I think everyone assumes that basic accuracy specs are the same on every machine tool. Just about everybody’s seen laser checks, and everyone assumes that the specs are relatively universal.

If you go back in history, you can see from the 1960s to the 1990s there was significant improvement in positioning accuracy and repeatability. Accuracy has moved from about two-thousandths in the ’60s to the millionths, where we’re at today. Repeatability has happened the same way, from about a thousandth to about 40 millionths, so there have been significant advances.

But the question is, how do you really measure this? What you have to understand is that there are a number of components that have to be taken into account. These include understanding the difference between accuracy and repeatability, unidirectional versus bidirectional measurements, lost motion, deviation, mean, error band, and confidence.

For instance, if you think about the way you make most parts, you make them bidirectional; therefore, I’d be more interested in bidirectional than unidirectional. All of these things deal with the confidence you can have in the stated levels under a large percentage of the time.

For an inspection method, you can have a static, no-load accuracy derived either in a statistical or non-statistical way. With a statistical inspection method, you’d have a bi-directional or multi-pass inspection where you have a level of confidence in the accuracy, or you can have a non-statistical uni-pass inspection that doesn’t take into account the average accuracy of the machine.

I think you can quickly see how stated accuracies and repeatability, without some description of how they were derived, really can have very little meaning. When you put these numbers in a spreadsheet, they really don’t tell you what the machine tool will do, unless you really understand what those numbers are.

Accuracy vs. Repeatability
In order to understand those numbers, let’s talk a little about accuracy and repeatability. If you take two targets with holes in them, where all shots hit within the bull’s-eye are scattered with varying spaces between the holes, what you have is accuracy without repeatability. This is due to the individual scatter of each shot.

If you take a second bull’s-eye, and a cluster of close shots is just below the bull’s-eye, what you have is good repeatability. In other words, you don’t have good accuracy but you have very little variation between shots, and therefore a repeatable situation.

If you’re going to buy a machine tool, you can fix a targeting error, or move the target to the center, and then have both accuracy and repeatability. So that makes repeatability important, not just accuracy.

Something else that must be kept in mind is lost motion. Let’s now imagine that the target is moving, as parts do when machining. Often a bias is found to the left as you’re moving toward the target and to the right as you’re moving away. In other words, it’s inaccurate as the part moves. This makes it especially important to have a bi-directional measurement, because such a measurement can take into account movement of the part much more effectively than a unidirectional measurement.

The next thing we want to talk about is confidence level. When you start talking about statistical analysis, it usually boils down to a bell-shaped curve, with the bulk of measurements plus or minus 1 sigma. By the time you get to +/- 3 sigma, you’ll have three measurements out of 1,000 that are outside the bulk of the bell curve. Understanding this statistical dispersion as a standard deviation is important to understanding how accurate your machine is, understanding the mean or target value, and error band relative to the target.

If I were looking for a machine tool, I’d be looking for bi-directional measurements and a good confidence level relative to those measurements.

As an example of a standard, let’s look at the NMTBA approach. It’s not used much anymore, but it did address all of these elements. For instance, it addressed accuracy and repeatability using a bi-directional approach, it addressed positioning, and it established a confidence level around both the moving forward and backward direction. It utilized a +/- 3 sigma confidence level by addressing the points seven times, to create a bell curve for both positive and negative directions. What this tells us is we have a total confidence level of 99.73 percent that the value will fall in the established bell curve. Now I have a high confidence level that clearly defines the accuracy and repeatability of this particular machine tool. To find the lost motion, you calculate the difference between the mean of the two bell curves.

If you do this a number of ways, you can then understand how the different standards compare. If you establish the NMTBA standard at 100 percent accurate, just for an example, and compare it to the other standards, many standards vary as much as 2:1 and 3:1. That’s not to say one standard is better than another, but that the numbers can vary dramatically depending on which standard the machine manufacturer uses. So if you take numbers from different manufacturers and compare them, but they aren’t the same standard, you’ll be misled by the numbers.

It gets even worse when you try to compare different standards in repeatability, where variations can be as much as 10:1. Lost motion has the same issue, where the variation can be as much as 3:1. You need to be aware of the standards and what the number represents if you decide to put specs in a spreadsheet.

Another thing to consider is scale feedback. Typically, scale feedback reduces variability by measuring the final position of the moving element relative to the fixed scale. This can allow for better surface finish by reducing the variability of positioning and repeatability. Obviously, the machine itself has to have the rigidity and stiffness to support that. The runoff technique on a scale machine can be of any of the standards. One thing to be very careful is that some manufacturers use the specs of the scale feedback, not the axis of the machine tool. That’s why you’ll often seen +/- 1 micron or even less. What they’re doing is using the scale repeatability as the machine repeatability, which isn’t always the case.

To add to the mix, there are several other issues to keep in mind. For instance, in a basic three-axis machine, you’ll have roll, pitch, yaw, parallelism, straightness, and all per axis. The accuracies are typically stated per linear axis, so they aren’t taking into account the geometric and kinematic issues. You should also be concerned with these types of specs, because they can be more important than the linear specs depending on your specific job. Squareness, straightness, parallelism, roll, pitch, and yaw must be considered.

How do you compare? Well, because reported accuracies and respectabilities are derived using different evaluation and measurement techniques, you need to get back to the basic technique used to derive those numbers. We’re seeing a lot of action today talking about establishing a new, more useful standard. One recent standard is the ASME 5.4 “ball-bar” test and volumetric testing using a laser, though no major standard has really taken hold yet.