A Mathematical Model to Describe the Inner Contour of Moineau Stators

What is it about?

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.

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Photo by Jeswin Thomas on Unsplash

Photo by Jeswin Thomas on Unsplash

Why is it important?

Mathematical model was developed, which helps to improve and develop the new chamber boring process. The derived equation can be used to describe the epitrochoid-similar bore profile exactly, such that this approach can be utilized for a subsequent Laplace-transformation and a regulated and undisturbed machining sequence can be achieved.

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