A Finite element approach to determine the unknown location of the heat sources within engineering structures.

The performance of many engineering structures which contain heat sources are affected by the existence of the change in temperature. In some cases, this is an absolute change in temperature, but in others it is the thermal gradients within their assembled components that influence the integrity of their overall performance. One application that is the subject of ongoing investigation into thermal behaviour is machine tools for precision manufacturing. On such machines, several internal and external heat sources introduce unwanted energy into the machine structure. The effect of temperature gradients in these elements is a reduction in the positional accuracy and repeatability, which compromises the machine’s ability to produce accurate, repeatable parts. Numerous techniques are employed to compensate such errors, but if the exact spatial location of the internal heat sources within the structure remains an unknown parameter, then the modelling of the thermal displacement and compensation is fundamentally compromised. Without the original machine designs, the location of such heat sources may well be unknown.

The focus of this thesis is to devise an approach which can assist in determining the unknown spatial location of the internal heat sources in a structure, based only on observable data. This is challenging, because one must know the temperature field of the structure to know the heat source location. However, the temperature measurements of the structure can normally only be observed externally.

The approach taken requires analysis in both transient and steady state heat transfer stages. Mathematical calculations and Finite Element Analysis (FEA) on Computer-Aided Design (CAD) models are used to provide a theoretical approach that is then validated through controlled thermal experiments. A steel plate is used throughout the work to prove the concept, first as a one-dimensional (1D) problem with observation on a single
boundary and then a two-dimensional (2D) problem with observation on two perpendicular boundaries.

The analytical approach applied to the FEA simulated data yielded the unknown location of the internal heat source in the 1D structure under steady state conditions with the accuracy better than 95%. Analysis in the transient phase yielded an accuracy of up to 97%, but also provided the strength of the heat source with an accuracy up to 96%. For the 2D problem, the location of the heat source was estimated using thermal experimental data, lumped capacitance techniques, and interpolation of the temperature gradient against the various locations of the heat source.

Future work should extrapolate the methods proposed in this thesis to estimating the location of heat sources in three-dimensional structures and assemblies, so it could be readily adopted by researchers when specifying temperature sensor locations and thermal compensation models for precision machine tools.