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Analytical Compliance Model for Right Circle Flexure Hinge Considering the Stress Concentration Effect

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Abstract

In this paper, an analytical compliance model for right circle flexure hinge (RCFH) is presented with the stress concentration in consideration. The stress concentration caused by changes in RCFH’s cross-section usually happens at the weakest point. It has been shown to seriously affect RCFH’s compliance calculation. Based on the virtual work theory, superposition relationship of the deformation, as well as Castigliano’s second theorem, RCFH’s analytical compliance model considering the stress concentration effect is established. The model is calculated as a series of closed-form equations which are related with geometric dimensions and employed material. Complicated definite integrals existing in these compliance equations are proved to be correctly calculated through comparisons with other literatures. Finally, in order to examine the validity of the established model, finite element analysis (FEA) is conducted. The relative errors between the theoretical values obtained by the established model and FEA results are found within 20% for a wide range of geometric dimensions.

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References

  1. 1.

    Lobontiu, N. (2002). Compliant mechanisms: Design of flexure hinges. Boca Raton: CRC Press.

  2. 2.

    Lobontiu, N., & Garcia, E. (2003). Two-axis flexure hinges with axially-collocated and symmetric notches. Computers & Structures,81(13), 1329–1341.

  3. 3.

    Liu, P. B., Yan, P., Zhang, Z., & Leng, T. T. (2015). Flexure-hinges guided nano-stage for precision manipulations: Design, modeling and control. International Journal of Precision Engineering and Manufacturing,16(11), 2245–2254.

  4. 4.

    Bhagat, U., Shirinzadeh, B., Clark, L., Chea, P., Qin, Y., Tian, Y., et al. (2014). Design and analysis of a novel flexure-based 3-DOF mechanism. Mechanism and Machine Theory,74, 173–187.

  5. 5.

    Bhattacharya, S., Chattaraj, R., Das, M., Patra, A., Bepari, B., & Bhaumik, S. (2015). Simultaneous parametric optimization of IPMC actuator for compliant gripper. International Journal of Precision Engineering and Manufacturing,16(11), 2289–2297.

  6. 6.

    Sattler, R., Plötz, F., Fattinger, G., & Wachutka, G. (2002). Modeling of an electrostatic torsional actuator: Demonstrated with an RF MEMS switch. Sensors and Actuators, A: Physical,97, 337–346.

  7. 7.

    Tian, Y., Shirinzadeh, B., & Zhang, D. (2010). Closed-form compliance equations of filleted V-shaped flexure hinges for compliant mechanism design. Precision Engineering,34(3), 408–418.

  8. 8.

    Tian, Y., Shirinzadeh, B., Zhang, D., & Zhong, Y. (2010). Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis. Precision Engineering,34(1), 92–100.

  9. 9.

    Qin, Y. D., Zhao, X., Shirinzadeh, B., Tian, Y. L., & Zhang, D. W. (2018). Closed-form modeling and analysis of an XY flexure-based nano-manipulator. Chinese Journal of Mechanical Engineering,31(1), 7.

  10. 10.

    Wang, D. H., Yang, Q., & Dong, H. M. (2011). A monolithic compliant piezoelectric-driven microgripper: Design, modeling, and testing. IEEE/ASME Transactions on Mechatronics,18(1), 138–147.

  11. 11.

    Wang, J., Yang, Y., Yang, R., Feng, P., & Guo, P. (2019). On the validity of compliance-based matrix method in output compliance modeling of flexure-hinge mechanism. Precision Engineering. https://doi.org/10.1016/j.precisioneng.2019.02.006.

  12. 12.

    Zettl, B., Szyszkowski, W., & Zhang, W. J. (2005). On systematic errors of two-dimensional finite element modeling of right circular planar flexure hinges. Journal of Mechanical Design,127(4), 782–787.

  13. 13.

    Shen, Y., Chen, X., Jiang, W., & Luo, X. (2014). Spatial force-based non-prismatic beam element for static and dynamic analyses of circular flexure hinges in compliant mechanisms. Precision Engineering,38(2), 311–320.

  14. 14.

    Zettl, B., Szyszkowski, W., & Zhang, W. J. (2005). Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: The equivalent beam methodology. Precision Engineering,29(2), 237–245.

  15. 15.

    Paros, J. M., & Weisbord, L. (1965). How to design flexure hinges. Machine Design,37(27), 151–156.

  16. 16.

    Valentini, P. P., & Pennestrì, E. (2017). Elasto-kinematic comparison of flexure hinges undergoing large displacement. Mechanism and Machine Theory,110, 50–60.

  17. 17.

    Yang, M., Du, Z., & Dong, W. (2016). Modeling and analysis of planar symmetric superelastic flexure hinges. Precision Engineering,46, 177–183.

  18. 18.

    Li, Y., Xiao, S., Xi, L., & Wu, Z. (2014). Design, modeling, control and experiment for a 2-DOF compliant micro-motion stage. International Journal of Precision Engineering and Manufacturing,15(4), 735–744.

  19. 19.

    Wu, Y., & Zhou, Z. (2002). Design calculations for flexure hinges. Review of Scientific Instruments,73(8), 3101–3106.

  20. 20.

    Lobontiu, N., Garcia, E., & Canfield, S. (2003). Torsional stiffness of several variable rectangular cross-section flexure hinges for macro-scale and MEMS applications. Smart Materials and Structures,13(1), 12–19.

  21. 21.

    Tseytlin, Y. M. (2002). Notch flexure hinges: An effective theory. Review of Scientific Instruments,73(9), 3363–3368.

  22. 22.

    Yong, Y. K., Lu, T. F., & Handley, D. C. (2008). Review of circular flexure hinge design equations and derivation of empirical formulations. Precision Engineering,32(2), 63–70.

  23. 23.

    Chen, G., & Howell, L. L. (2009). Two general solutions of torsional compliance for variable rectangular cross-section hinges in compliant mechanisms. Precision Engineering,33(3), 268–274.

  24. 24.

    Hearn, E. J. (1997). Mechanics of materials, 3th. Oxford: Butterworth-Heinemann.

  25. 25.

    Xu, N., Dai, M., & Zhou, X. (2017). Analysis and design of symmetric notch flexure hinges. Advances in Mechanical Engineering. https://doi.org/10.1177/1687814017734513.

  26. 26.

    Li, T. M., Zhang, J. L., & Jiang, Y. (2015). Derivation of empirical compliance equations for circular flexure hinge considering the effect of stress concentration. International Journal of Precision Engineering and Manufacturing,16(8), 1735–1743.

  27. 27.

    Awtar, S., Slocum, A. H., & Sevincer, E. (2007). Characteristics of beam-based flexure modules. Journal of Mechanical Design,129(6), 625–639.

  28. 28.

    Linß, S., Schorr, P., & Zentner, L. (2017). General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges. Mechanical Sciences,8(1), 29.

  29. 29.

    Meng, Q. (2012). A design method for flexure-based compliant mechanisms on the basis of stiffness and stress characteristics. Doctoral dissertation, University of Bologna.

  30. 30.

    Young, W. C., Budynas, R. G., & Sadegh, A. M. (2002). Roark’s formulas for stress and strain. New York: McGraw-Hill.

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Acknowledgements

This research was funded by the Foundation of the National Natural Science Foundation of China (No. 61733012), the Foundation of the National Natural Science Foundation of China (No. 61703303), the Natural Science Foundation of Tianjin City (No. 17JCQNJC04100), the Project supported by State Key Laboratory of Precision Measuring Technology and Instruments (No. PILAB1705) and the Research Project of Tianjin Municipal Education Committee (No. 2017KJ086).

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Correspondence to Xingfei Li.

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Tuo, W., Li, X., Ji, Y. et al. Analytical Compliance Model for Right Circle Flexure Hinge Considering the Stress Concentration Effect. Int. J. Precis. Eng. Manuf. (2020) doi:10.1007/s12541-019-00306-7

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Keywords

  • Right circle flexure hinge
  • Compliance model
  • Stress concentration
  • Finite element analysis