# Re: accuracy of ratio

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Posted by Bill S on May 12, 2002 at 18:13:29:

In Reply to: accuracy of ratio posted by steve green on May 05, 2002 at 23:59:12:

Hi Steve,
Just as Dan points out, The index should exactly match the hobber's index formula (usually given as
[Mconst x Hob Starts]/Teeth)
to cut 0 degree lead angle (except for whatever misalignment is between workpiece axis and table travel direction, as Micheal observes). To ideally get 0 degree lead, the workpiece rotation must be exactly synchronized with cutter rotation.
But imagine that the index ratio deviates by a very small amount, as it did in your example. Imagine also that the hob runs for a long time without table feed engaged, and with the cutter running "in mesh" with the workpiece. Eventually all the teeth would progressively be cut away. Why? Because the cutter will be displaced slightly but continously in a direction normal to the teeth of the workpiece for as long as the machine runs. Of course, the cutter isn't actually moving at all, but because the workpiece rotates slightly faster (or slower) than it should to stay meshed with the cutter, the effect is as though the cutter were shifting along its axis. Again, this small displacement between cutter and workpiece is not a machine motion like table feed or hob shift. It is a relative motion between the cutter and the workpiece in a direction perpendicular to the teeth.
Now let's suppose that the table feed is engaged and the cutter moves through the workpiece. In cutting the gear, feed motion combines with slight but continuous displacements of the cutter normal to the gear teeth to create a lead angle. This is how a helix angle is cut when using a hobber without a differential. The rate of feed is calculated based on the intentional index ratio "error" and precisely controlled by feed change gears to produce the desired helix angle.
OK, I got off the subject somewhere back there ;^)
I think you were maybe trying to cut a prime gear without using the equivalent prime change gear. The FAQ page describes some ways to do that, but cutting an "almost" spur prime change gear using an approximate ratio is good. It's probably the only way possible on a non-differential hobber.
Cut the gear with as high a table feed rate as practical for the material, etc. You can't eliminate the lead error completely, but the highest table feed will produce the smallest lead error.
Hope this helps

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