Kirk Wallace wrote: > On Sat, 2009-05-09 at 15:07 -0400, John Kasunich wrote: > >> Kirk Wallace wrote: >> > ... snip > >> I assumed the rack >> >>> base and top are horizontally midway between the rack center line and >>> the 20 degree peaks, such that the X length of the rise, flats and falls >>> are equal. Here is my rack and pitch circle: >>> >> I think that assumption might not be valid. I believe the height above >> the pitch line, and the depth below the pitch line have names - addendum >> and dedendum IIRC, and they are not necessarily equal to each other. In >> particular, for a pinion with a small tooth count like yours, the >> dedendum is made less to avoid undercutting the teeth - the undercut >> shows up in your last image. That would result in weak teeth if the >> gear was heavily stressed. >> > > A thought I had on this, is that for different gears of the same pitch > to work together they need to have the same base rack form. Since a gear > and it's mate can be derived from the top or bottom of the base rack > form, the base form should be symmetrical. A non-symmetrical base form > could be used, but I think the gear pair will only work with its > original mate. Actually, the more I think, the rack base and top lines > don't even count, because the mesh zone is well within these limits. I > could do the derivation again with a sawtooth instead of a trapezoidal > form. I suspect the way to adjust the addendum/dedendum is with pressure > angle, but this is just a hunch at this point. I think I have enough to > make what I need, so I'm not sure how far I'll get on this issue. Some > engineers have made a life on these matters, I've only got spare time. > > >>> http://www.wallacecompany.com/machine_shop/gears/rack_and_pitch_circle.png >>> (Short URL) http://alturl.com/7t8a >>> >>> The first pinion tooth form guess is the complementary shape of the rack >>> > ... snip > >>> The problem is, have I made any mistakes? Is there a better, easier way? >>> >> I think your derivation of the shape is correct. There is probably a >> mathematically purer way (one that doesn't involve small increments of >> motion that you then blend into the form). But I like your way better. >> > > Wikipedia covers the involute equations, but I suspect the mesh points > are not on obvious function points. > > >> Note that what you did on paper is what happens in metal when you hob a >> gear. Imagine that your rack is actually one side of an acme threaded >> > ... snip > > My one real CNC employer had an old gear hob machine. The problem was it > was easy to stand and watch it, right through your break. Another > problem was that when the guy that runs it retires, the machine gets > scrapped. > > >> The other approach is to buy a gear cutter with the proper form. Note >> that unlike a hob (which can be used to cut gears with any number of >> teeth), a gear cutter is designed for a specific range of teeth. I >> think there is usually a set of 8 to cut everything from 12 tooth >> pinions thru many tooth gears up to a rack (basically a gear with an >> infinite number of teeth). >> > > Gear cutting tools are too expensive for me since I usually need one or > a few of each. Having a way to make any gear without special tooling > would be a big plus. One reason I am looking at a 2m - 10mm gear is that > I can use a .063" end mill to cut a thin version. > It has been my understanding that the number eight cutter will cut a gear with 12 and 13 teeth. If you get below 12 teeth there has to be undercutting for the teeth to run right without chafing against each other. I would think that a 10 tooth gear would need to be generated with a hob or a gear shaper. There was some information on the South Bend lathe list where a fellow claimed that a perfect generated tooth for can be cut by useing a tap running on the perifery of a gear blank and feeding across the face. The blank is left to freewheel and be pulled around by the tap. He claims it makes a perfect tooth??? Doug
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