The present work aims to determine mathematical equations that describe the behavior of the components of the volumetric error in Three Coordinates Measuring Machines (3CMM). A general methodology using techniques of multiple regressions is presented. Such methodology, applied to a moving bridge type 3CMM, has made it possible to obtain, in a simple way, three regression equations from data collected through a direct calibration procedure, more specifically, the space grid method. The proposed model was statistically and experimentally evaluated. The statistic evaluation covers the calculation of the correlation coefficient of the samples, a residue analysis and the hypothesis verification. The experimental evaluation was made through the comparison of results expected by the model with the results obtained from the measurements of a ball bar. From these results, it is possible to verify that the model is adequate and that it is good in predicting volumetric errors in the machine.
Space grid method; ball bar; multiple regression; Abbè offsets and least squares
