RECENT DEVELOPMENTS IN PROFILE EXTRUSION: AUTOMATIC DESIGN OF EXTRUSION ... · PDF fileRECENT DEVELOPMENTS IN PROFILE EXTRUSION: AUTOMATIC DESIGN OF EXTRUSION DIES AND CALIBRATORS

RECENT DEVELOPMENTS IN PROFILE EXTRUSION:

AUTOMATIC DESIGN OF EXTRUSION DIES AND CALIBRATORS

J. M. Nóbrega and O. S. Carneiro

Institute for Polymers and Composites, Department of Polymer Engineering, University of Minho, Campus de Azurém,

4800-058 Guimarães, Portugal

e-mail: [email protected]; [email protected]

This work describes the current state of the numerical codes that have been developed, by the authors, to aid the design

of tools for thermoplastic profile extrusion. The main problems associated with the automatic design approach

employed both for the extrusion die, forming stage, and calibrator, cooling/calibration stage, will be described. Two

case studies are employed to illustrate the current code capabilities.

Introduction

Thermoplastic profiles have a large-scale application in the construction, medical, electric and

electronic industries, among others. The term profile is commonly used to designate products of

constant cross section that are obtained by the extrusion process.

A typical extrusion line for the production of thermoplastic profiles generally comprises an

extruder, a die, a calibration/cooling system, a haul-off unit and a saw, as shown in Figure 1.

Figure 1 - Typical profile extrusion line (Battenfeld Extrusionstechnik GmbH).

The major objective of any extrusion line is to produce the required profile at the highest rate and

quality [1]. These goals are usually conflicting, i.e., the increase in speed generally affects the

product quality negatively, and vice-versa. Therefore, the improvement of the extrusion line

performance demands a systematic approach and a careful study of the phenomena involved in the

Anais do 9o Congresso Brasileiro de Polímeros

process [2]. The die and the calibration system are the extrusion line components that play a central

role in the establishment of the product dimensions, morphology and properties and are also those

that establish the maximum allowable production rate [3].

The difficulties to be faced in the design of an extrusion die are closely related to the complexity of

the profile to be produced. In fact, while the design of an extrusion die for the production of a rod is

almost straight-forward, in the case of a complex window profile it can be an extremely complex

process. From the geometrical point of view the extrusion die flow channel must transform a

circular cross section, corresponding to the melt leaving the extruder, into a shape similar to that of

the profile. Due to the large number of phenomena and restrictions involved and to the complexity

of the polymer melt rheological behaviour, extrusion die design was, and still is, more an art than a

science [4]. The design process is usually based on trial-and-error procedures, which are strongly

dependent on the designer knowledge and experience [4], often requiring several trials. As a

consequence, the design process is usually very time, material and equipment consuming, affecting

product price and performance [5], since it does not guarantee the achievement of an optimum

solution.

The complex behaviour of the polymer melt during flow through the die, together with the expected

slight variations of the operating conditions/polymer rheological properties, make it very difficult to

produce the required melt extrudate cross-section with precise and stable dimensions. For this

reason, the calibration/cooling system is used to establish the final most relevant dimensions of the

profile while cooling it down until a temperature that guarantees its shape along the downstream

stages [3]. Moreover, as the profile progresses along the line, it is subjected to a variety of external

forces (such as friction, buoyancy and compression), being necessary to guarantee that it is strong

enough to withstand these forces without deforming [3]. From a thermal point of view, the

calibration/cooling system must also ensure fast rate uniform cooling of the extrudate in order to

induce the adequate morphology and a reduced level of thermal residual stresses [6]. In practical

terms, the temperature gradient along both the profile contour and its thickness must be minimized

[7] and its average temperature at the calibration/cooling system outlet must fall bellow the

solidification temperature, in order to avoid subsequent melting [8]. Furthermore, to ensure that the

profile will be properly handled, before the saw point, all cross section temperatures must fall

bellow the solidification temperature.

Currently, and do to the availability of software packages for the mathematical modelling of

polymer melt flows, the trial-and-error design approach, usually employed for extrusions dies and

calibrators, is being progressively transformed from experimental into a numerical based operation

being, however, still dependent on the designer’s experience. The advantages of these approaches


are an overall reduction in the cost of the project and a higher probability of finding the optimal

solution. Recently, there is a trend towards the automatic design concept. The idea is to turn the die

design fully automatic, i.e., without any user intervention, and to guarantee the achievement of the

optimal solution.

This work describes the current state of the numerical codes that have been developed, by the

authors, to aid the design of extrusion dies [9] and calibrators [10] for thermoplastic profile

extrusion, based on the automatic design concept.

Extrusion Dies

The use of an automatic design approach for extrusion dies requires the resolution of some

problems, which include: i) the need to parameterize the die flow channel in order to enable an easy

modification of its geometry during the optimisation process; ii) the minimisation of the

computation time and hardware requirements needed for recurrent 3-D flow modelling. The

multiple simulations involved in an optimisation process make this feature critical since that, in

practical terms, the process should be performed within an acceptable time; iii) the need to evaluate

the quality, or performance, of each trial solution (die geometry), as in each iteration the required

automatic decisions will be based on this information. Evaluation is a key step of the optimisation

process since it will drive the search towards the final, optimal, solution; iv) the availability of an

efficient optimisation technique able to automatically search the space of possible solutions until an

optimum is reached. The developed algorithm that solves all these issues, involves the steps

illustrated in the flowchart shown in Figure 2.

Figure 2 – Extrusion dies optimisation methodology flowchart.


To illustrate the developed methodology the optimisation of the profile shown in Figure 3

was performed. The flow channel geometry was optimised using the methodology described

considering two different approaches: one exclusively based on length optimisation (which

will define DieL) and other exclusively based on thickness optimisation (defining DieT).

To access the results obtained, three modular instrumented extrusion dies were designed and

manufactured: one using the same ratio length/thickness for all elemental sections (DieINI),

matching the initial trial of the optimisation algorithm, and two corresponding to the

optimised geometries (DieL and DieT) proposed by the die design routines.

Figure 3 – Cross section of the parallel zone of the die as a case study.

The improvements obtained by the optimisation routines are illustrated in Figure 4 that

shows pictures of the polymer melt emerging from the dies and the corresponding computed

velocity fields. For the initial trial die (DieINI), the excessive flow verified in the thicker ES

produces a clearly visible melt rippling. This effect vanished in the optimised dies.

V [m/s]

(a) DieINI (b) DieL (c) DieT

Figure 4 – Velocity contours and polymer melt leaving the die flow channel (photo taken during extrusion): (a) DieINI; (b) DieL; (c) DieT.


Calibrators

For the calibrator the aim of the optimisation methodology is to automatically find the set of

calibrators/annealing zones lengths that results in the most rapid and even cooling of he extruded

plastic profile. The integration of the different routines needed for this purpose is illustrated in

Figure 5.

Pre-Processor

Geometry Mesh

3D Temperature field calculation (FVM)

Temperature

Trial Parameters

Performance Evaluation

∑=

=

n

i

iiobj FF1

α

Modification of the controllable geometrical parameters until the optimum is reached

Pre-Processor

Geometry Mesh

3D Temperature field calculation (FVM)

Temperature

Trial Parameters

Performance Evaluation

∑=

=

n

i

iiobj FF1

α

Modification of the controllable geometrical parameters until the optimum is reached

Figure 5 - Calibration stage optimisation methodology flowchart.

During the optimisation process, a pre-processor is used to generate automatically the

computational grid corresponding to each geometry proposed by the optimisation algorithm. A

typical mesh is illustrated in Figure 6, for both the metallic (calibrator) and plastic (extruded profile)

domains.

(a) (b) Figure 6- Geometry (a) and typical mesh (b) used in the calculations (due to symmetry only ¼ of the geometry was modelled).

The optimisation algorithm implemented is based on the non-linear SIMPLEX method [11]. The

process starts with ‘n+1’ trial solutions randomly generated, being n the number of degrees of

freedom (or of optimisation variables). After the corresponding heat transfer simulations, the worst


solution is rejected and is replaced by a new trial solution proposed by the algorithm. The

calculation finishes when the standard deviation of the objective function of the set of ‘n+1’

solutions is lower than a prescribed value.

To illustrate the usefulness to the previously described optimisation methodology, it was used to

improve the cooling efficiency of a calibration system, through the optimisation of the cooling units

and annealing zones lengths distributions. For this purpose the cooling of the rectangular hollow

profile shown in Figure 7(a) was studied considering the following general conditions: kp=0.18

W/mK; kc=0.18 W/mK; ρp=1400 kg/m3; cp=1000 J/kgK; vp= 2 m/min; Tm= 180 ºC, Tf=18ºC;

hi=500 W/m2K.

(a) (b)

Figure 7 - Cooling of a rectangular hollow profile problem (dimensions in mm): cross section geometry (a) and calibration system layout (b).

As shown in Figure 7(b) the calibration system layout is defined by 5 variables: three LCx, variable

defining the length of Calibrator x, plus two Dij, variable corresponding to the annealing zone

length between Calibrators i and j.

The results obtained along the optimisation process, in terms of the objective function, are depicted

in Figure 8. These values show that the implemented optimisation methodology was able to

improve the performance of the calibration system. To be able to evaluate the gain in performance,

Table1 contains the results obtained for the ‘Optimum Solution’, proposed by the optimisation

methodology, and the ‘Equal Length’ geometry, where both the total calibration and annealing zone

lengths were uniformly distributed by the three calibrators and two annealing zones, respectively.

These results show that the ‘Optimum Solution’ has a better performance than the solution usually

adopted in extrusion practise.


86.00

86.02

86.04

86.06

86.08

86.10

86.12

86.14

86.16

86.18

86.20

86.22

1 3 5 7 9 11 13

Iteration

Fo

bj

Figure 8 – Objective function evolution along the optimisation process.

Table 1 – Results obtained for the ‘Equal Length’ and ‘Optimum’ geometries, in terms of average temperature and corresponding standard deviation.

Geometry T [ºC] Tσ [ºC]

Equal Length 107.7 21.1

Optimum Solution 108.8 17.8

Conclusion

In this work, the optimisation codes developed for the automatic design of extrusion dies and calibrators

were briefly described and its application was illustrated with two case studies.

As shown, both codes were able to improve the performance of the respective tools in a fully automatic

process, i.e., without any user intervention.

Acknowledgements

The authors gratefully acknowledge funding by FEDER via FCT, Fundação para a Ciência e

Tecnologia, under the POCI 2010 (project POCI/EME/58657/2004) and Plurianual programs

References

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