≪ View Page

Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Beide Seiten der vorigen RevisionVorhergehende Überarbeitung
Nächste Überarbeitung		Vorhergehende Überarbeitung
en:grundlagenhandbuch:drehmoment_und_antriebsleistung [2026/06/12 15:27] – deppe2en:grundlagenhandbuch:drehmoment_und_antriebsleistung [2026/06/16 11:11] (aktuell) – [Enthalpy model with heat flow] neelest
Zeile 317: Zeile 317:
 First of all, a specific enthalpy curve of a semi-crystalline plastic is considered (Picture 1). At the crystallite melting temperature, the plastic has a corresponding specific enthalpy depending on the type. This enthalpy is divided in PAM into $\Delta h_f$ solid enthalpy (enthalpy change to increase the solid temperature) and $\Delta h_a$ melting enthalpy (enthalpy required to dissolve the crystalline regions). First of all, a specific enthalpy curve of a semi-crystalline plastic is considered (Picture 1). At the crystallite melting temperature, the plastic has a corresponding specific enthalpy depending on the type. This enthalpy is divided in PAM into $\Delta h_f$ solid enthalpy (enthalpy change to increase the solid temperature) and $\Delta h_a$ melting enthalpy (enthalpy required to dissolve the crystalline regions).
  
-{{ :en:grundlagenhandbuch:drehmoment_und_antriebsleistung:en_sigma150_dlg_grundlagenhandbuch_drehmoment_und_antriebsleistung_009.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_drehmoment_und_antriebsleistung_009.png?nolink&600 |}}
  
 **Picture 1:** Specific enthalpy curve of a partially crystalline polymer **Picture 1:** Specific enthalpy curve of a partially crystalline polymer
Zeile 418: Zeile 418:
 With the relationships shown, the individual required drive powers between two support points or the individual elements can be determined and visualized in SIGMA. Finally, the individual calculated element powers must be added up to obtain the total power. The sole consideration or difference of the initial and final enthalpy to determine the power leads to errors in various cases. This is the case, for example, if the melt temperature drops once during the extrusion process due to fillers and the melt is then heated again. The subsequent heating of the melt must be done by new energy from outside. This requires a further input of power, which would be neglected if the initial and final enthalpy were simply compared. With the relationships shown, the individual required drive powers between two support points or the individual elements can be determined and visualized in SIGMA. Finally, the individual calculated element powers must be added up to obtain the total power. The sole consideration or difference of the initial and final enthalpy to determine the power leads to errors in various cases. This is the case, for example, if the melt temperature drops once during the extrusion process due to fillers and the melt is then heated again. The subsequent heating of the melt must be done by new energy from outside. This requires a further input of power, which would be neglected if the initial and final enthalpy were simply compared.
  
 +====Enthalpy model with heat flow====
 +The enthalpy model neglects the heat flow between the polymer and the barrel wall. While in larger industrial extruders the proportion of heating power to total power is small compared to the drive power, neglecting the heat flow can lead to significant errors, particularly in smaller laboratory extruders or processes with a large temperature difference between the melt and the barrel.
 +
 +To account for the heat flow, the heat transfer coefficient is calculated according to [[en:grundlagenhandbuch:drehmoment_und_antriebsleistung#references |[TM00]]]. First, the Brinkmann number is calculated and then the Nusselt number is regressed from it.
 +
 +$$Br=\frac{K*v_{0}^{n+1}}{\lambda*\Delta T*h^{n-1}}\tag{60}$$
 +
 +$$Nu=2,9*Br^{0,8}\tag{61}$$
 +
 +The heat transfer coefficient can then be calculated using the thermal conductivity of the melt and the channel height:
 +
 +$$\alpha=\frac{Nu*\lambda}{h}\tag{62}$$
 +
 +The heat flow is calculated as follows:
 +
 +$$\dot Q=\alpha*l_{Node}*U_{Barrel}*\frac{b_{eff}}{b_{max}}*\Delta T\tag{63}$$
 +
 +The heat flow is subtracted from the calculated specific enthalpy difference according to equation 46 in order to determine the corrected drive power. This calculation is performed when the 'Enthalpy w. heat flow' power model is selected.
 ==== Validation ==== ==== Validation ====
  
 The new power model was implemented and verified in SIGMA. Identical to other models, the new power model was compared with the values of the experimental investigations to validate the model. The deviations of different process points and material combinations are shown in the following picture. The new power model was implemented and verified in SIGMA. Identical to other models, the new power model was compared with the values of the experimental investigations to validate the model. The deviations of different process points and material combinations are shown in the following picture.
  
-{{ :en:grundlagenhandbuch:drehmoment_und_antriebsleistung:en_sigma150_dlg_grundlagenhandbuch_drehmoment_und_antriebsleistung_0010.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_drehmoment_und_antriebsleistung_0010.png?nolink&600 |}}
  
 **Figure:** Comparison of experimental investigations and simulations **Figure:** Comparison of experimental investigations and simulations
Zeile 441: Zeile 459:
  
 [TK78] Tadmor, Z.; Klein, I: Engineering Principles of Plasticating Extrusion, Robert E. Krieger Publishing Company, Huntington, New York, 1978 [TK78] Tadmor, Z.; Klein, I: Engineering Principles of Plasticating Extrusion, Robert E. Krieger Publishing Company, Huntington, New York, 1978
 +
 +[TM00] Tenge, S.; Mewes, D.: “Experimental investigation of the energy balance for the metering zone of a twin screw extruder”; Polymer Engineering & Science; Volume 40; 2000; S. 277–289