The calibration certificate for a CMM arm provides the single point and volumetric performance test results. The single point value indicates the maximum variation that can be expected when measuring the same point repeatedly. The volumetric value compares the instrument's measurements of gauge blocks of known lengths to the actual lengths, providing a measure of accuracy. However, these values are obtained under ideal laboratory conditions and may not reflect real-world measurement performance, which can be affected by temperature variations, vibrations, imperfect workpiece geometry and mounting rigidity. The instrument only needs to perform better than the manufacturer's specification on these tests, not achieve the actual test results.

1. How to understand calibration and performance of portable CMM
arms. By William Plutnick, Swiss Metrology
Figure 1 Typical portable CMM Arm
What is the accuracy of the measurements you get from your instrument? Is a question I often get from
my customers. In the past I often repeated what was stated on the calibration certificate. Recently I
started to realize that this information really didn’t tell you precisely what you expect on any particular
project, other than the fact that the instrument passed calibration at an accredited lab some time back.
Well, if the job required measuring a single point over and over and the distance between two nearly
perfect spheres then I guess it would, but “real” measurement is never that pretty. Add to that fact the
measurement of non-perfect circle, cylinders, imperfect planes, and surfaces. In addition circle
algorithms that compound error in complex ways make this is complicated. Maybe the best answer is,
“it depends.” So, I thought I would try and analyze this and see if I could come up with some guidelines
that could reasonable describe what accuracy could be expected. As with any task, one has to start
somewhere and I thought to start with the calibration certificate, since that is the only hard numbers
that are provided with the instrument and discussion of this topic invariably always lead to this
document. I thought maybe it was worth the time to explain what a typical CMM arm calibration
certificate is really telling you. The two main items of interest are the Single Point and Volumetric
performance test results. We will examine these two in this article and then, later we will look at how
this applies to real world measurements. A typical calibration certificate will have a Single Point
specification something like this:

2. Single Point
In the big measurement picture, single point is the margin of values that the instrument should be
expected to exhibit during repeated measurements or in other words how much is the biggest variation
between measuring the same point. The manufacturer has to determine this when qualifying the
product for sale as a metrology instrument. The Single Point value is determined by the single-point
articulation performance test specified in ASME B89.4.22. “Methods for performance Evaluation of
Articulated Arm CMM’s.” For this evaluation, the device is mounted with a ball probe and is used in
conjunction with a fixed socket that is located in 3 locations. 0-20% of arm travel, 20-80% of arm travel,
and <80% of ball travel. Ten readings are taken at each location. The maximum and minimum values in
the (X,Y,Z) data sets are determined. The maximum is subtracted from the minimum and divided by 2.
This is done for all 3 positions. The three largest values are compared to the stated instrument
specification. If they are less than the stated specification then the instrument “passes”.
What is interesting to note here is that the value on the certificate is not the value determined by your
instrument, but it is the manufacturer’s specified value for that model of instrument. The certificate is
issued when your instrument either meets or exceeds this value (in this case exceeds is misleading
because the actual value has to be less than the specified in order to “pass.” you’re particularly well
cared for instrument will probably perform much better than this, but, it is not reported on the
certificate because the specification only states that your instrument performs within range of the
specified value. For example, for this particular instrument during this calibration, the largest single
point max-min/2 was .0076, or almost 4 times better than what is required to meet the specification.
Although one most consider that these are performed in ideal laboratory conditions with rigidly
mounted arm and highly accurate socket. These conditions will probably seldom be encountered in the
field. Furthermore, this value does not tell you how close your instrument reads to a particular standard
length, that evaluation comes next in the volumetric.
Volumetric
In the big measurement picture, Volumetric is a measure of error. It is a comparison between a
traceable SI artifacts via an ISO17025 accredited lab and the device being calibrated. As in Single Point
above, the procedure is determined from ASME B89.4.22. The procedure involves repeated
measurements within the range of the instrument. The range of the instrument can be thought of as a
sphere with the first joint of the instrument being the sphere center. The sphere is divided into

3. quadrants from which 2 ball bars (see Figure 2 below) are employed. The 2 ball bars consist of a “short”
bar that is between 50% and 75% of the radial length of the arm and a “long” bar that is between 120%
and 150% of the arm length. The bars are positioned horizontally, vertically, and at 45 degrees. The
operator measures the spheres at the end of the bars. The operator must record five measurement
points per sphere. A center to center distance between the spheres is then calculated. Since this is a
measurement to a “known” standard temperature, vibration and measurement technique is important.
For example, length of ball bar must be compensated for temperature for data analysis.
Figure 2 Typical Ball Bar used in Volumetric Calibration
The analysis section of the Volumetric evaluation involves calculating temperature adjusted length
between centers of ball bar, subtracting the measured value from this and noting this as a length
deviation. This is repeated for all quadrants with both the “long” and “short” bar. The maximum
deviation is reported and compared to the manufacturers stated specification for the instrument. If your
instrument is less than the value specified for the instrument the instrument has “passed” and like single
point above your instrument may have done considerably better than the stated specification. For
example in the calibration of this particular instrument the maximum deviation from the standard is 2.5
times better than required, but again, this is in nearly perfect laboratory conditions, not likely to be seen
in the field. The volumetric is probably what most people are asking when they want to know the
accuracy of the instrument, but as always, your actual results may vary. In actual measurement
situations, temperature may vary, vibrations may be present, features will have varying degrees of form,
mounting of part and instrument may not be sufficiently rigid, etc. These will all detract from the
volumetric number that has appeared on the certificate.
For further information see: ASME B89.4.22 “Methods for Performance of Evaluation of Articulated Arm
Coordinate Measuring Machines,” The American Society of Mechanical Engineers.