Prediction of cutting forces in ball-end milling by means of geometric analysis

A new geometric model of ball-end milling is proposed. The relationships among undeformed chip thickness, rake angle, cutting velocity, shear plane area and chip flow angle in ball-end milling are clearly described. The shear plane area of the shear deformation zone and the effective frictional area on tool face are calculated. The three-dimensional cutting forces in the tool axis system are then obtained by minimum energy method. The transformation matrices, including the effects of the axial depth of cut, helix angle, tool rotational angle, and indentation action of the tool tip, are presented. The three-dimensional cutting forces can be predicted via matrix transformation. A force model for a two-flute cutter is developed and a four-flute model is also obtained by superposing the two-flute model. Based on the basic geometric modeling, the cutting forces along horizontal and vertical directions are predicted. Several unveiled phenomena, such as the influence on cutting forces of the different engaged regions between cutting edge and undeformed chip thickness, and indentation action on tool tip that influences the Z-direction force, have been illustrated. Experiments are conducted to verify the developed model. It shows that the predicted cutting forces agree with the experimental data both in trends and values.