How a strain gauge works
A strain gauge is a thin metal foil pattern glued to a part. When the part stretches, the foil gets longer and thinner and its resistance rises; when it is compressed, the resistance falls. The change is tiny, so gauges are wired in a Wheatstone bridge that turns it into a measurable voltage.
The formulas
- Strain: ε = ΔL ÷ L, usually given in microstrain (µε, 10⁻⁶).
- Resistance change: ΔR = R × GF × ε, where GF is the gauge factor, about 2 for metal foil gauges.
- Bridge output (small strains): Vout ≈ Vex × GF × ε × N ÷ 4, where N is the number of active arms: 1 for a quarter bridge, 2 for a half bridge and 4 for a full bridge.
- Stress in the elastic range: σ = E × ε, with E the Young’s modulus.
Example
A 350 Ω gauge with GF = 2 on steel (E = 200 GPa) at 1,000 µε, in a quarter bridge at 5 V:
- ΔR = 350 × 2 × 0.001 = 0.7 Ω;
- output ≈ 5 × 2 × 0.001 ÷ 4 = 2.5 mV, or 0.5 mV/V;
- stress: 200,000 MPa × 0.001 = 200 MPa (about 29,000 psi).
The exact quarter-bridge output is slightly lower, Vex × (GF ε ÷ 4) ÷ (1 + GF ε ÷ 2), about 2.497 mV here. The difference grows with large strains.
Choosing the bridge
- Quarter bridge: one active gauge, cheapest, but sensitive to temperature and lead resistance.
- Half bridge: two active gauges, for example one on each side of a beam in bending. Doubles the output and cancels temperature effects.
- Full bridge: four active gauges, the standard in load cells. Four times the output and the best compensation.
Load cells are specified in mV/V: a 2 mV/V load cell at full load and 10 V excitation gives 20 mV.
Practical tips
- Use an instrumentation amplifier or a 24-bit bridge ADC; the signals are in millivolts or less.
- Excitation of 2 to 10 V is common. Higher voltage gives more signal but more self-heating.
- Temperature changes create apparent strain. Use self-temperature-compensated gauges matched to the material, or a dummy gauge.
- Surface preparation and adhesive curing matter as much as the electronics.
- Typical elastic moduli: steel about 200 GPa, aluminum 69 GPa, titanium 110 GPa, concrete 25 to 40 GPa.