The major part of production cost of a manufacturing product is set during the design stage and especially by the tolerancing choice. Therefore, a lot of work involves trying to simulate the impact of these choices and provide an automatic optimization. For integrating this modeling in computer aided design (cad) software, the tolerancing must be modeled by a mathematical tool. Numerous models have been developed but few of them are really efficient. Two advanced models are “T-map” model developed by Joseph K. Davidson and “deviation domain” developed by Max Giordano. Despite the graphical representation of these two models seems to be similar, they have significant differences in their construction and their resolution method. These similarities and differences highlight the needs of tolerancing modeling tool in each kind of problems, especially in case of assembly with parallel links.

References

References
1.
Geometrical Product Specifications (GPS)
,
2006
, “
Geometrical Tolerancing—Tolerances of Form, Orientation, Location and Run-Out
,” NF-EN-ISO-1101.
2.
ASME-Y14.5
,
2009
, “Dimensioning and Tolerancing: Engineering Drawing and Related Documentation Practices.”
3.
Chase
,
K. W.
, and
Parkinson
,
A. R.
,
1991
, “
A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies
,”
Res. Eng. Des.
,
3
, pp.
23
37
.10.1007/BF01580066
4.
Shen
,
Z.
,
Ameta
,
G.
,
Shah
,
J. J.
, and
Davidson
,
J. K.
,
2005
, “
A Comparative Study of Tolerance Analysis Methods
,”
ASME J. Comput. Inf. Sci. Eng.
,
5
(
3
), pp.
247
256
.10.1115/1.1979509
5.
Shah
,
J. J.
,
Ameta
,
G.
,
Shen
,
Z.
, and
Davidson
,
J. K.
,
2007
, “
Navigating the Tolerance Analysis Maze
,”
Comput.-Aided Des. Appl.
,
4
(
5
), pp.
705
718
.
6.
Chavanne
,
R.
, and
Anselmetti
,
B.
,
2009
, “
Quick GPS: Rapid Tolerancing of an Isolated Part
,”
11th CIRP International Conference On Computer Aided Tolerancing, Geometric Variations Within Product Life-Cycle Management
,
Annecy, France
.
7.
Singh
,
G.
,
Ameta
,
G.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2009
, “
Worst-Case Tolerance Analysis of a Self-Aligning Coupling Assembly Using Tolerance-Maps
,”
Proceedings of the 11th CIRP International Conference on Computer Aided Tolerancing
,
Annecy, France
.
8.
Germain
,
F.
, and
Giordano
,
M.
,
2007
, “
A New Approach for Three-Dimensional Statistical Tolerancing
,”
Proceedings of CIRP-CAT
,
Erlangen, Germany
.
9.
Ameta
,
G.
,
Samper
,
S.
, and
Giordano
,
M.
,
2011
, “
Comparison of Spatial Math Models for Tolerance Analysis: Tolerance-Maps, Deviation Domain, and TTRS
,”
ASME J. Comput. Inf. Sci. Eng.
,
11
(
2
), p.
021004
.10.1115/1.3593413
10.
Davidson
,
J. K.
,
Mujezinovic
,
A.
, and
Shah
,
J. J.
,
2002
, “
A New Mathematical Model for Geometric Tolerances as Applied to Round Faces
,”
ASME J. Mech. Des.
,
124
(
4
), pp.
609
622
.10.1115/1.1497362
11.
Coxeter
,
H.
,
1969
,
Introduction to Geometry
,
2nd ed.
,
John Wiley & Sons
,
New York
.
12.
Giordano
,
M.
,
Pairel
,
E.
, and
Samper
,
S.
,
1999
, “
Mathematical Representation of Tolerance Zones
,”
Global Consistency of Tolerances
,
F. V.
Houten
, and
H.
Kals
, eds.,
Proceedings of the 6th CIRP International Seminar on Computer-Aided Tolerancing, Kluwer Academic, University of Twente
,
Enschede, The Netherlands
.
13.
Fukuda
,
K.
,
2004
, “
From the Zonotope Construction to the Minkowski Addition of Convex Polytopes
,”
J. Symb. Comput.
,
38
(
4
), pp.
1261
1272
.10.1016/j.jsc.2003.08.007
14.
Jian
,
A. D.
,
Ameta
,
G.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2005
, “
Tolerance Analysis and Allocation Using Tolerance-Maps for a Power Saw Assembly
,”
CIRP: Models for Computer Aided Tolerancing in Design and Manufacturing
,
Springer
,
Netherlands
, pp.
267
276
.
15.
Mansuy
,
M.
,
Giordano
,
M.
, and
Hernandez
,
P.
,
2011
, “
A New Calculation Method for the Worst Case Tolerance Analysis and Synthesis in Stack-Type Assemblies
,”
Comput.-Aided Des.
,
43
, pp.
1118
1125
.10.1016/j.cad.2011.04.010
16.
Ameta
,
G.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2007
, “
Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies
,”
ASME J. Comput. Inf. Sci. Eng.
,
7
(
4
), pp.
347
359
.10.1115/1.2795308
17.
Ameta
,
G.
,
Davidson
,
J. K.
, and
Shah
,
J.
,
2010
, “
Influence of Form on Tolerance-Map-Generated Frequency Distributions for 1D Clearance in Design
,”
Precis. Eng.
,
34
(
1
), pp.
22
27
.10.1016/j.precisioneng.2008.02.002
18.
Ameta
,
G.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2010
, “
Statistical Tolerance Allocation for Tab-Slot Assemblies Utilizing Tolerance-Maps
,”
ASME J. Comput. Inf. Sci. Eng.
,
10
(
1
), p.
011005
.10.1115/1.3249576
19.
Giordano
,
M.
,
Samper
,
S.
, and
Petit
,
J.-P.
,
2007
, “
Tolerance Analysis and Synthesis by Means of Deviation Domains, Axi-Symmetric Cases
,”
Models for Computer Aided Tolerancing in Design and Manufacturing
,
Springer
,
Netherlands
, pp.
85
94
.
20.
Davidson
,
J.
, and
Shah
,
J.
,
2002
, “
Geometric Tolerances: A New Application for Line Geometry and Screws
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
216
(
1
), pp.
95
103
.10.1243/0954406021524837
21.
Ameta
,
G.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2007
, “
Tolerance-Maps Applied to a Point-Line Cluster of Features
,”
ASME J. Mech. Des.
,
129
(
8
), pp.
782
792
.10.1115/1.2717226
22.
Mujezinovic
,
A.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2004
, “
A New Mathematical Model for Geometric Tolerances as Applied to Polygonal Faces
,”
ASME J. Mech. Des.
,
126
(
3
), pp.
504
518
.10.1115/1.1701881
23.
Desrochers
,
A.
,
2003
,
A CAD/CAM Representation Model Applied to Tolerance Transfer Methods
,
ASME J. Mech. Des.
,
125
(
1
), pp.
14
22
.10.1115/1.1543974
24.
Desrochers
,
A.
, and
Clment
,
A.
,
1994
, “
A Dimensioning and Tolerancing Assistance Model for CAD/CAM systems
,”
Int. J. Adv. Manuf. Technol.
,
9
(
6
), pp.
352
361
.10.1007/BF01748479
25.
Anselmetti
,
B.
,
2006
, “
Generation of Functional Tolerancing Based on Positioning Features
,”
Comput.-Aided Des.
,
38
(
8
), pp.
902
919
.10.1016/j.cad.2006.05.005
26.
Kamali-Nejad
,
M.
,
Vignat
,
F.
, and
Villeneuve
,
F.
,
2006
, “
Simulation of the Geometrical Defects of Manufacturing
,”
Int. J. Adv. Manuf. Technol.
,
45/7
(
7–8
), pp.
631
648
.
27.
Adragna
,
P.-A.
,
Samper
,
S.
, and
Favrelire
,
H.
,
2010
, “
How Form Errors Impact on 2D Precision Assembly With Clearance?
,”
Precision Assembly Technologies and Systems
,
Springer
,
Berlin Heidelberg
, pp.
50
59
.
You do not currently have access to this content.