Change gear calculation

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.