Thermal modelling using dynamic mode decomposition for thermal error compensation in the temperature domain

Thermal errors significantly impact the performance of precision machine tools. Compensation enables control of these errors in a flexible manner but depends on the prediction accuracy of models. Thermal error compensation is often performed in the displacement domain, but in certain applications can be done in the temperature domain using models that predict the thermal distribution. These predictions are used to regulate external heat sources such that the effects of thermal errors at the point of interest are controlled. In most instances, reduced order models for predicting thermal distribution are obtained from analytical tools such as finite element analysis (FEA). However, these methods require the boundary conditions to be well-defined, which may be suboptimal when the resulting model is applied under different sets of conditions such as a moving heat disturbance. This paper explores the performance of Dynamic Mode Decomposition (DMD) for modelling thermal dynamics in a thin aluminium plate, representing a hot inkject printer head. DMD is an efficient, empirical, reduced-order modelling approach that obtains locally linear models of nonlinear dynamics. FEA simulation of a moving heat load is used to obtain modelling data. DMD is observed to extract and model low frequency dynamics associated with heat conduction and convection. The models produced have prediction residuals that fall within ± 0.25 ℃. This has potential application in implementation of a thermal error compensation controller.