The purpose of this work is to establish an analytical model and standard way to predict the performance characteristics of a four-point contact, or gothic arch type, rolling element ball bearing. Classical rolling element bearing theory, as developed by Jones, has been extended to include the complex kinematics of the four-point contact bearing; thereby providing complete elementwise attitude and internal load distribution of the bearing under operating conditions. Standard performance parameters, such as element contact stresses, contact angles, inner ring deflections, nonlinear stiffness's, torque, and L10 life, are solved explicitly via standard Newton–Raphson techniques. Race control theory is replaced with a minimum energy state theory to allow both spin and slip to occur at the ball-to-raceway contact. The developed four-point model was programed within the orbis software program. Various test cases are analyzed and key analytical results are compared with the Jones four-point contact ball bearing analysis program, the Wind Turbine Design Guideline, DG03, and traditional two-point (angular contact) analysis codes. Model results for the internal distribution of ball loads and contact angles match the Jones program extremely well for all cases considered. Some differences are found with the DG03 analysis methods, and it is found that modeling a four-point contact bearing by overlaying two opposed angular contact bearings can result in gross errors.

References

References
1.
Hamrock
,
B. J.
, and
Anderson
,
W. J.
,
1972
, “
Arched-Outer-Race Ball-Bearing Analysis Considering Centrifugal Forces
,”
NASA Report No. TN D-6765
.
2.
Nelias
,
D.
, and
Leblanc
,
A.
,
2007
, “
Ball Motion and Sliding Friction in a Four-Contact-Point Ball Bearing
,”
ASME J. Tribol.
,
129
(
4
), pp.
801
808
.
3.
Jones
,
A. B.
,
1964
, “
The Mathematical Theory of Rolling-Element Bearings
,”
Mechanical Design and Systems Handbook
,
McGraw-Hill
,
New York
.
4.
Leveille
,
A. R.
,
1997
, “
The Non-Reversible Nature of Ball Bearing Internal Geometry
,”
REBG International Bearing Symposium
, Orlando, FL.
5.
Jones
,
A. B.
,
1946
, “
Analysis of Stresses and Deflections
,” Vol.
1
,
General Motors Corp.
,
Bristol, CT
.
6.
Harris
,
T. A.
,
2001
,
Rolling Bearing Analysis
,
4th ed.
,
Wiley
,
New York
.
7.
Chapman
,
J. J.
, and
Boness
,
R. J.
,
1975
, “
The Measurement and Analysis of Ball Motion in High Speed Deep Groove Ball Bearings
,”
ASME J. Lubr. Technol.
,
97
(
3
), pp.
341
348
.
8.
ANSI
,
1990
, “
Load Ratings and Fatigue Life for Ball Bearings
,” American National Standards Institute, New York, Standard No. Std. 9-1990.
9.
Harris
,
T. A.
,
Rumbarger
,
J. H.
, and
Butterfield
,
C. P.
,
2009
, “
Wind Turbine Design Guideline, DG03: Yaw and Pitch Rolling Bearing Life
,” National Renewable Energy Laboratory, Golden, CO, Report No. NREL/TP-500-42362.
10.
ISO
,
2006
, “
Static Load Ratings
,” International Organization for Standardization, Geneva, Switzerland, Standard No. ISO-76.
You do not currently have access to this content.