Internal Loading Distribution in Statically Loaded Ball Bearings, Subjected to a Combined Radial and Thrust Load, Including the Effects of Temperature and Fit

Authors: Mário C. Ricci

Abstract:

A new, rapidly convergent, numerical procedure for internal loading distribution computation in statically loaded, singlerow, angular-contact ball bearings, subjected to a known combined radial and thrust load, which must be applied so that to avoid tilting between inner and outer rings, is used to find the load distribution differences between a loaded unfitted bearing at room temperature, and the same loaded bearing with interference fits that might experience radial temperature gradients between inner and outer rings. For each step of the procedure it is required the iterative solution of Z + 2 simultaneous nonlinear equations – where Z is the number of the balls – to yield exact solution for axial and radial deflections, and contact angles.

Keywords: Ball, Bearing, Static, Load, Iterative, Numerical, Method, Temperature, Fit.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071128

References:

[1] Stribeck, R. "Ball Bearings for Various Loads," Trans. ASME 29, 420- 463, 1907.
[2] Sjoväll, H. "The Load Distribution within Ball and Roller Bearings under Given External Radial and Axial Load," Teknisk Tidskrift, Mek., h.9, 1933.
[3] Jones, A. Analysis of Stresses and Deflections, New Departure Engineering Data, Bristol, Conn., 1946.
[4] Rumbarger, J. "Thrust Bearings with Eccentric Loads," Mach. Des., Feb. 15, 1962.
[5] Harris, T. Rolling Bearing Analysis, 4th ed., John Wiley & Sons Inc., New York, 2001.
[6] Ricci, M. C. Internal loading distribution in statically loaded ball bearings subjected to a thrust load with variable eccentricity, to be presented at DINCON-09 8th Brazilian Conference on Dynamics, Control and Applications, May, 18-22, Bauru, Brazil, 2009.
[7] Ricci, M. C. Internal loading distribution in statically loaded ball bearings subjected to a combined radial and thrust load, to be presented at 6th ICCSM International Congress of Croatian Society of Mechanics, Sept. 30 to Oct. 2, Dubrovnik, Croatia, 2009.
[8] Ricci, M. C. Internal loading distribution in statically loaded ball bearings subjected to a combined radial, thrust, and moment load, to be presented at 60th International Astronautical Congress, October, 12-16, Daejeon, South Korea, 2009.
[9] Hamrock, B. J. and Anderson, W. J. Arched-Outer-Race Ball-Bearing Considering Centrifugal Forces. NASA TN D-6765, 1972.
[10] Hertz, H. "On the contact of Rigid Elastic Solids and on Hardness," in Miscellaneous Papers, MacMillan, London. 163-183, 1896.
[11] Hamrock, B. J. and Anderson, W. J. Rolling-Element Bearings. NASA RP 1105, 1983.