Skip to main content
Log in

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pohl D.W.: Dynamic piezoelectric translation devices. Rev. Sci. Instrum. 58(1), 54–57 (1987). doi:10.1063/1.1139566

    Article  MathSciNet  Google Scholar 

  2. Zhang Z.M., An Q., Li J.W., Zhang W.J.: Piezoelectric friction–inertia actuator—a critical review and future perspective. Int. J. Adv. Manuf. Technol. 62(5–8), 669–685 (2012). doi:10.1007/s00170-011-3827-z

    Article  Google Scholar 

  3. Nguyen, H.X., Edeler, C., Fatikow, S.: Modeling of piezo-actuated stick–slip micro-drives: an overview. In: Proceedings of the 4th International Conference on Smart Materials, Structures and Systems, printed in Adv. Sci. Technol., vol. 81, pp. 39–48. doi:10.4028/www.scientific.net/AST.81.39 (2012)

  4. Hunstig, M., Hemsel, T., Sextro, W.: Anregungskonzepte und Modellierung piezoelektrischer Trägheitsmotoren. 7. Paderborner Workshop Entwurf mechatronischer Systeme. HNI-Verlagsschriftenreihe, Band 272, Paderborn, pp. 129–141, ISBN 978-3-939350-91-0 (2010)

  5. Breguet, J.-M.: Stick and Slip Actuators. PhD Dissertation. Swiss Federal Institute of Technology ETH Zurich (1998)

  6. De Wit C., Olsson H., Astrom K., Lischinsky P.: A new model for control of systems with friction. IEEE Trans. Autom. Control 40, 419–425 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Altpeter, F.: Friction Modeling, Identification and Compensation. PhD Dissertation. Swiss Federal Institute of Technology ETH Zurich (1999)

  8. Peng J.Y., Chen D.B.: Modeling of piezoelectric-driven stick–slip actuators. IEEE/ASME Trans. Mechatron. 99, 1–6 (2010)

    Google Scholar 

  9. Dupont P., Hayward V., Armstrong B., Altpeter F.: Single state elastoplastic friction models. IEEE Trans. Autom. Control 47, 787–792 (2002)

    Article  MathSciNet  Google Scholar 

  10. Edeler, C.: Modellierung und Validierung der Krafterzeugung mit Stick–Slip-Antrieben für nanorobotische Anwendungen, Ph.D. dissertation, Carl von Universität Oldenburg, Germany (2011)

  11. Dahl, P.R.: A Solid Friction Model. Aerosp. Coop. El Segundo CA, No. ADA041920, p. 31 (1968)

  12. Grzemba, B., Pohrt, R., Teidelt, E., Popov, V.L.: Maximum micro-slip in tangential contact of randomly rough self-affine surfaces. Wear 309, 256–258 (2014)

  13. Geike, T., Popov, V.L.: Mapping of three-dimensional contact problems into one dimension. Phys. Rev. E 76, 036710 (5 pp) (2007)

  14. Geike T., Popov V.L.: Reduction of three-dimensional contact problems to one-dimensional ones. Tribol. Int. 40, 924–929 (2007)

    Article  Google Scholar 

  15. Popov V.L.: Basic ideas and applications of the method of reduction of dimensionality in contact mechanics. Phys. Mesomech. 15, 9–18 (2012)

    Google Scholar 

  16. Popov V.L.: Method of reduction of dimensionality in contact and friction mechanics: a linkage between micro and macro scales. Friction 1(1), 41–62 (2013)

    Article  Google Scholar 

  17. Hunstig M., Hemsel T., Sextro W.: Stick–slip and slip–slip operation of piezoelectric inertia drives. Part I: ideal excitation. Sens. Actuators A Phys. 200, 90–100 (2013)

    Article  Google Scholar 

  18. Hunstig M., Hemsel T., Sextro W.: Stick–slip and slip–slip operation of piezoelectric inertia drives—part II: frequency-limited excitation. Sens. Actuators A Phys. 200, 79–89 (2013)

    Article  Google Scholar 

  19. Bregander, A., Breguet, J.-M.: Performance improvements of stick–slip positioners. In: Proceedings of the 2003 International Symposium on Micromechanics and Human Science, pp. 59–66 (2003)

  20. Edeler, C., Jasper, D.: Laser-based structuring of piezoceramics for mobile microrobots. In: Proceedings of the European Conference on Mechanism Science (2008)

  21. Edeler, C., Meyer, I., Fatikow, S.: Simulation and measurements of stick–slip microdrives for nanorobots. In: European Conference on Mechanism Science (2010)

  22. Popov V.L.: Contact Mechanics and Friction: Physical Principles and Applications, English ed. Springer, Heidelberg (2010)

    Book  Google Scholar 

  23. Hertz, H.: Über die Berührung fester elastischer Körper (german). J. für Die Reine Und Angewandte Mathematik 92,156–171 (1826)

    MathSciNet  Google Scholar 

  24. Popov V.L., Psakhie S.G.: Numerical simulation methods in tribology. Tribol. Int. 40, 916–923 (2007)

    Article  Google Scholar 

  25. Popov V.L., Heß M.: Methode der Dimensionsreduktion in Kontaktmechanik und Reibung Eine Berechnungsmethode im Mikro- und Makrobereich. Imprint: Springer, Berlin (2013)

    Book  Google Scholar 

  26. Pharr G.M., Oliver W.C., Brotzen F.R.: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7(3), 613–617 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Ha X. Nguyen or Elena Teidelt.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nguyen, H.X., Teidelt, E., Popov, V.L. et al. Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction. Arch Appl Mech 86, 1771–1785 (2016). https://doi.org/10.1007/s00419-014-0934-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-014-0934-y

Keywords

Navigation