Making optimum use of an extruder from the economic point of view requires a comprehensive knowledge of the plasticizing process of polymeric materials. To date, decisions are made primarily on the basis of „empirical values“ and experimental investigations. In the course of the past few years, the SIGMA simulation program has been developed to become an alternative to the frequently employed trial-and-error-approach. It can be used in the design and optimization of extruders from the process engineering point of view. Apart from permitting time and cost savings, the calculation additionally provides information on individual parameters which influence the plasticizing of the material. The plasticizing process is rendered highly transparent and made accessible to calculation.

The following parameters can be calculated with the program:

• pressure profile
• filling degree distribution
• temperature profile
• melting curve
• residence time behavior
• drive power or requisite torque
• axial mixing coefficient
• degree of dispersion
• heating/cooling needed

The parameters listed above display differing degrees of mutual dependence. To achieve a physical-mathematical description of a problem of this complexity, solution methods were worked out for the individual parameters. When the individual models were implemented in a computer program, they were linked together to form a comprehensive model. The physical-mathematical computation models make allowance for the influencing factors of screw and barrel geometry, material behavior and process parameters.

The following basic principles were applied during modelling:

• the models are based on simple physical considerations
• simple mathematical models
• the aim is to achieve a closed analytical solution, if necessary achieved by simplifications
• with a sequence of differential equations, it is possible to work towards a solution through the linearization of intermediate results on a semi-logarithmic or log-log plot
• if no closed analytically solution exists, approximation equations are used which are based on numerical solutions
• statistical processes within the plasticizing unit are described by means of defined distribution functions

Using closed solutions or experimentally verified approximation solutions made it possible to implement very quick solution algorithms, thereby giving very short computation times. In this way, SIGMA can be used as a target-oriented, engineering tool for the layout of extruders.

NOTE:

Software- and hardware terms used in this manual are also registered trademarks. Therefore, they are marked by CAPITALS in ITALIC PRINT.

Software Engineering Team SIGMA (Email: software@ktp.upb.de)

Paderborn