Accuracy, repeatability, performance—knowing how to interpret specifications for measuring devices and systems is important. This month I’ll talk about accuracy specifications for video measuring machines, which I described last month. The concepts apply to other measuring devices as well. The concepts apply to other measuring devices as well.
Let’s start with a definition of accuracy: The degree of conformity of a measured or calculated value to its actual or specified value.
The measured or calculated value for a video measuring machine is typically a length, distance, or size value. Accuracy, therefore, is how closely the video measuring machine measures an actual or specified length, distance, or size. The degree of conformity is the accuracy specification where the smaller the accuracy value, the closer the conformity to the actual or specified value. The best-case scenario is an accuracy specification of zero, or exactly equal to the actual value. If only that were possible!
Straight, not curved
In this discussion, I’ll stick to length measurement and define length as a straight line of a known size between its two end points. (We’ll skip arcs.) The length specimen with the known value is the sample. Let’s assume the sample is long enough to require that the video system move between each end of the sample. When one end is measured, the sample or the optics must be moved so that the other end of the sample can be measured. The length measurement is calculated from the amount of stage travel between the specific locations of the start and end points.
Linear in which direction?
Before getting into accuracy specifications, there is the matter of dealing in three dimensions. You may recall from last month’s discussion of video measuring machines that the high-performing versions have three axes of motion. The orientation of the sample determines how many axes are involved in its measurement. This is important because there are accuracy specifications for one, two, and three axes of stage motion.
Single-axis measurement is straightforward. The sample is in line with one of the three system axes, so measurement is in that single axis.
Two-axis measurement is required when the sample lies at an angle to one of the two axes that together determine a plane. The sample lies in the plane of the two axes over which the system must move to measure its length. The most common situation is when the sample lies in the XY plane. To make this measurement, no motion in the Z (perpendicular) axis is needed. Therefore, any inaccuracy in the length measurement is due to the combined motion of the two axes (X and Y).
As you might expect, three-dimensional measurement is more complex. In this case, the sample doesn’t lie either in line with any single axis, or in a plane of any two axes (XY, XZ, YZ). Measuring the sample in three dimensions requires three axes of stage motion to measure its two end points.
Specifying length accuracy
There are two common conventions used for specifying length accuracy of video measuring machines. Both have a similar format for presenting the specification. The difference is in the confidence value of each.
One thing that is very important to understand about either accuracy specification is, the value is always +/–. The specification is commonly shown as a single value, but it must be understood to be one side of a double-sided value.
The older and still common specification is U95. This measurement uncertainty (U) specification means that 95 percent of all measurements will fall within the +/– values of this specification. This is meant to closely match the 2s (sigma) value of the distribution of measurements for the particular specification.
On the other hand, companies that specify accuracy relative to ISO 10360-2 use the Ex format, which is related to the maximum permissible error (MPE) of indication for size measurement. Note that this specification scheme does not have any statistical distribution factors applied to it.
The 1, 2, 3 of accuracy specifications
Whether E or U95, the specification uses a 1, 2, or 3 to specify whether it is for 1, 2, or 3 axes. Because 1 can mean any of three axes, it’s usually specified in some way such as:
E1(X) or E1(Z)
So 2 can mean a plane in any of two axes, and it usually includes the particular axes, such as:
E2(XY) or E2(YZ)
There is one thing that can be a source of confusion unless you pay particular attention to it. Some companies provide an E1 specification for more than one axis, but include it as a single specification. This can be easy to confuse with a corresponding E2 specification for the same two axes. These are not the same.
E1(X,Y) ≠ E2(XY)
Note the comma in the E1 expression, but not the E2 expression. This means that the E1 specification is the same for the single axis direction in either the X or the Y axis. That specification isn’t the same as the single E2 specification, which is for the combination of motion in both the X and Y axes.
E3 is the accuracy within an XYZ volume and is sometimes referred to as volumetric accuracy.
Accuracy-specification format
Depending on the units of measurement, ISO 10360-2 accuracy specifications are expressed in a form like this:
Ex = [k + (multiplier * L) / 1000] μm
Where:
E = the maximum permissible error, in microns, under the given conditions
X = 1, 2, or 3 refers to single-, two-, or three-axis accuracy, respectively
k = systemic or inherent machine error that is not length-dependent
multiplier = a constant that defines the travel-dependent error
L = the length of travel over which the accuracy specification is desired, in millimeters
μm = microns, the accuracy unit of measurement
And, as stated earlier, in all cases the result is one side of a +/– range.
Using the specification—an example
Example of a typical single-axis accuracy specification:
E1(Z) = (1.5 + 6L/1000) μm
E1(Z) = one side of the +/– linear measurement error in the Z-axis
1.5 = the constant; in this case there is a 1.5-μm uncertainty in this axis that is independent of any travel in this axis
6 = the stated multiplier; this is the travel-dependent component of the Z-axis measurement error
L = the length of travel for the measurement (or the length of the sample, in this case), in millimeters
Let’s use a sample length of 150 mm:
Substituting into the equation:
E1 = (1.5 + 6L/1000) μm
E1 = (1.5 + (6 * 150)/1000) μm
E1 = (1.5 + (900)/1000) μm
E1 = (1.5 + 0.9) μm
E1 = 2.4 μm
Therefore, measurements over 150 mm of travel in the Z-axis are accurate to within +/– 2.4 μm. We cannot tell the length of our sample to any better than +/– 2.4 μm (which is pretty impressive, since this represents an uncertainty of +/– 0.0016% of the total length of 150 mm).
This can be quite complicated, and, rather than continue now, I’ll discuss the accuracy funnel, calibration, and sources of error in my next column.
Yes, all these measurements matter.
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