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The significance of air pockets for modelling thermal errors of machine tools

It is well known, especially with the prevalence of compensation for geometric errors, that thermal error represents the most significant proportion of the total volumetric error of the machine tool. Thermal error in machine tools originates from changes to internal and external heat sources that vary the structural temperature of the machine tool resulting in the non-linear deformation of the machine structure. The ambient conditions inside and around the machine vicinity are varied not only by the external heat sources but, equally importantly but less well understood, by the machine itself when local air pockets are warmed inside the voids of the machine during the machining process. Air pockets are areas within the machine structure where the localized heat convection rate is reduced by the heat confined within them causing the temperature to vary slowly relative to the other places of the machine. This results in a relatively slower response of the associated structure. Consideration for this effect is an important, yet often ignored element of thermal modelling which deteriorates the prediction capability of many thermal models. 
This paper presents a case study where FEA (Finite Element Analysis) is used for the thermal modelling of a machine tool and the issue of air pockets is addressed by measuring and considering the temperature in voids. It was found that the consideration of the most significant air pockets improved the prediction capability of the FEA thermal model in the Z-axis direction from 50% to 62% when compared with the experimental results Z-axis. This paper highlights the significance of air pockets with regard to the thermal modelling and it is believed that the consideration of the temperature measurement inside voids of the machine structure and inclusion of their effect may significantly improve the performance of any thermal model.