Stability lobe and chatter prediction based on modified zeroth-order approximation in high-speed ball end milling process

In this study, dynamic force modelling was used to create a stability lobe diagram (SLD) using the modified zeroth-order approximation (ZOA) method for identifying chatter and non-chatter zones in high-speed ball end milling. SLD prediction models developed for flat end milling cutters may not be applicable to ball end milling cutters because this is only valid for end milling cutters with identical geometrical properties. The mechanics of cutting on the hemispherical portion of ball end milling cutter is very complex, thus, the hemispherical portion of the cutter was discretized into five discs with uniform spacing along the cutter axis. A mechanistic model was used to determine the dynamic cutting force coefficients in the tangential and radial directions and the characteristics equation was computed by applying the ZOA to all five discs. SLD was predicted using instantaneous cutting force coefficients and modal parameters such as stiffness constant, damping ratio, and natural frequencies. A modified ZOA Experiments were carried out to test the validity of the proposed modified ZOA method using various combinations of cutting parameters for chatter and non-chatter zones based on the predicted SLD. The validation experiments confirm the suitability of the proposed method very efficiently. Experiments were also carried out at various radial immersions, and it was discovered that at lower radial immersions, the cutting process was unstable, with the depth of cut, cutting speed, and feed remaining unchanged.