Fast Calculation of the Vibration Characteristics of the Five-Axis Machine Tool Based on Transfer Matrix Method for Multibody Systems

The five-axis machine tool is the core equipment in the modern manufacturing industry, and it is also a strategic cornerstone for the precision manufacturing of aerospace equipment and the autonomy of key components in national defense and military industries. To further enhance the precision, efficiency, and reliability of five-axis machine tools, the dynamic design is necessary. This research centers on the UMC-500 five-axis machine tool, with a primary focus on constructing its dynamic model. Specifically, the transfer matrix method for multibody systems (MSTMM) is employed to deduce the transfer equations corresponding to each constituent element of the system. Subsequently, leveraging the automatic derivation theorem, the overall transfer equation and the overall transfer matrix of the system are derived. Ultimately, through these analytical procedures, the natural frequencies and mode shapes inherent to the five-axis machine tool system are determined. From the mode shapes, low-order vibrations are concentrated in the cutting head, while high-order vibrations are mainly located on the worktable. To verify the efficacy of the method proposed in this paper, the natural frequencies and mode shapes of the machine tool in question were computed by the finite element analysis software ANSYS. The results show that the method in this paper is consistent with the finite element simulation, and its efficiency is higher than that of the finite element simulation. This research lays a foundational framework for the dynamic analysis, structural design, and performance optimization of five-axis machine tools.