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--- en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:exzentrische_knetbloecke [2025/05/24 23:04] – deppe2
+++ en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:exzentrische_knetbloecke [2025/11/02 21:46] (aktuell) – deppe2
@@ Zeile 10: / Zeile 10: @@
 $$-\frac{180°}{z} \leq \text{Staggering angle} \leq \frac{180°}{z}$$
-with i as **Number of flights** of the element. A negative angle identifies a reconveying kneading block, in contrast positive angle characterizes a conveying kneading block. Neutral kneading blocks are indicated by a Staggering angle of 180°/i.
+with i as **Number of flights** of the element. A negative angle identifies a reconveying kneading block, in contrast positive angle characterizes a conveying kneading block. Neutral kneading blocks are indicated by a Staggering angle of $$\frac{180°}{i}$$.
+{{ :en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:en_sigma150_dlg_eingabe_der_maschinenparameter_und_konfiguration_schneckenelemente_006.png?nolink |}}
 **Figure:** Input mask eccentrical kneading block
@@ Zeile 18: / Zeile 19: @@
 It is known that in a profile only one comb is scraped off with the housing. If the comb angle is zero, the eccentric profile can be generated by a displacement. The displacement is called eccentricity e. This generated eccentric profile is also tightly intermeshing. The shapes of the contours are not changed after the displacement. The following figure shows the displacement of the profiles.
+{{ :en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:en_sigma150_dlg_eingabe_der_maschinenparameter_und_konfiguration_schneckenelemente_007.png?nolink |}}
 **Figure:** Displacement of profiles with eccentricity
 If the comb angle is zero, the diameter ratio of the three-course profile is at the maximum point.
-Maximum diameter ratio of three-way profile (i=3)
+** Maximum diameter ratio of three-way profile (i=3)**
+$$D_{v,3} = D_{a,3 \max} = \frac{1}{2 \cdot \cos\left(\frac{\pi}{2 \cdot i}\right) - 1} = 1.366 \tag{Equation 3-13}$$
-Equation 3-13
-Outer diameter of three-course profile
+**Outer diameter of three-course profile**
-Equation 3-14
+$$D_{a,3} = \frac{2 \cdot a}{1 + \frac{1}{D_{v,3}}} \tag{Equation 3-14}$$
-Eccentricity e
-Equation 3-15
+**Eccentricity $e$**
+$$e = \frac{D_{a,2} - D_{a,3}}{2} \tag{Equation 3-15}$$
+**Inside diameter of three-course profile**
+$$D_{i,3} = 2 \cdot a - D_{a,3} \tag{Equation 3-16}$$
-Inside diameter of three-course profile
-Equation 3-16
 The graph below shows the standard profile and the eccentric profile. The black profile is centered and symmetrical over the rotation center O point. It is also symmetrical over 3 axes: AD, BE and CF. On the other hand, the red profile is symmetrical only over x-axis.
-**Illustration:** Profile geometry with Dv=1.366. Black: standard profile; red: eccentric profile.
+{{ :en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:en_sigma150_dlg_eingabe_der_maschinenparameter_und_konfiguration_schneckenelemente_008.png?nolink |}}
+**Figure:** Profile geometry with Dv=1.366. Black: standard profile; red: eccentric profile.
 This profile shows that the comb angles are zero. Therefore the flank angles of the standard profile are the same:
+$$\phi_{k,3} = \phi_{g,3} = 0 \tag{Equation 3-17}$$
-Comb angle: Equation 3-17
+**Comb angle:**
-Flank angle: Equation 3-18
-Outside radius: Equation 3-19
+$$\angle AOB = \angle BOC = \angle COD = \Omega_3 = 60° \tag{Equation 3-18}$$
-Inside radius: Equation 3-20
+**Flank angle:**
+$$R_{a,3} = \frac{D_{a,3}}{2} \tag{Equation 3-19}$$
+**Outside radius:**
+$$R_{i,3} = \frac{D_{i,3}}{2} = \left(a - \frac{D_{a,3}}{2}\right) \tag{Equation 3-20}$$
+**Inside radius:**
 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:** $$x_A = R_{i,3}; \quad y_A = 0$$
+**B:** $$x_B = R_{i,3} \cdot \cos 60° = \frac{1}{2}R_{i,3}; \quad y_B = R_{i,3} \cdot \sin 60° = \frac{\sqrt{3}}{2}R_{i,3}$$
+**C:** $$x_C = R_{i,3} \cdot \cos 120° = -\frac{1}{2}R_{i,3}; \quad y_C = R_{i,3} \cdot \sin 120° = \frac{\sqrt{3}}{2}R_{i,3}$$
+**D:** $$x_D = -R_{i,3}; \quad y_D = 0$$