Advertisement

Science China Technological Sciences

, Volume 59, Issue 9, pp 1320–1327 | Cite as

Stripe theory based numerical method for solving asymmetrical hysteresis of friction force in linear rolling guideways

  • Yang Zhao
  • YinHu Xi
  • JunHong MaoEmail author
  • Patrick Pat Lam Wong
Article
  • 82 Downloads

Abstract

Linear rolling guideways (LRGs) play an important role in precision engineering. In the pre-rolling region, the hysteretic friction force exerts great impacts on the positioning accuracy. Numerical and experimental studies of the hysteresis of friction force are presented in this paper. A model, which is based on the stripe theory and the simplified theory of rolling contact, is built to describe the transient hysteresis of the friction force. Then, the model is modified by taking the anelasticity effect into consideration. Experimentally, a linear motor direct-drive setup is utilized to measure the transient asymmetrical hysteresis of the friction force in the pre-rolling region of an LRG. The influences of the pre-rolling displacement and the dwelling time on the asymmetrical hysteresis of the friction force are studied. The numerical and experimental results are well correlated, which shows good accuracy of the model. The transient asymmetrical hysteresis of friction force in the pre-rolling region of LRGs can thus be determined using the model.

Keywords

pre-rolling friction anelasticity hysteresis linear rolling guideway 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Oiwa T, Katsuki M, Karita M, et al. Questionnaire survey on ultra- precision positioning. Int J Automat Tech, 2011, 5: 766–772CrossRefGoogle Scholar
  2. 2.
    Chen J S, Chen, K C, Lai Z C, et al. Friction characterization and compensation of a linear-motor rolling-guide stage. Int J Mach Tool Manu, 2003, 43: 905–915CrossRefGoogle Scholar
  3. 3.
    Al-Bender F, Symens W. Characterization of frictional hysteresis in ball-bearing guideways. Wear, 2005, 258: 1630–1642CrossRefGoogle Scholar
  4. 4.
    De Moerlooze K, Al-Bender F, Van Brussel H. Modeling of the dynamic behavior of systems with rolling elements. Int J Nonlinear Mech, 2011, 46: 222–233CrossRefGoogle Scholar
  5. 5.
    Fukada S, Fang B, Shigeno A. Experimental analysis and simulation of nonlinear microscopic behavior of ball screw mechanism for ultra- precision positioning. Precis Eng, 2011, 35: 650–668CrossRefGoogle Scholar
  6. 6.
    Xi Y H, Zhou Y, Zhang W, et al. An experiment method for measuring friction behaviors of linear rolling guides. Chin Sci Bull, 2014, 59: 3912–3918CrossRefGoogle Scholar
  7. 7.
    Harris T A, Kotzalas M N. Rolling Bearing Analysis, Fifth Edition: Advanced Concepts of Bearing Technology. Boca Raton/London/ New York: Taylor and Francis Group, LLC, 2007Google Scholar
  8. 8.
    Haines D J, Ollerton E. Contact stress distribution on elliptical contact surfaces subjected to radial and tangential forces. In: Proceedings of Institution of Mechanical Engineers, London, 1963. 177: 45–54Google Scholar
  9. 9.
    Kalker J J. A strip theory for rolling with slip and spin. In: Proc. Kon. Ned. Acad. van Wetenschappen, 1967, B70: 10–62Google Scholar
  10. 10.
    Kalker J J. Three-dimensional Elastic Bodies in Rolling Contact. Ordrecht/ Boston/London: Kluwer Academic Publishers, 1990CrossRefzbMATHGoogle Scholar
  11. 11.
    Johnson K L. Contact Mechanics. Cambridge: Cambridge University Press, 1985CrossRefzbMATHGoogle Scholar
  12. 12.
    Kalker J J. Simplified theory of rolling contact. Delft Progress Report, Series C, 1973. 11–10Google Scholar
  13. 13.
    Spiegelberg C, Björklund S, Andersson S. Simulation of transient friction of a cylinder between two planes. Wear, 2003, 254: 1170–1179.CrossRefGoogle Scholar
  14. 14.
    Vollebregt E A H, Wilders P. FASTSIM2: A second-order accurate frictional rolling contact algorithm. Comput Mech, 2011, 47: 105–116CrossRefzbMATHGoogle Scholar
  15. 15.
    Söderberg A, Spiegelberg C. Modeling transient behavior of a mechanical system including a rolling and sliding contact. ASME Tribology Division, TRIB, 2005, 16: 229–238CrossRefGoogle Scholar
  16. 16.
    Al-Bender F, De Moerlooze K. A model of the transient behavior of tractive rolling contacts. Adv Tribol, 2008, 214894. 1–17Google Scholar
  17. 17.
    Al-Bender F, Lampaert V, Swevers J. A novel generic model at asperity level for dry friction force dynamics. Tribol Lett, 2004, 16: 81–93CrossRefGoogle Scholar
  18. 18.
    Oleksowicz S, Mruk A. A basic theoretical model for friction process at microasperity level. Tribol T, 2011, 54: 691–700CrossRefGoogle Scholar
  19. 19.
    De Moerlooze K, Al-Bender F. Experimental investigation into the tractive prerolling behavior of balls in V-grooved tracks. Adv Tribol, 2008, 561280. 1–10Google Scholar
  20. 20.
    Goodman L E. Contact stress analysis of normally loaded rough spheres. J Appl Mech, 1962, 29: 515–522CrossRefzbMATHGoogle Scholar
  21. 21.
    Mindlin R D. Compliance of elastic bodies in contact. ASME T J Appl Mech, 1949, 16: 259–268MathSciNetzbMATHGoogle Scholar
  22. 22.
    Nowick A S. Anelastic Relaxation in Crystalline Solids (Vol. 1). New York: Academic Press, 2012. 8–9Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yang Zhao
    • 1
    • 2
  • YinHu Xi
    • 1
  • JunHong Mao
    • 1
    Email author
  • Patrick Pat Lam Wong
    • 2
  1. 1.Theory of Lubrication and Bearing Institute, Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing SystemXi’an Jiaotong UniversityXi’anChina
  2. 2.Department of Mechanical and Biomedical EngineeringCity University of Hong KongHong KongChina

Personalised recommendations