Conical Involute Gears (Bevel Gears)?

I have spent some time researching involute gears and came up with [www.thingiverse.com]
I would now like to have bevel gears (conical gears), but Im finding it much harder to find any reference to the mathematics behind them.
Can anyone point me to a source of information on the maths behind this type of gearing?

... i think for conical gears it's a simple projection of the contour-lines to a point on the axis representing the scewed angle, so 'normal' math for the countour could be enough

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Viktor
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Viktor's right. The profile is tapered to the intersection point of the gears' axes, which is the extension of their shaft axes. Because of the taper, profile-correct conical involutes can't be hobbed or cut with a tool on a single axis, those you buy are approximations.

So is the involute profile of the gear generated using a base radius which is based on the "outside pitch diameter" or the "back cone radius"? (refer to the attached image for what I mean by the quoted terms).

... it's the same as with a 'normal' gear - imagine moving the focus point away, until with a 'infinite' distance you have a common gear without conus - so your reference is the "outside pitch diameter" ...

Edited 1 time(s). Last edit at 07/15/2010 06:15AM by VDX.

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Viktor
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Victor,
I'm thinking about your analogy, and by that thought experiment, I think you are wrong.
If you move the pitch apex to infinity, the "outside pitch diameter" and the "back cone radius" describe the same thing, so it is not particularly enlightening. If however, you go the other way and make the pitch angle approach 90 degrees, the gear becomes a circular rack. If you used the "outside pitch diameter" circle to define the teeth, they would project in the plane of the circular rack. Projecting them back to the pitch apex would result in them being flat. If however you used the "back cone radius" (which is now infinite), its involute would form teeth that were flat and project vertically (which is what you expect for a rack).
Greg.

Hi Greg,

... it's not so clear with the analaogy - i think what you have to do is design a 'normal' gear-contour with your desired pitch ... inner or outer diameter, it's not essential ...

Then you define your focus point and draw from every construction point a line to the focus.

And last you draw your 'back cone radius' perpendicular to the 'outside pitch diameter' ... then you have to cut the outer lines and elongate the inner lines until the 'back cone radius', so you'll receive the same construction as in your sample ...

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Viktor
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Aufruf zum Projekt "Müll-freie Meere" - [reprap.org] -- Deutsche Facebook-Gruppe - [www.facebook.com]

Call for the project "garbage-free seas" - [reprap.org]

I think I have what is needed. I ended up creating a tooth with a tooth thickness using the outside pitch diameter and the tooth profile using the back cone radius [www.thingiverse.com]. The parameters for the pair of bevel gears that I chose to render for the thing show how the large gear is like a circular rack with almost straight teeth and the small gear is like a normal gear with clearly involute profile teeth.

Hello,

Detailed information have been given at the following journal papers.


Jesper Brauer, A general finite element model of involute gears , Finite Elements in Analysis and Design
Volume 40, Issues 13-14, August 2004, Pages 1857-1872

Börner, J., Humm, K. and Joachim, F., “Development of Conical Involute Gears (Beveloids) for Vehicle Transmission”, Gear Technology, Vol. 22, No 6, 28-35, 2005.