Estimation of Machine Tool Accuracy Based on Monte Carlo Simulation Using Movement Axes Geometric Errors Model

Abstract

Accuracy is one of the most important feature of a machine tool. Being able to estimate the overall accuracy of a machine tool represented by the total volumetric error can be a huge advantage in the design process. This paper provides overview of methods used for geometric error transfer modeling and volumetric error modeling. An error transfer rigid body model is derived and after that, a random linear guideway straightness error profile generator is proposed. This allows to simulate a movement axis with random straightness errors of rails and computed geometric errors of an assembled axis. Volumetric error of a 3-axis machine tool is then modeled using its kinematic scheme and homogenous transformation matrices with 21 kinematic errors. Using simulated axes as input to the volumetric model, an entire machine tool can be simulated. From that, the total volumetric error can be obtained and a Monte Carlo simulation carried out. This allows to analyze statistics of the total volumetric error and with slight input changes (rail straightness tolerance), a sensitivity analysis can be performed to determine the most influential errors in the machine tool.