Cutter-workpiece engagement calculation in 3-axis ball end milling considering cutter runout

In order to obtain desired surface quality, the machining parameters such as feed per tooth, spindle speed, axial and radial depth of cut have been selected appropriately by using a process model. The surface quality and the process stability are related to cutting forces which are more influenced by the instantaneous chip thickness and the cutter-workpiece engagement (CWE) region. To reach a high accuracy in cutting forces calculation it is primary to determinate the start and the exit angles on the (CWE) region. Unlike previous studies which calculated the (CWE) numerically. This paper proposes an analytical model to calculate the (CWE) region by determining the cutting instantaneous flute entry and exit angles. These locations are calculated according to the heights of axial depth of cut. The second proposed approach is to calculate the instantaneous undeformed chip thickness. These solutions are used to calculate accurately the cutting forces in the case of the 3 axis milling operations. To validate the model, a mechanistic cutting forces model was simulated and compared to the measured one. A good agreement between them was proved.