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Author Topic: Machining Bevels.  (Read 56391 times)
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Damo
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« Reply #105 on: December 10, 2013, 12:36:29 AM »

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

http://books.google.com.au/books?id=wZpaPKcQZxAC&pg=PT697&lpg=PT697&dq=octoidal+vs+involute&source=bl&ots=eN-tM7kbAd&sig=1eRWxY8froShIFqViarBfY6NmHQ&hl=en&sa=X&ei=haOmUuL4E4WfkAXKk4CoCw&ved=0CGUQ6AEwCTgK#v=onepage&q=octoidal%20vs%20involute&f=false
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ArtF
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« Reply #106 on: December 10, 2013, 08:37:21 AM »

Damo:

  Heres a photo of an octoidal generatio n. 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 manifista tion 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 spherical ly now a proper octoid? I highly suspect the answer to this is yes. If we consider just the infinitel y 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 modificat ion into that tooth. I would submit its the same process as folding the rack and then generatig n 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 considera tion, 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
 



* octoidalgenerator.jpg (378.68 KB, 904x1259 - viewed 501 times.)
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Damo
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« Reply #107 on: December 10, 2013, 03:30:48 PM »

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 microscop ically where the tooth flank is, so so miniscule ly, it's slightly "s" shaped. Would be nice to prove it mathemati cally. And remember this is just the crown gear, not yet bent around a smaller gear. What'd you think?
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Damo
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« Reply #108 on: December 10, 2013, 03:53:34 PM »

I think all the calculati ons 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. :-)
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ArtF
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« Reply #109 on: December 10, 2013, 03:59:51 PM »

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..th e entire issue will be the cutter shape.. so we'll see.. Smiley

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

Art
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Damo
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« Reply #110 on: December 10, 2013, 08:28:52 PM »

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 circumfer ence and 2 opposite tooth flanks are on the surface.
Cheers Damo

Not sure if this will work, am attaching 2 images


* octoid-1.jpg (40.04 KB, 1176x881 - viewed 389 times.)

* octoid-2.jpg (30.21 KB, 1176x881 - viewed 413 times.)
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ArtF
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« Reply #111 on: December 10, 2013, 08:59:26 PM »

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 interesti ng to note that the specifica tion for the calculati on of the bevel toothform produces a very bad looking curve in the
axial plane..it s only once you fold that to spherical that the curve looks correct as a semi-evolute..

Art
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ArtF
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« Reply #112 on: December 10, 2013, 09:08:49 PM »

Damo:

 Just found this out there..

>>While gear manufactu ring is well developed, with precision gears cut under
tight tolerance s 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 approxima tion, under which the tooth profile
is designed so as to yield a projectio n onto the tangent plane of the back cone
that matches the profile of an equivalen t 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/stachel/Duisburg_Proc.pdf

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

Art
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Damo
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« Reply #113 on: December 12, 2013, 02:11:48 AM »

Out of those 5 theorems, they lost me at the first.  Cheesy
Cheers Damo

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Damo
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« Reply #114 on: December 12, 2013, 03:13:21 AM »

Actually, i'm just happy i understan d the word "octoid" now.
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ArtF
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« Reply #115 on: December 12, 2013, 07:41:25 AM »

Words just dont work..do they. Smiley

Art
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John S
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« Reply #116 on: December 26, 2013, 12:46:28 PM »

Yes but will it cook the turkey on Gas MK 5 ?
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John S.
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CMcDaniel
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« Reply #117 on: February 24, 2015, 10:17:10 AM »

Hey Art, Anything new with the bevels or are You busy working on other things?
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ArtF
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« Reply #118 on: February 24, 2015, 02:26:25 PM »

Hi:

  Bevels will be dealt with in a waterline engraving module, but probably not till next fall.

Art
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Chuck
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« Reply #119 on: May 09, 2015, 10:34:57 PM »

Art,

Here is another paper on spiral bevel gear generatio n and inspectio n.

http://gear-net.com/report/rep-03.html

Also Klingelnb erg method is in a spread sheet with macros that create tooth form for Solid Works IGES inport.

https://www.youtube.com/watch?v=k-WdPTxinZk

Chuck in Wyoming

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