A Mathematical Model to Describe the Inner Contour of Moineau Stators

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

Institut für Spanende Fertigung, Technische Universität Dortmund, Baroper Str. 303, 44227 Dortmund
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


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.


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


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