Rack & Pinion pitch error on cnc router

[ncprogrammer]

We are having a debate about pitch error
on a machine driven by straight tooth
rack and pinion.

If a machine is setup with a parameter to define
the pitch (distance traveled) when the machine is
new and then later, the pinion wears or has the engagement
into the rack changed--- does this change the actual
pitch (distance traveled for one revolution) ??? Hence
accumulating error as it travels further ??

Another thought was that as long as the pinion is
engaged in the rack, it will travel the same distance
per rev no matter how loosely it is engaged.

Which way is correct ???

Thanks in advance.

 

[rlincolnh]

Pitch is pitch is pitch, as long as everything stays in engagement. But (and I'm no gear expert, some specialist will surely answer here), if the teeth on the rack and on the pinion wear such that they finish up with different pressure angles on their teeth, the transverse motion along the rack will not be a direct linear function of the angular rotation of the pinion i.e. 1 degree of rotation of the pinion will not give you a transverse motion of ((1/360)*pitch) at every point during a single rotation of the pinion. There will be a cyclic non-accumulating error during each revolution of the pinion.

I would be interested to know how tooth wear manifests itself in this regard. Any experts out there?

 

[Pekelder]

rlincolnh, that is one of the effects you might encounter I guess (I'm als absolutly not an expert).
Another thing is, with a rack and pinion, you should think of it as a strip and a wheel. Because it is a rack and pinion, slip is not an option, that is good. But the diameter of the wheel is not a constant with wear. The teeth can be pushed further into the rack, defining another pitch-diameter. It will not matter much, but it might show. This is only a problem wen you change the distance between the rack and the axis of the pinion (!), but to reduce backlash, that might have been done.

Regards,

Pekelder

 

[EnglishMuffin]

In this reply I am assuming the rack has not worn (you seem to imply this). I am also assuming that these are involute teeth (virtually certain - such a rack has straight sided teeth). You refer to two different possibilities - first that the radial engagement of the pinion in the rack may have changed, and secondly that the pinion may have worn. The involute tooth form has a unique property which is such that radial displacement of the teeth in a mesh has no effect on the constant-velocity action of the teeth whatsoever, as long as they remain in engagement. Of course, there will be a significant effect on the backlash. In the case of a rack and pinion, all that will happen is that the pitch plane will move further up the rack teeth - the pitch cylinder on the pinion will remain the same. In the case of wear, on the other hand, assuming for the sake of argument that a uniform amount is worn off the pinion profile normal to its surface, then the profile would no longer strictly be a correctly generated involute, (although the pressure angle would still be the same - that is determined by the unworn rack). The pitch plane would then move in and out slightly during a tooth mesh cycle, causing a cyclic variation in velocity. The effective pitch, however, would still remain the same.