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Institute for Structural Analysis
Umformsimulation mit LS-DYNA und ETA/DYNAFORMInstitute for Structural Analysis
Beurteilung und Beeinflussung der Beurteilung und Beeinflussung der Zuverlässigkeit von Tiefziehprozessenin der frühen Entwurfsphasein der frühen Entwurfsphase
Stephan PannierWolfgang GrafMichael KaliskeMichael Kaliske
Kathrin GrossenbacherMarkus GanserMarkus GanserArnulf Lipp
Martin LiebscherMartin LiebscherHeiner Müllerschön
Introduction
Motivation
charge A too many rejects in reliablecharge Bcharge A y j
production process production processcharge B
• numerical verification afterwards
• source of trouble - delivery tolerances
Institute for Structural Analysis 2
Introduction
Definition
reliability analysis
reliability analysis
reliability analysis
design process manufacturing
t
• reliability analysis in an early design stages
modifications of design parameters easier
less expensive modifications
Institute for Structural Analysis 3
• identification of alternative design spaces
Introduction
Example
• e.g. input: 2 draw bead forces, 1 binder forceresult: thinning of blank
• simple deep drawing example – 3 input quantities, 1 results quantity
result: thinning of blank
Institute for Structural Analysis 4
Introduction
Example
• e.g. input: 2 draw bead forces, 1 binder forceresult: thinning of blank
• simple deep drawing example – 3 input quantities, 1 results quantity
result: thinning of blank
Institute for Structural Analysis 5
Introduction
Solution statement
reliability assessment
no rejects rejectsno rejects
identification of permissible design and uncertainty ranges
j
unmodifieddesign
and uncertainty ranges
design specification of alternative design spaces
• preconditionspreconditions
rare, vague information about uncertainty ranges
arbitrary structural behavior, no one-to-one functions
Institute for Structural Analysis 6
applicability of alternative design ranges in industrial environment
Institute for Structural AnalysisInstitute for Structural Analysis
Reliability analysis
Reliability analysis
Uncertainty modeling
uncertainty
aleatoric epistemic
randomness perception/evaluation
objective data subjective assessment
• abundant (objective) data• discrete random events• gambling
• limited (subjective) data• imprecise measurements• linguistic quantification
Institute for Structural Analysis 8
• experience/expert knowledge
Reliability analysis
Uncertainty modeling
objective information
f(x) µ(x)f(x) µ=01
f(x)~
µ=1
x
randomness
x
fuzziness
xfuzzy
randomnessrandomness
subjective information
Institute for Structural Analysis 9
j
Reliability analysis
Fuzzy set
1
• general definition
convexity• convexity
• -level discretization • -level optimization
Institute for Structural Analysis 10
Reliability analysis
Fuzzy structural analysis
fuzzy inputquantity
fuzzy inputquantity
mappingmapping
"-level optimization"-level optimization" level optimization" level optimization
fuzzy resultquantity
Institute for Structural Analysis 11
Institute for Structural AnalysisInstitute for Structural Analysis
Specification of lt ti d i alternative design spaces
Specification of alternative design spaces
General scheme
constraints identificationof partition
alternative design spaces
generation of point set
pac
ein
put
s
z=f(x) x=f-1(x)
cesu
lt s
pac
Institute for Structural Analysis 13
res
Specification of alternative design spaces
Dimensionality problem
• 3D • 2D
• more than sensitive 3 input quantities
Institute for Structural Analysis 14
Specification of alternative design spaces
General scheme
constraints identificationof partition
alternative design spaces
generation of point set
pac
ein
put
s
z=f(x) x=f-1(x)
cesu
lt s
pac
Institute for Structural Analysis 15
res
Specification of alternative design spaces
Partition
permissible
constraint
non-permissible
le len- le n- le
per
mis
sibl
per
mis
sibl
non
per
mis
sibl
non
per
mis
sibl
Institute for Structural Analysis 16
p pp p
Specification of alternative design spaces
Cluster analysis – objective
- pairwise disjoint
preconditions on clusters
- nonempty
- reproduce point set
Institute for Structural Analysis 17
Specification of alternative design spaces
Cluster analysis – objective
homogeneity • homogeneitypoints in a same cluster should be as similar as possible
heterogeneity
• heterogeneityg ypoints of different clusters should be as dissimilar as possible
determination of an appropriate cluster configuration ; optimization task
Institute for Structural Analysis 18
predefined number of clusters - challenge
Specification of alternative design spaces
General scheme
constraints identificationof partition
alternative design spaces
generation of point set
pac
ein
put
s
z=f(x) x=f-1(x)
cesu
lt s
pac
Institute for Structural Analysis 19
res
Specification of alternative design spaces
Alternative design space(s)
h ll h b id l convex hull vs.hypercuboid
hypercuboids per cluster vs.maximal possible hypercuboids
interacted design variables hypercuboid
bases on available
ambitiousand expensive
available point set
interaction-free detection design variables of number of
non-connected input spaces
Institute for Structural Analysis 20
Institute for Structural AnalysisInstitute for Structural Analysis
Examples
Rosenbrock function
Rosenbrock function z=f(x,y)
xy
permissibility condition
x x
yy y
Institute for Structural Analysis 22
z z
Metal forming example I
Model
crack sensitive area
computational model FLD
results
Institute for Structural Analysis 23
Metal forming example I
Reliability assessment – Fuzzy Analysis
Input parameters Delivery tolerances Fuzzy quantitiesp p
yield stress
tensile
Rp02
Rm
y
180 … 230
340 … 420
y q
<180, 205, 230>
<340, 380, 420>strength
hardeningexponent
n 0.20 … 0.30 <0.20, 0.22, 0.30>
anisotropy R90 1.80 … 4.00 <1.80, 2.40, 4.00>
1.0
Institute for Structural Analysis 24
Metal forming example I
Reliability assessment – fuzzy analysis
• evaluated results
cracking
(Grossenbacher 2008)
cracking
thinning
f lt tit• fuzzy result quantity
number of -levels: 5
rain
t
determined intervalbounds of -level: co
nstr
simulations runs: 150
Institute for Structural Analysis 25
Metal forming example I
Constraints
cross-plot: n – R90cross-plot: Rp02 – Rm
Institute for Structural Analysis 26
permissible non-permissible
Metal forming example I
Partitioning – cluster analysis
cross-plot: n – R90cross-plot: Rp02 – Rm
Institute for Structural Analysis 27
not assigned non-permissibleCluster Cluster
Metal forming example I
Partitioning – cluster analysis
3 cl ste 4 cl ste 5 cl ste3 cluster 4 cluster 5 cluster
Institute for Structural Analysis 28
Metal forming example I
Alternative design space
cross-plot: n – R90cross-plot: Rp02 – Rm
Institute for Structural Analysis 29
permissible non-permissiblealternative design space
Metal forming example II
Model
Institute for Structural Analysis 30
Metal forming example II
Input quantities
1.0
Institute for Structural Analysis 31
Metal forming example II
Reliability assessment – fuzzy analysis
• evaluated results
− geometry
− cracking (FLC)
− manufacturing
aint
• fuzzy result quantity
b f l l 2
cons
tra number of -levels: 2
determined intervalbounds of -level: bounds of level:
simulations runs: 232
Institute for Structural Analysis 32
Metal forming example II
Demonstrator
Determination of Determination of alternative design spaces
Institute for Structural Analysis 33
Conclusions
Conclusions
• assessment of reliability in an early design stages reasonable
• determination of alternative design spacesinstead of an optimal design
• detection of non-connected point sets with cluster analysis
li bilit i d li d
• assignment of hypercuboids to clusters − only permissible points
• applicability is underlined by means of an industry-relevant example
Institute for Structural Analysis 34
Institute for Structural Analysis
Umformsimulation mit LS-DYNA und ETA/DYNAFORMInstitute for Structural Analysis
Beurteilung und Beeinflussung der Beurteilung und Beeinflussung der Zuverlässigkeit von Tiefziehprozessenin der frühen Entwurfsphasein der frühen Entwurfsphase
Stephan PannierWolfgang GrafMichael KaliskeMichael Kaliske
Kathrin GrossenbacherMarkus GanserMarkus GanserArnulf Lipp
Martin LiebscherMartin LiebscherHeiner Müllerschön
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