Research on PIGEs identification method for spherical S-trajectory of five-axis machine tools based on dual quaternion modeling

To bridge the gap between double-ball bar (DBB) measurement trajectories and real-world machining conditions, and to overcome the limitations of inadequate error identification, this paper proposes a five-axes synchronous spherical S-trajectory derived from the S-shaped test piece of ISO10791-7:2020, which is scaled and sphericized to achieve spatial coordinated movement of both linear and rotary axes. This paper constructs kinematic and differential linearized error models using dual quaternion theory to achieve linear mapping of geometric errors to tool pose errors. An error identification model is constructed based on DBB measurements and forward kinematics, and error decoupling is achieved using the least squares method. The spherical S-trajectory is validated through simulation and experimental comparisons. The mean relative error (MRE) and root mean square error (RMSE) of the errors identified by this trajectory are 1.68% and 3.91 × 10 −4 , respectively, which are significantly lower than those of the XYC/XZ trajectories (MRE = 1.92%, RMSE = 5.27 × 10 −4 ), indicating superior identification accuracy. Experimental results show that the average relative deviation between the error identification results of the spherical S-trajectory and the XYC/XZ trajectories is only 4.5%, which effectively validates the precision and reliability of the spherical S-trajectory in PIGEs identification.