Chen, J. Wang, and X. Liu, Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges. Journal of Mechanical Design, 2014. 136(3).
[28] N. Lobontiu, et al., Stiffness characterization of corner-filleted flexure hinges. Review of Scientific Instruments, 2004. 75(11): p. 4896-4905.
[29] Z. Yang, Y. Bai, X. Chen, Simultaneous optimal design of topology and size for a flexure-hinge-based guiding mechanism to minimize mass under stiffness and frequency constraints. Engineering Optimization, 2017.49(6):p. 948-961.
[30] N. Lobontiu, J. S. N Paine, E. Garcia, et al., Corner-filleted flexure hinges. Journal of Mechanical Design, 2001. 123(3): p. 346-352.
[31] Q. Meng, Y. Li, and J. Xu, New empirical stiffness equations for corner-filleted flexure hinges. Mechanical Sciences, 2013. 4(2): p. 345-356.
[32] F. P. Beer, Mechanics of Materials, McGraw Hill, New York, 2012.
[33] W. Young, R Budynas, Sadegh A. Roark's Formulas for Stress and Strain, seventh ed., McGraw Hill, New York, 2002.
[34] R. C. Juvinall. Stress, Strain, and Strength., McGraw Hill, New York, 1967.
Cite This Article
  • APA Style

    Li Rui-qi, Wu Bai-sheng, Chen Xin, Yang Zhi-jun. (2018). Analytical Solution of Stiffness for a Corner-Fillet Leaf-Spring Type Flexure Hinge with a Long Fatigue Life. International Journal of Mechanical Engineering and Applications, 6(3), 64-72. https://doi.org/10.11648/j.ijmea.20180603.14

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    ACS Style

    Li Rui-qi; Wu Bai-sheng; Chen Xin; Yang Zhi-jun. Analytical Solution of Stiffness for a Corner-Fillet Leaf-Spring Type Flexure Hinge with a Long Fatigue Life. Int. J. Mech. Eng. Appl. 2018, 6(3), 64-72. doi: 10.11648/j.ijmea.20180603.14

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    AMA Style

    Li Rui-qi, Wu Bai-sheng, Chen Xin, Yang Zhi-jun. Analytical Solution of Stiffness for a Corner-Fillet Leaf-Spring Type Flexure Hinge with a Long Fatigue Life. Int J Mech Eng Appl. 2018;6(3):64-72. doi: 10.11648/j.ijmea.20180603.14

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  • @article{10.11648/j.ijmea.20180603.14,
      author = {Li Rui-qi and Wu Bai-sheng and Chen Xin and Yang Zhi-jun},
      title = {Analytical Solution of Stiffness for a Corner-Fillet Leaf-Spring Type Flexure Hinge with a Long Fatigue Life},
      journal = {International Journal of Mechanical Engineering and Applications},
      volume = {6},
      number = {3},
      pages = {64-72},
      doi = {10.11648/j.ijmea.20180603.14},
      url = {https://doi.org/10.11648/j.ijmea.20180603.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijmea.20180603.14},
      abstract = {Flexure hinges as the displacement guiding and amplifying mechanism or sensing component are widely used for micro-actuators and sensors. However, the existing flexure hinges, leaf-spring or notch type, cause serious stress concentration which severely weaken the fatigue life of compliance mechanism. Therefore, developing long fatigue life flexure hinges is very important for high working frequency actuators and sensors, such as fast-tool-servo. Corner-fillet leaf-spring type flexure hinge could provide large displacement with lower stress. Stiffness expressions of it with both fixed-fixed and fixed-guided boundary conditions are derived by using Castigliano’s theorem. The main influence factors for stress concentration are investigated and the formulas of stress concentration factor are obtained in terms of ratio of fillet radius to the minimum thickness. These analytical formulas have been verified by comparing with finite element analysis (FEA) results. Stress-life method is chosen to research the influence of fillet radius on fatigue life and the results indicate fillet radius can improve fatigue life of flexure hinge effectively. The proposed analytical solution is the fundamental of optimal design of a leaf-spring type flexure hinge based mechanism with fatigue life constraints.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Analytical Solution of Stiffness for a Corner-Fillet Leaf-Spring Type Flexure Hinge with a Long Fatigue Life
    AU  - Li Rui-qi
    AU  - Wu Bai-sheng
    AU  - Chen Xin
    AU  - Yang Zhi-jun
    Y1  - 2018/06/29
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ijmea.20180603.14
    DO  - 10.11648/j.ijmea.20180603.14
    T2  - International Journal of Mechanical Engineering and Applications
    JF  - International Journal of Mechanical Engineering and Applications
    JO  - International Journal of Mechanical Engineering and Applications
    SP  - 64
    EP  - 72
    PB  - Science Publishing Group
    SN  - 2330-0248
    UR  - https://doi.org/10.11648/j.ijmea.20180603.14
    AB  - Flexure hinges as the displacement guiding and amplifying mechanism or sensing component are widely used for micro-actuators and sensors. However, the existing flexure hinges, leaf-spring or notch type, cause serious stress concentration which severely weaken the fatigue life of compliance mechanism. Therefore, developing long fatigue life flexure hinges is very important for high working frequency actuators and sensors, such as fast-tool-servo. Corner-fillet leaf-spring type flexure hinge could provide large displacement with lower stress. Stiffness expressions of it with both fixed-fixed and fixed-guided boundary conditions are derived by using Castigliano’s theorem. The main influence factors for stress concentration are investigated and the formulas of stress concentration factor are obtained in terms of ratio of fillet radius to the minimum thickness. These analytical formulas have been verified by comparing with finite element analysis (FEA) results. Stress-life method is chosen to research the influence of fillet radius on fatigue life and the results indicate fillet radius can improve fatigue life of flexure hinge effectively. The proposed analytical solution is the fundamental of optimal design of a leaf-spring type flexure hinge based mechanism with fatigue life constraints.
    VL  - 6
    IS  - 3
    ER  - 

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Author Information
  • Micro and Nano Processing Equipment and Technology Key Laboratory of Guangdong Province, Guangdong University of Technology, Guangzhou, China

  • Micro and Nano Processing Equipment and Technology Key Laboratory of Guangdong Province, Guangdong University of Technology, Guangzhou, China

  • Micro and Nano Processing Equipment and Technology Key Laboratory of Guangdong Province, Guangdong University of Technology, Guangzhou, China

  • Micro and Nano Processing Equipment and Technology Key Laboratory of Guangdong Province, Guangdong University of Technology, Guangzhou, China

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