Computer aided design of extrusion forming toolsgec.di.uminho.pt/Discip/MInf/cpd1314/MNobrega_PolymExtrus.pdf · Extrusion Dies – Flow Distribution Optimisation ij j j k ij ii ij

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

[email protected] / [email protected]

http://www.uminho.pt/default.aspx

Introduction - Profile Extrusion

Extruder Die Calibration/Cooling Haul-off Saw


Introduction - Profile Extrusion


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



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



Trial Parameters


n

i

ii

iobj

iobj

A

A

tL

tLk

V

VF

1

2

min

2

,

111



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



Pre-Processor

Geometry Mesh



Trial Parameters


n

i

ii

iobj

iobj

A

A

tL

tLk

V

VF

1

2

min

2

,

111



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:


Equations to Solve


jiij

j i

uu

x x

Constitutive equation (Gen. Newtonian):


Pre-Processor

Geometry Mesh



Trial Parameters


n

i

ii

iobj

iobj

A

A

tL

tLk

V

VF

1

2

min

2

,

111



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:


Equations to Solve


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



Trial Parameters


n

i

ii

iobj

iobj

A

A

tL

tLk

V

VF

1

2

min

2

,

111



Admissible L/t value

Flow Balance

Area Weighting


Objective Function



Pre-Processor

Geometry Mesh



Trial Parameters


n

i

ii

iobj

iobj

A

A

tL

tLk

V

VF

1

2

min

2

,

111



SIMPLEX Method (SM)

Experimental Method (EM) Modification of the controllable geometrical




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



DieINI – Initial trial

DieL – Length optimisation

DieT – Thickness optimisation

DieLS – Length optimisation + Flow separators

Optimizations performed



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


ES1ES2ES3ES4ES5ES6


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


ES1ES2ES3ES4ES5ES6


2 4 6 8 10

- Mesh Refinment

V/

Vo

bj

V/

Vo

bj



DieIni

DieL DieT

Velocity [m/s]

DieLS



DieIni

DieL DieT




Calibrators – Problem Statement

TsTT


Calibrators - Pre-processor


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



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



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



Pre- Processor

Geometry Mesh


Temperature

Input Data


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


Temperature

Input Data


n

i

iiobj FF1








Optimisation algorithm

Non-linear SIMPLEX method

Pre- Processor

Geometry Mesh


Temperature

Input Data


n

i

iiobj FF1











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:


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)



Geometry

Mesh



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?



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



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%



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;



• 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.




• Development of ISPH numerical modelling code (D.F.

Cordeiro, PhD/Cooperation Project USP);



• Development of ISPH numerical modeling code (D.F.




Documents

Computer aided design of extrusion forming toolsgec.di.uminho.pt/Discip/MInf/cpd1314/MNobrega_PolymExtrus.pdf · Extrusion Dies – Flow Distribution Optimisation ij j j k ij ii ij