In the field of CNC milling, chatter has been a hot research topic, which is related to machining quality, precision and cost. Stability lobe diagram (SLD) reflects the vibration of the machining system under different process parameters and cutter axis vectors that is significant for optimization. The accurate dynamic characteristics of the machining system is the prerequisite for stability analysis. Finite element simulation is mainly aimed at small diameter cutter system, and accuracy is poor. The most widely used method is hammer test, but the equipment is expensive, the operation is too professional and it cannot reflect the dynamic characteristics of the machining system in working status. This paper proposes an undetermined coefficient method for the general cutter system to identify the modal parameters, that are the natural frequency, stiffness and damping ratio, just based on the very simple experiment of three-axis half-immersion milling in horizontal plane. Firstly, considering the exact in-cut cutting edge and the instantaneous cutting force coefficient corresponding to the axial factor and the chip thickness, the dynamic model of three-axis milling machining for the general cutter is established. Secondly, two implicit conditions of stable critical speed and cutting depth are derived based on feedback control theory in the frequency domain. Thirdly, the two sets of critical cutting depth and the chatter frequency under arbitrary speeds are obtained by using the dichotomy. With the method proposed in this paper, one of the two is used to solve a series of modal parameter sets, and the other of the two is used to extract the optimal modal parameters in the modal parameter sets. Finally, taking the identified modal parameters as known conditions to search the points one by one in the two-dimensional space composed of the rotational speed and the cutting depth, and judge whether it meets the critical conditions. SLD can be obtained by connecting the points that satisfy critical conditions together. Based on the previous experiment of flat-end cutter, it verified the feasibility of the modal parameter identification method in the paper. In the designed three-axis milling experiment of the ball-end cutter, the in-cut cutting edge simulation and the cutting force coefficient identification were carried out, and the modal parameters of the cutter system were also obtained successfully. The plotted lobe diagram was verified by the spectrum analysis result of the vibration signal collected by the acceleration sensor.

在数控铣削领域，颤振一直是研究的热点，涉及到加工质量，精度和成本。稳定性凸角图（SLD）反映了不同工艺参数和刀具轴矢量下加工系统的振动，这对于优化很重要。加工系统的准确动态特性是进行稳定性分析的前提。有限元仿真主要针对小直径刀具系统，精度较差。最广泛使用的方法是锤击测试，但设备昂贵，操作过于专业且不能反映工作状态下加工系统的动态特性。本文针对通用刀具系统提出了一种不确定的系数方法来识别模态参数，即固有频率，刚度和阻尼比，仅基于非常简单的水平面三轴半浸铣实验。首先，考虑到精确的切削刃和与轴向因素和切屑厚度相对应的瞬时切削力系数，建立了通用刀具三轴铣削加工动力学模型。其次，基于频域中的反馈控制理论，推导出了稳定的临界速度和切削深度的两个隐含条件。第三，通过二分法获得了任意速度下的两组临界切削深度和颤振频率。使用本文提出的方法，可以使用两者之一来求解一系列模态参数集，两者中的另一个用于提取模态参数集中的最优模态参数。最后，以识别出的模态参数为已知条件，在由转速和切削深度组成的二维空间中逐点搜索点，判断其是否满足临界条件。可以通过将满足关键条件的点连接在一起来获得SLD。在此基础上，采用平头铣刀进行了实验，验证了本文模态参数辨识方法的可行性。在设计的球头铣刀三轴铣削实验中，进行了刀内切削刃模拟和切削力系数识别，并成功获得了刀具系统的模态参数。