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--- en:berechnungen:einrieselverhalten [2024/07/21 12:58] – neelest
+++ en:berechnungen:einrieselverhalten [2025/01/20 10:56] (aktuell) – gelöscht cschall
@@ Zeile 1: / Zeile 1: @@
-======Feed section ======
-FIXME
-===== 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)
-{{ :berechnungen:abbildung_9_9_en.svg?700 |}}
-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.
-{{ :en:berechnungen:abbildung_9_10_en.svg?700 |}}
-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.
-{{ :en:berechnungen:abbildung_9_11_en.svg?700 |}}
-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.