Strain gauges · Measurement

Strain Gauge Apparent Strain Calculator

Calculate thermal resistance change and apparent strain of a strain gauge from grid temperature coefficient, thermal expansion of part and grid, and gauge factor.

DMSKeil 2017
01

Inputs

Linear model; α_R and α_B are actually temperature dependent, which is why manufacturers give the temperature response as a polynomial. If the bridge is balanced at measuring temperature the response is irrelevant.

02

Results

Enter values and run the calculation.

Method

What is calculated?

Temperature changes alter the grid resistance directly (α_R) and through the difference in thermal expansion between part and grid, which forces a strain on the grid. Both add to the load strain and appear as a zero shift. Self-compensating gauges are pre-treated so that α_R just cancels the expansion difference for a given material (eq. 2.31).

Equations

(ΔR/R₀)therm = α_R·ΔT + k·(α_B − α_M)·ΔT (Keil Gl. 2.29)

ε_s = (ΔR/R₀)therm / k

Selbstkompensation: α_R = −k·(α_B − α_M) (Keil Gl. 2.31)

Limits

Assumptions and typical mistake

Linear model; α_R and α_B are actually temperature dependent, which is why manufacturers give the temperature response as a polynomial. If the bridge is balanced at measuring temperature the response is irrelevant.

Adding the datasheet temperature response (already in µm/m) on top of this result, or confusing α_R with the temperature dependence of the gauge factor (eq. 2.28).

Inputs

What you enter – and where the values come from

Temperature coefficient of grid resistance α_R [10⁻⁶/K]
Temperature coefficient of the measuring-grid resistance: it states by how many millionths electrical resistance changes per kelvin even without mechanical load. Manufacturers tune it to a specimen material, creating a self-compensating strain gauge. Source: datasheet or thermal-output graph for the gauge batch. If the individual coefficient is not given, use the published thermal-output curve as the governing correction.
Thermal expansion of the part α_B [10⁻⁶/K]
Thermal expansion coefficient of the part the gauge is bonded to: by how many µm/m it expands freely per kelvin. The bonded gauge is stretched along with it. Source: material tables; ferritic steel ≈ 11–12, austenitic steel ≈ 16, aluminium ≈ 23, titanium ≈ 9, plastics 50–100 (·10⁻⁶/K).
Thermal expansion of the grid α_M [10⁻⁶/K]
Thermal expansion coefficient of the grid material itself. The difference from the part's expansion forces a strain on the grid that looks like a reading. Source: constantan (standard grid) ≈ 14.5·10⁻⁶/K, Karma ≈ 13; stated in the gauge datasheet.
Gauge factor k
The gauge factor is the sensitivity of the strain gauge: it states how much the electrical resistance changes when the gauge is stretched (ΔR/R = k·ε). Without it no strain can be computed from an electrical signal. Source: printed on every gauge package or in the manufacturer datasheet, typically 2.0 to 2.1 for constantan foil gauges; valid at room temperature. The same value must be set in the amplifier.
Temperature change ΔT from balancing [K]
The temperature change is the difference between the temperature at bridge balancing and the temperature during measurement. Only this difference produces temperature-related errors; if balanced at measuring temperature it is zero. Source: thermocouple or resistance thermometer at the measuring point or cable.
Nominal resistance R₀ [Ω]
The nominal resistance is the electrical resistance of the unloaded strain gauge. It sets how large the absolute resistance change is for a given strain and how much current flows for a given excitation. Source: printed on the gauge package; standard values 120 Ω and 350 Ω, less often 700 Ω or 1000 Ω. Higher values mean less self-heating and less cable influence.
Context

What this calculator is for

Judging whether a steel-matched gauge is usable on aluminium without a compensation gauge, and estimating zero drift when temperature changes during a test.

What comes next

  1. Enter thermal expansion coefficients of part and grid plus α_R of the gauge lot.
  2. Enter the temperature difference between balancing and measurement.
  3. Subtract the apparent strain from the reading or provide a compensation circuit per ch. 4.3.
Results

How to read the results

  • The apparent strain is what the reading shows at ΔT without load – after zero balancing at the initial temperature.
  • Measured strain minus apparent strain = mechanical strain, provided no compensation gauge is used.
  • If the α_R for self-compensation is far from the datasheet value, the gauge does not match the material – use a half bridge with compensation gauge (circuit II).
Result quantities

What each value means

Thermal resistance change (ΔR/R₀)therm [‰]
Relative resistance change of the strain gauge caused solely by temperature. Use it to diagnose zero drift during heating when no mechanical load acts.
Absolute resistance change [Ω]
The same thermal resistance change in ohms for the given nominal resistance.
Apparent strain ε_s [µm/m]
Apparent strain: the amplifier displays this value although the part carries no mechanical load. Subtract it from the reading or eliminate it with a compensation gauge. Positive = the reading fakes tension.
α_R for full self-compensation [10⁻⁶/K]
Grid temperature coefficient a self-compensating gauge would need for exactly this material so the apparent strain becomes zero. Compare with the material matching in the gauge datasheet.
Source

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 2.4.2 temperature response, eqs. (2.29)–(2.31); sec. 4.3 temperature compensation.

The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.

FAQ

Frequently asked questions

Why does a steel-matched gauge on aluminium show strain?

Aluminium expands about 12·10⁻⁶ per kelvin more than steel; the difference is forced onto the grid and appears as tensile strain.

Does a compensation gauge help?

Yes: an unloaded gauge of the same lot on the same material in the adjacent arm cancels the response in the bridge (Keil circuit II).

What about the gauge factor at temperature?

The gauge factor changes per eq. 2.28 with α_k·ΔT, typically only a few per mille up to 100 °C; that is a sensitivity error, not a zero error.