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Is the diametral pitch of a worm gear determined the same way as that of a spur gear, or is the determining factor the pitch of the worm, being derived the same way as a screw thread?
Thanks.
The D.P. of the gear is the same as the worm. The tooth profile on the gear is concave with the center lower (i.e. closer to the hub) than the perimeter, since it must mate with the worm.
The pitch of the worm is determined from the lead at the pitch line, just like a rack.
Here's a set of formulae from page 150 of the Boston Gear catalog:
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Leigh W3NLB
[This message has been edited by Leigh (edited 01-13-2006).]
[This message has been edited by Leigh (edited 01-13-2006).]
Leigh
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Apologies to anyone who read my original response and got confused. I use CP only rarely and got it mixed up. That fact came to me over a plate of Sweet & Sour Chicken and I hastened back to correct it. Sorry, but it should be correct now. Corrected post follows:
Worms are measured in the same way as any other gear. In the English world, gear pitches are specified either in diametral pitch (DP) or circular pitch (CP). But, it is far more common to use DP. The reason for this is to simplify the math by eliminating the use of Pi in most equations. Note the difference in the Boston Gear equations up above for Pitch Diameter. The equation that uses DP is simpler, while the one that uses CP contains the constant Pi. Please note that I did specify "English" above. Metric gear specs are in Module and work somewhat differently.
However, when you are going to cut a worm gear on the lathe, you will probably be working in terms of TPI or CP. If you have a spec in terms of CP then, that is just the reciporical of the TPI figure to use. TPI = 1/CP That's easy.
But in the far more common case, you will have a DP spec and will need to convert it to CP or TPI. TPI = 1/CP = 3.1416/DP.
As to which way it is "determined", that depends on the intended use and any gear can be looked apon in either manner or in both. As I said, most gears are specified in terms of DP because the math is simpler. And that is really the determining factor for choosing one way or the other; which way has the simplest math.
DP is most common, but there may be a reason for using CP. For instance, the rack and pinion in most dial style calipers are based on a rack that has 40 TPI. So the CP is 1/40" or 0.025" and the DP is Pi*40 or 125.664. But this is not a pitch that I would expect Boston Gear to stock. If you want a stock gear, better think in terms of DP.
But then if you are rolling your own and want the TPI on the lathe to be an even number for cutting the worm, then specifing an even number CP will be best. Any even number DP will not work out even on the lathe gearing due to that pesky Pi factor. Note that Pi is an irrational number so no gear ratio can ever be exact. So if I were going to make both the worm and a hob for cutting the worm wheel on my lathe, I would try to choose an even number CP. But this choice is simply up to the engineer/designer.
Paul A.
[This message has been edited by Paul Alciatore (edited 01-13-2006).]
Paul A.
SE Texas
And if you look REAL close at an analog signal,
You will find that it has discrete steps.
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