Modelling time-domain vibratory deflection response of thin-walled cantilever workpieces during flank milling

While machining thin-walled workpieces, the chatter and corresponding damage to the machined surface can be avoided if that is predicted well in advance. Currently, investigations of machining vibrations mainly rely on experiments, which are costly and difficult to perform and FEM simulation methods that are many times computationally cumbersome. This work presents a mathematical model to obtain time domain forced vibration deflection response of a thin rectangular cantilever plate for any time and space varying external loads. The model is adapted for a milling process to obtain machining vibration response of a thin impeller blade by simplifying its geometry as a thin rectangular cantilever plate. The developed model was verified by checking the natural frequencies and mode shapes obtained by the model with the Finite Element simulation results for a thin cantilever plate. Peripheral milling experiments were performed to machine a thin rectangular cantilever plate of Ti-6Al-4V alloy on a vertical 3-axis CNC milling machine. Milling forces and workpiece acceleration were acquired during machining. Workpiece material properties and moving machining forces obtained by Linear Edge Force Model are input to the model. The model was validated by comparing vibratory deflection of thin cantilever plate obtained by the model and by the acquired experimental data. In general, the developed model can be used to obtain time-domain forced vibration response of thin rectangular cantilever plate workpieces.