Parametric curve and curve matching

Question

I am trying to design this pump which has asymmetric profile rotor rotating in opposite direction.

I created the spline in cad software using different point which more or less matches the profile, but I think there should be a mathematical way to create this.

Is it possible?

Additional information:

• Diameter of both holes is 200mm
• The centre of the rotors axes are spaced 150mm apart
• Arrows show the rotating directions
• The rotors revolve at the same rate.
• The rotors are not inter-connected. They do not drive each other, but they should rotate while constantly in touch with each other.

EDIT: or even is it possible if I define a spline for one rotor, I can get an equation for another rotor mathematically?

Answer 1

In your CAD software, look for 'roots pump'.

Design video

https://www.youtube.com/watch?v=xZ0OZChb-MI . I believe the person who made the video has mislabelled the red and blue circle parameter boxes.

Also see https://www.youtube.com/watch?v=DIui7lSv76I

If I get a chance, I'll see if I can provide a mathematical derivation

Answer 2

I believe for every chosen "Ying" rotor design, there exists a corresponding "Yang" rotor design among the asymmetric pairs.

What is needed is a review differential equations of involutes and evolutes rather than Bezier curve approach to determine their matching profiles.

The above is a Claw type pair convex/concave vacuum pump differently profiled pair with some advantage over epicycloid /spirograph designs apparently. Probably the two lobe Roots pump design is modified.

Hope no patent infringement issues in reverse engineering attempt.