A stochastic model for volumetric errors

Abstract

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