Re: general gear enquiry

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Posted by Dan O on October 11, 2000 at 15:16:00:

In Reply to: general gear enquiry posted by Carey Hablous on October 09, 2000 at 17:12:28:

Using normal involute mathematics in order to mesh both members must share the
normal base pitch. Normal base pitch is calculated as the normal circular pitch
(pi/normal diametral pitch) times the cosine of the pressure angle. Because the
cone must have a constant number of teeth, the diametral pitch must change
(ratio of number of teeth to pitch diameter) as you traverse it. In order to keep
the same base pitch therefore you must have a pressure angle that varies as
one moves along it. The cosine of a 14.5 degree pressure angle is .9961, while
the cosine of a 30 degree pressure angle is .8660. The 30 degree pressure angle
is not very suitable for a rolling application, while only a 87% variation in diametral
pitch is available even by varying from 14.5 degrees to 30 degrees. This may only
say that the traditional involute mathematics of typical gearing might not be the
correct shape for this. I wouldn't want to discourage thought about this, but in order
to have smooth and continuous meshing using the involute curve we must satisfy
some common basic principles, such as sharing a common normal to the base
diameters, and such. As the gear reduction from high to low of a typical transmission
is many times more than this 87%, we have obvious problems. The solution
may be a good one, though not using the involute and hard gearing. I might not
even have identified the most serious flaw in the reasoning, though to be more
optimistic perhaps a new meshing process can be found to do this...

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