Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:berechnungen:druckverlauf [2025/01/13 18:00] – neelest
+++ en:berechnungen:druckverlauf [2025/07/03 13:34] (aktuell) – cschall
@@ Zeile 1: / Zeile 1: @@
 ======Pressure profile======
-The same conditions must be met for the calculation of the pressure profile as for the throughput or dosing time calculation. This applies to all input data ([[en:eingabe_der_schneckendaten:eingabe_der_schneckendaten|geometry]],
+-> [[en:grafische_darstellung_der_ergebnisse:druckverlauf|For graphical representation of the pressure curve]]
+To calculate the pressure profile, the same conditions as for throughput and dosing time calculations must be fulfilled. This applies to all input data ([[en:eingabe_der_schneckendaten:eingabe_der_schneckendaten|geometry]],
 [[en:materialdaten:allgemeineangaben|material data]]
 and [[en:eingabe_der_verfahrensparameter:eingabe_der_verfahrensparameter|processing parameters]]).
-Additionally, the point of calculation (just //PSI//) for which the pressure
+Additionally, the calculation position (only in //PSI//) must be defined, for which the pressure profile along the screw length is to be calculated.
-profile of the screw length shall be calculated has to be defined.
+The same equations as those used in the throughput calculation are applied.
-The pressure curve is calculated back to the location of the melt vortex formation (OSW).
-The pressure curve calculation starts at the screw tip. The calculated throughput is used to determine the pressure loss within a calculation interval and added to the previous absolute pressure. The pressure in the screw vestibule (at the screw tip) results from the set back pressure.
+The pressure profile is calculated from the screw tip back to the location of the melt pool formation. Before this location, solid conveying takes place, which shows an exponential pressure build-up.
-The pressure curve is calculated isothermally at the melt temperature in each step and then multiplied by a correction factor. From a physical point of view, this correction factor ensures that the calculation is carried out at a temperature that allows the pressure and throughput behaviour to match. This is necessary because the flow rate must be calculated according to a mixed isothermal-non-isothermal approach, but the pressure curve must be calculated either isothermally or non-isothermally.
+The pressure profile calculation begins at the screw tip. Based on the calculated throughput, the pressure drop within a computation interval is determined and added to the previous absolute pressure. In injection molding machines, the pressure in the screw antechamber (at the screw tip) results from the set back pressure.
+==== Pressure Profile Calculation for Barrier and Wave Screws ====
-==== Pressure profile calculation for the barrier section ====
+=== Assumption of Equal Pressure Gradient ===
+Barrier screws can only be calculated analytically under the simplifying assumption of an equal pressure gradient in the melt and solid channels. Although this allows for rapid calculation, the simplification reduces simulation accuracy.
-In order to calculate a barrier as described above, the assumption of an equal pressure gradient must be made. However, as each additional assumption increases the inaccuracy of the simulation, the so-called nodal point method was implemented to eliminate this assumption, whose calculation process generates a grid in the flow area similar to the FEM calculation method.
+=== Network Calculation / Matrix Model ===
-Here, individual intervals are formed for the barrier web, solids channel and melt channel and for each section between the individual balance points, the change in flow is described by the linear pressure-throughput equation. These equations form a linear system of equations. The equations only describe the flow development along the channel direction, so that the established network corresponds to the subdivision of the geometry into the required intervals of constant conditions.
+To eliminate the above-mentioned simplifying assumption, the so-called matrix model was additionally implemented. Its calculation process is similar to the FEM method, generating a mesh within the flow domain. The //Matrix Model// is an analogy model based on network theory from electrical engineering.
-{{ :en:berechnungen:abbildung_9_13_en.svg?700 |}}
+This method is optionally available for barrier screws as an alternative to the equal pressure gradient assumption but is always used for wave screws.
-In order to be able to solve the resulting system of equations with the known solution algorithms, it must be reduced by taking boundary conditions into account.
+A network is generated from the screw geometry, consisting of simple geometries (rectangular channels). For each of these simple geometries, a //voltage source// (drag flow) and a resistance (pressure flow) are defined. From the network of voltage sources and resistances, a matrix (linear system of equations) is generated and solved. Given a specified pressure drop in the zone, this allows determination of not only the throughput but also the pressure for each segment of the geometry, making the pressure profile across the section available.
-{{ :en:berechnungen:abbildung_9_14_en.svg?700 |}}
-For the closed barrier zone, the mass flow pointing towards the first node or away from the last node in the channel direction can be set to zero. If, on the other hand, an open barrier zone is calculated, it is sufficient to change the boundary condition in order to be able to calculate this design. In this case, the pressure difference between the first and last nodes of the solid and melt channels is set to zero due to the lack of geometric separation.
+{{ :berechnungen:druckverlauf:abb_barriere_netzwerktheorie_en.svg?nolink&700 |}}
-==== Pressure curve calculation for wave screws ====
+To solve the resulting system of equations, it must be reduced by incorporating boundary conditions.
+For a closed barrier zone, the mass flow into the closed inlet or out of the closed outlet can be set to zero. For an open barrier section and for wave screws, due to the lack of separation at the beginning and end of the section, the pressure difference between the channels is set to zero.
-The calculation of the pressure curve in wave zones is similar to the calculation of the //node point method// in barrier zones. The //node point method// is an analogue model of network theory from electrical engineering.
+{{ :berechnungen:druckverlauf:abb_barriere_netzwerktheorie_randbedingung_en.svg?nolink&700 |}}
-A network is formed from the geometry of the screw, which is made up of simple geometries (rectangular channels). A //voltage source// (drag flow) and a resistance (pressure flow) are defined for each of these simple geometries. A matrix is created and solved from the network of stress sources and resistances so that, for a given pressure difference in the zone, not only the flow rate but also the pressure is obtained for each of the simple geometries, so that the pressure curve over the zone is also known.
 ===Further topics===
   * [[en:berechnungen:einfache_berechnung|]]
+  * [[en:berechnungen:prozess_iterieren]]
   * [[en:berechnungen:durchsatz|]]
   * [[en:berechnungen:druckverlauf|]]
@@ Zeile 39: / Zeile 41: @@
   * [[en:berechnungen:temperaturverlauf|]]
   * [[en:berechnungen:leistung_und_schubspannungen|]]
+  * [[en:berechnungen:schergeschwindigkeit]]
   * [[en:berechnungen:verweilzeit|]]
   * [[en:berechnungen:verweilzeitverteilung|]]