Abstract: The cutting edge curve of the ball nose end mill was established by using the "S" shaped equal lead spiral, and the grinding edge curve was used as the grinding basis, and the grinding scheme of the grinding wheel grinding trajectory is planned with the three traveling orthogonal vectors of the grinding point on the cutting edge curve as the reference coordinate system. On this basis, the mathematical model of the rake face and the rake face with the normal rake angle is established, and the grinding depth of the rake face of the ball nose end mill is obtained by obtaining the traveling orthogonal vector of the grinding point at any time in the grinding process. The posture of grinding the rake face of the grinding wheel is planned by the traveling orthogonal vector of the grinding point, the rake angle of the rake face method and the corresponding depth of each grinding point of the rake face, and the posture of the rake face grinding is planned by the traveling orthogonal vector of the grinding point, the normal angle of the rake face and the corresponding width of each grinding point of the rake face, and finally the motion trajectory of the grinding wheel grinding milling cutter is formed by traversing the entire cutting edge curve. The experimental results show that the error of each structural parameter of the ball nose milling cutter can be guaranteed to be within 5%, which verifies the accuracy of the grinding trajectory model of the grinding wheel and establishes a theoretical basis for the grinding of the ball nose end mill.

Key words: ball end mills, grinding wheel grinding trajectory, variational orthogonal vector, front knife face, back rake face