In this paper, the cutting force calculation of ball-end mill processing was modeled mathematically. All derivations of cutting forces were directly based on the tangential, radial, and axial cutting force components. In the developed mathematical model of cutting forces, the relationship of average cutting force and the feed per flute was characterized as a linear function. The cutting force coefficient model was formulated by a function of average cutting force and other parameters such as cutter geometry, cutting conditions, and so on. An experimental method was proposed based on the stable milling condition to estimate the cutting force coefficients for ball-end mill. This method could be applied for each pair of tool and workpiece. The developed cutting force model has been successfully verified experimentally with very promising results. the diameter of cutter [mm] the diameter of cutter [mm] the number of flutes on the cutter the helix angle on the cutter [deg] the cutter pitch angle [deg] the full axial depth of cut [mm] the differential axial depth of cut [mm] the lag angle at an axial depth of cut z [deg] the lag angle at maximum axial depth of cut z=a [deg] the instantaneous immersion angle of flute number j, ( j = 1 – N f ) [deg] the instantaneous immersion angle of flute number j in z cutting depth, ( j = 1 – N f ) [deg] the instantaneous chip thickness at immersion angle ϕ j [mm] the chip width [mm] the edge length of the cutting segment [mm] the radius of a circle on xy plane at an arbitrary point (P) on cutting edge [mm] the feed per tooth [mm/tooth] the axial immersion angle at z axial depth of cut tangential shearing force coefficient [N/mm2] radial shearing force coefficient [N/mm2] axial shearing force coefficient [N/mm2] tangential edge force coefficient [N/mm] radial edge force coefficient [N/mm] axial edge force coefficient [N/mm] the differential tangential cutting force [N] the differential radial cutting force [N] the differential axial cutting force [N] the differential feed cutting force [N] the differential normal cutting force [N] the cutting force in the feed direction [N] the cutting force in the normal direction [N] the cutting force in the axial direction [N] the average cutting force in the feed direction [N] the components of linear model force in the feed direction [N] the average cutting force in the normal direction [N] the components of linear model force in the normal direction [N] the average cutting force in the axial direction [N] the components of linear model force in the axial direction [N] 
A combination method of the theory and experiment in determination of cutting force coefficients in ball-end mill processes