The Strain Gauge
The humble strain gauge, technically, speaking, is not a transducer as it doesn’t transfer energy from one form to another. However, given it is fundamental to a wide range of engineering analysis in the modern world, and Flintmore have extensive experience working with them, it felt wrong to exclude it from transducer Thursdays!
The strain gauge was first proposed in the early 20th Century. The fundamental idea for a typical strain gauge is based on the fact that the longer a conductor the higher the resistance becomes as described in the equation below. When a conductor is put under strain, its length changes, and we can see a resultant change in resistance. Even better, the response (for small strains) is linear! A very coveted relationship in instrumentation.
R = ρ L /A
A very basic strain gauge could be made by bonding a piece of wire to the object to be measured and attempting to measure any changes in resistance. However, a problem arises, strain in metals is typically measured in micro-strain, thousandths of a percent of change in length, this produces a tiny change as a fraction of original resistance. To measure this over a short single strip of wire, the wire would have to extremely thin to get a large enough value of resistance to measure, when such a thin and short wire is exposed to the voltage used to polarise the bridge, it will heat up and potentially fail.
We could extend the length of the wire used along the axis of stress, allowing it be thicker whilst maintaining a practical resistance, but this means we can no longer approximate the stress at a point. So what do we do if we want to measure strain in a small area (as is typical) to gain ideas about stress concentrations and deformation of our specimen? The genius of the strain gauge is looping the wire back and forth over the same small area, such that the effective length of the wire is much higher, whilst still being localised to an area of a few milimetres. This allows the wires to have reasonable cross sectional area, minimising overheating from the polarisation current. Typically this is achieved by inscribing the gauge on a piece of foil which is bonded to a polymer film.
The resistance change is measured using the ubiquitous wheatstone bridge. With modern measurement equipment very very small imbalances in the bridge can be measured, by working out the corresponding change in resistance changes in the order of micro-strain can be practically measured. In the 1930’s the change would have been measured with a calibrated galvanometer, a transducer we covered in a previous transducer thursday.
And if that was all one needed to know about strain gauges then a whole chunk of our work would be delightfully simple!
Practically there is far more to consider. Those of you who paid attention in science might know that the little ‘resistivity’ term lurking in the above equation varies in response to temperature. If our strain gauge is, let’s say 120 Ohms, fairly typical, and made of copper, less typical, changes in temperature of a few degrees can cause variances in the order of ohms. This is massively more than the milli-ohm changes that we are expecting to measure for small strains. Worse still, metals, typically the materials on which strain gauges are applied, also change shape with temperature introducing strains that aren’t related to load! Even worse, the small current that we use to polarise the bridge causes heating as well, further changing resistance. If we’re trying to measure the response to changes in load, especially over extended periods this can be a real problem. How do we mitigate this? Especially in environments where we can’t control the temperature?
Test Engineers have developed a number of tricks over the years to mitigate this. The first step is in the gauge itself, certain alloys are particularly insensitive to temperature fluctuations and strain gauges are usually made of these materials, typically constantan.
Another step is to take ‘cold zeros’; if we’re conducting a simple test over a period where temperature change will be minimal, and the bridges have already been polarised, we can ‘zero’ the gauges, we assume all variation from the zero over the course of the test is due to changes is strain. This is the simplest approach, but is not valid in a wide number of scenarios.
When using principal gauges, the next best approach to cold zeroes is to have a dummy gauge, this is attached to an unloaded sample of similar material. Often both approaches will be used in tandem. The assumption is that any thermal effects are the same in both the unloaded and loaded sample, so any differences can be assumed to be from genuine strain. This too has some drawbacks, if the target for measurement is very large getting another piece that is comparable can be prohibitive. Flintmore has been involved in projects where the object to instrumented weighed several tonnes, with so much ‘thermal inertia’ it changed temperature very slowly, this was both an advantage as cold zeroes were largely a valid approach. However it also meant that using a dummy gauge would have required an unloaded sample of steel of similar size, which was rather impractical. But what if we can use the sample itself?
A typical strain gauge, as has been described above, is what I have been calling a ‘principal gauge’. It is, in essence, a single piece of wire and measures strain along a single axis. There are, however, other arrangements; some of these are used to increase the effective ‘gauge factor’: the change in resistance to a given strain. This raises the sensitivity by reducing the comparative effect of noise. Many of these arrangements can be used to also cancel out temperature effects, one is the ‘Poisson pair’. The Poisson pair is formed from two principal gauges at right angles. One is aligned with the principal strain axis and, in this arrangement, the other measures strain that results from Poissons ratio. By arranging them on the same arm of the bridge with the correct factors, it pushes up the effective gain. Because thermal stress largely occurs in all directions the gauges increase (or decrease) by the same amount, this keeps the bridge arm balanced and so the effect cancels out. The same is true for the wires from the gauges to the data acquisition system, so long as comparable wires are used for both the principal and Poisson gauge and they are routed the same way. The gauges still drift a little, but this is typically limited to less than 10 micro strain over tens of hours. Unfortunately Poisson gauges have a disadvantage, their response to out of plain strains i.e. strains that are not aligned with the principal gauge, is somewhat complex and they are best suited to scenarios in which the direction of the strain field is known or easily predicted. This still allows them to be used in the vast majority of use cases.
Another arrangement is termed the strain gauge ‘rosette’, this contain 3 gauges at 45 degrees to one another, forming a full 90 degree sweep. With the third gauge the Poisson effects, thermal effects, and principal effects can, theoretically at least, be determined. However, in most cases, the added complexity of a full rosette is unwarranted.
Just working with thermal effects is a massive ice-berg, we haven’t touched on bonding strain gauges to the surface in question, which can be just as complex. Noise reduction, wiring type, and positioning are all factors that come in to play when working with the strain gauge. Their use has become an art, it almost always being possible to improve one’s knowledge of them. Many books have been written to codify and pass on this knowledge, with a wide array of resources online. In part this is why strain gauges remain so well used, they are well understood and a mature instrumentation technology.
Whilst other techniques for strain measurement have arisen over time, including finite element analysis to estimate strains by modelling, the strain gauge remains a cutting edge tool for strain measurement, both for verification and for health monitoring of active systems. Strain gauges form part of another widely used ‘transducer’: the load cell. These are essentially a calibrated set of strain gauges where the load-strain response is known.
In future we will explore other strain measurement systems, including digital image correlation, strain-sensitive-coatings and the foil strain gauges cousin; the piezo-gauge.
Flintmore have worked with strain-gauges in static, dynamic and transient use cases, do you have a job that could use the insight of practical strain measurement? Verification of FEA? Creep measurement? Get in contact with us today.
Further Reading
National Instruments have an excellent article on the practical use of strain gauges. National Instruments equipment remains our prefered choice for measuring strain: https://www.ni.com/en/shop/data-acquisition/sensor-fundamentals/measuring-strain-with-strain-gages.html
RS give a similar article to ours. RS transducer articles can be a good starting point to gain understanding of different transducers, particularly the potential trade offs between types:
https://uk.rs-online.com/web/content/discovery/ideas-and-advice/strain-gauges-guide
If you’re looking for a real deep dive, check out HBK’s extensive article series on strain gauge use and selection:
And, as you might be coming to expect from us, we still highly recommend the wikipedia article which gives a good overview of the subject:
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