Modelling and analysis of chatter in the heavy-load multi-DoF plastic forming process

Regenerative chatter is an unstable and detrimental vibration phenomenon stemming from the regenerative excitation of time-delay dynamic systems. Currently, research on regenerative chatter predominantly focuses on machining process, wherein chatter occurs when the process frequency aligns closely with the natural frequency of the tool-holder system. However, in plastic forming process conducted by heavy-load multi-DoF forming machine (MDFM), the process frequency is far smaller than the natural frequency of the tool-holder system. Despite this, chatter still occurs in the actual plastic forming process, challenging the explanatory capacity of existing chatter models developed for machining process. This paper aims to a new chatter model and a new chatter generation mechanism for multi-DoF plastic forming process (MPFP). Firstly, the flexible-rigid coupled dynamic model of the MDFM is established based on the Lagrangian method. Then, a time-delay dynamic model of MDFM is developed incorporating material deformation and tool-blank contact in forming process. Subsequently, the time-delay dynamic model is simplified based on the static position, and a stability model for MDFM is established using the fully discrete method. Based on the above dynamic and stability model, the vibration and 3D stability lobe diagram are theoretically calculated and experimentally validated, showing prediction error of vibration about 18% and that of stability about 11%. Besides, a new chatter generation mechanism different from the machining process is revealed. That is, in the machining process, chatter arises from the phase difference between the regenerative exciting force and vibration due to the high process frequency, whereas in the forming process, chatter arises from the larger of exciting force than the damping force, namely arises from insufficient damping. This work introduces an innovative chatter model and elucidates a novel chatter generation mechanism, which holds substantial implications for vibration research and offers high application potential in MPFP.