Formulation of Friction Forces in LM Ball Guides

LM 볼가이드의 마찰력 정식화

Oh, Kwang-Je;Khim, Gyungho;Park, Chun-Hong;Chung, Sung-Chong

  • Received : 2015.10.30
  • Accepted : 2015.12.09
  • Published : 2016.02.01


Linear motion (LM) ball guides with rolling contact are core units of feed-drive systems. They are widely applied for precision machinery such as machine tools, semiconductor fabrication machines and robots. However, the friction force induced from LM ball guides generates heat, which deteriorates positioning accuracy and incurs changes of stiffness and preload. To accurately analyze the effects and apply the results to precision machine design, mathematical modeling of the friction force is required. In this paper, accurate formulation of the friction force due to rolling, viscous, and slip frictions is conducted for LM ball guides. To verify the reliability of the developed friction model, experiments are performed under various assembly, load and velocity conditions. Effects of frictional components are analyzed through the formulated friction model.


Friction Model;Hertz Contact;Linear Motion Ball Guide;Rolling Friction;Slip Friction;Viscous Friction


  1. Oh, K. J., Khim, G. H., Park, C. H. and Chung, S. C., 2015, "Mathematical Modeling of Friction Force in LM Ball Guides," Journal of the KSPE, Vol. 32, No. 5, pp. 423-429.
  2. KIMM., 2014, "Development of Platform Technology for Machine Accuracy Simulation II," Research Report, Korea Institute of Machinery & Materials.
  3. Kim, K. H., Park, C. H., Song, C. K., Lee, H. S. and Kim, S. W., 2000, "The Accuracy Design of LM Guide System in Machine Tools," Journal of the KSPE, Vol. 23, No. 7, pp. 692-695.
  4. Ohta, H. and Tanaka, K., 2010, "Vertical Stiffness of Preload Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail," Journal of Tribology, Vol. 132, pp. 1-9.
  5. Shimizu, S., 1999, "Stiffness Analysis of Linear Motion Guide System," International Journal of the JSPE, Vol. 33, No. 3, pp. 163-167.
  6. Kim, K. H., Park, C. H., Lee, H. and Kim, S. W., 2002, "Analysis of the Motion Errors in Linear Motion Guide," Journal of the KSPE, Vol. 19, No. 5, pp.139-148.
  7. Oh, K., Park, C. H. and Chung, S. C., 2014, "Identification of Static and Dynamic Frictions in Ballscrew Servos," Proceedings of the ASPE Annual Meeting, Vol. 59, pp. 246-250.
  8. Jang, S. H., Khim, G. and Park, C. H., 2013, "An Experimental Prediction of Heat Generation Caused by Friction Force on Linear Motion Guide," Proceeding of the KSPE, pp. 489-490.
  9. Harris, T. A., 2001, Rolling Bearing Analysis, John Wiley and Sons, New York, pp. 183-230.
  10. Stolarski, T. A. and Tobe, S., 2000, Rolling Contacts, Professional Engineering Publishing Limited, pp. 76-80.
  11. Hamrock, B. J. and Dowson, D., 1981, Ball Bearing Lubrication: The Elasto-hydrodynamics of Elliptical Contacts, John Wiley and Sons, pp. 187-218.
  12. Weisberg, S., 2005, Applied Linear Regression, John Wiley and Sons, pp. 194-206.

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