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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?

  • 0
    Are the two rotors revolving in different directions? Which direction(s) are they revolving in? Are they revolving at the same rate? Should they interlock so that one drives the other? – 2017-02-25
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    yes, you can see the arrows of rotating direction. yes they are revolving at the same rate. no they do not drive each other, but they should rotate while constantly in touch of each other – 2017-02-25
  • 0
    I couldn't see the arrows, working on a small screen. What is the radius of the two 'holes', and how far apart are the two spaced? – 2017-02-25
  • 0
    center distance between two holes is 150 while their diameter being 200, i.e. 50mm overlap. – 2017-02-25
  • 0
    Is there a constraint on the size of the red spindles, minimum or maximum? – 2017-02-25
  • 0
    it should not be too small. but no rigid constraints. – 2017-02-25
  • 0
    where does the requirement for a beizer line come into the problem? – 2017-02-27

2 Answers 2

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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.

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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