DOI QR코드

DOI QR Code

Modified sigmoid based model and experimental analysis of shape memory alloy spring as variable stiffness actuator

  • Sul, Bhagoji B. (Department of Instrumentation and Control Engineering, National Institute of Technology) ;
  • Dhanalakshmi, K. (Department of Instrumentation and Control Engineering, National Institute of Technology)
  • Received : 2018.08.07
  • Accepted : 2019.05.10
  • Published : 2019.09.25

Abstract

The stiffness of shape memory alloy (SMA) spring while in actuation is represented by an empirical model that is derived from the logistic differential equation. This model correlates the stiffness to the alloy temperature and the functionality of SMA spring as active variable stiffness actuator (VSA) is analyzed based on factors that are the input conditions (activation current, duty cycle and excitation frequency) and operating conditions (pre-stress and mechanical connection). The model parameters are estimated by adopting the nonlinear least square method, henceforth, the model is validated experimentally. The average correlation factor of 0.95 between the model response and experimental results validates the proposed model. In furtherance, the justification is augmented from the comparison with existing stiffness models (logistic curve model and polynomial model). The important distinction from several observations regarding the comparison of the model prediction with the experimental states that it is more superior, flexible and adaptable than the existing. The nature of stiffness variation in the SMA spring is assessed also from the Dynamic Mechanical Thermal Analysis (DMTA), which as well proves the proposal. This model advances the ability to use SMA integrated mechanism for enhanced variable stiffness actuation. The investigation proves that the stiffness of SMA spring may be altered under controlled conditions.

Keywords

References

  1. Hadi, A., Yousefi-Koma, A., Elahinia, M., Moghaddam, M.M. and Ghazavi, A. (2010), "A shape memory alloy spring-based actuator with stiffness and position controllability", J. Syst. Control Eng. Proc. I Mech E, 225 Part I. https://doi.org/10.1177/2041304110394570.
  2. Liang, C. and Rogers, C.A. (1997), "Design of shape memory alloy springs with applications in vibration control", J. Intel. Mat. Syst. Str., 8, 314-322. https://doi.org/10.1177/1045389X9700800404.
  3. Dhanalakshmi, K., Umapathy, M., Ezhilarasi, D. and Bandyopadhya, B. (2011), "Design and implementation of fast output sampling feedback control for shape memory alloy actuated structures", Smart Struct. Syst., 8(4), 367-384. http://dx.doi.org/10.12989/sss.2011.8.4.367.
  4. Kardan, I., Abiri, T., Kabganian, M. and Vahabi, M. (2013), "Modeling of shape memory alloy springs using a neural network", J. Theor. Appl.Mech., 51 (3), 711-718.
  5. Zhang, J., Yin, Y. and Zhu, J. (2013), "Sigmoid - based hysteresis modeling and high speed tracking control of SMA -artificial muscle", Sensor. Actuat. A - Phys., 201, 264-273. https://doi.org/10.1016/j.sna.2013.07.036.
  6. He, J. and Toi, Y. (2013), "Improved constitutive modeling for phase transformation of shape memory alloys", J. Solid Mech. Mater. Eng., 7(1), 11-26. https://doi.org/10.1299/jmmp.7.11.
  7. Kumon, M., Mizumoto, I. and Iwai, Z. (2007), "Shape memory alloy actuator with simple adaptive control", IEEE 0-7695-2882-1/07.
  8. Kciuk, M., Chwastek, K., Kluszczynski, K. and Szczyglowski, J. (2016), "A study on hysteresis behaviour of SMA linear actuators based on unipolar sigmoid hyperbolic tangent functions", Sensor. Actuat. A - Phys., 243, 52-58. https://doi.org/10.1016/j.sna.2016.02.012.
  9. Cortez-Vega, R., Chairez, I., Luviano-Juarez, A. and Feliu-Batlle, V. (2018), "A hybrid dynamic model of shape memory alloy spring actuators", Measurement, 114, 340-353. https://doi.org/10.1016/j.measurement.2017.08.041.
  10. Holanda, S.A., Silva, A.A., de Araujo, C.J. and de Aquino, A.S. (2014), "Study of the complex stiffness of a vibratory mechanical system with shape memory alloy coil spring actuator", Shock Vib., Article ID 162781, 11 pages. http://dx.doi.org/10.1155/2014/162781.
  11. Wolf, S., Grioli, G., Eiberger, O., Friedl, S., Grebenstein, M. and Carloni, R. (2016), "Variable stiffness actuators: review on design and components", IEEE/ASME T. Mechatron., 21(5), 2418-2430. DOI: 10.1109/TMECH.2015.2501019.
  12. Enemark, S., Savi, M.A. and Santos, I.F. (2015), "Experimental analysis of dynamical systems and involving shape memory alloys", Smart Struct. Syst., 15(6), 1521-1542. http://dx.doi.org/10.12989/sss.2015.15.6.1521.
  13. Wang, T.M., Shi, Z.Y., Liu, D., Ma, C. and Zhang, Z.H. (2012), "An accurately controlled antagonistic shape memory alloy actuator with self-sensing", Sensors MDPI Publications, 12(6), 7682-7700. https://doi.org/10.3390/s120607682.
  14. Raczka, W., Konieczny, J. and Sibielak, M. (2011), "Mathematical model of a shape memory alloy spring intended for vibration reduction systems", Trans. Tech. Publications, 177, 65-75. https://doi.org/10.4028/www.scientific.net/SSP.177.65.
  15. Lagoudas, D.C. (2008), Editor, Shape Memory Alloys, Modeling and Engineering Applications, Springer Science + Business Media, LLC.
  16. Sul, B.B. and Dhanalakshmi, K. (2017), "Sigmoid based force modeling and shape recovery characteristics of SMA spring actuator", Proceedings of the 14th IEEE International Conference INDICON, 15th -17th December 2017, IIT Roorkee, India.
  17. Ikuta, K. (1990), "Micro/miniature shape memory alloy actuator", Proceedings of the IEEE International Conference on Robotics and Automation, 2156-2161.
  18. Da Silva, N.J., Grassi, E.N.D., de Brito Simoes, J. and de Araujo, C.J. (2009), "Dynamic mechanical analysis of a NiTi shape memory alloy: An experimental study", Proceedings of the COBEM 2009, Gramado, RS, Brazil.
  19. Bendame, M. (2010), "Mathematical modeling and control of nonlinear oscillators with shape memory alloys", M. S. Theses, Wilfrid Laurier University.
  20. Van Ham, R., Sugar, T.G., Vanderborght, B., Hollander, K.W. and Lefeber, D. (2009), "Compliant actuator design", IEEE Robotics and Automation Magazine, 81-94. www.sciencebuddies.com; Ben Finio, Ph.D.