In order to calculate the pressure profile it is necessary to fulfil the same conditions as for the throughput calculation of both the throughput and the metering time calculation. This also applies for all input data geometry, material data and processing parameters. Additionally, the point of calculation (just PSI) for which the pressure profile of the screw length shall be calculated has to be defined.

The pressure profile is calculated back to the point of melt pool formation (OSW). If it was not possible to determine the point of melt pool formation on account of missing data, REX/PSI will calculate up to the end of the feed section. The profile from the front edge of the hopper to the last point calculated is reflected by a logarithmic formulation.

The pressure profile calculation starts with the screw tip. The calculated throughput is used to determine the pressure loss between two calculation points and this is then added to the previous absolute pressure. The pressure in the screw vestibule (at the screw tip) results from the adjusted impact pressure.

The pressure profile is calculated isothermally at the melt temperature for each step and is subsequently multiplied by a correction factor. This correction factor has in physical terms the effect that the calculation performed at a temperature that permits the pressure and throughput behavior to coincide. This is necessary, since the throughput has to be calculated on the basis of a mixed isothermal/non-isothermal formulation while the pressure profile has to be calculated either isothermally or nonisothermally.

In order to calculate the barrier screw in the way described a constant pressure gradient has to be assumed. However, since every additional assumption increases inaccuracy, the so-called „Matrix model“ was implemented to eliminate this assumption. Its calculation method is similar to the FEM calculation method.

Here, single intervals are built for barrier flight, solid and melt channel and for each section between the individual balance points, the change in the flow is described by means of a linear equation. These equations form a linear system of equations. The equations only describe the development of the flow in the direction of the channel, which means that the mesh of the division of the geometry into the required intervals corresponds to constant conditions.

Before the resulting equation system can be solved with the familiar algorithms used to solve linear equation systems, it is first necessary to reduce the system. This reduction is achieved by allowing boundary conditions.

In the closed barrier section, the mass flow towards the first node, or away from the last node in the channel direction, can be taken as being equal to zero. If an open barrier section is calculated, by contrast, it is sufficient to alter the boundary condition in order to be able to calculate this design. Because of the lack of a geometrical separation, the pressure difference between the first and last nodes of the solids and melt channel is set at zero.

For a clear-cut solution of the system it is necessary to know about the mass flow. Here an iterative calculation helps, i.e. in the first step, the pressure-throughput behavior of the standard sections is calculated for a known pressure at the screw tip without considering the barrier section. In the second step, this throughput is taken to solve the equation system for the barrier section. Since the overall pressure requirement for the screw is equal to the sum of the pressure requirements of the individual screw sections, the calculated pressure requirement for the barrier section can be added to the pressure requirement of the remaining screw sections that was calculated in the first step.

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