A mathematical modeling method for the "S" edge curves of a ball end mill

To simplify the mathematical model for the "S" edge curves of a ball end mill and derive the composite edge curve equations of the intersection of two space planes and the sphere, this paper proposed and applied the "Single Sphere Method" and "Dual Spheres Method" to deduce the mathematical expressions of the deflection angle and helical angle of the flat edge curves on a ball end mill's spherical part. The results have shown that the mathematical relationship between the deflection angle and the helical angle is equal, thus simplifying the mathematical model of the plane edge curves on the spherical part with an equal relationship between the two angles. This reduces the complexity of the derivation process of the plane edge curves and provides an effective method for the composite edge curves' modeling of the intersections of two or more space planes and the spherical part of the ball end mill.