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Cutting edge of a sphere portion (end cutting edge) of the ball end mills is treated as the intersection of a spherical surface and a rake face approximated by a plane surface. The cutting edge configuration is geometrically analyzed, and variation of inclination angle and normal rake angle along the cutting edge is discussed. In addition, it is assumed that the line elements along the curved cutting edge of the sphere portion do not undergo extension or contraction, and the modified condition of sidecurl of the chip is introduced. Then a cutting model and energy method developed for the drilling process is extended to the milling process. Expressions such as area of the shear plane and projected area of the cutting cross-section on the rake face are derived for slot milling. From the analytical results obtained through energy method, it is found that the center of side-curl of the chip is fixed near the top of the sphere portion of ball end mills and the chip is produced under this restricted condition. Furthermore, predicted result shows that Stabler's chip flow rule does not hold for the milling with ball end mills.

Prediction of Chip Formation and Cutting Forces in Milling with Ball End Mills. (1st Report). Geometry of a Ball End Mill and Cutting Model.