Parametric modeling and estimation of geometric errors for a rotary axis using double ball-bar

Abstract

In this study, the geometric errors of the rotary axis of machine tools are modeled parametrically and estimated using a double ball-bar. To estimate the geometric errors from the measured data, they are defined as position-dependent/position-independent geometric errors. The position-dependent and position-independent geometric errors are modeled as nth-order polynomials with C1-continuity and constants, respectively. Additionally, the set-up errors which are inevitable during the installation of the double ball-bar are modeled as constants to increase the accuracy of the estimation process. The measurement paths are designed to increase the sensitivity of the geometric errors in the measured data. The position of the balls constituting the double ball-bar is calculated in the reference coordinate system using the homogeneous transform matrices. The ball-bar equation is applied to determine the relation between the measured data and geometric errors. The linearized relations between them are derived by eliminating the higher-order error terms. The parameters of the modeled geometric errors and set-up errors are calculated using the least squares method. Finally, the geometric errors are estimated using the calculated parameters. The validity of the proposed method is tested through simulations and it is used to estimate the geometric errors of the rotary axis of five-axis machine tools.