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Inhomogeneous chamber states in screw spindle vacuum pumps
(2024) Pleskun, Heiko; Brümmer, Andreas; Pelz, Peter F.
In the present work, inhomogeneous pressure distributions in working chambers of screw spindle vacuum pumps (SSVP) are investigated, which occur due to a superposition of a drag-driven and a pressure driven flow, especially at low chamber pressures and high rotational speeds. As a result of the rotation, a mass flow is caused in the working chambers in the direction of the moving rotor teeth, which is dammed up in the profile engagement. This causes a pressure gradient in the opposite direction, which compensates for this. The static pressure in the working chamber is therefore location-dependent. This mechanism leads to a significant increase in the applied gap mass flow rates, since the gap entry density is greater than in a homogeneous working chamber due to the local pressure increase. During the filling process, the inhomogeneous pressure distribution means that less mass can be sucked into the machine and the filling efficiency is reduced as a result. To calculate the inhomogeneous pressure distribution, the working chamber is first abstracted as a rectangular channel in which all walls have a wall velocity corresponding to the kinematic relationships. Subsequently, a one-dimensional differential equation is formulated, which is based on a superposition of the mass flow rates of a pressure-driven flow and a drag-driven flow. Depending on the gas rarefaction, the geometry and the gas-surface interaction, a closure problem arises, which is solved separately using analytical solutions and results from the direct simulation Monte Carlo (DSMC) method. The one-dimensional model is validated in two ways. On the one hand, a vacuum test rig is set up for experimental validation, in which the inhomogeneity in a working chamber is measured via three pressure measurement points. This shows good agreement between measurements and model. On the other hand, three-dimensional computational fluid dynamics (CFD) simulations are carried out, which confirm the admissibility of a reduction of the model to a one-dimensional flow. Transient CFD simulations are also used to investigate the chamber filling process with an expanding computational mesh. By dimensional analysis, it is shown that the inhomogeneity in the working chamber coincides on one curve each for both chamber filling and encapsulated working chambers, so that analytically determinable functionals are derived and implemented in the chamber model simulation software KaSim. Subsequently, a test machine is simulated and compared with existing measurement results. It is obtained that the simulation results of SSVPs can be significantly improved with the help of the inhomogeneous model of working chambers. Since the machine is significantly more inefficient at operating points with higher chamber inhomogeneity, the evaluation of the functionals depending on the required operating point is suitable for a rough design of new machines.
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MathOA-SuS: Entwicklung verstehensorientierter Aufgaben im Kontext eines digitalen formativen Assessments im Rahmen der Lehrkräfteausbildung
(Gesellschaft für Didaktik der Mathematik, 2025) Heinrich, Daniel C.; Block, Jan; Hattermann, Mathias; Strunk, Franziska; Bach, Volker
Im "Lehren und Lernen in der digitalen Welt" stellt die Auswahl, Evaluation und Synthese von digitalen Aufgaben für den eigenen Unterricht eine zentrale Aufgabe für zukünftige und aktuelle Lehrkräfte dar. Um die angehenden Lehrerinnen und Lehrer des gymnasialen Lehramts bereits in der Ausbildung hierauf vorzubereiten, evaluieren und konzipieren diese im vorgestellten Seminarkonzept eigene digitale Aufgaben mit individuellem Feedback nach fachdidaktischen Prinzipien. In diesem Beitrag möchten wir die Qualität der erstellen Aufgaben hinsichtlich Diagnostik und formativem Feedback beleuchten.
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MS 07 - Frühe mathematische Bildung
(Gesellschaft für Didaktik der Mathematik, 2025) Lüken, Miriam; Schuler, Stephanie; Bruns, Julia
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Datenbasierte Entscheidungsbäume mit unplugged Datenkarten als Einstieg in das maschinelle Lernen
(Gesellschaft für Didaktik der Mathematik, 2025) Fleischer, Yannik; Biehler, Rolf; Podworny, Susanne
Die Integration von maschinellem Lernen in den Schulunterricht gewinnt zunehmend an Bedeutung. Im ProDaBi-Projekt wurde eine Unterrichtseinheit für die Sekundarstufe I entwickelt, in der Lernende mithilfe von analogen Datenkarten datenbasierte Entscheidungsbäume erstellen. Drei Studien mit Schülerinnen und Schülern zeigten, dass Grundlagen von datenbasierten Entscheidungsbäume erfolgreich erlernt und angewendet werden können. Herausforderungen lagen in der optimalen Nutzung von Strategien wie Sortieren oder Gruppieren der Datenkarten und der datenbasierten Argumentation.
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