Internal Loading Distribution in Statically Loaded Ball Bearings Subjected to a Centric Thrust Load: Alternative Approach
An alternative iterative computational procedure is
proposed for internal normal ball loads calculation in statically
loaded single-row, angular-contact ball bearings, subjected to a
known thrust load, which is applied in the inner ring at the geometric
bearing center line. An accurate method for curvature radii at
contacts with inner and outer raceways in the direction of the motion
is used. Numerical aspects of the iterative procedure are discussed.
Numerical examples results for a 218 angular-contact ball bearing
have been compared with those from the literature. Twenty figures
are presented showing the geometrical features, the behavior of the
convergence variables and the following parameters as functions of
the thrust load: normal ball loads, contact angle, distance between
curvature centers, and normal ball and axial deflections.
[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. Ball bearings subjected to a variable eccentric thrust load,
DINCON-09 Proceedings of the 8th Brazilian Conference on Dynamics,
Control and Applications, May, 18-22, Bauru, Brazil, 2009. ISBN: 978-
85-86883-45-3.
[7] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings, ICCCM09 1st International Conference on Computational
Contact Mechanics, Program and Abstracts, p. 21-22, Sept. 16-18,
Lecce, Italy, 2009.
[8] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial and thrust load, including the
effects of temperature and fit, Proceedings of World Academy of
Science, Engineering and Technology, Volume 57, September 2009,
WCSET 2009, Amsterdam, Sept. 23-25, 2009. ISSN: 2070-3724.
http://www.waset.org/proceedings.php.
[9] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial and thrust load, 6th ICCSM
Proceedings of the 6th International Congress of Croatian Society of
Mechanics, Sept. 30 to Oct. 2, Dubrovnik, Croatia, 2009. ISBN 978-
953-7539-11-5.
[10] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial, thrust, and moment load,
Proceedings of the 60th International Astronautical Congress, October,
12-16, Daejeon, South Korea, 2009. ISSN 1995-6258.
[11] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to an eccentric thrust load, Submitted to
Mathematical Problems in Engineering, 2009.
[12] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial, thrust, and moment load,
including the effects of temperature and fit, to be presented at 11th Pan-
American Congress of Applied Mechanics, January, 04-10, Foz do
Iguaçu, Brazil, 2010.
[13] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a centric thrust load: numerical aspects, submitted
to World Congress of the Academy of Science, Engineering and
Technology, Rio de Janeiro, Mar. 29-31, 2010.
[14] Ricci, M. C. Ball bearing under thrust load using an accurate method
for curvature sum and difference, submitted to VI Congresso Nacional
de Engenharia Mecânica, CONEM 2010, Aug. 18-22, 2010.
[15] Hamrock, B. J. and Anderson, W. J. Arched-Outer-Race Ball-Bearing
Considering Centrifugal Forces. NASA TN D-6765, 1972.
[16] Hertz, H. "On the Contact of Rigid Elastic Solids and on Hardness," in
Miscellaneous Papers, MacMillan, London. 163-183, 1896.
[17] Hamrock, B. J. and Anderson, W. J. Rolling-Element Bearings. NASA
RP 1105, 1983.
[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. Ball bearings subjected to a variable eccentric thrust load,
DINCON-09 Proceedings of the 8th Brazilian Conference on Dynamics,
Control and Applications, May, 18-22, Bauru, Brazil, 2009. ISBN: 978-
85-86883-45-3.
[7] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings, ICCCM09 1st International Conference on Computational
Contact Mechanics, Program and Abstracts, p. 21-22, Sept. 16-18,
Lecce, Italy, 2009.
[8] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial and thrust load, including the
effects of temperature and fit, Proceedings of World Academy of
Science, Engineering and Technology, Volume 57, September 2009,
WCSET 2009, Amsterdam, Sept. 23-25, 2009. ISSN: 2070-3724.
http://www.waset.org/proceedings.php.
[9] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial and thrust load, 6th ICCSM
Proceedings of the 6th International Congress of Croatian Society of
Mechanics, Sept. 30 to Oct. 2, Dubrovnik, Croatia, 2009. ISBN 978-
953-7539-11-5.
[10] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial, thrust, and moment load,
Proceedings of the 60th International Astronautical Congress, October,
12-16, Daejeon, South Korea, 2009. ISSN 1995-6258.
[11] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to an eccentric thrust load, Submitted to
Mathematical Problems in Engineering, 2009.
[12] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a combined radial, thrust, and moment load,
including the effects of temperature and fit, to be presented at 11th Pan-
American Congress of Applied Mechanics, January, 04-10, Foz do
Iguaçu, Brazil, 2010.
[13] Ricci, M. C. Internal loading distribution in statically loaded ball
bearings subjected to a centric thrust load: numerical aspects, submitted
to World Congress of the Academy of Science, Engineering and
Technology, Rio de Janeiro, Mar. 29-31, 2010.
[14] Ricci, M. C. Ball bearing under thrust load using an accurate method
for curvature sum and difference, submitted to VI Congresso Nacional
de Engenharia Mecânica, CONEM 2010, Aug. 18-22, 2010.
[15] Hamrock, B. J. and Anderson, W. J. Arched-Outer-Race Ball-Bearing
Considering Centrifugal Forces. NASA TN D-6765, 1972.
[16] Hertz, H. "On the Contact of Rigid Elastic Solids and on Hardness," in
Miscellaneous Papers, MacMillan, London. 163-183, 1896.
[17] Hamrock, B. J. and Anderson, W. J. Rolling-Element Bearings. NASA
RP 1105, 1983.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:58249", author = "Mário C. Ricci", title = "Internal Loading Distribution in Statically Loaded Ball Bearings Subjected to a Centric Thrust Load: Alternative Approach", abstract = "An alternative iterative computational procedure is
proposed for internal normal ball loads calculation in statically
loaded single-row, angular-contact ball bearings, subjected to a
known thrust load, which is applied in the inner ring at the geometric
bearing center line. An accurate method for curvature radii at
contacts with inner and outer raceways in the direction of the motion
is used. Numerical aspects of the iterative procedure are discussed.
Numerical examples results for a 218 angular-contact ball bearing
have been compared with those from the literature. Twenty figures
are presented showing the geometrical features, the behavior of the
convergence variables and the following parameters as functions of
the thrust load: normal ball loads, contact angle, distance between
curvature centers, and normal ball and axial deflections.", keywords = "Ball, Bearing, Static, Load, Iterative, Numerical,Method.", volume = "4", number = "5", pages = "454-9", }
