Posted by BillS on April 17, 2007 at 15:02:12:
In Reply to: Re: How Do I Make A Pinion gear for lathe chuck posted by Bob Nisbet on April 16, 2007 at 16:13:58:
I thought the way you found 11T for the pinion was clever!
I'm still skeptical about cutting the teeth without allowing for a true angle between teeth (Tooth Angle, or angle between adjacent teeth, is usually 1-3 degrees). I'm not sure if I understand cutting in steps and regrinding the cutter, but I'm keeping an open mind.
A number of people have asked the same basic question about doin' bevels on a milling machine, so I thought I'd take a wack at it! Trying to describe the process turned out to be longer than expected, but here is my "long-winded" attempt.
A bevel gear machine uses two flat-sided cutters, each with a tip no larger than the small-end tooth space. Two cutters are used to form each tooth one at a time, through a series of reciprocating shaper-like strokes. You could say that the space between cutting edges of both tools form a diminishing rack form. The cutting edges are on a collision course just beyond the small end, and would surely collide except they alternate in their stroke. Each cutter operates in adjacent tooth spaces, thus surrounding each tooth.
At each cutter stroke, the pinion rolls a small amount about its axis, and the axis swings above (and below) the imaginary point where pinion and gear axes intersect.
The cutter profile is flat yet angled on one side for pressure angle to represent 1/2 of a rack form. The incremental movements of roll and swing occurring between each cutter stroke are small but they accumulate over a wider range of roll and swing angles, so the "generated" tooth surfaces take the classic involute curve of conjugate gearing. When a tooth is complete, the blank witdraws from the cutters and indexes to position for the next tooth.
There's nothing that says you have to use two cutters. It's important only if you want to consistently control tooth dimensions in a productive way :^).
I think the real challenge for a milling machine approach is to approximate the roll and swing movements for each cut, and to duplicate these motions for each tooth flank. That would be 22 flanks, and maybe 5-10 roll/swing positions/passes per flank?
One rotary milling tool could be used in a well controlled setup. It would have one cutting side ground at a 20 deg angle to the cutter face, long enough to go full depth of cut, and the other side left flat faced. The point width of the cutter would be as small as the tooth space at the small (toe) end of the pinion.
The jig/fixture needs to be able to pivot about +/-15 degrees or so about a point out in front of the pinion and then be locked in that position. The point of pivot should be located where the larger gear's axis would hit the table if the gear were meshed with the pinion. This needs to be fairly accurately located. Don't use a bolt, but a pin to locate this pivot position. The distance is very close to half the diameter of the large gear, and should be measured from the pinion's heel (large end).
Now to the process as I see it.
You will need the pinion's Tooth Angle, and I can calculate it for you if you send me the number of teeth in the large gear. I'll assume 11T for the pinion.
Pivot 1/2 the Tooth Angle from the table axis. This moves the tooth line off of the table axis. Now move the table cross feed by an amount equal to cutter point width to compensate for the point width of the cutter. Turn the cutter around, swing the jig 1/2 Tooth Angle to the other side of table axis and reverse the cross feed offset to compensate for tool point width. Conventional mill from the other direction, and take 11 cuts.
Looking at the pinion tooth profile it should have a rack form. Looking from the side, there should be tooth taper with teeth separated by the Tooth Angle. The width at root should be very close to that of the large gear.
Next comes the "generating motion" part.
Pivot the jig to about 15 degrees in the same direction from table travel. Now comes the tricky part - Unlock the 44T gear so that you can rotate or "roll" the pinion slightly with respect to your index mechanism. Don't move anything else.
Bring the cutter to the small end of the pinion. Notice the pinion space doesn't align with the cutter any more. Roll the pinion so the small-end tooth space lines up with the cutter. You have to "eye-ball" this, since the cutter will interfere with the blank and not pass into the tooth space. Put your index mechanism at the new location and lock it for a cut. Raise the cutter slightly and take a trial cut. You should only be touching/tapering the top tooth edge. If it "looks right" (it will take more off at the heel than the toe) then take the cutter back down to its reference depth. It should still be taking a small tapering cut along the full tooth. Don't worry if the cutter "nicks" the opposing flank - there is stock to be removed from it later. Remember, you're only concerned with one flank on each tooth. Index and do each tooth with this setting.
Next, pivot the jig back toward the table axis, say to about 10 degrees. Repeat the same steps above, unlocking the index, rotate the pinion, relock the index to align the cutter close to the tooth space. Take a trial cut. This time, the cut should be small and about half-way down the tooth, neither touching the top land or the bottom root. Index and cut all the teeth in this new position. You should begin to imagine the approximate curvature in the tooth profile.
Turn the cutter around on the arbor and approach from the other end ot the work (to conventional mill again). and cut the opposing flanks. Shift out 15 deg, then 10 deg taking finishing cuts at each new "roll" position of the pinion.
That's how I would imagine doing it on a milling machine. Not an easy process!
Sounds like you want to "form" the involute curve and approximate the Tooth angle in a step wise way. Let us know how it works out.
Remember, every line of each surface should converge at the point where gear and pinion axes intersect. The exception is the tooth root surface. Root surface lines converge at a point on the pinion axis just before reaching the gear axis. This is due to an amount of clearance that is normally added to the tooth space's working depth. But for your project, this would be a small consideration.
If you followed this to the bitter end, you can see the challenge. For those who wonder why anyone would go to the bother, well - good question! But here it is for the MacGiver in all of us...
I hope others will jump in with their 2 cents!
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