fuel tank design optimization in extrusion blow...
TRANSCRIPT
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Fuel Tank Design Optimization in Extrusion Blow Moulding
F. Thibault
RTS 2009
March, 11th 2009
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Competitiveness and quality of life of Canadians through research and innovation
• 21 institutes and facilities across Canada
• 4,150 full-time employees
• 1,200 guest workers
NRC Research FacilitiesIRAP Office
Overview:National Research Council
Overview:National Research Council
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OverviewExpertise: Simulation of Deformable Materials
Forming processes– Blow moulding, thermoforming, micro-forming
Modelling of deformable structures – Finite elements, geometric modelling, material
deformations
– Coupled with mechanical, chemical, electrical, biological behaviour
Integration and interaction with hardware platforms– Control, imaging and haptics
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Industrial Materials Forming
Development of in-house simulation software
with 20 industrial users worldwide
Industrial material forming and characterization lab Industrial material forming and characterization lab Industrial material forming and characterization lab Industrial material forming and characterization lab
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Automotive Blow Moulded
Parts
Seat back
WindShield Washerreservoir Fuel tank accessories
Air ducts
Air ducts
Cooling liquidreservoir
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Different Types of Automotive
Fuel Tanks
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Outlook
• Die Technology Overview for Plastic Fuel Tank (PFT) Manufacturing
• PFT Simulation Capabilities
• Design Optimization– Parison length optimization
– Die geometry optimization
– VWDS optimization
– Barrier layer optimization
• Illustration of some Case Studies
• Concluding Remarks
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Parison Programming(Vertical Wall Distribution System-VWDS)
Programmedparisonshowingheavier
wallthickness
for greatestexpansion
area
1
2
3
4
5
6
7
8
% Gap Opening (θθθθ)
Programming Points or Extrusion Time (sec)
1 2 3 4 5 6 7 8
20%
0%
40%
60%
80%
100%
0% open 100% openDie
Mandrel
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Illustration of VWDS for PFT
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Die Shaping
(Static Flexible Deformable Ring-
SFDR)
• Non-symmetric parts• Avoid mandrel retooling (flexibility)• Geometry constant along extrusion
Adjusting SFDR-Screws
Exit Die Cross Section
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Partial Wall Distribution
System (PWDS)
Actuator Movements:Deformable Bushing
Pull (+)
Push (-)
Pull (+)
Push (-)
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Illustration of
VWDS-SFDR-PWDS
Technology
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IMI Simulation Capabilities
for PFT
• Fluid mechanics inside the die• Solid mechanic outside the die• Phenomenological model for
• Diameter swell• Thickness swell• High Wessenberg number
Extrusion
Parison Inflation
• Multilayer viscoelastic nonlinear deformation using membrane finite elements• K-BKZ material model used for stress-strain deformation curve
6 layers of polymers
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Typical Simulation of
PFT Process
• Parison extrusion with VWDS/SFDR/PWDS
• Pinch plates at the top
• Stretching pins at the bottom
• Pinch plates at the bottom
• Pre-blow pressure
• Mold clamping
• High pressure to get final PFT shape
Process Steps
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Optimization Formulation
s)constraint(equality,10)(
)sconstraintinequality(NCON1,0)(
)variablesdesign(NDV1,
function)(objective)(
max,min,
NEQUkkh
iiG
tosubject
jXXX
ngmanipulatiby
XFMin
jjj
==
=≤
=≤≤
r
boundsupperX
boundslowerX
→
→
max
min
:SpaceDesign
r
r
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BlowDesign Optimization
Scheme
Initial Design Simulate Process
Evaluate
objective function &
constraints
Update
design variables
Stop
Converge?no
yes
Optimization Loop
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Constraints
: Design variables vector
: Search direction
: Step length
: iteration number
X
α
S
j
q
j SXX ⋅+=+ α1
The standard line search algorithm is used to update design variables as the following
Updating Design Variables
where α is the optimal step length found along the direction Sq so that
)(min qqj
SXF ⋅+αα
q
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BlowDesign Optimization
Flowchart
Parison Length Optimization
Die Shaping Optimization
VWDS Optimization
+PWDS Optimization
SFDR ?
Yes
VWDS ?
Yes
Parison Length
is OK?
No
Stop
No
Yes
No
Die shaping
Die Programming profile
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Parison Length Optimization
sconstrainton
tosubject
XXX
variabledesignnextthengmanipulatiby
TargetPLn)(simulatio PLF(X)Min
max,11min,1 <<
−=
Remark:
The simulated parison length takes into account the sag and/or swell
effects
Targeted
parison length
(PL)
)(),( exttTimeExtrusionQFlowrateX =r
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Die Shaping Optimization(SFDR)
Extruded Parison
270o205o 235o220o
270o
235o220o205o
Inflated Parison
(Gmin, Gmax)i
Inflation
mandrel
bushing
Average inflated parison thickness
for each die point ( )iT ,pointdie
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( )
sconstraintno
tosubject
NDiePjGapGapGap
variablesdesignnextthengmanipulatiby
NDieP
TT
XFMin
jjj
NDieP
i
podieipodie
,1,
)(
max,min,
1
intint,2
=<<
−
==∑
=σ
Die Shaping Optimization
where is the mean of the average inflated parison thicknessintpodieT
Remark:The algorithm manipulates the maximum die gap (mandrel shaping) to get a uniform material distribution on each die point around the inflated parison
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Programming ProfileOptimization (VWDS)
Mandrel Opening (%)
Extr
usio
n T
ime (
t)
1
2
3
4
5
6
Q (kg/m3)T (°C)
D
∆L1
∆L2
∆L3
∆L4
∆L5
∆L6
Parison length segment
T1
T2
T3
T4
T5
T6
Inflation
Average programming
point thickness
T1,min
T2,min
T3,min
T4,min
T5,min
T6,min
Minimum programming
point thickness
Manipulate the mandrel opening (%) to target1. A uniform inflated parison thickness (algorithm #1)2. A minimum inflated parison thickness (algorithm #2)taking into account the sag and/or swell during the parison extrusion
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Design Objective Function
1
)( 2
arg
−
−=∑
n
TTMin
etti
thicknesspartσ
By manipulating
Gap opening limits
Uniform part thickness
Constant parison length
Subject to constraints
Ti = Ttarget
Plength = PL
θmin < θ < θmax
Parison Programming (text, θ)
Stroke Positions (S1, S2)
Flowrate (Q)
Fix Angle & Prog. Points S1 S2
text, θ
Q
Programming ProfileOptimization (algorithm #1)
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Programming ProfileOptimization (algorithm #2)
Design Objective Function
Gap opening limits
Minimum inflated parison thickness (j=1,NProgP)
Constant parison length
∫Ω
Ω= dSTWeightPartMin ρ)(
Subject to constraints
Tj,min > Tmin
Plength = PL
θmin,i < θi < θmax,i
By manipulating
Parison Programming (text, θ)
Stroke Positions (S1, S2)
Flowrate (Q)
Fix Angle & Prog. Points S1 S2
text, θ
Q
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Case Study #1 (Jerry Can)
Problem Description:• Objective: Target a uniform part thickness = 3.0 mm
• Design Variables: Gap opening, die gap (Gmax), flowrate (Q),
PWDS stroke motions (S1, S2)
• Material : PP Pro-Fax SV152 (Montell)
• Parison length : 430 mm
• Fix extrusion time : 30 sec
• Number of prog. points: 10
• Initial gap opening : 60%
• Die Geometry : Gmin = 2 mm, Gmax = 10 mm (circular)
• Initial PWDS : S1 = 0.0 (0º), S2 = 0.0 (180º)
• Four Optimizations will be performed:
• VWDS, VWDS+PWDS, VWDS+SFDR, VWDS+SFDR+PWDS
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σ T
2.5 mm
9.4 mm
VWDS
0.63
3.02
VWDS+PWDS
2.6 mm
9.7 mm
0.51
3.03
VWDS+SFDR
2.4 mm
12.3 mm
0.45
3.06
VWDS+SFDR+PWDS
2.8 mm
12.0 mm
0.4
3.1
0.5 5.0 mm
Target value
Initial Design
6.8 mm
0.83
3.38
Optimization Results
3.0
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• PFT of Vitec (Detroit area)
• Material: HDPE/LDPE
• Parison length: 1405 mm
• Extrusion time: 120 sec
• Minimum PFT thickness: 3.4 mm(before shrinkage)
• Die technology (VWDS, no PWDS)
Case Study #2
(optimization of VWDS)
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Objective Function &
Parison Length History
1.02E+04
1.03E+04
1.04E+04
1.05E+04
1.06E+04
1.07E+04
1.08E+04
1.09E+04
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Optimization Iteration [-]
Pari
so
n W
eig
ht
[g]
1.30E+03
1.32E+03
1.34E+03
1.36E+03
1.38E+03
1.40E+03
1.42E+03
1.44E+03
1.46E+03
1.48E+03
1.50E+03
Pari
so
n L
en
gth
[m
m]
Parison Weight
Parison Length
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VWDS Optimization
Results
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120
Extrusion Time [s]
Die
Gap
Op
en
ing
[%
]
Initial Design
Iter. #1
Iter. #5
Iter. #10
Iter #15
Final Design
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Parison & Inflated Parison
Thickness History
Initial
Design Iter #2 Iter #5 Iter #10 Iter #15 Iter #20 Iter #30
Tmin
3.52
21.99 mm
3.4
15.0 mm
3.4
15.0 mm
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Targeting Non-Uniform Inflated
Parison Thickness on Specific Area
(ZONING)
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Inflated Parison Thickness = 3.4 mmFitting Component Area = 6.0 mm
Targets:
# Target ID, Prog1 -> Prog2, Die1 -> Die2, Thickness
Target, 1, 1, 5, 1, 17, 3.4
Target, 2, 6, 7, 15, 16, 6.0
Target, 3, 8, 12, 1, 17, 3.4
Thickness Target Definition
for the Case Study
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Inflated Parison Thickness
Optimization Results
Thick
(mm)
Initial Design Iter #3 Iter #6 Iter #9 Iter #11
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VWDS or
Programming Profile
Optimization Results
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Extrusion Time (s)
Die
gap
Op
enin
g (
%)
Initial Design
Iter #3
Iter #6
Iter #11
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Permeability Analysis Capability
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Mathematical Model
Henry’s Solubility Law
pSC ⋅=
Solubility Coefficient
2
2
x
CD
t
C
∂
∂=
∂
∂
Fick’s Law of diffusion
000 =<<= Chxt
sCCxt ==> 00
00 ==> Chxt
Initial Condition
Boundary Condition
Diffusion Coefficient
Fick’s second Law of diffusion
2
2
x
pSD
t
pS
∂
∂⋅=
∂
∂
Initial Condition
000 =<<= phxt
Boundary Condition
sppxt ==> 00
00 ==> phxt
Permeability Coefficient
Adhesive LLDPE
Virgin HDPE
EvOH barrier
Regrind HDPE
Virgin HDPE
h0
C=Cs
C=0 C=0
inside
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Parting lineon the part
Contact on the inflated parison Pinch-Off Zone
• If a parting line node is within a distance tolerance to inflated parison node located in the flash, then this node is located in the pinch-off zone
top
bottom
Automatic Pinch-Off
Zone Detection
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Barrier Layer Optimization
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Barrier Layer Optimization
Case Study
• Material: HDPE virgin & recycled, EvOHLLDPE adhesive
• Parison length: 1800 mm
• Extrusion time: 130 sec
• Minimum PFT thickness: 3.4 mm(before shrinkage)
• Hydrocarbon emission constraint: 10 mg/day
• Die Shaping, VWDS, PDWS
(Courtesy of Kautex)
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Diffusion Parameters of
PFT Layers
20
50
2.5
0.3
2.5
24.7
Layer
Percentage
[%]
6.8e-2
6.8e-2
1.49e-1
5.0e-4
1.49e-1
6.8e-2
Solubility
Coefficient
[g/g]
5.5e-12Regind HDPE
5.0e-13EvOH Barrier
5.5e-12Virgin HDPE
5.5e-12LLDPE adhesive
8.2e-12LLDPE adhesive
5.5e-12Virgin HDPE
Diffusion
Coefficient
[m2/s]
PFT Layers of
Initial Design
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Permeation Results for
the Initial Design
Thickness[mm]
Thickness profile after deflashing
21.7 kg
Daily Emission: = 90.8 mg/day i
NElem
i
i SFlux ⋅∑=1
PermeationFlux
[mg/day/m2]
0.3% EvOH
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EBM Process Optimization withDaily Permeation Constraint
[10 mg/day]
Thic
kness [m
m]
19.9 kg
Iteration #1
18.7 kg
Iteration #3
17.6 kg
Iteration #6
2.98
13.16
Initial Design
21.7 kg
Hydro
carb
on E
mis
sio
n
[mg/d
ay/ m
2]
3.30% EvOH10.2 mg/day
3.6% EvOH9.98 mg/day
3.81% EvOH9.98 mg/day
0.3% EvOH90.8 mg/day
3.21
12.0
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Adaptative Remeshing during Optimization
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Case Study of TI-Automotive
• Material: HDPE
• Parison length: 2180 mm
• Extrusion time: 110 sec
• Initial die opening: 50%
• Minimum PFT thickness: 3.4 mm(before shrinkage)
• VWDS (No Die Shaping), PWDS
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Thickness Profile HistoryThickness Profile History
Initial design #iter 1 #iter 3 #iter 5
1952 nodes
3840 elements5322 nodes
10580 elements
14445 nodes
28826 elements
34286 nodes
68508 elements
5.1
Thick
(mm)
20.5
3.4
Thick
(mm)
25
7.6 min 17.8 min 53.4 min 130.1 min
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Refinement Details at
last Iteration
Refinement Details at
last Iteration
Front View
Bottom Top
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Refinement Details at
last Iteration
Refinement Details at
last Iteration
Middle
Front View
Middle
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Concluding RemarksConcluding Remarks
• Efficient simulation technology to model and mimic PFT manufacturing
• Adequate optimization tools to get the optimal design
• Recently working on TSBM fuel tank optimization (new technology to reduce fuel emission)