A mutual mapping model of cross-sections between the axial and normal planes of ball screws based on the forming of helical ball track.

This paper presents a novel axial-normal plane mutual interconversion algorithm for ball screws, which effectively bridges the gap between design and actual product. It is pivotal in streamlining processes across the design, manufacturing, and inspection phases of ball screws. By forming the ball track, the mutual mapping matrix between the axial and normal planes addresses key challenges and enhances engineering applications has been developed. The method simplifies the complex interaction within ball screws, offering a comprehensive model for better understanding and application. Empirical evaluations demonstrate the efficiency and precision of our algorithm. In 3D modeling tests, it processes 10,000 points in merely 5 ms, with an impressively low maximum relative error of 0.001%. Further testing in product detection confirms the robustness of the model, maintaining a maximum relative error under 0.5%. This high precision and efficiency underscore the algorithm's value in enhancing design, manufacturing, and inspection processes. Overall, our research offers significant practical engineering benefits, thereby advancing ball screw technology.