Modeling of Time-Varying Surface Roughness Considering Wear Overlap Per Tooth in Ball End Finish Milling

In multi-axis ball end finish milling, the continuous change in cutting contact points produces complex wear overlapping zones. Moreover, each flute bears different actual cutting depths and contact points leading to inconsistent wear overlap distribution per tooth, which significantly affects the surface quality. Therefore, it is necessary to consider the wear overlap distribution per tooth to improve the surface roughness prediction accuracy. To address this issue, a time-varying surface roughness model is proposed considering wear overlap distribution per tooth. First, the model of wear overlap distribution per tooth considering the actual cutting depth and contact point is developed using the combined effects of the milling mechanism per tooth and the element wear model through the worn cutting edge trajectory. Then, the wear overlap distribution per tooth is embedded in the theoretical model of surface roughness through the geometric relationship of tool–workpiece engagement and milling radius model of worn cutter per flute under wear overlapping zones. Finally, the proposed method is validated through a case study. The testing results demonstrate that the wear overlap distribution per tooth and machined surface roughness could be forecasted exactly and effectively by the proposed method.