Calculating pitch diameter from measurement over pins 1

[markarnold]

I am reviewing specifications of an older pinion gear design where changes to the specifications were not complete. The measurement over pins was changed to modify the backlash between the pinion and its mating rack. My problem is I need to update the amount of rack movement for a given rotation of the pinion gear. Of course, I then need to know the updated pitch diameter. There are five sizes of gears of which I need to determine the pitch diameter. I have not found a way to translate the measurement over pins into the pitch diameter. The gears are 20° pressure angle spur gears. Any help is appreciated.

 

[diamondjim]

If you have an modified pinion
or a standard pinion the rack
would move the same distance
for either one. It is a function
of the number of teeth in the
pinion and the angle of rotation.
ie if the pinion had 10 teeth,
the rack would move 10 rack teeth
forward regardless of the profile
shift.

 

[markarnold]

diamondjim, then I need to verify the tooth pitch on the rack to determine how much linear movement each tooth on the rack translates to.

 

[diamondjim]

The tooth to tooth spacing on the
rack is simply pi divided by the
diametral pitch
or pi times the module.

So each pinion would move the rack
by one space if 360/n degrees of
rotation takes place on the pinion.
n is the number of teeth

 

[markarnold]

OK, lets say I have a pinion gear that was originally designed with 16 teeth and a pitch diameter of 1.000 inches. Then the diametral pitch=16 (number of teeth divided by the pitch diameter) Later, the pitch diameter was changed to 1.034. Would that then make the diametral pitch=15.474? The mating rack started out with a diametral pitch of 16 and an indicated pitch diameter of the pinion of 1.000. This pitch diameter was then updated to the aforementioned 1.034. Would this not require a change to the diametral pitch of the rack as well? Sorry for what seems like basic gear questions. I need to be able to translate what I'm measuring actually meets specifications as well as clarifying our specifications that we do have.

 

[diamondjim]

No the basic pitch diameter at
the 20 degree pressure remains
constant and so does the circular
pitch at that diameter.
It is true that distance to the rack
would increase but the rotation of
either the normal pinion or the
modified pinion should advance the
rack the same amount. That is the
advantage of the involute system in
also allowing profile changes that
retain same gear ratios and basic
circular pitch. It is true that
the tooth thickness and the tooth
space are not the same value for
modified tooth profiles. 10 degree
of rotation of either will produce the
same advance in the rack. I know this is
confusing. The base diameter of both
standard and modified tooth pinions
are the same.

 

[markarnold]

OK, it makes sense now. The tooth may decrease in thickness, but the actual pitch between the teeth will not change. So the ratios will remain the same. Thanks for your help!

 

[tap90291]

Anybody know of a good manufacturer for a steel rack gear 20 degree P.A. with a module of 1.5 and 2 I have some metric gearing on some equipment and people like boston go down to about 4-5.

Thanks in advance.

TAP

 

[israelkk]

THK