In order to verify
that the calculations are correct you will need the circular
pitch. You can use the "Gear calculations" in ShopCalc
to find this or use the following formula that use Pi in
the form of the approximate fraction of 22 / 7:
This means you will need at least 1 gear with teeth that are
multiples of 11 (33, 44, 55, 66, 88).
For metric
module.
circular pitch (in millimetres) = metric module x Pi
eg For 1.25 metric module 1.25 x 3.1416 = 3.927 mm
For diametrical
pitch.
circular pitch (in inches) = Pi / Diametrical pitch
eg for 20 diametrical pitch = 3.1416 / 20 =
0.1571 inches
The metric module formula
metric module 22 ---------------- x -- lead screw pitch 7
eg | 1.25 22 ---- x -- 3 7 |
The decimal 1.25 must be changed to a whole number, in this case multiply by 4. |
Now we have | 5 22 110 55 -- x -- = --- = -- 12 7 84 42 |
Lets prove the calculations by
circular pitch = 3 {pitch of lead screw} x 55 / 42 = 3.929 mm
Diametrical pitch formula
lead screw TPI 22 ----------------- x -- diametrical pitch 7
eg | 8 22 176 44 -- x -- = --- = -- 20 7 140 35 |
Lets prove the calculations by
circular pitch = 0.125 {pitch of lead screw} x 44 / 35 = 0.1571 inches
If you have a metric
lathe and need to make a diametrical pitch worm or an imperial
lathe and need to cut a metric module worm you will have to
incorporate the transposition gears in you change gear drive
train.
If you have a quick change (Norton) gear box on your lathe you
can also set the gear box to cut other pitches and effectively
change the pitch of your lead screw giving several combinations
for one set of gears. Setting the to cut 16 tpi then
the example gears would make 40 diametrical pitch and setting the
lead screw to cut 4 tpi we would get 10 diametrical pitch.
Unfortunately changing the pitch the lead screw is set to cut
does not work out so well with metric module.