Robust measurement method and uncertainty analysis for position-independent geometric errors of a rotary axis using a double ball-bar

In this study, we propose a robust and simple method using double ball-bar to measure position-independent geometric errors of a rotary axis involving single axis control during the measurement. The standard uncertainty for the proposed method is analyzed to quantify the confidence interval of the measurement result. Two measurement paths are planned to measure the position-independent geometric errors, including two offset errors and two squareness errors of a rotary axis. An error synthesis model using homogenous transform matrices and a ball-bar equation to represent the relation between the positions of two balls and the measured distance between them are used. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants and added to the design position of the balls. Their effects on the measurement result are investigated in detail. Furthermore, a novel fixture consisting of flexure-hinges located at the tool nose is developed to minimize the set-up errors of the ball and to robustly keep the position of the ball during measurements. Finally, the proposed method is validated using simulation and is applied to the rotary axis located on a five-axis machine tool.