GearHeads Forum

Gearify wrote: Here is my question for you though, Nate. By whatever definition you're working with, what is the pressure angle measured from on a non-circular gear? In circular gears, the line tangent to the roll lines at the point of contact is always perpendicular to the line through the centers of rotation (which gives us some nice properties). On non-circular gears (especially the more eccentric ones) the tangent line can be quite far from perpendicular to the line through the center.

If measured from (p1-p2) I feel that there would be severe disortions where t1-t2 differs significantly. But if from t1-t2, the gears may not "push" on eachother properly and the entire benefit of involute teeth is compromised.

Thoughts?

Nate wrote:

Gearify wrote: Here is my question for you though, Nate. By whatever definition you're working with, what is the pressure angle measured from on a non-circular gear? In circular gears, the line tangent to the roll lines at the point of contact is always perpendicular to the line through the centers of rotation (which gives us some nice properties). On non-circular gears (especially the more eccentric ones) the tangent line can be quite far from perpendicular to the line through the center.

I don't know what the official definition is or even if there is one for non-circular gears.  Art and I discussed the same question in the other thread.   As far as I'm concerned, the preferred usage is the angle off p1-p2, but I worked this stuff out for myself.  Other people will have other notions.

If measured from (p1-p2) I feel that there would be severe disortions where t1-t2 differs significantly. But if from t1-t2, the gears may not "push" on eachother properly and the entire benefit of involute teeth is compromised.

Thoughts?

Mechanically speaking you probably want to measure the angle from p1-p2 and live with the distortions.   That's what I was trying to describe, and, mechanically, you want the action to be close to that line.  There's a lot of freedom in tooth profiles, so the roll line tangent line can somtimes also work.

In the illustration, if we imagine that we're turning the red gear clockwise as the master and the yellow gear is the slave and the gear flanks are roughly perpendicular to the t1-t2 line, then it's likely that the gears would just separate.

ArtF wrote: ...
I think Nates idea is a really good one. Ill probably play with it in the coming months to see if it improves on hobbing, but I have read papers
on the hobbing being superiour simply because it deals with degenerate solutions to Nates idea. Its like the tips of the teeth on high K areas
of the curve, the hob finds it naturally, the involute equations start to produce some nasty overlap that needs to be dealt with.. at least thats
what Ive experienced so far.
...

Gearify wrote: ...
We can define the pressure lines as a series of "snap shots" where the line is chosen to pass through the contact point at a particular point in time. So there is in a sense a "jump" from one pressure line to the next as the position of the line switches for each tooth, to pass through the varying point of contact of the roll lines. This jump may produce some abrupt changes in stress and pressure that may be undesirable (am I wrong?).

One could, however, define a MOVING pressure line.  Such a pressure line would always be intersecting the point of contact between the roll lines, and the point of contact would linearly travel along this "floating" pressure line.
...

Gearify wrote:...
So imagine in the video you posted, imagine that the height of the red line would instantaneously jump to a different vertical height every time a new tooth engaged.