A Mathematical Model to Describe the Inner Contour of Moineau Stators

Özkaya, E.1, a; Fuß, M.2, b; Biermann, D.1, c

1)
Institut für Spanende Fertigung, Technische Universität Dortmund, Baroper Str. 303, 44227 Dortmund
2)
Beratende Gesellschaft für Tiefbohr- und Zerspanungstechnik GmbH, Dorstfelder Hellweg 60, 44149 Dortmund

a) ekrem.oezkaya@tu-dortmund.de; b) m.fuss@bgtb.de; c) dirk.biermann@tu-dortmund.de

Kurzfassung

Bore holes with a large length to diameter ratio of up to l/d = 100 are typically produced using the single-tube deep hole drilling method also named BTA (Boring and Trepanning Association) deep hole drilling method. However, there are various technical applications requiring deep, complex, epitrochoid-similar and helical inner contours, such as stators used in Moineau motors and pumps. According to the current state of the art, epitrochoid-similar contours for small diameters with large drilling depths can only be produced using a special machining process which is referred to a chamber-boring process. In this paper, a developed mathematical model will be presented that describes the epitrochoid-similar contour exactly. This allows the determination of the position-dependent speed and acceleration of the tool, which are necessary for designing the joints and components of the tool system. In addition, this mathematical model can be used for a subsequent Laplace-transformation, so that could be used for a further optimization of the process dynamic in the future.

Schlüsselwörter

Design for manufacturing, machining processes, modeling and simulation, process engineering

Veröffentlichung

ASME Journal of Manufacturing Science and Engineering, 143 (2021) 4, doi: 10.1115/1.4048437