Accuracy evaluation of geometric error calibration using a laser tracer via a formulaic approach

Abstract

In this work, we examine the accuracy of the geometric error calibration of machine tools using a laser tracer, via the multilateration or sequential multilateration principle. An uncertainty analysis of geometric errors or target point coordinates, based on the Monte-Carlo method, is often adopted to assess the accuracy of measurement results. However, this approach is not comprehensive, and can be time-consuming. This paper adopts the average volumetric localization accuracy to assess the quality of geometric error calibration, where the accuracy is evaluated approximately by means of a formulaic method, based on the multivariate law of propagation of uncertainty. Using this method, the accuracy of measurement results can be denoted quantitatively with a single indicator, and the influence of measurement strategy on measurement accuracy can be analyzed more intuitively. To further improve the average volumetric localization accuracy, we employ an optimization method for the measurement path, based on the greedy algorithm. Simulations and experiment are then conducted to verify the proposed method; the results show that both the laser tracer setup and measurement path have a great deal of influence on the measurement accuracy of geometric errors.