Tolerance analysis is increasingly becoming an important tool for mechanical design, process planning, manufacturing, and inspection. It provides a quantitative analysis tool for evaluating the effects of manufacturing variations on performance and overall cost of the final assembly. It boosts concurrent engineering by bringing engineering design requirements and manufacturing capabilities together in a common model. It can be either worst-case or statistical. It may involve linear or nonlinear behavior. Monte Carlo simulation is the simplest and the most popular method for nonlinear statistical tolerance analysis. Monte Carlo simulation offers a powerful analytical method for predicting the effects of manufacturing variations on design performance and production cost. However, the main drawbacks of this method are that it is necessary to generate very large samples to assure calculation accuracy, and that the results of analysis contain errors of probability. In this paper, a quasi-Monte Carlo method based on good point (GP) set is proposed. The difference between the method proposed and Monte Carlo simulation lies in that the quasi-random numbers generated by Monte Carlo simulation method are replaced by ones generated by the method proposed in this paper. Compared with Monte Carlo simulation method, the proposed method provides analysis results with less calculation amount and higher precision.

References

References
1.
Polini
,
W.
,
2011
, “
Geometric Tolerance Analysis
,”
Geometric Tolerances
,
Springer
,
Berlin
, pp.
39
68
.
2.
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
(
1
), pp.
23
37
.
3.
Roy
,
U.
,
Liu
,
C.
, and
Woo
,
T.
,
1991
, “
Review of Dimensioning and Tolerancing: Representation and Processing
,”
Comput. Aided Des.
,
23
(
7
), pp.
466
483
.
4.
Zhang
,
H.
, and
Huq
,
M.
,
1992
, “
Tolerancing Techniques: The State-of-the-Art
,”
Int. J. Prod. Res.
,
30
(
9
), pp.
2111
2135
.
5.
Nigam
,
S. D.
, and
Turner
,
J. U.
,
1995
, “
Review of Statistical Approaches to Tolerance Analysis
,”
Comput. Aided Des.
,
27
(
1
), pp.
6
15
.
6.
Hong
,
Y.
, and
Chang
,
T.
,
2002
, “
A Comprehensive Review of Tolerancing Research
,”
Int. J. Prod. Res.
,
40
(
11
), pp.
2425
2459
.
7.
Marziale
,
M.
, and
Polini
,
W.
,
2009
, “
A Review of Two Models for Tolerance Analysis of an Assembly: Vector Loop and Matrix
,”
Int. J. Adv. Manuf. Technol.
,
43
(
11–12
), pp.
1106
1123
.
8.
Marziale
,
M.
, and
Polini
,
W.
,
2011
, “
A Review of Two Models for Tolerance Analysis of an Assembly: Jacobian and Torsor
,”
Int. J. Comput. Integr. Manuf.
,
24
(
1
), pp.
74
86
.
9.
Polini
,
W.
,
2012
, “
Taxonomy of Models for Tolerance Analysis in Assembling
,”
Int. J. Prod. Res.
,
50
(
7
), pp.
2014
2029
.
10.
Chen
,
H.
,
Jin
,
S.
,
Li
,
Z.
, and
Lai
,
X.
,
2014
, “
A Comprehensive Study of Three Dimensional Tolerance Analysis Methods
,”
Comput. Aided Des.
,
53
(
2
), pp.
1
13
.
11.
Gupta
,
S.
, and
Turner
,
J. U.
,
1993
, “
Variational Solid Modeling for Tolerance Analysis
,”
IEEE Comput. Graphics Appl.
,
13
(
3
), pp.
64
74
.
12.
Li
,
B.
, and
Roy
,
U.
,
2001
, “
Relative Positioning of Toleranced Polyhedral Parts in an Assembly
,”
IIE Trans.
,
33
(
4
), pp.
323
336
.
13.
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
, pp.
263
274
.
14.
Whitney
,
D. E.
,
Gilbert
,
O. L.
, and
Jastrzebski
,
M.
,
1994
, “
Representation of Geometric Variations Using Matrix Transforms for Statistical Tolerance Analysis in Assemblies
,”
Res. Eng. Des. Theory Appl. Concurrent Eng.
,
6
(
4
), pp.
191
210
.
15.
Davidson
,
J.
,
Mujezinovic
,
A.
, and
Shah
,
J.
,
2002
, “
A New Mathematical Model for Geometric Tolerances as Applied to Round Faces
,”
ASME J. Mech. Des.
,
124
(
4
), pp.
609
622
.
16.
Jaishankar
,
L. N.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
, eds.,
2013
, “
Tolerance Analysis of Parallel Assemblies Using Tolerance-Maps® and a Functional Map Derived From Induced Deformations
,”
ASME
Paper No. DETC2013-12394.
17.
Jiang
,
K.
,
Davidson
,
J. K.
,
Liu
,
J.
, and
Shah
,
J. J.
,
2014
, “
Using Tolerance Maps to Validate Machining Tolerances for Transfer of Cylindrical Datum in Manufacturing Process
,”
Int. J. Adv. Manuf. Technol.
,
73
(
1–4
), pp.
465
478
.
18.
Desrochers
,
A.
, and
Clément
,
A.
,
1994
, “
A Dimensioning and Tolerancing Assistance Model for CAD/CAM Systems
,”
Int. J. Adv. Manuf. Technol.
,
9
(
6
), pp.
352
361
.
19.
Clément
,
A.
,
Desrochers
,
A.
, and
Riviere
,
A.
,
1991
, “
Theory and Practice of 3-D Tolerancing for Assembly
,”
CIRP International Working Seminar on Computer-Aided Tolerancing
, Penn State University, State College, PA, May 16–17, pp.
25
55
.
20.
Clément
,
A.
, and
Riviere
,
A.
, eds.,
1993
, “
Tolerancing Versus Nominal Modeling in Next Generation CAD/CAM System
,”
3rd CIRP Seminar on Computer Aided Tolerancing-Tolérancement Géométrique
, Ecole Normale Supérieure de Cachan, Paris.
21.
Desrochers
,
A.
,
Ghie
,
W.
, and
Laperrière
,
L.
,
2003
, “
Application of a Unified Jacobian—Torsor Model for Tolerance Analysis
,”
ASME J. Comput. Inf. Sci. Eng.
,
3
(
1
), pp.
2
14
.
22.
Ghie
,
W.
,
Laperriere
,
L.
, and
Desrochers
,
A.
,
2007
, “
Re-Design of Mechanical Assemblies Using the Unified Jacobian–Torsor Model for Tolerance Analysis
,”
Models for Computer Aided Tolerancing in Design and Manufacturing
,
Springer
,
Berlin
, pp.
95
104
.
23.
Ghie
,
W.
,
Laperrière
,
L.
, and
Desrochers
,
A.
,
2010
, “
Statistical Tolerance Analysis Using the Unified Jacobian–Torsor Model
,”
Int. J. Prod. Res.
,
48
(
15
), pp.
4609
4630
.
24.
Teissandier
,
D.
,
Couétard
,
Y.
, and
Gérard
,
A.
,
1999
, “
A Computer Aided Tolerancing Model: Proportioned Assembly Clearance Volume
,”
Comput. Aided Des.
,
31
(
13
), pp
805
817
.
25.
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
,
Berlin
, pp.
85
94
.
26.
Dantan
,
J.-Y.
, and
Ballu
,
A.
,
2002
, “
Assembly Specification by Gauge With Internal Mobilities (GIM)—A Specification Semantics Deduced From Tolerance Synthesis
,”
J. Manuf. Syst.
,
21
(
3
), pp.
218
235
.
27.
Dantan
,
J.-Y.
,
Mathieu
,
L.
,
Ballu
,
A.
, and
Martin
,
P.
,
2005
, “
Tolerance Synthesis: Quantifier Notion and Virtual Boundary
,”
Comput. Aided Des.
,
37
(
2
), pp.
231
240
.
28.
Spotts
,
M. F.
,
1959
,
An Application of Statistics to the Dimensioning of Machine Parts
.
29.
Bender
,
A.
,
1968
, “
Statistical Tolerancing as it Relates to Quality Control and the Designer (6 Times 2.5 = 9)
,”
SAE
Technical Paper No. 680490.
30.
Chase
,
K. W.
, and
Greenwood
,
W. H.
,
1988
, “
Design Issues in Mechanical Tolerance Analysis
,”
Manuf. Rev.
,
1
(
1
), pp.
50
59
.
31.
Evans
,
D. H.
,
1975
, “
Statistical Tolerancing: The State of the Art—II: Methods for Estimating Moments
,”
J. Qual. Technol.
,
7
, pp.
1
12
.
32.
Evans
,
D. H.
,
1971
, “
An Application of Numerical Integration Techniques to Statistical Tolerancing—II: A Note on the Error
,”
Technometrics
,
13
(
2
), pp.
315
324
.
33.
Evans
,
D. H.
,
1972
, “
An Application of Numerical Integration Techniques to Statistical Tolerancing—III: General Distributions
,”
Technometrics
,
14
(
1
), pp.
23
35
.
34.
Parkinson
,
D.
,
1982
, “
The Application of Reliability Methods to Tolerancing
,”
ASME J. Mech. Des.
,
104
(
3
), pp.
612
618
.
35.
Lee
,
W.-J.
, and
Woo
,
T.
,
1990
, “
Tolerances: Their Analysis and Synthesis
,”
J. Eng. Ind.
,
112
(
2
), pp.
113
121
.
36.
Taguchi
,
G.
,
1978
, “
Performance Analysis Design
,”
Int. J. Prod. Res.
,
16
(
6
), pp.
521
530
.
37.
D'Errico
,
J. R.
, and
Zaino
,
N. A.
,
1988
, “
Statistical Tolerancing Using a Modification of Taguchi's Method
,”
Technometrics
,
30
(
4
), pp.
397
405
.
38.
DeDoncker
,
D.
, and
Spencer
,
A.
,
1987
, “
Assembly Tolerance Analysis With Simulation and Optimization Techniques
,”
SAE
Technical Paper No. 870263.
39.
Lin
,
C.-Y.
,
Huang
,
W.-H.
,
Jeng
,
M.-C.
, and
Doong
,
J.-L.
,
1997
, “
Study of an Assembly Tolerance Allocation Model Based on Monte Carlo Simulation
,”
J. Mater. Process. Technol.
,
70
(
1
), pp.
9
16
.
40.
Bruyère
,
J.
,
Dantan
,
J.-Y.
,
Bigot
,
R.
, and
Martin
,
P.
,
2007
, “
Statistical Tolerance Analysis of Bevel Gear by Tooth Contact Analysis and Monte Carlo Simulation
,”
Mech. Mach. Theory
,
42
(
10
), pp.
1326
1351
.
41.
Dantan
,
J.-Y.
, and
Qureshi
,
A.-J.
,
2009
, “
Worst-Case and Statistical Tolerance Analysis Based on Quantified Constraint Satisfaction Problems and Monte Carlo Simulation
,”
Comput. Aided Des.
,
41
(
1
), pp.
1
12
.
42.
Wu
,
F.
,
Dantan
,
J.-Y.
,
Etienne
,
A.
,
Siadat
,
A.
, and
Martin
,
P.
,
2009
, “
Improved Algorithm for Tolerance Allocation Based on Monte Carlo Simulation and Discrete Optimization
,”
Comput. Ind. Eng.
,
56
(
4
), pp.
1402
1413
.
43.
Qureshi
,
A. J.
,
Dantan
,
J.-Y.
,
Sabri
,
V.
,
Beaucaire
,
P.
, and
Gayton
,
N.
,
2012
, “
A Statistical Tolerance Analysis Approach for Over-Constrained Mechanism Based on Optimization and Monte Carlo Simulation
,”
Comput. Aided Des.
,
44
(
2
), pp.
132
142
.
44.
Chase
,
K. W.
,
Gao
,
J.
,
Magleby
,
S. P.
, and
Sorenson
,
C.
,
1996
, “
Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies
,”
IIE Trans.
,
28
(
10
), pp.
795
808
.
45.
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
.
46.
Chase
,
K. W.
,
1999
, “
Tolerance Analysis of 2-D and 3-D Assemblies With Small Kinematic Adjustments
,” ADCATS Report No. 94-4.
47.
Grossman
,
D. D.
,
1976
, “
Monte Carlo Simulation of Tolerancing in Discrete Parts Manufacturing and Assembly
,”
Report No. STAN-CS-76-555
.
48.
Hua
,
L. K.
, and
Wang
,
Y.
,
1981
,
Application of Number Theory to Numerical Analysis
,
Springer
,
Berlin
.
49.
Chung
,
K.-L.
,
1949
, “
An Estimate Concerning the Kolmogroff Limit Distribution
,”
Trans. Am. Math. Soc.
,
67
, pp.
36
50
.
50.
Halton
,
J. H.
,
1960
, “
On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals
,”
Numerische Math.
,
2
(
1
), pp.
84
90
.
51.
Armillotta
,
A.
,
2014
, “
A Static Analogy for 2D Tolerance Analysis
,”
Assem. Autom.
,
34
(
2
), pp.
182
91
.
You do not currently have access to this content.