Journal of Theoretical
and Applied Mechanics

57, 1, pp. 59-72, Warsaw 2019
DOI: 10.15632/jtam-pl.57.1.59

### An extended contact model of the angular bearing

Jan Kosmol
The article presents a new contact model of an angular bearing, called the extended model.
The model takes account of the effects of centrifugal load caused by thr rotating ring of the
bearing and the issue of elasticity. Present models, encountered in literature and referred
to in the article as classical, consider the centrifugal force caused by the rotating ball only.
Results of analytical research on the extended model and of FEM simulation show explicitly
that the contact angles of bearings, and thus contact loads, differ very much from those
values obtained in the classical model. These differences are disadvantageous for designing
bearing assemblies, since contact loads are greater than those obtained in the classical model.
This means, among others, that the present structures with angular contact bearings are
in reality subject to greater loads than the constructor has envisaged. The motto of the
article is to design analytical calculation models in such a form which would enable the
constructor to estimate contact loads, just using a standard scientific calculator or MS
Excel type applications; so that there would be no need for solving complex models using
numerical methods.
Keywords: contact model, angular bearing, FEM

#### References

Abele E., Altintas Y., Brecher C., 2010, Machine tool spindle units, CIRP Annals – Manufacturing

Technology, 59, 781-802

Alfares M.A., Elsharkawy A., 2003, Effects of axial preloading of angular contact ball bearings

on the dynamics of a grinding machine spindle system, Journal of Materials Processing Technology, 136, 48-59

Altintas Y., Cao Y., 2005, Virtual design and optimization on machine tool spindles, Annals of

the CIRP, 54, 1, 379-382

Antoine F., Abba G., Molinari A., 2005, A new proposal for explicit angle calculation in

angular contact ball bearing, Journal of Mechanical Design, 128, 2, 468-478

Cao Y., Altintas Y., 2007, Modelling of spindle-bearing and machine tool systems for virtual

simulation of milling operations, International Journal of Machine Tools and Manufacture, 47, 1342-1350

Chen J.-S., Hwang Y.-W., 2006, Centrifugal force induced dynamics of motorized high-speed

spindle, International Journal of Machine Tools and Manufacture, 30, 10-19

Chojnacki M., 2016, Experimental research of motion resistance in angular bearings (in Polish),

M.Sc. Thesis, Silesian University of Technology, Gliwice

Harris T., Kotzalas M., 2013, Essential Concepts of Bearing Technology. Rolling Bearing Analysis, 5th Ed., Taylor & Francis Group, London

Jędrzejewski J., Kwaśny W., 2010, Modelling of angular contact ball bearings and axial displacements

for high-speed spindles, CIRP Annals-Manufacturing Technology, 59, 377-383

Jiang S., Mao H., 2010, Investigation of variable optimum preload for machine tool spindle,

International Journal of Machine Tools and Manufacture, 50, 19-28

Kosmol J., 2016, Determination of Motion Resistances in High-Speed Spindle Angular Bearings,

Monograph, Silesian University of Technology Publisher, Gliwice

Kosmol J., Gatys R., 2016, Simulation research of the influence of rotational speed on contact

loads in angular bearings (in Polish), Inżynieria Maszyn, 21, 1, 32-45

Musiał J., Styp-Rekowski M., 1999, Analytical and experimental method of determination

of the coefficient of motion resistance in rolling friction (in Polish), Proceedings of Conference

“Problems of Unconventional Bearing Configuration”, Łódź, 59-65

Muszyński M., 2017, Experimental research of motion resistance in angular bearings (in Polish),

M.Sc. Thesis, Silesian University of Technology, Gliwice

Noel D., Rithou M., Furet B., Leloch S., 2013, Complete analytical expression of the stiffness

matrix of angular contact ball bearing, Journal of Tribology, 135, 4

Palmgren A., 1951, Rolling Bearings (in Polish), PWT, Warszawa, 235

Styp-Rekowski M., 1999, Problems of the Internal Resistance of Motion in an Angle Bearing

(in Polish), University Press of Technology and Agriculture Academy in Bydgoszcz, Thesis, 99,

Bydgoszcz