1 computational methodology for the prediction of functional requirement variations across the...
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1
Computational Methodology for the Prediction of Functional Requirement Variations Across the Product Life-Cycle
Guillaume Mandil
Alain Desrochers
Alain Rivière
2
Problem
Parts of Mechanisms are generally specified for the assembly stage of their life cycle
Useful values of Functional Requirements are usually taken under other conditions
How to link theses values ?
3
Definitions and concepts
Nominal dimension : A Tolerance : [al;au] Mean dimension :
Dimension chain : j1 = B-A Calculation of functional
requirement values
aualA
1j
bublB
€
A = A +au + al
2
4
Sources of functional requirement variations
Uncertainties due to Tolerances stack-up : analysis of tolerance zones made thanks to existing techniques
Changing environment (variation of mechanical load or temperature) : Elastic deformation of parts.
5
Functional requirements variations across the life-cycle Elastic deformation
Variation of tolerance zone width is insignificant relatively to mean dimension variation.
Aalau AAalau
)1(1 Sj)1(SA )2(SA
)2(SB)1(SB
)2(1 Sj
6
Functional requirements variation across life-cycle Width of uncertainty for Functional
Requirement is not varying along life cycle Loads variations affect the mean value of
the Functional Requirement
Tolerance analysis/synthesis made once at the initial stage.
Variations due to the changing environment are evaluated on the mean values
7
Functional requirements variation across life-cycle
Life-cycle stage
Stage “Si”
Stage “Sf”
Value ofFunctional Requirement
- 0 +
Interference possible motion
j1
Mean value
€
j1
8
Three kind of calculations
Dependent of known variables Dimension driven
What will be the value of a given functional requirement after thermal dilatation of the parts?
Functional requirement drivenWhich dimension has to be chosen in order to obtain a given value of a functional requirement after thermal dilatation?
Geometry drivenWhich loads are acceptable in order to ensure the respect of a functional requirement at two stages Si and Sf of the life-cycle?
Example of FR management along the product life cycle
9
Check of initial Design (Dimension Driven)
Meet Final Functional Requirements
Product validated
no
Yes
Redesign to fit final requiments (Functional Requirement Driven)
Meet Initial Functional Requirements
Yes
no
Calculation of Acceptable Load variation (Geometry Driven)
10
Simple application case :Geometry
e1 e2 e3
j1 j3j2
b2 b3b1
Presentation of the case studied and corresponding dimensions chains
€
j1= b1− e1
j2 = e2 − b2
j3 = b2 + b3 − e2 − e3
⎧
⎨ ⎪
⎩ ⎪
11
Simple application case :Hypothesis Stepping from “Si” to “Sf” life-cycle stages Wheel shaft made of Aluminium Frame made of steel Dimension known at 20°C Deformation of parts due to thermal
dilatation only Design variables : dimensions of the frame
12
Uncertainties onFunctional Requirements
For all dimensions tolerance zones are 0.2mm width
Uncertainties on Functional Requirements are deduced thanks to dimension chains relationj1 has a 0.4mm width uncertainty zonej2 has a 0.4mm width uncertainty zonej3 has a 0.8mm width uncertainty zone
13
Calculation 1Dimension driven
Life-cycle stage
Stage “Si” @ 20°C
Stage “Sf”@ 50°C
Value of j1- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
Value of j2- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
Value of j3- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
0.05
0.450.25
0.079
0.4790.279
0.2
0.60.4
0.610
1.0100.810
0.05
0.850.45
-0.431
0.369-0.031
14
Calculation 2Functional Requirement driven
Life-cycle stage
Stage “Si” @ 50°C
Stage “Sf”@ 20°C
Value of j1- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
Value of j2- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
Value of j3- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
0.05
0.450.25
0.071
0.4710.271
0.1
0.50.3
-0.310
0.09-0.110
0.1
0.90.5
0.581
1.3810.981
15
Calculation 3Geometry driven
Life-cycle stage
Stage “Si” @ 20°C
Stage “Sf”
Allowable final temperature
Value of j1- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
Value of j2- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
Value of j3- 0 +
Inte
rfere
nce
Mot
ion
Poss
ible
0.1
0.50.3
0.05
0.450.25
0.1
0.50.3
0.2
0.60.4
0.1
0.90.5
0.05
0.850.45
91.0°C 25.9°C 22.8°C
16
ConclusionPerspectives High-level management of Functional
Requirement along life-cycle.
Need of an extension to 3D Results from Finite Elements calculation
used to quantify dimension variations Use of TTRS/MGRE to obtain relations
between individual dimension.
Further Work
Use of a parametric representation (vectorisation) for 3D mechanism. [Serré] (TTRS / MGRE)
Dimension chains viewed as loop of vectors
Deformations viewed as variations of representation vectors
17
Further Work
Use of a deformed mesh to deformed BRep transfer. [Louhichi]
Association of the deformed mechanism to an ideal and FR compatible “neighbour”.
Calculation of the distance between deformed and associated parameterisation vectors
deduction of minimal functional requirement [Serré]
18
19
Computational Methodology for the Prediction of Functional Requirement Variations Across the Product Life-Cycle
Guillaume Mandil
Alain Desrochers
Alain Rivière
Discussion
20
Modèle Géométrique CAO
Spécifications Fonctionnelles (GPS)
Paramètres de conception
Simulation Éléments Finis
Paramètres de calcul
Maillages résultats
SATT / EGRM
Modèle CAO
Déformé
Vectorisation
21
22
Discussion :Contribution du LISMMA?
Utilisation des relations de dépendance en 3D comme équation pour caractériser des conditions fonctionnelles.
Pour les mécanismes iso-statiques ?
23
Three kind of calculations
Choice of functional requirement under study and extraction of the corresponding dimension chain
Extraction of individual dimensions along dimension chain
Calculation of mechanical deformations
Integration of calculated deformations in the corresponding
mean dimension
Calculation of final functional requirement value with dimensions
updated values
Comparison of the results with designer intent or with specifications
at final stage.
Choice of functional requirement under study and extraction of the
corresponding dimension chain
Specification of initial functional requirement
Distribution of functional requirement : deduction of initial dimension values
Calculation of parts deformations
Deduction of final values for individual dimensions
Optional calculation of functional requirement at final stage
Comparison of the results with designer intent or with specifications
at final stage.
Choice of functional requirement under study and
extraction of the corresponding dimension chain
Specification of initial and final values for functional
requirement
Distribution of functional requirement: deduction of initial
dimension values
Calculation of thermo-mechanical load variations from
initial to final condition
Optional Calculation of final dimensions
Dimension driven Functional requirement driven Geometry driven
24
Calculation 1Dimension driven
Hypothesis
ti = 20°C
tf = 50°C
e1 = at 20°C
e2 = at 20°C
e3 = at 20°C
b1 = at 20°C
b2 = at 20°C
b3 = at 20°C
Results
at 50°C
at 50°C
at 50°C
at 50°C
at 50°C
at 50°C
j1 =[0.079 ; 0.479] mm at 50°C
j2 =[0.610 ; 1.010] mm at 50°C
j3 =[-0.431 ; 0.369] mm at 50°C
What will be the value of a given functional requirement after thermal dilatation of the parts?
mm1,060
mm1,01440
mm1,060
0,160.3 mm
0,11439.7 mm
0,160.8 mm
1 60.043e mm2 1441.028e mm3 60.043e mm1 60.322b mm2 1440.218b mm3 60.822b mm
25
Calculation 2Functional requirement driven
0,160.893 mm
Hypothesis
ti = 50°C
tf = 20°C
j1 =[0.05 ; 0.45] mm at 50°C
j2 =[0.2 ; 0.6] mm at 50°C
j3 =[0.05 ; 0.85] mm at 50°C
e1 = at 50°C
e2 = at 50°C
e3 = at 50°C
b1 = at 50°C
b2 = at 50°C
b3 = at 50°C
Results
at 20°C
at 20°C
at 20°C
at 20°C
at 20°C
at 20°C
j1 =[0.071 ; 0.471] mm at 20°C
j2 =[-0.310 ; 0.09] mm at 20°C
j3 =[0.581 ; 1.381] mm at 20°C
Which dimension has to be chosen in order to obtain a given value of a functional requirement after thermal dilatation?
0,11440.628 mm
0,160.293 mm
0,160.043 mm
0,160.043 mm
0,11441.028 mm
2 1440.109b mm1 60.27b mm
3 60.87b mm
3 60e mm
1 60e mm2 1440e mm
0,160.893 mm
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