Hybrid multibody system method for the dynamic analysis of an ultra-precision fly-cutting machine tool

The dynamics of an ultra-precision machine tool determines the precision of the machined surface. This study aims to propose an effective method to model and analyze the dynamics of an ultra-precision fly-cutting machine tool. First, the dynamic model of the machine tool considering the deformations of the cutter head and the lathe head is developed. Then, the mechanical elements are classified into M subsystems and F subsystems according to their properties and connections. The M-subsystem equations are formulated using the transfer matrix method for multibody systems (MSTMM), and the F-subsystem equations are analyzed using the finite element method and the Craig–Bampton reduction method. Furthermore, all the subsystems are assembled by combining the restriction equations at connection points among the subsystems to obtain the overall transfer equation of the machine tool system. Finally, the vibration characteristics of the machine tool are evaluated numerically and are validated experimentally. The proposed modeling and analysis method preserves the advantages of the MSTMM, such as high computational efficiency, low computational load, systematic reduction of the overall transfer equation, and generalization of its computational capability to general flexible-body elements. In addition, this study provides theoretical insights and guidance for the design of ultra-precision machine tools.