# How is the equivalent spur gear diameter of a helical gear equal to (d/cos^2α)?

The book I've got says that the equivalent spur gear radius(re) = (Semi-major axis)^2/(Semi-minor axis) of the ellipse made by the cut-section normal to the teeth of the helical gear. There is no explanation provided for the given relation and is what I seek.

• Your title question and body question don't match each other. But the main idea of evaluating a helical gear is to treat it as a straight spur gear, albeit a larger one. You do this by taking a section normal to the helix angle of the teeth, the equivalent diameter of this is the nominal diameter/cos helix angle. What is the book you are referencing?
– jko
Apr 1 at 18:31
• The title asks the question straightforward whereas the body gives the little background given while deriving the relation in the title. The book I'm referencing is a local publication with limited credibility and poor quality. I would like to attach a picture but don't know how. Apr 5 at 13:55
• This (re) = (Semi-major axis)^2/(Semi-minor axis) relation is what has me confused and the one in the title is derived by substituting r/cos(helix angle) for the semi-major axis and r for the semi-minor axis Apr 5 at 14:02
• The equivalent spur gear diameter for a helical gear is the diameter divided by the cosine of the helix angle, nothing is squared. The re radius doesn't make sense either, you end up with a value greater than the major axis itself. I wouldn't put too much value in your source.
– jko
Apr 5 at 16:23
• Thanks a lot, I had begun suspecting as much after asking around a bit. Should I delete this question? Apr 8 at 13:49