Sphericity error evaluation method of multi-axis machine tool based on spherical S-shaped trajectory

Sphericity error, as a critical indicator of multi-axis machine tool linkage accuracy, directly influences the performance optimization of intelligent manufacturing systems through its computational efficiency and precision. This study proposes an error evaluation method based on spherical S-shaped trajectories. This method achieves digital transformation in machine tool accuracy detection through the deep integration of computer-aided design (CAD) and high-performance computing (HPC) technologies. By generating parametric S-shaped motion trajectories through computer numerical control (CNC) systems and synchronously capturing triaxial linkage position deviation data via real-time data acquisition modules, a high-density point cloud dataset is constructed. At the algorithmic level, a GPU-accelerated parallelized least squares method is employed for preliminary sphere center positioning, achieving a hundredfold acceleration in matrix operations through architectural optimization. Furthermore, an evolutionary algorithm-optimized minimum circumscribed zone model is introduced. This method utilizes multi-objective optimization strategies to identify optimal sphere center coordinates within the Pareto solution set. The experimental results demonstrate that the proposed algorithm significantly reduces computational time on computer clusters compared to traditional methods, providing real-time and precise feedback for digital twin systems.