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 machine tool in 3-dimensional workspace, and proposes a new model helping the prediction of the tolerances of products caused by uncertainties of a machine tool without going through very costly and time-consuming production evaluation. The probability of the volumetric error within the prescribed tolerance in the case of a vertical type 3-axis machine tool is obtained in 3-dimensional graphical form and the beta distribution is adopted to obtain a distribution that can better approximate the real distribution of the sum of the variables. The direction of approach of a tool/workpiece is considered when the stochastic error parts of a machine tool are evaluated. In addition, we verified experimentally that the stochastic parts of the volumetric error are also affected by the direction of approach of a tool/workpiece.