Dies ist eine alte Version des Dokuments!
Feed section
For the calculation of the feeding behavior the input of tribological and technological data is required.
Realization of the theoretical principles
With regard to the processing the solid sections can be divided into three sections:
I. Hopper and hopper opening
II. Flow section without pressure built-up along the screw channel (∆p = 0)
III. Conveying section with pressure built-up (∆p > 0)
Most of the popular research and mathematical models focus on the third section ($∆p > 0$). This takes place among other things in case of a calculation with REX/PSI in which the solid conveying is considered.
In order to explain the data, the kinematic ratio in the screw channel is briefly set out in the following: Usually the filling ratio $f$ of the screw refers to the volume of the screw channel. Because of its geometrical shape the plastic pellet does not fill a screw channel completely. Therefore the filling ratio can theoretically never be 1, according to this definition. Here, the filling ratio is defined differently in order to operate with the regularities used in the literature:
$$f = \frac {\dot m_{spez} (n)} {\dot m_{spez 0} (n→0)}$$
First, the specific throughput ($\dot m_{spez}$, throughput per screw speed in [kg/rotation]) is constant with increasing screw speed and then continuously drops over the entire rotational range. Only when the screw channels are completely filled the solid conveying behavior is linear in the lower rotational range.
In order to describe this decrease mathematically, the filling ratio of the screw refers to the lower speed range (from the mathematical point of view this is the initial increase of the throughput diagram).
The following figure shows the development of the measured throughput speed behavior to the filling ratio resulting from it.
From the definition of the filling ratio, the following results for the calculation of the throughput $\dot m$:
$$\dot m (n) = f \cdot \dot m_{spez 0} \cdot n$$
According to this equation, in addition to the filling ratio function the specific throughput $\dot m_{spez0}$ of the lower speed range has to be known for the calculation of the throughput. In this case (completely filled screw channels, $f=1$, $Δp = 0$) the following throughput relation applies:
$$\dot m_{spez0} = \frac {\dot m}{n}|_{n→0} = ρ_s \cdot π \cdot D_a \cdot A_{quer} \cdot \frac {tan φ \cdot tan α}{tan α + tan φ}$$
with: $n$ = rotational speed, $ρ_s$ = bulk density, $D_a$ = diameter of the screw, $A_{quer}$ = channel cross section, $α$ = conveying angle, $φ$ = pitch
Using the Schneider approach the conveying angle $α$ is calculated in the pressure neutral case.
Different possibilities to realise flow problems and solve them if necessary, are offered to the user. This can be done by integration of the feed grooves or by enlargement of the feed opening. It always has to be taken into consideration that the issued results refer to the maximum throughput to be achieved. The following figure shows how the present results can be combined with the plasticization.
The blue curve (flow-dominated throughput) describes the maximally achievable throughput on the basis of the feed conditions. Due to the fact that not more material can arrive in the first screw sections, more polymer cannot be melted. The red curves show the throughput behavior depending on the counterpressure. If no counterpressure exists, the maximal throughput is achieved. The throughput behavior is feed dependent. With increasing counterpressure the throughput is influenced with regard to the counterpressure. Only with increasing counterpressure the feed conditions must also be considered. Thus, the user can immediately decide whether the pressure behavior of the screw is sufficient enough for compacting and melting the solid. Even if the throughput is flow-dominated, the calculation of the pressure throughput e.g. for the melt behavior in REX/PSI is melt-dominated. If a calculation shall be conducted flow-dominatedly, the throughput must be edited in the processing parameters.