Uncertainties in dimensional measurements due to thermal expansion

Thermal expansion is a source of uncertainty in dimensional measurements, which is often significant and in some cases dominant. Methods of evaluating and reducing this uncertainty are therefore of fundamental importance to product quality, safety and efficiency in many areas. Existing methods depend on the implicit assumption that thermal expansion is relatively uniform throughout the part and can therefore be corrected by scaling the measurement result. The uncertainty of this scale correction is then included in the uncertainty of the dimensional measurement. It is shown here that this assumption is not always valid due to thermal gradients resulting in significant shape changes. In some cases these are the dominant source of dimensional uncertainty. Methods are described to first determine whether shape change is significant. Where shape changes are negligible but thermal expansion remains significant then the established methods may be used. This paper describes the application of the Guide to the expression of Uncertainty in Measurement (GUM) uncertainty framework which provides an approximate solution for thermal expansion due to non-linearity and a non-Gaussian output function. The uncertainty associated with this approximation is rigorously evaluated by comparison with Monte Carlo Simulation over a wide range of parameter values. It is often necessary to estimate the expected uncertainty for a measurement which will be made in the future. It is shown that the current method for this is inadequate and an improved method is given.