Modal parameter identification of general cutter based on milling stability theory

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.