Working out diametrical pitch of a rack

[cooper1203]

Hi all, as i said in a previous post someone has shortened and moved the rack on my lathe. I am still having issues with the carriage movement and can only think of two reasons why.

1) the rack is in the wrong place (this seems unlikely to me because it moves about half way sweet as a nut)
2) mr bodge and bugger it has got some random rack from some where and hacked a bit off.

Hence i need to know the diametrical pitch to make sure that bit is right .

am i right in thinking that a rack is basically a round gear that has been straightened out ie if the length of the rack is 35" then the diameter of the "gear" would be 35/Pi. From there the dp can be worked out by the number of teeth on the rack + 2 divided by the diameter?

many thanks

 

[dbb-the-bruce]

Slightly tricky because a rack has an infinite diameter and DP is usually calculated as number of teeth divided by pitch diameter - both of which are infinite for a rack.

From "Gears and gear cutting - workshop practice series 17" Ivan Law (I strongly recommend the book if you are getting into gears)

Circular Pitch = 2 * T (thickness of tooth on root line, which is illustrated as simply the tooth spacing on a rack - distance between the same point on 2 teeth)

and diametrical pitch can be expressed as:

DP = pi / CP

So your answer is pi divided by twice the tooth spacing.

 

[cooper1203]

thanks ill try that ....i was getting some funky answers with my method

 

[RJSakowski]

Wikipedia has an extensive work on gears. Scroll down to the nomenclature section for all the involved math. https://en.wikipedia.org/wiki/Gear

 

[benmychree]

Machinery's Handbook is my go to for gear work.

 

[dbb-the-bruce]

I got that description partially wrong. Didn't look hard enough at the illustration this morning when I was in a hury.

Circular pitch is simply the measured tooth spacing for the case of a rack. The CP = 2 * T comes from measuring the thickness of a tooth at the pitch line which is the middle of the tooth. For a rack, the teeth and valley profiles are the same, the valley is just inverted. So CP is twice that measurement. DP is still pi / CP (tooth spacing).

The way to think of it is a rack is just a gear with an infinite diameter. Most texts fail to explain it that way. The involute tooth shape on gear teeth is what you get when you "bend" trapezoidal teeth around a circle.

I really do recommend the book above as the author does an excellent job developing the concepts in a way that truly explains it rather than most "handbooks" that simply state formulas for lines drawn on a diagram without explaining how the lines got there and what them mean.

 

[cathead]

I like John York's thinking. There are pictorials in actual size in the handbook that one can use for comparison
purposes.

 

[brino]

another thought...... How about checking the gear that mates with the rack as well.

If your lathe has been modified it might be that gear has been replaced.

Brian

 

[Weldingrod1]

Don't forget pressure angle! With a rack it's any easy measurement... 14.5 degrees is the old school number.

Sent from my SM-S911U using Tapatalk

 

[cooper1203]

@ Brino i will do as far as dp etc

@ weldingrod would pressure angle have anything to do with it jamming halfway down