Calculating corrected center distance

[gearcutter]

Would anyone be willing to let me know if below is correct/incorrect? It's based on my understanding of the subject.
Operating P.C.D.s can only be used to calculate center distance for spurs and helicals if the amount of correction given to one member is equally inverse to the amount given to the other, eg. +0.50 and -0.50. If the corrections are not equally inverse to each other then centers can only be calculated from tooth thicknesses based on the difference between the "no longer equal" operating pressure angles.

 

[EnglishMuffin]

Philrock :

Changing the CD does not change the profile shift of either gear if you have already defined them. The profile shift of a gear can be defined and measured quite independently of any center distance you intend to use. In addition, when measuring a gear, you cannot distinguish between the amount of basic rack infeed introduced to provide backlash and the design amount of the profile shift, unless you happen to know what either of them were intended to be in advance. And you might, for example, have a first gear that meshes with one or more other gears. I hope you are not suggesting that whatever you might do with the other gears would alter the design properties of the first gear.

 

[hablew]

EnglishMuffin,

Your 07Feb 06 10:34 posting has a simple mistake;

You posted
(x1+x2)/zm = (inv(alpha)-inv(alpha'))/tan(alpha)

I think that needs to be
(x1+x2)/zm = (inv(alpha')-inv(alpha))/tan(alpha)

Otherwise everything looked good.

I've been struggling through this issue on a set of gears and found this posting very helpful - you guys really know your stuff. I've learned a lot.

Where I'm now stuck is applying backlash to a gear set. Most Hobs are only a 2.157/Diametral Pitch deep thus if you make an enlarged gear you still can only cut it so deep. IE the middle of the tooth profile doesn't occur at the theoretical pitch diameter anymore.

This whole exercise (Enlarged pinions/smaller gears) is an effort to lower slip ratios which essentially lowers the sliding velocity at the pinion root. Sliding velocities are bad from what I've recently read (Drago).

 

[diamondjim]

Enlarged pinions are generally designed to avoid
undercutting as well as strengthen the teeth
and to balance the strengths of the two members.

Center distance changes are a sin function
while the tan function is used to calculate
the change in tooth thickness.

If gears are cut with 20 degree pressure tools,
the pressure line at the theoretical pitch line
remains constant at 20 degrees although the tooth
thickness varies as the cutter is sunk deeper
into the part.

Gears do not have operating pressure angles
until they are assembled together at a defined
center distance.

What makes things even more confusing is the
fact that some use the term corrected pitch
line or corrected pressure angle. The corrected
pitch line is the pitchline of the part where
the tooth thickness equals the tooth space.
Just to add a little fun to this serious topic.