Aiming at the problem of chatter suppression in the turning process of slender shaft workpiece,a 2 DOF model was proposed to analyze the metal cutting process of flexible workpiece in the state space domain.The modal decoupling effect of slender shaft workpiece in face turning operation was analyzed,the 2 DOF model was theoretically analyzed in state space,and the analytical expression of system eigenvalue formed by cutting process and workpiece was obtained.The stability of the system was analyzed to determine the no flutter condition,and the functional relationship between the natural frequency of the system and the cutting speed was obtained through model simulation.The machining of slender shaft workpiece was actually tested on CNC lathe.The results show that for the C45 steel slender shaft workpiece with the initial diameter of 38.2 mm,the simulated and measured frequencies converge to 7928 Hz under the same cutting conditions,and the minimum cutting speed is 105 m/min,which verifies the validity of the model.This model can be used to predict the stability limit of slender shaft workpiece more accurately,then to effectively prevente chatter.