Tool path point algorithm and optimization for freeform surface CNC machining

To reduce the manufacturing cost of optical freeform surfaces, this study establishes a mathematical model for grinding using a wheel tool and coordinate transformation of tool positioning. A novel tool path point computation method based on rotational transformation is developed. Through optimization and experimental validation, the effectiveness of the algorithm is verified. After logical optimization of the rotational transformation tool path point algorithm, surface form error was reduced from 40μm to 15μm, a 62.5% improvement. Additionally, to address the slow computational speed of the algorithm, speed optimization was performed. Timing tests using MATLAB show that the calculation time was reduced from 2.72 hours to 2.77 seconds under the same data conditions, significantly enhancing both speed and the density of computable tool path points.