Application of Sherman–Morrison–Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component.

How to consider the mass loading effects and stiffness modification effects of materials removed on dynamic characteristics in a thin-walled component milling process is an essential problem. Sherman–Morrison–Woodbury formula can be employed and extended to estimate the corrected frequency response function (FRFs) without the material removing effect. In the paper, a novel method, named as structural dynamic modification method with equal mass, to predict the dynamic stable lobe diagram (DSLD) of the thin-walled workpiece milling process is proposed. The whole cutting process is divided into multi-cutting steps with equal length. The presented method is to regard material removal of each cutting step as a modification (or reanalysis) of structure so as to estimate the corrected FRFs based on the so-called Sherman–Morrison–Woodbury formula. The input data of the method is only two sets of the dynamic characteristics of original (unmachined) and finial (machined) structures, which can be easily obtained using experimental modal analysis (EMA) or finite element method (FEM). The accuracy of the method is dependent of the number of cutting step. FEM is highly recommended, and EMA mainly enables the damping ratio of FEM model to be readjusted. The efficiency is higher than one of the methods reported in literatures because it is not necessary to re-build and re-mesh FEM model each time, and the modal analysis can be implemented automatically through pre-programs. Meanwhile, using Sherman–Morrison–Woodbury formula at active coordinates only can greatly improve computational efficiency. Additionally, the probability of singularity occurring is very low comparing with that in the existing methods. Once the dynamic characteristics changing with respect to tool positions are identified, a specific DSLD can then be predicted by using these characteristics along the machining direction. And the cutting parameters for thin-walled components milling can be also optimized to avoid chatter vibration and improve the chatter-free material removal rate and surface finish. Finally, the results are verified by dynamic and milling tests with thin-walled workpiece. [ABSTRACT FROM AUTHOR]