Towards understanding the geometric error coupling effect on squareness error identification in circular tests

For circular tests, the measurement data are simultaneously affected by the coupling effect of position-dependent geometric errors (PDGEs) and squareness errors. Consequently, identification method that solely considers squareness errors struggle to accurately determine the true squareness error values. To address this issue and obtain the actual squareness error, the identification method considering the geometric error coupling effect is proposed. The PDGE values and the distance data of the geometric error coupling effect are obtained based on the multi-instrument measurement data fusion, enabling the establishment of a squareness error identification model that incorporates PDGEs. The validity of the identification results is corroborated through volumetric error prediction, yielding a maximum deviation of 18.9 µm between the predicted and measured volumetric errors. The prediction accuracies of the proposed method and Ballbar 20 software, characterized by the root-mean-square error between the predicted and measured volumetric errors, are 6.7 and 20.4 µm, respectively. This indicates that the proposed method prediction results are closer to the measured values. The proposed method mathematically elucidates the coupling effect of PDGEs and squareness errors for circular tests.