- Joined
- Feb 1, 2015
- Messages
- 9,645
Circular pitch, p, of a gear is the distance between teeth along the pitch diameter and is related to the diametral pitch by p = π/d.p. Circular pitch of a gear is the equivalent of lead or pitch in screw threads.
Diametral pitch is limited to whole numbers, and since the circular pitch, which is what would be of interest when cutting a worm gear, is π divided by a whole number, the change gear ratio must necessarily be an irrational number. Gears by their very nature must have rational numbers which means that to cut worm gears on lathe with a conventional lead screw, an approximation must be used for the gear train.
Looking at my chart of all possible threads that can be cut on a Grizzly G0602, it appears that there are a number of diametral pitch worm gears that could be cut to better than .1% accuracy using the stock change gears. If I add the 127 tooth transposing gear to the list, I would expect that a number of others would pop up.
Diametral pitch is limited to whole numbers, and since the circular pitch, which is what would be of interest when cutting a worm gear, is π divided by a whole number, the change gear ratio must necessarily be an irrational number. Gears by their very nature must have rational numbers which means that to cut worm gears on lathe with a conventional lead screw, an approximation must be used for the gear train.
Looking at my chart of all possible threads that can be cut on a Grizzly G0602, it appears that there are a number of diametral pitch worm gears that could be cut to better than .1% accuracy using the stock change gears. If I add the 127 tooth transposing gear to the list, I would expect that a number of others would pop up.