Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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Estimation of Axial Displacement in High-speed Spindle Due to Rotational Speed

회전속도에 따른 고속 스핀들의 돌출량 예측에 관한 연구

  • Received : 2011.12.05
  • Accepted : 2012.03.05
  • Published : 2012.06.01
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Abstract

This paper presents an estimation procedure for axial displacement in spindle equipped with angular contact ball bearings due to rotational speed. High-speed spindle-bearing system experiences axial displacement due to thermal expansion and rotational speed-dependent characteristics of angular contact ball bearings. This paper deals with the axial displacement caused by the rotational speed-dependent effects such as centrifugal force and gyroscopic moments. To this end, a bearing dynamic model is established that includes all the static and dynamic properties of angular contact ball bearing. An analytical formula to calculate the axial displacement based on contact angles between ball and races is derived to discuss the physics regarding the axial displacement in spindle. The proposed dynamic model is compared with a reference and a commercial program. Numerical examples are presented to show the effects of centrifugal force and gyroscopic moment on the axial displacement. The proposed model is also validated with an experimental result.

Keywords

References

  1. Harris, T. A., "Rolling Bearing Analysis," John Wiley & Sons, 1990.
  2. Hagiu, G. D. and Gafitanu, M. D., "Dynamic characteristics of high speed angular contact ball bearings," Wear, Vol. 211, No. 1, pp. 22-29, 1997. https://doi.org/10.1016/S0043-1648(97)00076-8
  3. Hong, S. W. and Shin, Y. C., "Dynamic analysis of rotor systems with angular contact ball bearings subject to axial and radial loads," Proceeding of the 1st International Symposium on Stability Control of Rotating Machinery, Paper No. 4009, 2001.
  4. Abele, E., Altintas, Y., and Brecher, C., "Machine tool spindle units," CIRP Annals: Manufacturing Technology, Vol. 59, No. 2, pp. 781-802, 2010. https://doi.org/10.1016/j.cirp.2010.05.002
  5. Senda, H., Sato, R., and Moriwaki, T., "Estimation of thermal displacement under varying rotational condition of spindle," Transaction of the JSME, Vol. 70, No. 698, pp. 2813-2818, 2005.
  6. Chen, J. S. and Hsu, W. Y., "Characterizations and models for the thermal growth of a motorized high speed spindle," International Journal of Machine Tools and Manufacture, Vol. 43, No. 11, pp. 1163-1170, 2003. https://doi.org/10.1016/S0890-6955(03)00103-2
  7. Jedrzejewski, J. and Modrzycki, W., "Compensation of thermal displacements of high-speed precision machine tools," Journal of Machine Engineering, Vol. 7, No. 1, pp. 108-114, 2007.
  8. Zverv, I., Pyoun, Y.-S., Lee, K.-B., Kim, J.-D., Jo, I., and Combs, A., "An elastic deformation model of high speed spindles built into ball bearings," Journal of Materials Processing Technology, Vol. 170, No. 3, pp. 570-578, 2005. https://doi.org/10.1016/j.jmatprotec.2005.05.038
  9. Jedrzejewski, J. and Kwasnya, W., "Modelling of angular contact ball bearings and axial displacements for high-speed spindles," Journal of Manufacturing Technology, Vol. 59, No. 1, pp. 377-382, 2010.
  10. Chen, J.-S. and Hwang, Y.-W., "Centrifugal force induced dynamics of a motorized high-speed spindle," International Journal of Advanced Manufacturing Technology, Vol. 30, No. 1-2, pp. 10-19, 2006. https://doi.org/10.1007/s00170-005-0032-y
  11. Bae, G. H., Lee, C. H., Hwang, J. H., and Hong, S. W., "Evaluation of axial displacement in high-speed spindle supported by angular contact ball bearings," Proc. of KSPE Autumn Conference, pp. 299-300, 2011.
  12. de Mul, J. M., Vree, J. M., and Maas, D. A., "Equilibrium and associated load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting friction-part I: general theory and application to ball bearings," ASME Journal of Tribology, Vol. 111, No. 1, pp. 142-148, 1989. https://doi.org/10.1115/1.3261864
  13. Hwang, J., Shim, J. Y., Hong, S. W., and Lee, D. W., "Accuracy simulation of precision rotary motion systems," Journal of the KSPE, Vol. 26, No. 3, pp. 285-291, 2011.
  14. Jorgensen, B. R. and Shin, Y. C., "Dynamics of spindle-bearing systems at high speeds including cutting loads effects," ASME Journal of Manufacturing Science and Technology, Vol. 120, No. 2, pp. 387-394, 1998. https://doi.org/10.1115/1.2830138
  15. Lee, C. W. and Hong, S. W., "Asynchronous harmonic response analysis of rotor-bearing systems," International Journal of Analytical and Experimental Modal Analysis, Vol. 2, No. 2, pp. 51-65, 1990.
  16. Jorgensen, B. R., "Robust modeling of high speed spindle-bearing dynamics under operating conditions," Ph.D. Dissertation, School of Mechanical Engineering, Purdue University, 1996.

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