Modeling, identification, and measurement of geometric errors for a rotary axis of a machine tool using a new R-test

Geometric errors are important factors that affect the accuracy of multi-axis CNC machine tools. In this paper, three aspects of research work are carried out. First, two kinds of error modeling methods are proposed, i.e., tool tip coordinates error modeling (TTC) and kinematic chain transmission error modeling (KCT). This work resolves the theoretical confusion existing in the error modeling process in the past. Second, left matrix multiplication and right matrix multiplication have different meanings for geometric error modeling; this paper makes a detailed analysis and summarizes four identification algorithms for geometric errors based on the above theory. Third, a new R-test device is developed. For the traditional commercial R-test, it is usually difficult to adjust the position and orientation, so it is hard to directly obtain the vectors of the sensor axes and to ensure that the intersection of the sensor axes and the center of precision ball coincide accurately. However, this new R-test with the addition of positioning datums and a sliding table overcomes these problems. The calibration of the R-test is described in detail. Finally, a four-point measurement experiment for identifying the geometric errors of a rotary axis has been conducted, and the effectiveness of the measurement method is verified by a prediction experiment and a comparative experiment of double ball bar (DBB).