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.

在多轴球头端面精铣中，切削接触点的连续变化会产生复杂的磨损重叠区域。此外，每根排屑槽具有不同的实际切削深度和接触点，导致每齿的磨损重叠分布不一致，从而显着影响表面质量。因此，需要考虑每齿的磨损重叠分布，以提高表面粗糙度预测精度。为了解决这个问题，提出了一种考虑每齿磨损重叠分布的时变表面粗糙度模型。首先，利用每齿铣削机构和通过磨损切削刃轨迹的元素磨损模型的组合效应，开发了考虑实际切削深度和接触点的每齿磨损重叠分布模型。然后，通过刀具-工件啮合的几何关系和磨损重叠区下每刃磨损刀具的铣削半径模型，将每齿的磨损重叠分布嵌入到表面粗糙度的理论模型中。最后，通过案例研究验证了所提出的方法。测试结果表明，该方法可以准确有效地预测每齿磨损重叠分布和加工表面粗糙度。