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--- en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:exzentrische_knetbloecke [2025/08/17 01:24] – deppe2
+++ en:eingabe_der_maschinenparameter_und_konfiguration:schneckenelemente:exzentrische_knetbloecke [2025/11/02 21:46] (aktuell) – deppe2
@@ Zeile 24: / Zeile 24: @@
 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)**
-$$D_{v,3} = D_{a,3 \max} = \frac{1}{2 \cdot \cos\left(\frac{\pi}{2 \cdot i}\right) - 1} = 1.366$$
+$$D_{v,3} = D_{a,3 \max} = \frac{1}{2 \cdot \cos\left(\frac{\pi}{2 \cdot i}\right) - 1} = 1.366 \tag{Equation 3-13}$$
-Equation 3-13
-Outer diameter of three-course profile
+**Outer diameter of three-course profile**
-$$D_{a,3} = \frac{2 \cdot a}{1 + \frac{1}{D_{v,3}}}$$
+$$D_{a,3} = \frac{2 \cdot a}{1 + \frac{1}{D_{v,3}}} \tag{Equation 3-14}$$
-Equation 3-14
-Eccentricity e
+**Eccentricity $e$**
-$$e = \frac{D_{a,2} - D_{a,3}}{2}$$
+$$e = \frac{D_{a,2} - D_{a,3}}{2} \tag{Equation 3-15}$$
-Equation 3-15
-Inside diameter of three-course profile
+**Inside diameter of three-course profile**
-$$D_{i,3} = 2 \cdot a - D_{a,3}$$
+$$D_{i,3} = 2 \cdot a - D_{a,3} \tag{Equation 3-16}$$
-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.
@@ Zeile 54: / Zeile 50: @@
 This profile shows that the comb angles are zero. Therefore the flank angles of the standard profile are the same:
-$$\phi_{k,3} = \phi_{g,3} = 0$$
+$$\phi_{k,3} = \phi_{g,3} = 0 \tag{Equation 3-17}$$
-Comb angle: Equation 3-17
-$$\angle AOB = \angle BOC = \angle COD = \Omega_3 = 60°$$
+**Comb angle:**
-Flank angle: Equation 3-18
-$$R_{a,3} = \frac{D_{a,3}}{2}$$
+$$\angle AOB = \angle BOC = \angle COD = \Omega_3 = 60° \tag{Equation 3-18}$$
-Outside radius: Equation 3-19
+**Flank angle:**
-$$R_{i,3} = \frac{D_{i,3}}{2} = \left(a - \frac{D_{a,3}}{2}\right)$$
+$$R_{a,3} = \frac{D_{a,3}}{2} \tag{Equation 3-19}$$
-Inside radius: Equation 3-20
+**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.