Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:berechnungen:durchsatz [2025/01/13 17:55] – neelest
+++ en:berechnungen:durchsatz [2025/07/03 13:33] (aktuell) – cschall
@@ Zeile 1: / Zeile 1: @@
 ======Throughput======
-===== Throughput =====
+===== Throughput Calculation=====
-If the throughput or the dosing time (optional) is specified together with the dosing volume (necessary) in the process parameters, the throughput is not calculated, but all further calculations are carried out with the specified throughput.
+If the throughput or dosing time (optional) is specified together with the dosing volume (mandatory) in the process parameters, then the throughput is not calculated. Instead, all subsequent calculations are performed using the specified throughput.
-The following content describes the melt-dominated throughput calculation. If a grooved bushing is used in the process, this determines the throughput (see [[en:berechnungen:einfache_berechnung|]] and [[en:berechnungen:nutbuchsenberechnung|]]). \\ The calculation of the [[en:berechnungen:feststofffoerderung|]] is coupled with the melt-dominated throughput calculation.
-As a standard feature, a linear temperature profile beginning at the front edge of the
+The following section describes the melt-dominated throughput calculation. If a grooved bushing is used in the process, it determines the throughput (see [[en:berechnungen:einfache_berechnung|]] and [[en:berechnungen:nutbuchsenberechnung|]]). \\ The [[en:berechnungen:feststofffoerderung|]] is carried out in conjunction with the melt-dominated throughput calculation.
-hopper $T_G$ / $T_K$ and progressing to the point of the isothermal throughput calculation with
-a specified melt temperature is assumed (see also [[en:berechnungen:einfache_berechnung|necessary process parameters]]).
-Next, the reference zone is determined; this is the screw zone (no shear or mixing section) with the lowest channel depth. The reference zone is used to determine the average shear rate there.
+Two melt-dominated throughput models are distinguished: the equivalent zone model and the interval-based model, which will be introduced with REX 19.0 / PSI 17.0.
-The mean shear rate for this section is
-obtained from the circumferential velocity, the screw back speed and the channel
-depth. This shear rate is used to establish the current rheological material data. The
-following approach is adopted here:
-If the flow curve is available in the form of the Carreau data, a tangent is drawn to the
+Initial temperature and pressure profiles are assumed prior to the throughput calculation. This is necessary to determine the viscosities required for throughput estimation. For more information, see [[prozess_iterieren|]].
-Carreau curve at the appropriate shear rate and temperature. The power law
-parameters are then established for this tangent.
-After these pre-calculations the actual throughput respectively metering time
-calculations are conducted.
-<details><summary>**only vented screws **</summary>
+For both models, degassing screws form a special case: the throughput is calculated solely based on the geometry of the first screw stage (before degassing), with the backpressure at the degassing location physically set to 1 bar. Consequently, the backpressure at the screw tip has no effect on the mass throughput.
-The vented screws are an exception here, where the location of the specified melt temperature is already set at the start of the degassing zone. The temperature curve then remains constant.
+Additionally, for both models, pressure losses across shearing and mixing elements are calculated analytically. This also applies to all sections computed using network theory/matrix model (node method for barrier screws, always for wave screws). See also [[druckverlauf|Pressure Calculation]].
-With venting extruders the throughput is calculated on the basis of the geometry of
-the first screw stage, where the counterpressure at the venting point is set at 0 bar
-corresponding to the physical conditions.
-For vented screws, the reference zone must be located BEFORE the first degassing zone.
-</details>
-In the first step, the total pressure difference (specified back pressure minus hopper pressure) is assumed for all screw zones (excluding shearing and mixing parts) and an initial mass flow rate is therefore determined. Based on this mass flow rate, the pressure loss across all shearing and mixing parts as well as the non-return valve (PSI only) is calculated and subtracted from the pressure difference so that a simplified linear pressure gradient is obtained across all feed, (de)compression, metering and barrier zones. This pressure gradient is used to calculate the throughput in an iterative process, which in turn influences the pressure loss across the shearing and mixing parts present. A throughput-dependent back pressure (see [[en:eingabe_eines_werkzeugs:eingabe_eines_werkzeugs_mit_geometriedaten|Input of a tool]] or [[en:eingabe_eines_werkzeugs:eingabe_einer_werkzeugkennlinie|Input of a die characteristic]] can also be taken into account via the iterative calculation.
+==== Melt-Dominated Equivalent Section Model  ====
-<details><summary>**only PSI**</summary>
+First, a reference section is determined—this is the screw section (excluding shearing and mixing elements) with the smallest channel depth. For degassing screws, the reference section must be located before the first degassing section. This reference section is used to determine the average shear rate, which in turn is used to determine the viscosity using the given melt temperature at the end of the screw.
-At the beginning of the calculation of the metering time the screw is in the front screw
-stage and will be retracted by 0.1* diameter. Thus, the length of the feed section is
+Based on the screw geometry and the temperature profile, factors for throughput calculation are determined. The throughput is then calculated using these geometry-dependent factors only for the reference section and the associated pressure drop.
-cut by this amount and a new temperature profile is assigned to each screw stage.
+In the first step, the entire pressure difference (specified backpressure minus hopper pressure) is assumed to apply across the entire screw (excluding shearing and mixing elements), and an initial mass throughput is calculated.
-The characteristic values of the throughput equation are determined for the screw
+This value is then used to calculate pressure losses across all shear and mixing sections and, in the case of //PSI//, the non-return valve. These pressure losses are subtracted from the pressure difference to yield a simplified linear pressure gradient across the feeding, compression, metering, and barrier sections.
-stage and the throughput is calculated afterwards. Using the cross sections of the
+With this pressure gradient, an iterative process is used to determine the throughput, which in turn affects the pressure losses across the shearing and mixing elements.
-barrel the proportion between the screw back speed and the melt conveyed in the
+Additionally, this iterative process can take into account a throughput-dependent backpressure (see [[en:eingabe_eines_werkzeugs:eingabe_eines_werkzeugs_mit_geometriedaten|]] or [[en:eingabe_eines_werkzeugs:eingabe_einer_werkzeugkennlinie|]]).
-screw vestibule enables the determination of the screw back speed. The required
-metering time of 0.1 d for the shortening of the effective screw length can be
+==== Melt-Dominated Interval-Based Model  ====
-obtained by dividing the screw shift through the determined screw back speed.
-In order to determine the entire metering time the single times for the metering path
+The interval-based model does not require a reference section.
-divided into 0.1 D steps are added up. Besides the metering time the throughput for
+Unlike the equivalent Section model, no global geometry-based factors are used. Instead, local screw geometry, temperature, pressure, and—if applicable—the calculated degradation level of the plastic are considered in each calculation interval.
-the calculation point is defined, which is the basis for further calculations for this
-screw stage.
+This is done using a generalized regression equation, which calculates the pressure loss for a given throughput based on local screw geometry and viscosity.
-</details>
+Because the throughput remains constant along the entire screw, a specific throughput is assumed, and the pressure loss across each calculation interval is computed to determine the overall pressure drop across the screw.
+The calculated total pressure difference is compared with the target pressure difference, and an iterative solution is performed to find the throughput at which both the inlet and outlet pressures match their target values.
-The prerequisite for the throughput calculation is:
-  * A defined screw geometry that begins with a [[en:eingabe_der_schneckendaten:einzugs-_metering-_und_entgasungszone|feed zone]], i.e. a zone with a constant flight depth. The length of the feed zone must be at least equal to the metering stroke (//PSI only//).
-  * A defined [[en:eingabe_der_zylinderdaten:eingabe_der_zylinderdaten|cylinder]] whose length is identical to the length of the screw, or at most twice the length of the screw.
-  * The [[en:materialdaten:rheologische_materialdaten|rheological material behaviour]].
-  * The [[en:materialdaten:thermodynamische_daten|glass transition temperature $T_g$]] for amorphous thermoplastics or the [[en:materialdaten:thermodynamische_daten|crystallisation temperature $T_k$]] for semi-crystalline thermoplastics.
-  * The [[en:materialdaten:dichtedaten_bzw._spezifisches_volumen|density or volume function]] for the melting range must also be entered.
-  * The [[en:eingabe_der_verfahrensparameter:eingabe_der_verfahrensparameter|process parameters]]: (i) speed, (ii) mass temperature at the screw tip (REX) at the start and end of dosing (PSI), (iii) pressure at the screw tip (REX) or in the screw vestibule (PSI), (iv) dosing path (PSI). If only one of the two melt temperatures (PSI) is known, both entries can be assigned the same value.
 ===Further topics===
   * [[en:berechnungen:einfache_berechnung|]]
+  * [[en:berechnungen:prozess_iterieren]]
   * [[en:berechnungen:durchsatz|]]
   * [[en:berechnungen:druckverlauf|]]
@@ Zeile 63: / Zeile 42: @@
   * [[en:berechnungen:temperaturverlauf|]]
   * [[en:berechnungen:leistung_und_schubspannungen|]]
+  * [[en:berechnungen:schergeschwindigkeit]]
   * [[en:berechnungen:verweilzeit|]]
   * [[en:berechnungen:verweilzeitverteilung|]]