Modeling of contact line and efficient numerical solution for helical groove grinding of cylindrical end mills

Precision grinding of the helical flutes of cylindrical end mills is a key process in their manufacturing. Accurately establishing the grinding contact line model is of great significance for improving tool quality and efficiency. Aiming at the limitations of existing models in generality and numerical solving efficiency, a universal mathematical model for the contact line that comprehensively considers tool geometric parameters, wheel profile, and kinematic relationships. An efficient numerical solving strategy based on a multi-interval bisection method is proposed, which stably obtains all solutions of the contact line equation and effectively avoids missing roots and singular solutions. Validation with multiple tool specifications shows that the model accurately characterizes the grinding contact relationship, and the numerical algorithm outperforms traditional methods in both computational efficiency and accuracy, providing a reliable theoretical foundation and technical support for high-precision CNC tool grinding.