Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen RevisionVorhergehende ÜberarbeitungNächste Überarbeitung | Vorhergehende Überarbeitung | ||
| en:berechnungen:leistung_und_schubspannungen [2025/06/18 14:36] – cschall | en:berechnungen:leistung_und_schubspannungen [2025/07/03 13:34] (aktuell) – cschall | ||
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| Zeile 11: | Zeile 11: | ||
| The accuracy of the power calculation therefore depends on the other curves. If experimental values are already known (e.g. flow rate), it is advisable to [[en: | The accuracy of the power calculation therefore depends on the other curves. If experimental values are already known (e.g. flow rate), it is advisable to [[en: | ||
| - | For an accurate power calculation, | + | For an accurate power calculation, |
| - | The temperature control power is calculated in the same way for all models and is made up of the melt film and the melt vortex. The temperature gradient on the cylinder wall is determined for both areas and the required temperature | + | The temperature control power is calculated in the same way for all models and is made up of the melt film and the melt pool. The temperature gradient on the cylinder wall is determined for both areas and the required temperature |
| - | [[en: | + | [[en: |
| The following models calculate the drive power and the required torque of the extruder. Power losses (e.g. in the gearbox) are not taken into account. \\ | The following models calculate the drive power and the required torque of the extruder. Power losses (e.g. in the gearbox) are not taken into account. \\ | ||
| Zeile 21: | Zeile 21: | ||
| ===== Isothermal power model ===== | ===== Isothermal power model ===== | ||
| - | When calculating the power, a distinction is made between the melting and melting-on areas. In the melting area, i.e. from the start of the first heating zone to the location of the melt vortex | + | When calculating the power, a distinction is made between the melting-delay |
| - | film can be determined. The power conversion in the pure solids area between the hopper and the first heating zone is neglected, as no pressure has yet built up there and the solids friction forces on the cylinder wall are negligibly small compared to the melt film friction forces. | + | |
| - | The calculation for the other zones results in a summation of the wall shear stresses on the cylinder. | + | The calculation for the further |
| < | < | ||
| Zeile 52: | Zeile 51: | ||
| and therefore also: | and therefore also: | ||
| - | $P_{drive} = \delta h_{temperature} * \dot{m}_{melt} + \delta p * \dot{V} - \dot{Q}$ | + | $P_{drive} = \Delta h_{temperature} * \dot{m}_{melt} + \Delta p * \dot{V} - \dot{Q}$ |
| //The enthalpy model is recommended for plating extruders.// | //The enthalpy model is recommended for plating extruders.// | ||
| Zeile 58: | Zeile 57: | ||
| ===== Calculation of the heat flows ===== | ===== Calculation of the heat flows ===== | ||
| - | In order to calculate the drive power, the energy supply and dissipation | + | In order to calculate the drive power, the energy supply and cooling |
| {{ : | {{ : | ||
| Zeile 64: | Zeile 63: | ||
| ==== Calculation of convection in the melt vortex ==== | ==== Calculation of convection in the melt vortex ==== | ||
| - | The calculation of convection in the melt vortex | + | The calculation of convection in the melt pool (SW) is based on the assumption of a plane wall with longitudinal flow around it. This results in the following dimensionless key figures: |
| $$\text{The Reynolds number } Re=\frac{L_{char} \cdot \rho \cdot v_0}{\eta}$$ | $$\text{The Reynolds number } Re=\frac{L_{char} \cdot \rho \cdot v_0}{\eta}$$ | ||
| Zeile 84: | Zeile 83: | ||
| $$\dot q_{SF} = \frac{dT}{d \xi} \Bigg \vert_{\xi=1} \cdot \frac{\lambda}{\overline \delta}$$ | $$\dot q_{SF} = \frac{dT}{d \xi} \Bigg \vert_{\xi=1} \cdot \frac{\lambda}{\overline \delta}$$ | ||
| - | $$\dot q_{SF} = (T_Z-T_{Fl}) \left\{ 1 + Br_{SW} \left[ \frac{exp \left[ - \beta (T-T_{Fl}) \right] \cdot \left[ (1-A)e^A - 1 \right]}{A^2} \left( \frac{A}{e^A-1} \right)^{1+n} \right] \right\} \cdot \frac{\lambda}{\overline \delta}$$ | + | $$\dot q_{SF} = (T_Z-T_{Fl}) \left\{ 1 + Br_{SW} \left[ \frac{\left[ (1-A)e^A - 1 \right]}{A^2} \left( \frac{A}{e^A-1} \right)^{1+n} \right] \right\} \cdot \frac{\lambda}{\overline \delta}$$ |
| $$\text{with}$$ | $$\text{with}$$ | ||
| $$A = \frac{\beta}{n} (T_Z-T_{Fl})$$ | $$A = \frac{\beta}{n} (T_Z-T_{Fl})$$ | ||
| $$\text{and}$$ | $$\text{and}$$ | ||
| - | $$Br_{SW} = \frac{K \cdot v_{rel}^{1+n} \cdot \bar{\delta}^{1-n}}{\lambda (T_Z - T_{Fl})}$$ | + | $$Br_{SF} = \frac{K \cdot v_{rel}^{1+n} \cdot \bar{\delta}^{1-n}}{\lambda (T_Z - T_{Fl})}$$ |
| - | with the thermal conductivity $\lambda$, the mean melt film thickness $\overline \delta$, the cylinder temperature $T_Z$, the flow temperature (melting temperature) $T_{Fl}$, the temperature in the melt vortex $T$, the Brinkmann number in the melt film $Br_{SW}$, the temperature coefficient in the flow law $\beta$, the flow law exponent $n$, the consistency factor $K$ and the relative velocity between cylinder and solid bed $v_{rel}$. | + | with the thermal conductivity $\lambda$, the mean melt film thickness $\overline \delta$, the cylinder temperature $T_Z$, the melting temperature $T_{Fl}$, the Brinkmann number in the melt film $Br_{SF}$, the flow law exponent $n$, the consistency factor $K$ and the relative velocity between cylinder and solid bed $v_{rel}$. |
| The heat flow is also calculated from the heat flow density by multiplying it by the area of the solid bed: | The heat flow is also calculated from the heat flow density by multiplying it by the area of the solid bed: | ||
| Zeile 106: | Zeile 105: | ||
| * [[en: | * [[en: | ||
| * [[en: | * [[en: | ||
| + | * [[en: | ||
| * [[en: | * [[en: | ||
| * [[en: | * [[en: | ||