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...