An analysis of the volumetric error uncertainty of a three-axis machine tool by beta distribution

This paper addresses the stochastic nature of the volumetric error of a mac hine tool in 3-dimensional workspace, and proposes a new model helping the prediction of the tolerances of products caused by uncertainties of a machi ne tool without going through very costly and time-consuming production eva luation. The probability of the volumetric error within the prescribed tole rance in the case of a vertical type 3-axis machine tool is obtained in 3-d imensional graphical form and the beta distribution is adopted to obtain a distribution that can better approximate the real distribution of the sum o f the variables. The direction of approach of a tool/workpiece is considere d when the stochastic error parts of a machine tool are evaluated. In addit ion, we verified experimentally that the stochastic parts of the volumetric error are also affected by the direction of approach of a tool/workpiece. (C) 2000 Published by Elsevier Science Ltd.