Fellows Stub Tooth, 9 teeth on a 10 tooth blank? Help.. 1

If I understand you the gear is has 9 teeth but the actual pitch diameter is as the theoretical pitch diameter of 10 teeth. It seems that the designer used a profile shift (tooth correction) to reduce undercut. The amount of correction is such that the actual pitch diamter is 1.25.

For gear transmission rate calculations you need to use the number 9. For center distance calculations you need to use the pitch diameter of 1.25.

One more reason for tooth correction is to make the teeth stronger and maybe to reduce specific sliding.

When you cut 9 teeth in a 10 tooth blank, it usually means that you are using an enlarged od pinion to run with a reduced od gear on standard centers. It reduces the amount of undercut in the pinion and makes for a stronger tooth. This is usually done when you have a small number of teeth in the pinion and a large number of teeth in the gear. You calculate the od for 10 teeth but you only cut 9. Since you have a print, you cut the teeth to the size on the drawing. If you don't have a print, it becomes a lot more challenging

There are two questions in your proposed case.

1) The meaning of Fellows stub – tooth system

For example for DP 8/10:

a- use DP 8 for pitch diameter calculation

d = N / DP = 9 / 8 = 1.125 "

b- use DP 10 for addendum and dedendum calculation

addendum = a = 1 / DP = 1 / 10 = 0.1”

dedendum = 1,25 / DP = 1.25 / 10 = 0.125”

The above values are the same as DP 8 stub – tooth gear with 0.8 / DP addendum (addendum = 0.8 / 8 = 0.1” )
and 1 / DP dedendum ( dedendum = 1 / 8 = 0.125”).

2) The meaning of the use of 10 teeth blank for 9 teeth gear, for example.

This is an old and bad way of specification for one Profile Shift gear.

The pitch diameter for DP 8 gear with 10 teeth is

d = N / DP = 10 / 8 = 1.250”

The pitch diameter for DP 8 gear with 9 teeth is

d = N / DP = 9 / 8 = 1.125”

Profile shift = (1.250 – 1.125) / 2 = 0.125” / 2 = 0.0625 = x / DP

x = 0.0625 (DP) = 0.0625 (8) = 0.5

3) Conclusion:

The stub - gear mentioned will be better and clearer specified as:

DP = 8; N = 9; x = 0.5; addendum = 0.8 / DP and dedendum = 1 / DP