Tracking Down Tracking Errors

In the world of dimensional measurement, electronic gages make up a class of instruments that are capable of detecting extremely small dimensional variations on a surface element. The gage's electronic transducer can operate in a number of different ways, typically LVDT (Linear Variable Differential Transducer) or through a digital scale-based technology. The resulting signal can be amplified or counted and is then available for display on an electronic readout or it can be fed directly into a computer-based software system.

Most of these transducers are used in short-range comparative gages and can have sub-micron or millionth of an inch resolutions. Besides having extremely fine resolutions, fast response and the ability to collect data, another benefit of electronic gaging is that transducer signals can be combined in mathematical formulas to display dimensional or geometric conditions. The most common example is a differential measurement where two transducers combine to produce a reading of part size without regard to part position.

When parts are measured under ideal conditions—for example, when a part with perfectly flat and parallel dimensions is placed on the reference table of a gage that is extremely flat and perfectly perpendicular to the part—then results should be pretty good without the need for differential measurement. However, since neither we, our parts, nor our gages live in a perfect world, differential gaging can be a decided benefit to the application.

This type of signal combination is typically used on simple bench stands or on complex fixture gages having multiple checks, where the part position cannot be well controlled. In this case, any out-of-position is seen by both heads. Since the heads are combined differentially, this shift is canceled out and only the change of size is displayed. However, there is a catch.

There is a potential source of error that must be accounted for when trying to make very precise measurements using these fine resolution transducers. Each transducer has its own performance characteristics. These are repeatability, linearity and calibration accuracy. Knowing the performance characteristics of the transducers is important, but what you need to remember is that every additional transducer adds another source of error to the measurement.

These errors may or may not be additive, but when they are, they can produce significant errors in extremely demanding measurements. This “new” error is called tracking error. Normally two heads are added differentially to produce a diameter measurement. However, because of the manufacturing process, a two-point measurement will not always suffice, and three, four or even six transducers are combined to produce an average diameter. This can result in tracking error.

So how do you track tracking error? It requires a way to hold the transducers, a display, and a means of displacing all the gage heads equally. Let’s start with a basic two-headed differential check. After each transducer is calibrated with the amplifier, place them in a gage calibrator or bench stand where gage blocks can be used to precisely move each transducer by the same amount. If you are using gage blocks, select a set that will allow you to record at least three equally spaced points on each side of the transducer’s zero.

Mechanically position both transducers at electrical zero on the zero gage block. Then switch the heads to the amplifier’s differential mode and note the result in the display. Now replace the zero block with the series of gage blocks and record the values (or if using the calibrator, move it to displace the transducers at a number of points in their travel). The results should provide a linear trace, but there will likely be more error than when each head is tracked individually. This check should be performed with all the heads that would be used in the mathematical calculation to determine the worst case error of the system. In extreme cases it may be necessary to calibrate on the total system response, but mostly you are apt to see non-linear results over different areas of the signal’s range.

While it may not always be possible to correct for these errors over the short range, knowing where they are may help you optimize the position of the transducers, or to look for a different combination of transducers that provide the best results.