In dimensional metrology the international reference temperature is 20 °C (ISO 1:2016). Deviations from this temperature cause significant errors, especially when measuring large parts.
Thermal Expansion Coefficients
Linear thermal expansion coefficients of common materials at 20 °C:
- Steel: 11.5 × 10⁻⁶ /K
- Aluminium: 23.1 × 10⁻⁶ /K
- Stainless steel: 16–18 × 10⁻⁶ /K
- Invar: 1.2 × 10⁻⁶ /K (reference material)
- Ceramic (Zerodur): 0.05 × 10⁻⁶ /K
Correction Formula
When a measurement is reduced to the standard temperature:
Here αs is the standard’s and αp is the part’s expansion coefficient. If both have the same temperature and material, the correction largely cancels out — which is why the standard and the part should be brought to thermal equilibrium together before calibration.
The Abbe Principle and Error
The Abbe principle states that the measurement axis must coincide with the instrument’s scale axis. In calipers there is a distance between the scale axis and the measurement axis, so a rocking error arises when the jaws are not parallel. In micrometers this error is very small because the measurement axis coincides with the scale axis.
Calibration Points
Calibration according to ISO 3611 (micrometer) and ISO 13385 (caliper):
- At least 5 points at 10%, 30%, 50%, 70%, 100% of the range
- At least 3 repeated measurements at each point
- Gauge blocks (grade 0 or 1) are used as the reference
- The parallelism and flatness of the jaws are also checked separately
Practical tip
The part and the reference should be left in the same environment for at least 4 hours; after being handled by hand, allow at least 10–15 minutes of thermal stabilisation as well.