Abstract This paper proposes a Projection-Based Fitting Method (PBFM) for identifying eight positionindependent geometric errors (PIGEs), including squareness errors and linear offsets, associated with the two rotary axes of a five-axis machine tool. By using a touch probe and a precision sphere, the X, Y and Z positions of the rotary axes are measured at various angular configurations. These errors are then projected onto a 2D plane, where they form distinctive geometric patterns. By deriving error equations and fitting these projected patterns, the eight PIGEs can be effectively identified. To minimize the coupling effects among different error components, a two-stage geometric error identification process is introduced. In the first stage, squareness errors are calculated and compensated to reduce angular deviations. The second stage focuses on identifying and compensating for linear offsets, further improving the system’s overall accuracy. Compared to the conventional Least Squares Method (LSM), the proposed PBFM not only offers a more intuitive interpretation of how different errors affect the geometry of the projection patterns, but also shows greater robustness against outliers and measurement noise. Experiments were conducted on the five-axis machine tool with compensation data implemented directly to the Heidenhain controller. After compensation, the RMS errors for the A axis and C axis were reduced by over 77% and 90%, respectively. These results demonstrate that the proposed PBFM can significantly reduce geometric errors in rotary axes, confirming both the feasibility and effectiveness of the approach.
Zhang et al. (Tue,) studied this question.
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