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. -- Kirk Wallace http://www.wallacecompany.com/machine_shop/ http://www.wallacecompany.com/E45/index.html California, USA ------------------------------------------------------------------------------ The NEW KODAK i700 Series Scanners deliver under ANY circumstances! Your production scanning environment may not be a perfect world - but thanks to Kodak, there's a perfect scanner to get the job done! With the NEW KODAK i700 Series Scanner you'll get full speed at 300 dpi even with all image processing features enabled. http://p.sf.net/sfu/kodak-com _______________________________________________ Emc-users mailing list Emc-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/emc-users
