Episode #27: How Does Abbe Error Effect the Straightness and Flatness Performance?

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The Motion Control Show

Back in Episode 4, I talked about several different types of precision and the terms related that we need to know about when discussing linear mechanics.  Since then, I've been asked to expand upon and clarify a bit on the Abbe Error and how it effects the flatness and straightness.  I'm Corey Foster at Valin Corporation.  Let's see what we can learn.

So as a reminder, we don't measure the spot of where your application is when measuring the accuracy and precision of the stages.  We have to assume where that is.  You could be using a piece of paper or a piece of sheet metal or something right on top of it so it's really thin, but most applications have some load an inch or two above the carriage.  The manufacturers have to assume where that's going to be.  Out of practice they just assume maybe an inch, 25 millimeters probably, right above the carriage.  That's called the point of measurement as shown here.

Well, what's the Abbe error?  The Abbe error is the angle that can be caused by the motion of that carriage as it moves down the rails.  It could be roll error.  It could be pitch error.  It could even be yaw error.  But each one of those will cause an angular error of that point of measurement that's an inch over the carriage.  So as the angle changes, we get this linear error that is caused by that change in the angle.  Well, how do you calculate that?  If you measure the linear error then you can calculate the angle, but let's say we know the angle and we know the distance because we have defined that.  It is trigonometry at that point: distance times the tangent of the angle.  If the D is one inch like I said, we assume that, if it's 0.1 degree, times the tangent, times that one inch, that linear error is .0017 inches.  That's not very big.  Let's say we multiply that by 10 and it's one degree of angular error.  I've grossly exaggerated this, of course, but you can see how that error changes.  The tangent of that times the one inch is only .017 inches.  Again, not very big.  But in millimeters, that's almost half a millimeter, 0.43 millimeters.  If you're trying to position down to the micron level, 0.43 millimeters, 430 microns, that's huge!  And that is a huge error that has to be accounted for.  So again, as it's going down the track, you can see the straightness, it's going to wobble like this.  The flatness, it's going to wobble this way, and even in the yaw it's going to wobble back and forth this way.  Each one of those at that inch above the carriage is going to make that wobble around in different directions, and that's definitely going to create problems for the precision if you're needing a high precision stage.

I'm Corey Foster at Valin Corporation, I hope this helps.

If you have any questions or are just looking for some help, we're happy to discuss your application with you.  Reach out to us at (855) 737-4716 or fill out our online form.