Gearwheels shouldn't have any
secret for a modeller. The standardized way to gear design is by
using the modulo principle of gearwheels. You probably know that
circles have a relation with a number called Pi. This not
different for gearwheels. But for gearwheels someone (who
probably did not like Pi either) thought up an elegant method for
working with gearwheels. The Modulo M of a gear is the ratio of
the pitch(distance between two teeth) to Pi. So for a M = 1 wheel
the pitch is Pi = 3.14 and for M = 0.5 the pitch is 1.57. Now you
normally never calculate the pitch of gearwheel so this is no
problem, you may forget this. For work in our scale M has nice
round values of 0.2, 0.3 or 0.4 with of course an exception for
Englishmen. In using gearwheels there are two important
dimensions both are diameters. That is the overall diameter which
you need to see if a gearwheel fits in a certain space and the
effective working diameter which you need to calculate axle
distances between gearwheels. The working diameter is the
diameter at half height of the teeth. As the height of the teeth
is a constant these two are linked. In fact gearwheels can be
regarded as developed from cylinders rolling off against each
other with teeth introduced to prevent any slip between the two.
The diameter ratios giving the gear ratio. So let:
N = the number of teeth Do = Overall diameter Dw = Working diameter M = Modulo
then Dw = N * M and Do = (N+2) * M
See how elegant this is with round numbers there is no need for a calculator!
The distance Ad between two gearwheels 1 and 2 is:
Ad = ( Dw1 + Dw2 )/2 =( N1 + N2 ) * M / 2
We sometimes have use for the axle distance between worm and wormwheel:
Aww = Do worm /2 + (N-2)/2 * M
That's all there is to gearwheels for using them in practice. Note however that the above formula for the axle distance is the ideal distance. If your gearwheels don't have a central axle hole or are a bit oval, you will end up with a bind. So when designing a new gear put in a few hundredths of a mm extra for non ideal dimensions.
Now there is only one thing left
and that is the English DP value. As it is of English origin you
will not be surprised that there is a connection with another
awkward number (to be extinguished) namely 1 DP = 1" = 25.4
mm. This means that a100 DP gear seems to be near equal to M=0.25
and 64 DP gear is about M=0.4.
author: Henk Oversloot
date: 15 February 1999
originally published in the 2 MM Magazine august 1995