Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

Ballbar is widely used for geometric error measurement of the rotary axis, and the uncertainty analysis is of great significance to ensure the reliability of error identification. This study analyzes the measurement uncertainty based on the Monte Carlo method. First, this study clarifies the uncertainty mechanisms caused by tool setting error, translational axis motion error, and ballbar installation error, and proposes a measurement model comprehensively considering the uncertainty sources. In this study, the same ballbar measurement experiments were carried out 10 times in three measurement modes, and the standard deviation of the ballbar length change under different rotation angles was analyzed to ensure that the uncertainty of the geometric error can be effectively analyzed. Furthermore, the uncertainty of each error at different angles of the rotary axis is evaluated based on the measurement model. The results show that the translational axis motion error and tool setting error are important sources of uncertainty. The measurement uncertainty of the angle positioning error is the largest in A- and C-axis, and its standard uncertainty reaches 9.38 '' and 2.81 ''. After optimizing the sine and cosine terms in the identification model, the standard uncertainties of the angular positioning errors are reduced to 6.43 '' and 2.26 '', and also the estimated errors are close to the actual values, which verifies the validity of the uncertainty analysis method.