Analysis and prediction of cutting forces in end milling by means of a geometrical model

The geometrical analysis of a new three-dimensional force model of end milling is presented. The analysis includes description of the relative relationships among undeformed chip thickness, rake angle, cutting velocity, shear plane area and chip flow angle during peripheral and face milling processes. The shear plane area of the shear deformation zone and the effective frictional area on the tool face are calculated and the shear energy per unit time and frictional energy per unit time are formulated. The three-dimensional cutting forces in the tool axis system are then obtained. In the developed model, the depth of cut, helix angle, tool rotational angle, and indentation action of the tool tip are taken into account by individual transformation matrices. The three-dimensional cutting forces in a Cartesian system can be predicted via matrix transformation. Experiments conducted to verify the developed model showed that the predicted cutting forces agreed well with the experimental data both in trends and values.