Posted by BillS on July 09, 2009 at 13:04:56:
In Reply to: Re: Free Span Measurement Calculator posted by bill bamber on December 30, 2007 at 02:17:04:
Changing the OD doesn't change location of either base circle or pitch circle. Remember that base circle defines the originating point and amount of curvature of each involute curve.
The OD and root diameters are simply physical boundaries drawn across involute curves. Involute curves are "drawn" by the end of a string that unwinds from the imaginary base circle.
ODs are commonly changed for pinions to avoid undercut. Back in the good ole days, it was a good rule of thumb to figure an enlarged OD by adding a tooth to the OD calculation, but there was nothing magic about enlarging an OD this way. A more modern system that is used commonly today determines OD enlargement according to the gear to pinion ratio. In other words, the OD enlargement diminishes as the gear/pinion ratio gets smaller. Check out the Machininst handbook for "Pinion, enlarged addendums". The point to make here is that changing the OD doesn't change the pitch circle diameter. As a consequence, only the addendum (part of tooth above the pitch circle) and the dedendum (part of tooth below the pitch circle) change.
So, a span measurement shouldn't be affected by a change in OD - That's why it is an acceptable way to check for proper cutting depth, for much the same reason as using an over pin measurement. Certainly a reliable comparison when matching to a sample.
Span measurement is theoretically true when generating involute teeth using a rack form (i.e. hobbing),
but is slightly less so when shaping. Even less true when cutting teeth on an indexing mechanism where the cutter
is ground involute to cover a range of number of teeth.
But that's another story for another time...