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--- en:grundlagenhandbuch:geometriegroessen_des_gleichdrall-doppelschneckenextruders [2026/05/24 09:02] – [Shouldered Kneading Blocks] neelest
+++ en:grundlagenhandbuch:geometriegroessen_des_gleichdrall-doppelschneckenextruders [2026/06/16 14:37] (aktuell) – [Geometry of Tightly Intermeshing, Co-rotating Twin Screw Extruders] deppe2
@@ Zeile 9: / Zeile 9: @@
   * Modular setup of both screw and barrel (see figure)
-{{ :grundlagenhandbuch:geometriegroessen_des_gleichdrall-doppelschneckenextruders:eingesetzte_schneckenelemente:en_sigma150_dlg_grundlagenhandbuch_geometriegroessen_000.svg?700%nolink |}}
+{{ :en:grundlagenhandbuch:de_sigma150_dlg_grundlagenhandbuch_geometriegroessen_000.svg?nolink&700 |}}
 **Figure:** Modular setup of both screw and barre
@@ Zeile 330: / Zeile 330: @@
 Maximum diameter ratio of three-way profile ($i=3$)
-$$D_{v,3} = D_{v,3,max} = \frac{1}{2 \cdot \cos\left(\frac{\pi}{2 \cdot 3}\right) - 1} = 1.366  \tag{Equation 3-13}$$
+$$D_{v,3} = D_{v,3,max} = \frac{1}{2 \cdot \cos\left(\frac{\pi}{2 \cdot 3}\right) - 1} = 1.366  \tag{40}$$
 Outer diameter of three-course profile
-$$D_{a,3} = \frac{2 \cdot a}{1 + D_{v,3}} \tag{Equation 3-14}$$
+$$D_{a,3} = \frac{2 \cdot a}{1 + D_{v,3}} \tag{41}$$
 Eccentricity $e$
-$$e = \frac{D_{a,3} - D_{i,3}}{2} \tag{Equation 3-15}$$
+$$e = \frac{D_{a,3} - D_{i,3}}{2} \tag{42}$$
 Inside diameter of three-course profile
-$$D_{i,3} = 2 \cdot a - D_{a,3} \tag{Equation 3-16}$$
+$$D_{i,3} = 2 \cdot a - D_{a,3} \tag{43}$$
@@ Zeile 352: / Zeile 352: @@
 This profile shows that the comb angles are zero. Therefore the flank angles of the standard profile are the same:
-Comb angle: $\angle AOB = \angle BOC = \angle COD = \Omega_3 = 60° \tag{Equation 3-17}$
+Comb angle: $$\angle AOB = \angle BOC = \angle COD = \Omega_3 = 60° \tag{44}$$
-Flank angle: $\phi_{k,3} = \phi_{g,3} = 0 \tag{Equation 3-18}$
+Flank angle: $$\phi_{k,3} = \phi_{g,3} = 0 \tag{45}$$
-Outside radius: $R_{a,3} = \frac{D_{a,3}}{2} \tag{Equation 3-19}$
+Outside radius: $$R_{a,3} = \frac{D_{a,3}}{2} \tag{46}$$
-Inside radius: $R_{i,3} = \frac{D_{i,3}}{2} = \left(a - \frac{D_{a,3}}{2}\right) \tag{Equation 3-20}$
+Inside radius: $$R_{i,3} = \frac{D_{i,3}}{2} = \left(a - \frac{D_{a,3}}{2}\right) \tag{47}$$
 The coordinates of the points in the three-course standard profile can be calculated by these geometry sizes. Because the profile is symmetrical, only half the contour is selected as the calculation object.
-A: $x_A = R_{i,3}$; $y_A = 0$
+A: $x_A = R_{i,3}; y_A = 0\tag{48}$
-B: $x_B = R_{a,3} \cdot \cos 60° = \frac{1}{2}R_{a,3}$; $y_B = R_{a,3} \cdot \sin 60° = \frac{\sqrt{3}}{2}R_{a,3}$
+B: $x_B = R_{a,3} \cdot \cos 60° = \frac{1}{2}R_{a,3}; y_B = R_{a,3} \cdot \sin 60° = \frac{\sqrt{3}}{2}R_{a,3}\tag{49}$
-C: $x_C = R_{i,3} \cdot \cos 120° = -\frac{1}{2}R_{i,3}$; $y_C = R_{i,3} \cdot \sin 120° = \frac{\sqrt{3}}{2}R_{i,3}$
+C: $x_C = R_{i,3} \cdot \cos 120° = -\frac{1}{2}R_{i,3}; y_C = R_{i,3} \cdot \sin 120° = \frac{\sqrt{3}}{2}R_{i,3}\tag{50}$
-D: $x_D = -R_{a,3}$; $y_D = 0$
+D: $x_D = -R_{a,3}; y_D = 0\tag{51}$
 ==== Screw Mixing Elements ====
@@ Zeile 386: / Zeile 386: @@
 From the control volume ABC we get the equilibrium of flow rates:
-$$\dot{V} = k \cdot \dot{V}_{channel} \pm \dot{V}_{gap} \pm l \cdot \dot{V}_{groove}\tag{21}$$
+$$\dot{V} = k \cdot \dot{V}_{channel} \pm \dot{V}_{gap} \pm l \cdot \dot{V}_{groove}\tag{52}$$
 Where $l$ is the number of grooves between the points A and B. $l$ is calculated using the following equation:
-$$l = \frac{l_{Nut}}{2\pi} \cdot (2\pi - \Omega) \cdot \cos \varphi_s\tag{22}$$
+$$l = \frac{l_{Nut}}{2\pi} \cdot (2\pi - \Omega) \cdot \cos \varphi_s\tag{53}$$
 ==== Blister Elements ====
@@ Zeile 415: / Zeile 415: @@
 These sections are characterized by the following dimensionless numbers:
-$$k_1 = \frac{D_a}{D_z}\tag{23}$$
+$$k_1 = \frac{D_a}{D_z}\tag{54}$$
-$$k_2 = \frac{D_i}{D_a}\tag{24}$$
+$$k_2 = \frac{D_i}{D_a}\tag{55}$$
-$$cl = \frac{a}{D_z/2}\tag{25}$$
+$$cl = \frac{a}{D_z/2}\tag{56}$$
 ==== Thoothed Mixing Elements ====