Efficient prediction of varying dynamic characteristics in thin-wall milling using freedom and mode reduction methods

The realistic dynamic behavior of thin-wall milling is often captured by frequency response functions (FRFs) of the in-process workpiece (IPW). Present paper proposes a theoretical method to predict the FRFs of the IPW by reducing the initial matrix dimensions and the in-analysis modes of the workpiece. The freedom reduction technique combined with structural modification method is employed to reduce the number of initial workpiece degrees of freedom. Subsequently, based on the reduced mass/stiffness matrices, the resulting eigensolution is used to establish the mode reduction transformation matrix by including the most influential modes. Finally, the FRFs of the IPW are theoretically obtained without further iterations. Using the proposed approach, influences of tool position and material removal on the varying dynamic parameters of the IPW are studied.