Online analysis method to correlate the mode shape for forced vibration in milling thin-walled workpieces

Forced vibration is a type of stable vibration different from chatter, which reduces the machining quality of a formed surface. The forced vibration characteristics of a thin-walled workpiece are difficult to capture due to varied milling excitation, cutter runout, and position dependence. Currently, insight into forced vibrations is still lacking without effective analysis methods. To solve these problems, a single-point online characterization method correlated to the mode shape was proposed. The modal contribution equation for a milled thin-walled workpiece was obtained by correlating the structural dynamics with the cutting force characteristics. Then, correlation factors were integrated to construct a state-space model, and the Kalman filter algorithm was used to estimate the modal contribution coefficients online based on a single-point response signal. Next, the principal mode shape was determined to characterize the forced vibration characteristics. The effectiveness of the proposed method was demonstrated by comparison with the operational deflection shape (ODS) results. These results revealed the contribution mechanism of each mode shape to the forced vibration under position-dependent excitation and varied cutting parameters, from which the vibration forms could be monitored.