This article deals with the behavior of a planar joint taking surface defects into account. Two theoretical concepts are used: gap hull and difference surface. Gap hull represents the displacement space characterizing all possible relative displacements in a joint. Difference surface simplifies the study of contact between parts of that joint. A bijective relationship between these two concepts is developed and exploited. Two experimental methods are developed to validate these theoretical concepts. The first consists of measuring relative displacements between two parts of a planar joint using a measuring system designed specifically for this study. Results obtained from the first method are validated by comparing with the results of the second method in which the contacting surfaces of the planar joint are measured.

References

References
1.
Bhushan
,
B.
,
1998
, “
Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact
,”
Tribol. Lett.
,
4
(
1
), pp.
1
35
.10.1023/A:1019186601445
2.
Yu
,
M. M.-H.
, and
Bhushan
,
B.
,
1996
, “
Contact Analysis of Three-Dimensional Rough Surfaces Under Frictionless and Frictional Contact
,”
Wear
,
200
(
1–2
), pp.
265
280
.10.1016/S0043-1648(96)07313-9
3.
International Organization for Standardization
,
1983
,
ISO 1101: Geometrical Tolerancing—Tolerancing of Form, Orientation, Location and Run-Out—Generalities, Definitions, Symbols, Indications on Drawings, ISO, Geneva
, Switzerland.
4.
ASME Standard, ASME Y14.5M-1994,
1994
,
Dimensioning and Tolerancing
,
American Society of Mechanical Engineers
,
New York
.
5.
Chase
,
K. W.
,
Gao
,
J.
, and
Magleby
,
S. P.
,
1995
, “
General 2-D Tolerance Analysis of Mechanical Assemblies With Small Kinematic Adjustments
,”
J. Des. Manuf.
,
5
(
4
), pp.
263
274
.10.1142/S096031319500027X
6.
Gao
,
J.
,
Chase
,
K. W.
, and
Magleby
,
S. P.
,
1998
, “
Generalized 3-D Tolerance Analysis of Mechanical Assemblies With Small Kinematic Adjustments
,”
IIE Trans.
,
30
(
4
), pp.
367
377
.
7.
Giordano
,
M.
, and
Duret
,
D.
,
1993
, “
Clearance Space and Deviation Space
,”
3rd. CIRP Seminars on Computer Aided Tolerancing
, ENS Cachan, France, Apr. 27–28, pp.
115
128
.
8.
Bourdet
,
P.
, and
Clément
,
A.
,
1976
, “
Controlling Surface With a 3 Axis Measuring Machine
,”
Ann. CIRP
,
25/1
(STC Me), pp.
359
361
.
9.
Bourdet
,
P.
,
Mathieu
,
L.
,
Lartigue
,
C.
, and
Ballu
,
A.
,
1996
, “
The Concept of the Small Displacement Torsor in Metrology, Advanced Mathematical Tools in Metrology II, Series on Advances in Mathematics for Applied Sciences
,”
World Scientific
,
40
, pp.
110
122
.
10.
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2002
, “
Geometric Tolerances: A New Application for Line Geometry and Screws
,”
Proc. Inst. Mech. Eng., Part C
,
216
(
C1
), pp.
95
104
.10.1243/0954406021524837
11.
Grandjean
,
J.
,
Ledoux
,
Y.
, and
Samper
,
S.
,
2012
, “
On the Role of Form Defects in Assemblies Subject to Local Deformations and Mechanical Loads
,”
Int. J. Adv. Manuf. Technol.
,
65
(
9–12
), pp.
1769
1778
.10.1007/s00170-012-4298-6
12.
Samper
,
S.
,
Adragna
,
P.-A.
,
Favreliere
,
H.
, and
Pillet
,
M.
,
2009
, “
Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces
,”
ASME J. Comput. Inf. Sci. Eng.
,
9
(
4
), p.
041005
.10.1115/1.3249575
13.
Greenwood
,
J.
, and
Williamson
,
J.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. Lond. Ser. A
,
295
(
1442
), pp.
300
319
.10.1098/rspa.1966.0242
14.
Ledoux
,
Y.
,
Lasseux
,
D.
,
Favreliere
,
H.
,
Samper
,
S.
, and
Grandjean
,
J.
,
2011
, “
On the Dependence of Static Flat Seal Efficiency to Surface Defects
,”
Int. J. Pressure Vessels Piping
,
88
(
11–12
), pp.
518
529
.10.1016/j.ijpvp.2011.06.002
15.
Neville
,
K. S. L.
, and
Grace
,
Y.
,
2006
, “
The Modeling and Analysis of Butting Assembly in the Presence of Workpiece Surface Roughness Part Dimensional Error
,”
Int. J. Adv. Manuf. Technol.
,
31
(
5–6
), pp.
528
538
.10.1007/s00170-005-0222-7
16.
Stoll
,
T.
,
Wittman
,
S.
, and
Meerkamm
,
H.
,
2009
, “
Tolerance Analysis With Detailed Part Modeling Including Shape Deviations
,”
Proceedings of the 11th CIRP Conference on Computer Aided Tolerancing
, Geometric Variations Within Product Life-Cycle Management, Annecy, France, Mar. 26–27, pp.
231
243
.
17.
Morière
,
S.
,
Mailhé
,
J.
,
Linares
,
J.-M.
, and
Sprauel
,
J.-M.
,
2009
, “
Assembly Method Comparison Including Form Defect
,”
Proceedings of the 11th CIRP Conference on Computer Aided Tolerancing
, Geometric Variations within Product Life-Cycle Management, Annecy, France, Mar. 26–27, pp.
245
257
.
18.
Bourdet
,
P.
,
1987
, “
Contribution à la mesure tridimensionnelle: Modèle d'identification géométrique des surfaces, Métrologie fonctionnelle des pièces mécaniques, Correction géométrique des machines à mesurer tridimensionnelles
,” Ph.D. thesis, Université de Nancy. Lorraine, France.
You do not currently have access to this content.