A strain gauge (also spelled strain gage) is a device used to measure strain on an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. The gauge is attached to the object by a suitable adhesive, such as cyanoacrylate. Proper adhesion is critical, as any air gaps or flexibility in the bonding layer will introduce measurement errors known as creep or hysteresis. As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge, is related to the strain by the quantity known as the gauge factor.
History Edward E. Simmons and Professor Arthur C. Ruge independently invented the strain gauge. Simmons was involved in a research project by Dätwyler and Clark at Caltech between 1936 and 1938. They researched the stress-strain behavior of metals under shock loads. Simmons came up with an original way to measure the force introduced into the sample by equipping a dynamometer with fine resistance wires. Arthur C. Ruge, a professor at MIT, on the other hand, conducted research in seismology. He tried to analyze the behavior of a model water tank installed on a vibration table. He was not able to utilize the standard optical strain measurement methods of his time due to the small scale and low strains in his model. Professor Ruge (and his assistant J. Hanns Meier) had the epiphany of measuring the resistance change caused by strain in metallic wires cemented on the thin walls of the water tank model. The development of the strain gauge was essentially just a byproduct of other research projects. Edward E. Simmons and Professor Arthur C. Ruge developed a widely used and useful measurement tool due to the lack of an alternative at their times. Arthur C. Ruge realized the commercial utility of the strain gauge. His employer at MIT waived all claims on the right of the invention, as they did not predict the economic and large-scale usage potential. This prediction turned out to be false. The strain gauge applications were quickly gaining traction as they served to indirectly detect all other quantities that induce strain. Additionally, they were simple to install by the scientists, did not cause any obstruction or property changes to the observed object and thus falsifying the measurement results. Probably the last and most important property was the ease of transmission of the electrical output signal.
Physical operation
A strain gauge takes advantage of the physical property of electrical conductance and its dependence on the conductor's geometry. When an electrical conductor is stretched within the limits of its elasticity such that it does not break or permanently deform, it will become narrower and longer, which increases its electrical resistance end-to-end. Conversely, when a conductor is compressed such that it does not buckle, it will broaden and shorten, which decreases its electrical resistance end-to-end. From the measured electrical resistance of the strain gauge, the amount of induced stress may be inferred. A typical strain gauge arranges a long, thin conductive strip in a zig-zag pattern of parallel lines. This does not increase the sensitivity, since the percentage change in resistance for a given strain for the entire zig-zag is the same as for any single trace. A single linear trace would have to be extremely thin, hence liable to overheating (which would change its resistance and cause it to expand), or would need to be operated at a much lower voltage, making it difficult to measure resistance changes accurately.
Gauge factor The gauge factor G F {\displaystyle GF} is defined as:
G F = Δ R / R G ϵ {\displaystyle GF={\frac {\Delta R/R_{G}}{\epsilon }}}
where
Δ R {\displaystyle \Delta R} is the change in resistance caused by strain,
R G {\displaystyle R_{G}} is the resistance of the undeformed gauge, and
ϵ {\displaystyle \epsilon } is strain. For common metallic foil gauges, the gauge factor is usually a little over 2. For a single active gauge and three dummy resistors of the same resistance about the active gauge in a balanced Wheatstone bridge configuration, the output sensor voltage S V {\displaystyle SV} from the bridge is approximately:
S V = E V G F ⋅ ϵ 4 {\displaystyle SV=EV{\frac {GF\cdot \epsilon }{4}}}
where
E V {\displaystyle EV} is the bridge excitation voltage. Foil gauges typically have active areas of about 2–10 mm2 in size. With careful installation, the correct gauge, and the correct adhesive, strains up to at least 10% can be measured.
In practice
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