Wire and Cable Technology International — July/August 2014
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Nonlinear Models Help Tune Temperature Profile In Extruder Barrels
Abhay Bulsari

Temperature profile in the extruder barrel affects the throughput, melt temperature, exit pressure and several properties of the extruded insulation or secondary coatings. Specific throughput tends to vary with screw speed, which is undesirable during ramp ups, leading to waste of raw materials.
There are several degrees of freedom in the extruder temperatures, all of which affect the consequences of extrusion in complicated ways.

The cable industry today tends to carry out a few trial and error experiments to decide on the temperature profile crosshead temperature and also screw temperature, if the screw is equipped with a cooling water conduit. If a small number of experiments can be carried out, nonlinear models can be developed relating the temperatures and screw speed with throughput, melt temperature, exit pressure, etc. It is obvious that the relations are not very linear and therefore, linear statistical techniques have limitations. However, nonlinear models can be developed from experimental data to describe these complicated relations. This article describes the experience of this kind of a project recently carried out at Nexans in Halden, Norway.

For process development work, we are often interested in achieving certain product properties. In case of extrusion, all the zone temperatures are process variables that affect the extrusion and the product properties. In an extruder from Maillefer, there were six zones. The temperatures of each of the zones affected the final product as well as the extruder output variables including throughput, melt temperature, pressure, motor load and specific throughput as well as throughput linearity. Figure 1 shows the model structure for optimization of the temperature profile in an extruder.

Nonlinear Modeling

There is hardly any material behavior that is absolutely linear. It is therefore wise to treat the nonlinearities rather than ignore them. To treat the nonlinearities, one can use new techniques of nonlinear modeling, like feed-forward neural networks. The proponents of linear techniques draw on their simplicity and the possibility of adding nonlinear terms in linear regression. Often this is not done, and is not efficient even if it is done. Nature does not follow the simplicities that we try to fit it in, using common linear techniques.

Nonlinear modeling can be carried out with a variety of methods. The older methods include linear regression with nonlinear terms, polynomial regression and nonlinear regression. These have several limitations. The newer methods include feed-forward neural networks, kernel regression, multivariate splines, etc., which do not require a prior knowledge of the nonlinearities in the relations. Figure 2 shows a typical feed-forward neural network.

Feed-forward neural networks have the so-called universal approximation capability1, which makes them particularly suitable for most function approximation tasks we come across in engineering and in the process industries. The user does not need to know the type and severity of nonlinearities while developing the models. In other words, we have freeform nonlinearities in feed-forward neural network models.

Feed-forward neural networks resemble structurally, and to a smaller extent functionally, the networks of neurons in biological systems. Like the networks of neurons in the brains, artificial neural networks also consist of neurons in layers directionally connected to others in the adjacent layers (see Figure 2).

There are many different types of neural networks, and some of them have practical uses in process industries2. Neural networks have been in use in process industries for about 20 years3. The multi-layer perceptron, a kind of a feed-forward neural network, is the most common one. Most neural network applications in industries are based on them including our earlier work on extrusion related to cables4-9.

In a feed-forward neural network of the kind shown in Figure 2, the output of each neuron i in the feed-forward neural network is usually given by:

where s is called the activation function, and is usually the logistic sigmoid, given by:

The incoming signals to the neuron are xj, and wij are the weights for each connection from the incoming signals to the ith neuron. The wi0 terms are called biases. This results in a set of algebraic equations, which relate the input variables to the output variables. Thus, for each observation (a set of input and output variables), the outputs can be predicted from these equations based on a given set of weights. The training procedure aims at determining the weights, which result in the smallest sum of squares of prediction errors.

There are a variety of training methods in use today. Backpropagation used to be the most common training method very many years back. Today, most people use good optimization methods10 instead.

Experimentation

A total of 26 experiments was carried out with different temperature profiles and screw speeds. These are called bleeding tests because no product is produced, and the extrudate just flows out of the crosshead, which is weighed to determine the throughput rate. The data is highly consistent, and small nonlinearities in the throughput are visible from the raw data.

Figure 3 shows throughput observations in blue as a function of screw speed, keeping the temperature profile constant. The points in red are melt temperatures and the points in green are pressures measured just before the crosshead. No experimental results had to be discarded.

It was possible to see clear effects from the raw experimental data. Some subsets of the experiments had variations in only one independent variable.

All of the four output variables increase with screw speed. And most of the zone temperatures increase the throughput and melt temperatures, but reduce the pressure and the motor load.

Nonlinear Modeling of Extrusion

Several nonlinear models were attempted for the four output variables. The selected models showed good statistical characteristics and a high degree of correlation. The statistics of the prediction errors for the four output variables (1-throughtput, 2-melt temperature, 3-pressure and 4-motor load) were as follows.

The selected models were implemented in a LUMET system, which is a set of software components for facile use of nonlinear models. This allowed us to study the behavior of the extruder in good detail and determine optimal temperature profiles.

Figure 4 shows the effect of screw speed on throughput for different zone 1 temperatures, while keeping other variables constant. A higher temperature generally leads to a higher throughput, but for some zones the effect can be the opposite, as can be seen from Figure 5 for zone 6 temperature. And Figure 6 shows the effect of screw speed on melt temperature at different zone 1 temperatures. The melt temperature increases with zone 1 tempeature, but the difference gets smaller at higher screw speeds.

Figure 7 presents the effect of the screw’s speed on pressure at different zone 4 temperatures. As can be seen, the pressure decreases with increasing temperatures.

Figure 8 on next page, presents the effect of the screw’s speed on the specific throughput at different zone 6 temperatures. The specific throughput is the throughput divided by the screw speed. As can be seen, the specific throughput decreases with screw speed and is lower at higher zone 6 temperatures.

Conclusions

Nonlinear modeling has been found to be a powerful tool for tuning the operating conditions of a large variety of processes including extrusion.

In the case of cable insulations, it is usually possible to achieve a higher throughput while keeping the melt temperature within limits by tuning the temperature profile of the extruder barrel. With a modest number of experiments followed by nonlinear modeling, it becomes possible to determine optimal conditions.

For more information on nonlinear modelling, extrusion and cables, visit the websites below.

Www.nonlinear-solutions-oy.com
www.mailleferextrusion.com
www.nexans.no

References:

1 Hornik, K., Stinchcombe, M. and White, H., “Multilayer feedforward networks are universal approximators,” Neural Networks, Vol. 2, (1989) 359-366.

2 A. Bulsari (ed.), Neural Networks for Chemical Engineers, Elsevier, Amsterdam, 1995.

3 A. Bulsari, ”Quality of nonlinear modelling in process industries”, Internal Report NLS/1998/2.

4 A. Bulsari and M. Lahti, “Nonlinear models guide secondary coating of OFCs”, Wire and Cable Technology International, Vol. 29, No. 5 (September 2001) 40-43.

5 A. Bulsari and M. Lahti, “How nonlinear models help improve the production economics of extrusion processes”, British Plastics and Rubber (September 2008) 30-32.

6 A. Bulsari and M. Lahti, “Muovialan tuotantoprosessien tehostaminen epälineaarisella mallintamisella”, Muovi, No. 8 (December 2008) 20-23.

7 A. Bulsari and M. Lahti, “Improving the throughput linearity of extruders”, Wire and Cable Technology International, Vol. 37, No. 3 (May 2009) 62-65.

8 A. Bulsari, M. Lahti and S. Sneck, “Nonlinear modeling for optical fibre cables”, Wire Industry, Vol. 70 (June 2003) 203-206.

9 A. Bulsari and M. Lahti, “Temperature profile in the extruder barrel matters”, British Plastics and Rubber (June/July 2010) 7-11.

10 P. E. Gill, W. Murray and M. H. Wright, Practical Optimisation, Academic Press, London (1981) 136-140.
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