Smart sequential multilateration measurement strategy for volumetric error compensation of an extra-small machine tool

Research on machine tools has mainly focused, during these last couple of decades, on methods of error mapping and compensation techniques in aim of improving their geometrical accuracy. Over the last ten years, new measurement methods based on tracking laser (TL) multilateration have appeared. These methods have generally been applied to large machine tools or coordinate measuring machines. However, compact extra-small (XXS) machines have rarely been approached. The aim of this paper is to provide an optimal experimental strategy for estimating volumetric errors and then compensating these machine tools in the best possible manner. The method is based on the sequential multilateration technique, using a TL. This study focuses on the calibration of the translation axes of a five-axis machine tool. In this work, the accuracy of the machine is defined as the mean error vector measured in the entire working volume of the machine. The influence of a great number of factors (TL positions, offset size, acquisition time, temperature, etc.) that could affect the accuracy of the machine tool is then studied. For that purpose, a Design of Experiment (DOE) is carried out to discriminate the effect of these parameters. A Screening process is thus first used to refine the set of factors. This set is then retained to obtain the Response Surface (RS) with its Statistical Confidence Boundaries (SCB). Finally, these factors are optimized to derive the smartest strategy for providing the smallest reduced residual volumetric error after compensation. The results of this optimization are validated by an experiment.