Uncertainties in the error compensation of coordinate measuring machines

Coordinate measuring machines (CMMs) are widely used in industry as accurate measuring devices of mechanical components. Most of these machines come with software algorithms to compensate for any residual errors that may be present in the machine. Mathematical models have been developed by metrology researchers that form the basis of these software algorithms. The research reported on herein is aimed at developing statistical models for estimating the uncertainties in the error compensation methodology. A kinematic model has been developed for a particular CMM to predict the errors due to geometric and kinematic error sources in the machine. This model has been used to error compensate the CMM. Three statistical techniques have been used to create uncertainty models of the error compensation methodology. These three models estimate the uncertainty in the error compensations implemented on the CMM. A Gaussian model, a model based on the bootstrap method, and a regression model have been developed. The Gaussian model assumes that the errors in the CMM are normally distributed, while the bootstrap method makes no assumptions pertaining to the distribution of these errors. The regression model is based on a conventional regression analysis of the error data. The error compensated CMM was tested using standard references and artifacts to validate the kinematic error model. The uncertainty estimates in the error compensations along three orthogonal trajectories of the probe tip are computed. It is found that the uncertainties computed by the bootstrap method are generally slightly smaller than those computed by the Gaussian model, both of these uncertainties being significantly larger than those computed by the regression method. The discrepancy between the bootstrap and the Gaussian model results indicates that the measurements of the errors in the motion of the linear axes of the CMM are not normally distributed. The measurements of the errors have a distribution which is slightly more peaked than what is expected from a normal distribution. The non-normalities in the distributions of these errors suggest that the bootstrap is a more appropriate technique for estimating uncertainties of the error compensations. The residual errors present in the three orthogonal trajectories of the probe tip, after incorporating the error compensations in these trajectories, were measured, and the total uncertainties in these measurements arising from the error compensation scheme and the measurement procedure are derived and displayed.