This paper analytically studies the effect of radial engagement on chatter stability when the flexibility is perpendicular to the feed motion, with thin-walled part milling being the most relevant industrial case. By studying the mean directional factor and its harmonics, the superior stability of the up-milling strategy over down-milling for both Hopf and flip chatter is demonstrated. The optimal engagement for a theoretical infinite stable depth of cut Hopf is obtained, as well as the expressions for the critical depth of cut. For flip chatter, three different cutting zones with different lobe shapes can occur depending on the radial engagement. It is also shown that while flip chatter cannot be completely eliminated by tuning the radial engagement alone, an engagement can be found in up-milling that maximises stability. Finally, the findings are validated through experimental tests.

本文分析研究了当柔性垂直于进给运动时径向啮合对颤振稳定性的影响，其中薄壁零件铣削是最相关的工业案例。通过研究平均方向因子及其谐波，证明了对于 Hopf 和翻转颤振，逆铣策略比顺铣策略具有优越的稳定性。获得了理论无限稳定切削深度 Hopf 的最佳啮合，以及临界切削深度的表达式。对于翻转颤振，根据径向啮合，可能会出现具有不同凸角形状的三个不同切削区域。研究还表明，虽然仅通过调整径向啮合无法完全消除翻转颤振，但可以在逆铣中找到使稳定性最大化的啮合。最后，通过实验测试验证了研究结果。