Ball bearings are complex components where local deformations are the main factor on the global behavior. One problem is the relation between a contact configuration and the load level. When those components are assembled, position errors have important effects on those contact configurations. A rigid ball bearing has very small clearances that give tolerances impossible to achieve. How can the designer write geometric specifications on the assembly taking into account bearing elastic behavior?. We propose a method to identify the limits of those errors according to the ball bearing limits and the clearances. The built model has been compared with industrial references with good accuracy.

References

References
1.
Bourdet
,
P.
, and
Clement
,
A.
, 1976, “
Controling a Complex Surface With a 3 Axis Measuring Machine
,”
CIRP Ann.-Manuf. Technol.
,
25
, pp.
359
361
.
2.
Clement
,
A.
,
Riviere
,
A.
, and
Serre
,
P.
,
A Declarative Information Model for Functional Requirements Computer-Aided Tolerancing
(
Chapman and Hall
,
London
, 1996). pp.
3
16
.
3.
Riviere
,
A.
,
Clement
,
A.
, and
Valade
,
C.
, 1997, “
The TTRS: 13 Oriented Constraints for Dimensioning, Tolerancing and Inspection
,”
Ser. Adv. Math. Appl. Sci.
,
45
, pp.
24
42
.
4.
Laperriere
,
L.
,
Ghie
,
W.
, and
Desrochers
,
A.
, 2002, “
Statistical and Deterministic Tolerance Analysis and Synthesis Using a Unified Jacobian-Torsor Model
,”
CIRP Ann.-Manuf. Technol.
,
51
(
1
), pp.
417
420
.
5.
Giordano
,
M.
,
Duret
,
D.
, and
Tichadou
,
S.
, 1992, “
Clearance Space in Volumic Dimensioning
,”
CIRP Ann.-Manuf. Technol
,
40
(
1
), pp.
565
568
.
6.
Teissandier
,
D.
,
Couetard
,
Y.
, and
Gerard
,
A.
, 1999, “
A Computer Aided Tolerancing Model: Proportioned Assembly Clearance Volume
,”
Comput.-Aided Des.
,
31
(
13
), pp.
805
817
.
7.
Davidson
,
J.K.
, and
Shah
,
J.J.
, 2002, “
Geometric Tolerances : A New Application for Line Geometry and Screws
,”
ImechE J. Mech. Eng. Sci.
,
216
(Part C), pp.
95
104
8.
Harris
,
T. A.
, 1991,
Rolling Bearing Analysis
,
3rd ed.
,
Wiley-Interscience, Hoboken, NJ
.
9.
Houpert
,
L.
, 2002, “
Ball Bearing and Tapered Roller Bearing Torque: Analytical, Numerical and Experimental Results
,”
Tribol. Trans., 1547-397X
,
45
(
3
), pp.
345
353
.
10.
Zamponi
,
L.
,
Mermoz
,
E.
,
Linares
,
J. M.
, and
Sprauel
,
J. M.
, 2009, “
Impact of geometrical Defects on Bearing Assemblies With Integrated Raceways in Aeronautical Gearboxes
,”
Mech. Mach. Theory
,
44
, pp.
1108
1120
.
11.
Bremner
,
D.
,
Fukuda
,
K.
, and
Marzetta
,
A.
, 1998, “
Primal–Dual Methods for Vertex and Facet Enumeration
,”
Discrete Comput. Geom.
,
20
, pp.
333
357
.
12.
Barber
,
C. B.
,
Dobkin
,
D. P.
, and
Huhdanpaa
,
H. T.
, 1996, “
The Quickhull Algorithm for Convex Hulls
,”
ACM Trans. Math. Softw.
,
22
(
4
), pp.
469
483
.
13.
Fukuda
,
K.
, 2009, “
cdd/cdd+ Reference Manual
,” Institute for Operations Research ETH-Zentrum, CH-8092 Zurich, Switzerland, http://www.ifor.math.ethz.ch/~fukuda/cdd_home/index.htmlhttp://www.ifor.math.ethz.ch/~fukuda/cdd_home/index.html
14.
Ballu
,
A.
, 2009, “
Measurement of Gap Hull for Model Validation, Product Verification and Maintenance
,”
Proceedings of the 11th International Conference on Computer Aided Tolerancing CIRP CAT2009
, Annecy, France, March 26–27.
15.
International Standard for Organisation, 1991, “
Rolling bearings—Internal clearance—Part 1: Radial internal clearance for radial bearings
,” ISO No. 5793.
16.
Teissandier
,
D.
, and
Dufaure
,
J.
, 2002, “
Tolerance Synthesis With Polytopes: Application to Radial Ball Bearing Arrangements
,”
Fourth International Conference on Integrated Design and Manufacturing in Mechanical Engineering
, Clermont Ferrand (France).
17.
Samper
,
S.
,
Petit
,
J. P.
, and
Giordano
,
M.
, 2006, “
Computer Aided Tolerancing-Solver and Post Processor Analysis
,”
Advances in Design
,
Springer Series in Advanced Manufacturing
, pp
487
497
.
18.
Habchi
,
W.
, and
Demirci
,
I.
, and
Eyheramendy
,
D.
, and
Morales
,
G.
, 2007, “
A Finite Element Approach of Thin Film Lubrication in Circular EHD Contacts
,”
Tribol. Int.
,
40
, pp.
1466
1473
.
19.
Hertz
,
H.
, 1881, “
On the contact of elastic solids, Zeitschrift ftir die Reine und angewandte Mathematik (in German)
,”
English translation in miscellaneous papers (translated by D.E. Jones and G.A. Schott) 99 146-62
.
Macmillan
,
London, UK
, (1986)
92
, pp.
156
171
.
20.
Hernot
,
X.
,
Sartor
,
M.
, and
Guillot
,
J.
, 2000, “
Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach
,”
ASME J. Mech. Des.
122
, pp.
83
89
.
21.
International Standard for Organization, 2006, “
Rolling Bearings—Static Load Ratings
,” I SO No. 76.
22.
Lundberg
,
G.
, and
Palmgren
,
A.
, 1947, “
Dynamic Capacity of Rolling Bearings
,”
Acta Polytech. Mech. Eng. Ser.
1
(
3
), pp.
7
8
.
23.
International Standard for Organization, 2008, ISO 1281-1:2008 “
Rolling bearings—Explanatory notes on ISO 281—Part 1: Basic dynamic load rating and basic rating life
.”
24.
American National Standards Institute, 1990, Std 11-1990, “
Load Rating and Fatigue Life for Roller Bearings
.”
You do not currently have access to this content.