computer aided design of extrusion forming...
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Computer aided design of extrusion
forming tools
J. M. Nóbrega and O. S. Carneiro
I3N/IPC –Institute for Polymers and Composites
Department of Polymer Engineering
University of Minho
Portugal
mnobrega@dep.uminho.pt / olgasc@dep.uminho.pt
Introduction - Profile Extrusion
Extruder Die Calibration/Cooling Haul-off Saw
Under development
Introduction - Design Approaches
Current
Traditional
% Time
?
$
Outline
•Extrusion Dies
• Problem Statement
• Flow Distribution Optimisation
• Flow Balance Strategies
• Optimisation
• Length vs Thickness Optimisation
• Conclusion
• Calibrators
• Problem Statement
• System Behaviour
• Optimisation Methodology
• Case Study
• Conclusion
• Conclusion
• Ongoing Work
Extruder Die Calibration/Cooling Haul-off Saw
Extrusion Dies – Problem Statement
Numerical
Velocity contours
Extrusion run
Unbalanced Balanced
Pre-Processor
Geometry Mesh
3D non-isothermal flow field calculation (FVM)
Velocity Pressure Temperature
Trial Parameters
Performance Evaluation
n
i
ii
iobj
iobj
A
A
tL
tLk
V
VF
1
2
min
2
,
111
Modification of the controllable geometrical
parameters until the optimum is reached
Extrusion Dies – Flow Distribution Optimisation
Trial Parameters
Pre-Processor
Geometry Mesh
3D non-isothermal flow field calculation (FVM)
Velocity Pressure Temperature
Trial Parameters
Performance Evaluation
n
i
ii
iobj
iobj
A
A
tL
tLk
V
VF
1
2
min
2
,
111
Modification of the controllable geometrical
parameters until the optimum is reached
Progressive mesh refinements
Cells along
Thickness
Number
of Cells
Time
[h:m:s]
2 15 496 0:00:36
4 92 248 0:12:15
6 272 220 1:12:17
8 593 928 4:28:36
10 688 024 6:43:42
PIV / 2.4 GHz
Pre-Processor
Frame 001 03 Mar 2003 grid
Extrusion Dies – Flow Distribution Optimisation
Pre-Processor
Geometry Mesh
3D non-isothermal flow field calculation (FVM)
Velocity Pressure Temperature
Trial Parameters
Performance Evaluation
n
i
ii
iobj
iobj
A
A
tL
tLk
V
VF
1
2
min
2
,
111
Modification of the controllable geometrical
parameters until the optimum is reached
0
j
j
x
u
j
ij
ij
iji
xx
p
x
uu
t
u
j
iij
iii
i
x
u
x
Tk
xx
Tcu
t
cT
Conservation of mass:
Conservation of linear momentum:
Conservation of energy:
3D non-isothermal flow field calculation (FVM)
Equations to Solve
Extrusion Dies – Flow Distribution Optimisation
jiij
j i
uu
x x
Constitutive equation (Gen. Newtonian):
Pre-Processor
Geometry Mesh
3D non-isothermal flow field calculation (FVM)
Velocity Pressure Temperature
Trial Parameters
Performance Evaluation
n
i
ii
iobj
iobj
A
A
tL
tLk
V
VF
1
2
min
2
,
111
Modification of the controllable geometrical
parameters until the optimum is reached
0
j
j
x
u
j
ij
ij
iji
xx
p
x
uu
t
u
j
iij
iii
i
x
u
x
Tk
xx
Tcu
t
cT
Conservation of mass:
Conservation of linear momentum:
Conservation of energy:
3D non-isothermal flow field calculation (FVM)
Equations to Solve
Extrusion Dies – Flow Distribution Optimisation
k ijij j ji iij p jk ik
k j i k k
u u uu u
t x x x x x
Constitutive equation (viscoelastic):
Pre-Processor
Geometry Mesh
3D non-isothermal flow field calculation (FVM)
Velocity Pressure Temperature
Trial Parameters
Performance Evaluation
n
i
ii
iobj
iobj
A
A
tL
tLk
V
VF
1
2
min
2
,
111
Modification of the controllable geometrical
parameters until the optimum is reached
Admissible L/t value
Flow Balance
Area Weighting
Performance Evaluation
Objective Function
Extrusion Dies – Flow Distribution Optimisation
Pre-Processor
Geometry Mesh
3D non-isothermal flow field calculation (FVM)
Velocity Pressure Temperature
Trial Parameters
Performance Evaluation
n
i
ii
iobj
iobj
A
A
tL
tLk
V
VF
1
2
min
2
,
111
Modification of the controllable geometrical
parameters until the optimum is reached
SIMPLEX Method (SM)
Experimental Method (EM) Modification of the controllable geometrical
parameters until the optimum is reached
Extrusion Dies – Flow Distribution Optimisation
Thickness
t2
t1 V2
V1
V3
V1
=
V3
V2
V3
V1
≠
V3
V2
V3
t2
t1
Die Flow Channel Haul-off
Speed
Final Profile Optimised
Variable Required
Profile
Extrusion Dies – Flow Balance Strategies
Length
t2
t1 V2
V1
Initial flow channel dimensions
ES 1 2 3 4 5 6
t i [mm] 2.0 2.5 2.5 3.0 2.0 4.0 L i [mm] 30.0 37.5 37.5 45.0 30.0 60.0
L i /t i 15.0 15.0 15.0 15.0 15.0 15.0
Extrusion Dies – Optimisation
Constitutive equation Mesh
Flow rate 20 kg/h
Melt inlet temperature 230 ºC
Outer die walls temperature 230 ºC
Inner (mandrel) die walls Adiabatic
Operating and thermal boundary conditions
THTHFT ,
2
12
0
1n
F
TT
TH11
exp
Extrusion Dies – Optimisation
DieINI – Initial trial
DieL – Length optimisation
DieT – Thickness optimisation
DieLS – Length optimisation + Flow separators
Optimizations performed
Extrusion Dies – Optimisation
DieL DieT
V/
Vo
bj
0.0
0.5
1.0
1.5
2.0
2.5
0:00
0:01
0:01
0:02
0:02
0:03
0:03
0:04
0:04
0:07
0:19
0:31
0:43
1:18
4:48
17:4
4
24:0
0
43:1
2
Calculation Time [hh:mm]
ES1ES2ES3ES4ES5ES6
Cells Along Thickness
2 4 6 8 10
- Mesh Refinment
0.0
0.5
1.0
1.5
2.0
2.5
0:00
0:01
0:01
0:03
0:05
0:07
0:12
0:25
0:38
0:52
1:20
2:02
3:11
4:29
8:25
9:45
11:0
8
16:3
5
22:4
0
34:4
1
59:0
0
66:2
8
88:4
6
111:
05
Calculation Time [hh:mm]
ES1ES2ES3ES4ES5ES6
Cells Along Thickness
2 4 6 8 10
- Mesh Refinment
DieLS
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
0:00
0:01
0:01
0:02
0:03
0:03
0:06
0:17
0:40
1:03
1:37
2:40
5:45
11:5
7
21:0
8
53:0
6
59:1
4
83:5
8
Calculation Time [hh:mm]
ES1ES2ES3ES4ES5ES6
Cells Along Thickness
2 4 6 8 10
- Mesh Refinment
V/
Vo
bj
V/
Vo
bj
Extrusion Dies – Optimisation
DieIni
DieL DieT
Velocity [m/s]
DieLS
Extrusion Dies – Optimisation
Extruder Die Calibration/Cooling Haul-off Saw
Calibrators – Problem Statement
TsTT
Calibrators – Numerical boundary conditions
Temperature
Imposed
Free convection
and radiation or
adiabatic
Contact
resistance
Adiabatic
Extrusion
Direction
Temperature
Imposed
Calibrators - Equations to solve
0
ppp
p
p
p
p
p
p wTz
cz
Tk
zy
Tk
yx
Tk
x
Polymer
Calibrator
0
z
Tck
zy
Tk
yx
Tck
xc
ccc
interface
interfaceinterface
cpi
p
pc
c TThn
Tk
n
Tk
Contact Resistance
Polymer-calibrator interface
3D Temperature field calculation (FVM)
Calibrators - Typical result
Calibrators - System Behaviour
Influence of boundary conditions, process and geometrical
parameters on the system performance (in terms of average
temperature and temperature uniformity)
Conclusion:
TT
In general Exceptions
X
70
92
114
136
158
180
0 100 200 300 400 500 600 700 800
Length, mm
T, ºC
0
5
10
15
20
25
30
T ,ºC
Die Calibrator 1
Calibrators - System Behaviour
70
92
114
136
158
180
0 100 200 300 400 500 600 700 800
Length, mm
T, ºC
0
5
10
15
20
25
30
T ,ºC
Die Calibrator 1 Calibrator 2 Calibrator 3
Calibrators - System Behaviour
70
92
114
136
158
180
0 100 200 300 400 500 600 700 800
Length, mm
T, ºC
0
5
10
15
20
25
30
T ,ºC
70
92
114
136
158
180
0 100 200 300 400 500 600 700 800
Length, mm
T, ºC
0
5
10
15
20
25
30
T ,ºC
Die Calibrator 1 Calibrator 2 Calibrator 3
Die Calibrator 1
Calibrators - System Behaviour
Pre- Processor
Geometry Mesh
3D Temperature field calculation (FVM)
Temperature
Input Data
Performance Evaluation
n
i
iiobj FF1
Optimisation: automatic generation of
solutions (modification of the controllable
geometrical parameters)
until the optimum is reached
Calibrators - Optimisation Methodology
T
n
i
ii
A
AT
T
f
1
T
n
i
ii
TA
ATTf
1
2
Cooling efficiency Temperature uniformity
TSobjTTKF
1000
0
KTT
KTT
S
S
where:
Pre- Processor
Geometry Mesh
3D Temperature field calculation (FVM)
Temperature
Input Data
Performance Evaluation
n
i
iiobj FF1
Optimisation: automatic generation of
solutions (modification of the controllable
geometrical parameters)
until the optimum is reached
Performance Evaluation
Calibrators - Optimisation Methodology
Optimisation algorithm
Non-linear SIMPLEX method
Pre- Processor
Geometry Mesh
3D Temperature field calculation (FVM)
Temperature
Input Data
Performance Evaluation
n
i
iiobj FF1
Optimisation: automatic generation of
solutions (modification of the controllable
geometrical parameters)
until the optimum is reached
Optimisation: automatic generation of
solutions (modification of the controllable
geometrical parameters)
until the optimum is reached
Calibrators - Optimisation Methodology
Calibrators - Case Study
- Number of calibration/cooling units <= 3
- Total calibration length (LCi) <= 600 mm
- Total system length (LCi + Dij + 10) <= 850 mm
- Cooling Fluid Temperature TCi [10ºC,26ºC]
Restrictions:
Die Calibrator 1 Calibrator 2 Calibrator 3
10 LC1 D12 LC2 D23 LC3
120
60
130
2
Ø8
12
70 TC1 TC2 TC3
Materials Properties
Kp = 0.18 W/mK
Kc = 14 W/mK
p = 1400 kg/m3
cp = 1000 J/kgK
General conditions for the simulations
Processing conditions
vp = 2 m/min
Tm = 180 ºC
Tf = 18 ºC
Ts= 80 ºC
Boundary conditions
Annealing zones: free convection and radiation
Polymer-calibrator interface: contact resistance
(hi = 425 W/m2K)
Calibrators - Case Study
7.00
9.00
11.00
13.00
15.00
17.00
19.00
75.00 76.00 77.00 78.00 79.00 80.00 81.00 82.00 83.00 84.00 85.00
[ºC]
[ºC
]
T
T
Ts
Local minimum?
Calibrators - Case Study
Die Calibrator 1
Calibrator 2
10 550 240 50
7.00
9.00
11.00
13.00
15.00
17.00
19.00
75.00 76.00 77.00 78.00 79.00 80.00 81.00 82.00 83.00 84.00 85.00
[ºC]
[ºC
]
T
T
Ts
TC1 = 10ºC TC2 = 26ºC
Calibrators - Case Study
Die Calibrator 1
Calibrator 2
10 550 240 50
7.00
9.00
11.00
13.00
15.00
17.00
19.00
75.00 76.00 77.00 78.00 79.00 80.00 81.00 82.00 83.00 84.00 85.00
[ºC]
[ºC
]
T
T
Ts
TC1 = 10ºC TC2 = 26ºC
Geometry T [ºC] T [ºC]
One Calibrator
(TC=18ºC) 84.9 16.6
Optimum Solution 78.5 7.9
- 52.4%
Calibrators - Case Study
Recent / Ongoing work
• Implementation of the wall Slip and free-surface
boundary conditions (L.L. Ferrás, Post-doctoral project);
• Development of unstructured numerical modelling
code (N.D. Gonçalves, PhD project);
• Implementation of viscoelastic constitutive equations
in an unstructured modelling code (S. Reddy, MSc
Eurheo project);
• Prediction of thermal induced stresses in calibration
in OpenFOAM (S. Reddy, Research Project);
• Development of high order interpolation schemes (R.
Costa, FCT Research Project, DMAT);
• Portability and Performance in Heterogeneous Many-
core Systems (R. Ribeiro, PhD Project, DI) -
OpenFOAM;
Recent / Ongoing work
• Development of multiscale modelling approaches (S.T.
Mould, PhD Project);
• Development of ISPH numerical modelling code (D.F.
Cordeiro, PhD/Cooperation Project, USP);
• Development of FSI methodologies for the design of
extrusion dies in OpenFOAM (M.R. Moosavi, Post-
doctoral grant);
• Modelling the cooling stage in profile extrusion using
OpenFOAM (R. Ananth, PhD project, MIT+Soprefa);
• Design of a new generation of car washing machines
(M. Sabet, PhD project, MIT+Petrotec);
• Characterisation of the heat transfer coefficient at the
polymer-metal interface in profile cooling (F. Araújo,
FCT Research Project);
• Development of ISPH numerical modeling code (D.F.
Cordeiro, PhD/Cooperation Project, USP);
Recent / Ongoing work
• Development of ISPH numerical modelling code (D.F.
Cordeiro, PhD/Cooperation Project USP);
Recent / Ongoing work
• Development of ISPH numerical modeling code (D.F.
Cordeiro, PhD/Cooperation Project, USP);
Recent / Ongoing work
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