This paper proposes an analytical chatter stability prediction for low frequency vibration assisted turning process, i.e. the modulated turning. Introducing low frequency tool modulations in machining is initially proposed to transform continuous cutting process into a discrete one so that chip-entanglement/jam could be eliminated. However, tool modulation assistance has a fundamental effect on chatter stability. This paper is the first attempt to uncover the regenerative chatter stability of the modulated turning process by a frequency-domain analysis. Tool engagement kinematics and the dynamic chip generation mechanism are modeled. It is understood that unlike conventional turning or milling processes, modulated turning process exhibits distinct stabilizing effects due to 1) short-time tool engagement and 2) multiple regenerative loops as the dynamic chip thickness is affected by past two revolutions. Considering the average immersion of the cutting tool (cutting duty cycle), a zero-th order frequency domain chatter stability model for the process is proposed. The developed model is used to quantify the effect of multi-delay regeneration and tool modulation parameters on the stability loop formation. The analytical stability solutions are benchmarked against the time domain digital simulation results, and both predictions are validated through orthogonal cutting experiments. It is shown that the proposed solution can accurately generate the Stability Lobe Diagram (SLD) of modulated turning for typical modulation conditions.

针对低频振动辅助转向过程，即调制转向，提出了一种分析性颤振稳定性预测。最初建议在加工中引入低频刀具调制，以将连续切削过程转换为离散切削过程，从而可以消除切屑缠结/卡纸。但是，工具调制辅助对颤振稳定性有根本的影响。本文是首次尝试通过频域分析揭示调制转向过程的再生颤振稳定性。对刀具啮合运动学和动态切屑产生机理进行了建模。可以理解，与传统的车削或铣削工艺不同，由于1）短时刀具啮合和2）多个再生回路，因此动态切屑厚度受过去两转的影响，因此，调制车削工艺表现出明显的稳定效果。考虑到切削工具的平均浸入度（切削占空比），提出了用于加工的零阶频域颤动稳定性模型。所开发的模型用于量化多延迟再生和工具调制参数对稳定性回路形成的影响。分析稳定性解决方案以时域数字仿真结果为基准，并且两个预测都通过正交切割实验进行了验证。结果表明，所提出的解决方案能够针对典型的调制条件准确地生成调制转弯的稳定波瓣图（SLD）。