Strain gauges · Measurement

Temperature response: apparent strain of a gauge under temperature change

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

DMSKeil 2017

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)

Procedure

Step by step

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

Typical mistake

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).

Practice

Application and limits

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

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.

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.

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