Hybrid modeling of thermo-elastic behavior of a three-axis machining center using integral deformation sensors

Although thermal effects are detrimental to machining accuracy, the industry still uses warm-up procedures that significantly lower productivity or energy-consuming thermal conditioning and air conditioning. On the other hand, the most of the research has focused until now on measuring the variation of the most significant error components and building phenomenological models with respect to structural temperatures. Collecting these data is however inherent with time-consuming optimal location algorithms and with high measurement uncertainty. The resulting models in the literature are hence too cumbersome for the industrial use. This paper proposes a new hybrid method, combining physical and phenomenological modeling, for calculating the thermally induced volumetric error based on integral deformation sensors (IDS). This measurement has a higher content of information than structural temperatures, since the machine component deformations are the outcome of all thermal sources and mechanisms combined, including environmental and process heat effects. Additionally, the physical model can be developed with simple equations of mechanics theory, so that a high predictability can be achieved already without any training. In order to increase the prediction accuracy even further, the influence of each IDS on the volumetric error can be calibrated based on direct measurements of the volumetric error, which can be done automatically by the machine-integrated measuring probe. To demonstrate the effectiveness of the proposed hybrid method, several thermal loadings were applied on a three-axis machining center retrofitted with nine IDS, while the dislocation between workpiece- and tool-side was measured every fifteen minutes.