Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
| en:scaleup_modul:scaleup_modul [2024/04/12 13:58] – angelegt admin | en:scaleup_modul:scaleup_modul [2025/09/04 13:13] (aktuell) – [Theoretical principles] neelest | ||
|---|---|---|---|
| Zeile 1: | Zeile 1: | ||
| ======ScaleUp module====== | ======ScaleUp module====== | ||
| + | |||
| + | If a process is to be scaled to a new machine size, this is possible with the Scale-Up module. The module is called up via //Process// > // | ||
| + | |||
| + | {{ : | ||
| + | |||
| + | ===== Operation of the scale-up module ===== | ||
| + | The Scale-Up module offers the option of scaling processes to larger or smaller production plants. The module is operated via the Project Scale-Up menu item, which takes you to a detailed dialogue window in which both the output variables of the current process and adjustments for the target process can be made. | ||
| + | |||
| + | You can choose between the target of a constant temperature difference (standard) and a constant heat flux density. A scale-up at constant temperature difference provides a very accurate scale-up. A scale-up at constant heat flux density is a theoretical scale-up operating point, which produces a higher mass throughput, but at the expense of scale-up accuracy. In particular, a later melting end is to be expected here. \\ | ||
| + | A ‘target’ greater than 0.66 is recommended, | ||
| + | |||
| + | ====Output variables of the process==== | ||
| + | |||
| + | In the dialogue that opens, the output variables of the process that describe the current operation of the machine are displayed first. These variables include: | ||
| + | |||
| + | * Screw diameter | ||
| + | * Screw length | ||
| + | * Mass temperature at the screw tip | ||
| + | |||
| + | These parameters define the starting point for the calculation and simulation of a scaled process. | ||
| + | |||
| + | ====Determining the target variables==== | ||
| + | |||
| + | You can define new variables for the target process that correspond to the requirements of the new machine or the new process. This provides flexibility to adapt the process to different machines or requirements. | ||
| + | If the target process contains a degassing zone, the scale-up module offers the option of calculating a modified length of the screw including the degassing zone (see [[en: | ||
| + | |||
| + | ====Creating and simulating the scaled process==== | ||
| + | |||
| + | By pressing the //OK// button, the scaled process is created and calculated based on the adjustments made. | ||
| + | |||
| + | {{ : | ||
| + | |||
| + | ====Comparison of the processes==== | ||
| + | |||
| + | After the calculation, | ||
| + | |||
| + | By default, a diagram showing the model law exponents and a diagram comparing the pressure curve and the melting curve are opened. Other curves and individual values can also be selected for comparison. The ‘//Open all standard diagrams// | ||
| + | |||
| + | Below the diagrams, you can show and hide the two machines involved in the scale-up process. If the screw lengths are different, you can right-click on the screw display to set either a common x-axis or separate x-axes for each process. | ||
| + | |||
| + | {{ : | ||
| + | |||
| + | ====Creation of the scaled process==== | ||
| + | |||
| + | If the scaled process meets the desired requirements, | ||
| + | |||
| + | The aim of the scale-up is to generate a process with a larger or smaller diameter while maintaining or changing the screw length and maintaining or changing the final melt temperature. The screw diameter or the screw length must be changed compared to the initial process. | ||
| + | |||
| + | |||
| + | ===== Theoretical principles ===== | ||
| + | |||
| + | The scale-up module is based on the similarity theory based on dimensionless key figures. The dimensionless key figures should be identical for the initial process and for the scaled process so that similar process behaviour can be achieved. | ||
| + | |||
| + | The scale-up exponents $\chi$ (Chi) and $\Psi$ (Psi) are calculated from the parameters entered. Alternatively, | ||
| + | The naming of the underlying exponents is explained in the following table: | ||
| + | |||
| + | ^ Name ^ Formula symbol ^ Meaning ^ Equation ^ | ||
| + | |Epsilon | $\epsilon$ | pitch exponent (always 1 in REX) | $\epsilon = log\left( \frac{tan(\varphi)}{tan(\varphi_0)}\right) \bigg/ log\left( \frac{D}{D_0}\right) +1$| | ||
| + | |kappa | $\kappa$ | viscosity shear rate exponent | $\kappa = -log\left( \frac{\eta}{\eta_0}\right) \bigg/ log\left( \frac{\dot{\gamma}}{\dot{\gamma}_0}\right)$| | ||
| + | |Xi | $\xi$ | mass temperature exponent | $\xi = -log\left( \frac{\vartheta}{\vartheta_0}\right) \bigg/ log\left( \frac{\dot{\gamma}}{\dot{\gamma}_0}\right)$| | ||
| + | |Omega| $\omega$ | length exponent | $\omega= log\left( \frac{\frac{L}{D}}{\left( \frac{L}{D}\right)_0}\right) \bigg/ log\left( \frac{D}{D_0}\right)$| | ||
| + | |||
| + | with | ||
| + | |||
| + | ^ Formula symbol ^ Meaning ^ | ||
| + | |$\varphi$| Gradient | | ||
| + | |$\eta$| viscosity | | ||
| + | | $\dot{\gamma}$ | shear rate | | ||
| + | | $\vartheta$ | temperature | | ||
| + | |$L$| length of the screw| | ||
| + | |$D$| Nominal diameter extruder | | ||
| + | |||
| + | When calculating the scale-up exponents $\chi$ (Chi, speed exponent) and $\Psi$ (Psi, gear depth exponent), a case distinction is made. | ||
| + | A distinction is made between | ||
| + | * Diameter remains the same | ||
| + | * Diameter does not remain the same | ||
| + | and | ||
| + | ***constant cylinder temperature**: | ||
| + | ***constant heat flux density**: Assumption that the area-related heat flow of the cylinder temperature control remains identical.\\ | ||
| + | |||
| + | The second assumption only describes a theoretical similarity. Under the assumption of constant heat flux density, a higher mass throughput is achieved during a scale-up compared to the assumption of constant cylinder temperature, | ||
| + | A compromise can be concluded from both assumptions, | ||
| + | This compromise can be set in REX using the ‘Target’ slider in the input screen. By default, the standard assumption of constant cylinder temperature is used due to the better scaling accuracy. However, the slider allows a setting at any position between the described boundary conditions. A ‘target’ greater than 0.66 is recommended, | ||
| + | |||
| + | ^ Case 1: Diameter unequal, constant cylinder temperature^ | ||
| + | |$\Psi=\frac{(2+\omega-\epsilon)(2-\kappa)}{4-3\kappa+2\xi}$| | ||
| + | |$\chi=\frac{\Psi(2+\xi)-(1+\omega-\epsilon+\xi)}{1-\xi}$| | ||
| + | |||
| + | ^ Case 2: Diameter unequal, constant heat flux density^ | ||
| + | |$\Psi=\frac{(2+\omega-\epsilon)(2-\kappa)}{3-2\kappa+\xi}$| | ||
| + | |$\chi=\frac{\Psi(1+\xi)-(1+\omega-\epsilon+\xi)}{1-\xi}$| | ||
| + | |||
| + | ^ Case 3: Diameter equal, constant cylinder temperature^ | ||
| + | |$\Psi=\frac{2-\kappa}{4-3\kappa+2\xi}$| | ||
| + | |$\chi=\frac{\Psi(2+\xi)-1}{1-\xi}$ (smooth tube extruder) | | ||
| + | |$\chi=\frac{\Psi(1+2\xi)-\xi}{1-\xi}$ (grooved barrel extruder) | | ||
| + | |||
| + | ^ Case 4: Diameter equal, constant heat flux density^ | ||
| + | |$\Psi=\frac{2-\kappa}{3-2\kappa+\xi}$| | ||
| + | |$\chi=\frac{\Psi(1+\xi)-1}{1-\xi}$ (smooth tube extruder) | | ||
| + | |$\chi=\frac{\xi(2\Psi-1)}{1-\xi}$ (grooved barrel extruder) | | ||
| + | |||
| + | The most important process and geometry parameters are calculated as follows: | ||
| + | |||
| + | ^ Screw length ^ | ||
| + | |$\frac{L}{L_0}=\left( \frac{D}{D_0} \right)^{1-\omega}$| | ||
| + | |||
| + | ^ Gear depth ^ | ||
| + | |$\frac{h}{h_0}=\left( \frac{D}{D_0} \right)^{\Psi(1+\xi)-\chi(1-\xi)+(2-\xi)}$ (diameter unequal, smooth tube extruder)| | ||
| + | |$\frac{h}{h_0}=\left( \frac{D}{D_0} \right)^{(3-2\xi+2\xi\Psi)-\chi(1-\xi)+\omega(1-\xi)}$ (unequal diameter, grooved barrel extruder)| | ||
| + | |$\frac{h}{h_0}=\left( \frac{L}{L_0} \right)^{\Psi(1+\xi)-\chi(1-\xi)}$ (diameter equal, smooth tube extruder)| | ||
| + | |$\frac{h}{h_0}=\left( \frac{L}{L_0} \right)^{2\Psi\xi+(1-\xi)(1-\chi)}$ (diameter equal, grooved barrel extruder)| | ||
| + | |||
| + | ^ Speed ^ | ||
| + | |$\frac{n}{n_0}=\left( \frac{D}{D_0} \right)^{-\chi}$ (diameter unequal)| | ||
| + | |$\frac{n}{n_0}=\left( \frac{L}{L_0} \right)^{-\chi}$ (diameter equal)| | ||
| + | |||
| + | ^ Throughput ^ | ||
| + | |$\frac{\dot{m}}{\dot{m}_0}=\left( \frac{D}{D_0} \right)^{2+\Psi-\chi}$ (diameter unequal, smooth tube extruder)| | ||
| + | |$\frac{\dot{m}}{\dot{m}_0}=\left( \frac{D}{D_0} \right)^{3+\omega-\chi}$ (diameter unequal, grooved barrel extruder)| | ||
| + | |$\frac{\dot{m}}{\dot{m}_0}=\left( \frac{L}{L_0} \right)^{\Psi-\chi}$ (diameter equal, smooth barrel extruder)| | ||
| + | |$\frac{\dot{m}}{\dot{m}_0}=\left( \frac{L}{L_0} \right)^{1-\chi}$ (diameter equal, grooved barrel extruder)| | ||
| + | |||
| + | < | ||
| + | * Potente, Helmut: Auslegen von Schneckenmaschinen-Baureihen. Modellgesetze und ihre Anwendung. Kunststoff-Fortschrittsberichte, | ||
| + | </ | ||
| + | |||
| + | ==== Modified length of degassing zones ==== | ||
| + | |||
| + | When creating the scale-up, the option //calculate modified length// can be selected for degassing extruders. \\ | ||
| + | If this setting is selected, the length of degassing zones is not calculated using the mathematical approaches described above, but with the aim of maintaining the degassing performance. | ||
| + | For this purpose, the specific surface renewal $\pi_{degassing}=\frac{\dot{m}}{\dot{A}_{degassing}} \thickapprox \left( \frac{D}{D_0}\right) ^{\varphi-\omega}$ with the pitch angle $\varphi$ and the dimensionless residence time $\frac{t_v}{t_{v, | ||
| + | |||
| + | When scaling the entire screw, the lengths of the scaled degassing zones are first calculated and the remaining residual length of the screw is taken into account according to the mathematical relationships in the upper section. | ||
| + | |||
| + | < | ||
| + | * Pohl, Max: High-Speed-Extrusion amorpher Polymere am Beispiel von Polycarbonat (PC) und Polymethylmethacrylat (PMMA). Dissertation, | ||
| + | * Schuler, W.: Degassing during polymer production and processing. Tagungsband: | ||
| + | </ | ||