≪ 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:entgasungsoberflaechenberechnung [2026/02/07 15:00] – deppe2en:grundlagenhandbuch:entgasungsoberflaechenberechnung [2026/08/03 13:36] (aktuell) – [Degassing efficiency of the process] paal
Zeile 1: Zeile 1:
 ====== Calculation of the degassing surface====== ====== Calculation of the degassing surface======
  
-==== Degassing Basic knowledge (Theory) ====+==== Material degradation and degassing ====
  
-Material degradation and degassing 
   * Thermal (oxidative, mechanical)   * Thermal (oxidative, mechanical)
   * Hydrolytic degradation   * Hydrolytic degradation
Zeile 48: Zeile 47:
 The surface (2) is the result of the multiplication of the height and the development of the channel, taking into account that no melt pool is formed in the contact zone. The surface (2) is the result of the multiplication of the height and the development of the channel, taking into account that no melt pool is formed in the contact zone.
  
-$$A_{Pool} = 2 \frac{\pi - \alpha_E}{\pi} \cdot \frac{2hL}{\sin \varphi} \tag{2}$$+$$A_{Pool} = 2 \frac{\pi - \alpha_F}{\pi} \cdot \frac{2hL}{\sin \varphi} \tag{2}$$
  
 For the determination of the melt film, the difference of the shell surface of the eight-shaped housing (filled with melt) and comb surfaces of the screw is drawn up, thereby the surface of the film is determined (see equation 3). For the determination of the melt film, the difference of the shell surface of the eight-shaped housing (filled with melt) and comb surfaces of the screw is drawn up, thereby the surface of the film is determined (see equation 3).
  
-$$A_{Film} = 2 \frac{\pi - \alpha_E}{\pi} D_a \pi L \left(1 - \frac{2e}{t \cos \varphi}\right)(1 - \varepsilon) \tag{3}$$+$$A_{Film} = 2 \frac{\pi - \alpha_F}{\pi} D_a \pi L \left(1 - \frac{2e}{t \cos \varphi}\right)(1 - \varepsilon) \tag{3}$$
  
 The surface renewal time is calculated by using Equation (4). The surface renewal time is calculated by using Equation (4).
Zeile 88: Zeile 87:
 On the basis of the course of the analytical and approximated solution it becomes clear that in the required interval [e/2; B/2], the solution is sufficiently precise, see Figure 4. The irregularity appears only outside the boundary. On the basis of the course of the analytical and approximated solution it becomes clear that in the required interval [e/2; B/2], the solution is sufficiently precise, see Figure 4. The irregularity appears only outside the boundary.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_004.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_004.png?nolink |}}
  
 **Figure 4:** Comparison of the analytical and approximated solution **Figure 4:** Comparison of the analytical and approximated solution
Zeile 94: Zeile 93:
 It is clear from Figure 6 that the theoretical calculation is based on the degree of filling. The filling level includes the current operating parameters of the extruder. This basic knowledge makes it possible to determine the channel height on the basis of the approximation equation with the necessary X-coordinate of the melt in equation 7. It is clear from Figure 6 that the theoretical calculation is based on the degree of filling. The filling level includes the current operating parameters of the extruder. This basic knowledge makes it possible to determine the channel height on the basis of the approximation equation with the necessary X-coordinate of the melt in equation 7.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_005.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_005.png?nolink |}}
  
 **Figure 5:** Methodology for determining the renewal of surfaces on the basis of theoretical foundations **Figure 5:** Methodology for determining the renewal of surfaces on the basis of theoretical foundations
Zeile 100: Zeile 99:
 Figure 6 shows the schematic sequence of the surface calculation for implementation in SIGMA. Figure 6 shows the schematic sequence of the surface calculation for implementation in SIGMA.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_006.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_006.png?nolink |}}
  
 **Figure 6:** Implementation of the surface renewal time and free surface calculation in SIGMA **Figure 6:** Implementation of the surface renewal time and free surface calculation in SIGMA
Zeile 106: Zeile 105:
 ===== Degassing efficiency of the process ===== ===== Degassing efficiency of the process =====
  
-The degassing efficiency is evaluated with the degassing reference parameter of Schuler (Equation 1. In this case taken place the determination for wetting and non-wetting polymer.+The degassing performance can be calculated using the following equation:
  
-$$\frac{c_{Start} - c_{End}}{c_{Start} - c_{Gleichgewicht}} = \frac{\left(\frac{A_{POOL}}{t_{POOL}} + \frac{A_{FILM}}{t_{FILM}} + \frac{A_{GRUND}}{t_{GRUND}}\right)}{\dot{m}} \tag{Equation 1}$$+$$\eta^* = \frac{c_{Start} - c_{End}}{c_{Start} - c_{Equilibrium}} = 2\rho\sqrt{ \frac{ D }{ \pi } } \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}} + \frac{A_{GROUND}}{\sqrt{t_{GROUND}}}\right)}{\dot{m}} \tag{8}$$
  
 After transposing of the equation can be the end concentration of low molecular component determined. Thereby is it possible to take a statement about the degassing efficiency. After transposing of the equation can be the end concentration of low molecular component determined. Thereby is it possible to take a statement about the degassing efficiency.
 +The degassing efficiency is evaluated with the degassing reference parameter of Schuler (Equation 9). 
  
-For wetting polymer is the Equation 2and for non-wetting polymer is the Equation 3 used.+$$\frac{c_{Start} - c_{End}}{c_{Start} - c_{Equilibrium}} \sim \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}} + \frac{A_{GROUND}}{\sqrt{t_{GROUND}}}\right)}{\dot{m}} \tag{9}$$
  
-$$EK_{Benetzend} = \frac{\left(\frac{A_{POOL}}{t_{POOL}} + \frac{A_{FILM}}{t_{FILM}} + \frac{A_{GRUND}}{t_{GRUND}}\right)}{\dot{m}} \tag{Equation 2}$$+In this case taken place the determination for wetting and non-wetting polymer. For wetting polymer is the Equation 10 and for non-wetting polymer is the Equation 11 used.
  
-$$EK_{Nicht-Benetzend} = \frac{\left(\frac{A_{POOL}}{t_{POOL}} + \frac{A_{FILM}}{t_{FILM}}\right)}{\dot{m}} \tag{Equation 3}$$+$$EK_{Wetting} = \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}} + \frac{A_{GROUND}}{\sqrt{t_{GROUND}}}\right)}{\dot{m}} \tag{10}$$ 
 + 
 +$$EK_{Non-Wetting} = \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}}\right)}{\dot{m}} \tag{11}$$
  
 The difference between both equation is that the surface area und renewal time at screw root is neglected, because in non-wetting case are not melt at screw root available. The difference between both equation is that the surface area und renewal time at screw root is neglected, because in non-wetting case are not melt at screw root available.