Machining Bevels.

[ArtF]

It IS hard to explain...near impossible I think. Only pictures can really show it. By Spiral generator I meant the code
that generates the helix. In a helical gear you use a true helix, but in bevel's a spiral is really just an arc of a circle
of cutter diameter which is offset from center of toothface by the helical angle. Again, hard to explain in words. I believe
I use the pitch cone distance as the cutter diameter for the purpose of the spirals but Id have to check the code..


Art
..

[Damo]

This link is about the best definition of an octoidal tooth form that sort of makes sense.

http://books.google.com.au/books?id=IAE ... te&f=false

[Damo]

Actually, I like this book, goes into the cutting tool manufacture in detail.

http://books.google.com.au/books?id=wZp ... te&f=false

[ArtF]

Damo:

  Heres a photo of an octoidal generation. If the rack in this picture were not bent into a circle, the output
woudl be an involute tooth. BUT, as I suspected if you simply bend the rack into a circle, the result is an
octoidal tooth. Thats why no math formulas seem to exist. Its a physical manifistation of the bending of the rack to a circular form.
  Now..the golden question. I generate my bevel "Involutes" by formulas derived from standard involute teeth ( so a linear rack ), BUT then I bend those teeth into a spherical form in order that they taper
correctly in a bevel. If a octoidal is generated by a straight rack bend round, then is a tooth generated from a linear rack but then folded spherically now a proper octoid? I highly suspect the answer to this is yes. If we consider just the infinitely thin outside tooth of a spur for example, mentally its easy to see that if you take this tooth and fold it upwards in bevel form so it fits a spere, you have folded a modification into that tooth. I would submit its the same process as folding the rack and then generatign the tooth prefolded. I would have to do a great deal of math to prove that though, its simply my intuition that tells me this is so..
  I will give this more consideration, but I highly suspect an octoidal tooth is what we have. It cannot, after, all be called an involute tooth as the process of folding it into a bevel has changed its shape, so if it isnt an involute..what is it?... I suspect perhaps its an octoid. Since the term "Octoid" refers only to its contact pattern and not its shape, I can only surmise this as yet..

  SO perhaps just putting out this tooth shape for grinding will work..
Art

[Damo]

Hi Alf, yes i think you're right. If you get a straight rack and project onto a sphere you will get 2 crown gears. But what happens to the tooth form when you get closer to the centre? This is where the octoid comes in. If you take one tooth flank of that crown gear, and another flank on the opposite side and imagine a surface that runs through those 2 flanks. As if you were holding a circular disc of paper and on one side twist it to that flank angle, then on the other side twist it to the other tooth flank angle. If you look at this shape side on, it looks like a figure "8". So microscopically where the tooth flank is, so so minisculely, it's slightly "s" shaped. Would be nice to prove it mathematically. And remember this is just the crown gear, not yet bent around a smaller gear. What'd you think?

[Damo]

I think all the calculations for a stanard involute are correct, just have to do one more function to them. Imagine a spur gear and the flat plane on the side of the spur gear, now all of a sudden that flat plane is spherical? Image the teeth. They are still an involute, just the world they live in is now a sphere. Now imagine 2 spur gears working together on parallel shafts, no imagine the flat plane on the side has become a sphere and the 2 shafts are now at right angles. Gives more meaning to me now of the work spherical involute.

[ArtF]

Damo:

  To the first question:  I cant imagine that piece of paper, though Im sure you can. Its the problem with such dicusions, their very hard
to describe in words. To the second comment.. exactly, I think when you take that spur tooth and fold it into a sphere you create a spherical
involute whos pattern of contact is then an octiod if its done correctly. Are mine? Christ only knows. I know they mesh very well, but if they pattern
on a figure 8... beats me.
  When I do finish the non-circ's in GT, I will visit the Gcode generator to add bevels. Since we're speaking only of using a ground cutter for these
the GCode will work fine no matter if we're rigth or wrong..the entire issue will be the cutter shape.. so we'll see..

  Ill have the Gcode put out so that the blank will have to be tilted to root angle..

Art

[Damo]

Hi Art, I tried to draw what I meant. Sort of looks like a potato chip. The line passes through 2 sets of axes at the same angle. From the side it looks like a figure 8. Imagine the rack going around the circumference and 2 opposite tooth flanks are on the surface.
Cheers Damo

Not sure if this will work, am attaching 2 images

[ArtF]

I see what you mean, it is a figure 8 on profile..  Im just not sure how that helps me in terms of getting the rigth profile..

Its interesting to note that the specification for the calculation of the bevel toothform produces a very bad looking curve in the
axial plane..its only once you fold that to spherical that the curve looks correct as a semi-evolute..

Art

[ArtF]

Damo:

Just found this out there..

>>While gear manufacturing is well developed, with precision gears cut under
tight tolerances and producing smooth motions, the geometry of gear meshing
is not yet fully exploited in the industry. For example, bevel gears are
still designed using Tredgold?s approximation, under which the tooth profile
is designed so as to yield a projection onto the tangent plane of the back cone
that matches the profile of an equivalent involute spur gear.

  This IS what Im doing. The tooth form IS created to be correct as a typical spur when viewed from the
tangent plane on the back face..

  This link explains how to make the correct  (if thats the correct word) method..
http://www.geometrie.tuwien.ac.at/stach ... g_Proc.pdf


  As you can see, its not something Ill jump into lightly.

Art