Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:grundlagenhandbuch:drehmoment_und_antriebsleistung:urspruenglicher_ansatz [2025/06/20 09:22] – deppe2
+++ en:grundlagenhandbuch:drehmoment_und_antriebsleistung:urspruenglicher_ansatz [2026/04/28 10:26] (aktuell) – gelöscht deppe2
@@ Zeile 1: / Zeile 1: @@
-====== Original Model ======
--> Erster Eintrag fehlt im Deutschen (Original Model)
-  *[[en:Grundlagenhandbuch:Drehmoment und Antriebsleistung:Ursprünglicher Ansatz:Schmelzebereich]]
-  *[[en:Grundlagenhandbuch:Drehmoment und Antriebsleistung:Ursprünglicher Ansatz:Aufschmelzbereich]]
-  *[[en:Grundlagenhandbuch:Drehmoment und Antriebsleistung:Ursprünglicher Ansatz:Schmelzewirbel]]
-===== Original Model =====
-The total power consumption is made up of solid friction and mixing friction in the feeding section, the power in the intermeshing zone of both screws, the power in the radial clearance over the screw tips, the power in the melt layer between solid material and the barrel wall, the power in the melt pool and in the melt section. In the calculation of the processes, the power consumption is considered to be negligibly tiny until the place of the first melt pool formation. As co-rotating twin screws, which will be used as a plasticating unit, usually possess a partly filled feeding zone, this is justifiable.
-In the estimation of the power consumption in [1] equations were represented, where the power is calculable in the general form:
-$$P = \int_0^z \int_{-\frac{b_{max}}{2}}^{+\frac{b_{max}}{2}} (\tau_{0x} r_{0x} + \tau_{0z} r_{0z}) dx \, dz \tag{1}$$
-With the wall shear stress:
-$$\tau_{0x} = K \left[\left(\frac{\partial v_x}{\partial y}\right)^2 + \left(\frac{\partial v_z}{\partial y}\right)^2\right]^{\frac{n-1}{2}} \frac{\partial v_x}{\partial y} \tag{2}$$
-$$\tau_{0z} = K \left[\left(\frac{\partial v_x}{\partial y}\right)^2 + \left(\frac{\partial v_z}{\partial y}\right)^2\right]^{\frac{n-1}{2}} \frac{\partial v_z}{\partial y} \bigg|_{y=h} \tag{3}$$
-if the shear rates at the wall for conveying elements with the represented approximation equations in the table are used.
-**Table: Estimation of the wall shear speeds (conveying elements: [1])**
-===== I. Conveying Elements =====
-$$C_x = \left[(1.368 + 2.634n^{0.1})e^{(n-1)}^{\frac{1}{n}}\right]$$
-$$0.55 \leq \pi_V \leq 1.00 \quad\quad C_z = 1 + 3n^{-0.2131}(1 - \pi_V)$$
-$$1.00 < \pi_V \leq 1.25 \quad\quad C_z = 1 + 3(1 - \pi_V)$$
-$$1.25 < \pi_V \leq 2.00 \quad\quad C_z = C_1 - C_2 \pi_V^{C_3}$$
-===== II. Kneading Blocks =====
-$$C_x = \frac{1}{\pi} + \sqrt{2}$$
-$$C_z = \frac{\pi + 1}{\pi} \cdot \frac{\dot{V}}{v_0 b_{max} h k}$$
-===== III. Reconveying Elements =====
-$$C_x = 1.75 + 1.75n$$
-$$0.00 \leq \pi_V \leq 1.00 \quad\quad C_z = (0.42 + 0.8828n)\pi_V + (1.75 + 1.9692n)$$
-For re-conveying elements, the two equations shown in table can be used. These approximation equations are based on a numerical solution of a system of differential equations, the systems of differential equations table [2]. The same prerequisites are used as were for the equations of the conveying elements [1].
-The estimation of the power consumption must differ in the 3 function sections in the figure on the barrel wall and in the melting section.
-**Figure:** Model for the power calculation.
-The calculation of the power consumption within each section is explained hereafter (for conveying elements and kneading blocks).