Analytical relationships for calculating three rolling element bearing loads (Fx, Fy, and Fz) and two tilting moments (My and Mz) as a function of three relative race translations (dx, dy, and dz) and two relative race tilting angles (dθy and dθz) have been given in a previous paper. The previous approach was suggested for any rolling element bearing type, although it has been recognized that the assumption of a constant rolling element-race contact angle is not well supported by deep groove ball bearings (DGBB) or angular contact ball bearings (ACBB). The new approach described in this paper addresses the latter weaknesses by accounting for the variation of the contact angle on the most loaded ball and also shows that misalignment effects on spherical roller bearing (SRB) loads are negligible. Comparisons between the simplified approach (option 1) and the “enhanced” numerical approach (option 2, which requires a summation of the load components on each ball with the appropriate contact angle included) is made, showing a good correlation as long as the relative misalignment remains reasonable or occurs in the plane corresponding to maximum radial displacement. Option 2 can, however, be recommended since it is easy to program and quite accurate at any misalignment level. Other pros and cons of both options are described. As in the previous paper, a full coupling between all displacements and forces, as well as roller and raceway crown radii, are considered, meaning that Hertzian point contact stiffness is used in roller bearings at low load with a smooth transition toward Hertzian line contact as the load increases. This approach is particularly recommended for programming the rolling element bearing behavior in any finite element analysis or multibody system dynamic tool, since only two nodes are considered: one for the inner race (IR) center, usually connected to a shaft, and another node for the outer race (OR) center, connected to the housing.

References

References
1.
Houpert
,
L.
,
1997
, “
A Uniform Analytical Approach for Ball and Roller Bearings
,”
ASME J. Tribol.
,
119
(
4
), pp.
851
857
.10.1115/1.2833896
2.
Houpert
,
L.
,
2014
, “
An Enhanced Study of the Load-Displacement Relationships for Rolling Element Bearings
,”
ASME J. Tribol.
,
136
(
1
), p.
011105
.10.1115/1.4025602
3.
Houpert
,
L.
,
2001
, “
An Engineering Approach to Hertzian Contact Elasticity– Part I
,”
ASME J. Tribol.
,
123
(
3
), pp.
582
588
.10.1115/1.1308043
4.
Houpert
,
L.
,
2001
, “
An Engineering Approach to Non-Hertzian Contact Elasticity–Part II
,”
ASME J. Tribol.
,
123
(
3
), pp.
589
594
.10.1115/1.1308042
5.
Eschmann
,
P.
,
Hasbargen
,
L.
, and
Weigand
,
K.
,
1978
,
Ball and Roller Bearings, Theory, Design and Application
,
2nd ed.
,
R.
Oldenbourg
, ed.,
Verlag
, München, Germany.
6.
Harris
,
T. A.
,
1991
,
Rolling Bearing Analysis
,
3rd ed.
,
Wiley-Interscience Publication
,
Wiley
, New York.
7.
Hoeprich
,
M. R.
,
1986
, “
Numerical Procedure for Designing Rolling Element Contact Geometry as a Function of Load Cycle
,”
SAE Technical Paper Series No. 850764
.10.4271/850764
8.
Houpert
,
L.
,
1995
, “
Prediction of Bearing, Gear and Housing Performances
,”
Proceedings of the Rolling Bearing Practice Today Seminar
,
Institution of Mechanical Engineers
,
London
,
UK
.
9.
Jones
,
A. B.
,
1960
, “
A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
,”
ASME J. Basic Eng.
,
82
(
2
), pp.
309
320
.10.1115/1.3662587
10.
Sjöval
,
S.
,
1933
, “
The Load Distribution Within Ball and Roller Bearings Under Given External Radial and Axial Load
,”
Tek. Tidskr., Mek.
, p.
9
.
11.
Tripp
,
J.
,
1985
, “
Hertzian Contact in Two and Three Dimensions
,” NASA Technical Paper No. 2473.
12.
Cretu
,
S.
,
1996
, “
Initial Plastic Deformation of Cylindrical Roller Generatrix Stress Distribution Analysis and Fatigue Life Tests
,”
Acta Tribol.
,
4
(
1–2
), pp.
1
6
.
13.
Houpert
,
L.
, and
Merckling
,
J.
,
1998
, “
A Successful Transition From Physically Measured to Numerically Simulated Bearings, Shafts, Gears and Housing Deflections in a Transmission
,”
Proceedings of the Conference GPC’98 Global PowerTrain Congress New Powertrain Materials and Processes
, Detroit, MI, Vol. 4, pp.
131
137
.
14.
Hauswald
,
T.
, and
Houpert
,
L.
,
2000
, “
Numerical and Experimental Simulations of Performances of Bearing System, Shaft and Housing; Account for Global and Local Deformations
,”
Proceeding of the Conference ‘SIA Seminar Fiabilité experimentale
,
Paris
,
France
.
15.
Houpert
,
L.
,
1999
, “
Numerical and Analytical Calculations in Ball Bearings
,”
Proceedings of the 8th European Space Mechanism and Tribology Symposium
,
Toulouse
,
France
.
16.
Houpert
,
L.
,
2010
, “
CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part I: Basic Tribology Concepts
,”
STLE Tribol. Trans.
,
53
(
1
), pp.
1
9
.10.1080/10402000903132093
17.
Houpert
,
L.
,
2010
, “
CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part II: Description of the Numerical Tool and its Outputs
,”
STLE Tribol. Trans.
,
53
(
1
), pp.
10
21
.10.1080/10402000903132101
18.
Houpert
,
L.
,
2010
, “
CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part III: Experimental Validation
,”
STLE Tribol. Trans.
,
53
(
6
), pp.
848
859
.10.1080/10402004.2010.496069
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