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en:berechnungen:druckverlauf [2024/10/17 20:07] – [Pressure curve calculation for wave screws] neelesten:berechnungen:druckverlauf [2025/07/03 13:34] (aktuell) – cschall
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 ======Pressure profile====== ======Pressure profile======
  
-In order to calculate the pressure profile it is necessary to fulfil the same conditions +-> [[en:grafische_darstellung_der_ergebnisse:druckverlauf|For graphical representation of the pressure curve]] 
-as for the throughput calculation of both the throughput and the metering time + 
-calculation. This also applies for all input data  +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:eingabe_der_schneckendaten:eingabe_der_schneckendaten|geometry]],+
 [[en:materialdaten:allgemeineangaben|material data]] [[en:materialdaten:allgemeineangaben|material data]]
-and [[en:eingabe_der_verfahrensparameter:eingabe_der_verfahrensparameter|processing parameters]]. +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 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.  +
- +
-==== Pressure profile calculation for the barrier section ====+
  
-In order to calculate the barrier screw in the way described a constant 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.
-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 +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.
-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.+
  
-{{ :en:berechnungen:abbildung_9_13_en.svg?700 |}}+==== Pressure Profile Calculation for Barrier and Wave Screws ====
  
-Before the resulting equation system can be solved with the familiar algorithms used +=== Assumption of Equal Pressure Gradient === 
-to solve linear equation systems, it is first necessary to reduce the system. This +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.
-reduction is achieved by allowing boundary conditions.+
  
-{{ :en:berechnungen:abbildung_9_14_en.svg?700 |}}+=== Network Calculation / Matrix Model ===
  
-In the closed barrier section, the mass flow towards the first node, or away from the +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.
-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. +This method is optionally available for barrier screws as an alternative to the equal pressure gradient assumption but is always used for wave screws.
-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. +
  
 +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.
  
-==== Pressure curve calculation for wave screws ====+{{ :berechnungen:druckverlauf:abb_barriere_netzwerktheorie_en.svg?nolink&700 |}}
  
-The content is currently being processed and will be made available shortly. Please be patient.+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.
  
-ToDo: Anpasssen wenn MA Gödeke fertig ist+{{ :berechnungen:druckverlauf:abb_barriere_netzwerktheorie_randbedingung_en.svg?nolink&700 |}}
  
 ===Further topics=== ===Further topics===
   * [[en:berechnungen:einfache_berechnung|]]   * [[en:berechnungen:einfache_berechnung|]]
 +  * [[en:berechnungen:prozess_iterieren]]
   * [[en:berechnungen:durchsatz|]]   * [[en:berechnungen:durchsatz|]]
-  * [[en:berechnungen:einrieselverhalten|]] 
   * [[en:berechnungen:druckverlauf|]]   * [[en:berechnungen:druckverlauf|]]
   * [[en:berechnungen:aufschmelzverlauf|]]   * [[en:berechnungen:aufschmelzverlauf|]]
   * [[en:berechnungen:temperaturverlauf|]]   * [[en:berechnungen:temperaturverlauf|]]
   * [[en:berechnungen:leistung_und_schubspannungen|]]   * [[en:berechnungen:leistung_und_schubspannungen|]]
 +  * [[en:berechnungen:schergeschwindigkeit]]
   * [[en:berechnungen:verweilzeit|]]   * [[en:berechnungen:verweilzeit|]]
   * [[en:berechnungen:verweilzeitverteilung|]]   * [[en:berechnungen:verweilzeitverteilung|]]