A new modeling approach for the dynamics of a micro end mill in high-speed micro-cutting

Abstract

This study presents a distributed parameter model for the transverse vibration analysis of a micro end mill. Owing to its geometrical nonuniformity, the micro end mill is spatially sub-structured into three distinct spinning elastic systems. With the application of the extended Hamilton’s principle to the energy expressions of the spinning elastic systems, the governing equations of each sub-structured system are obtained. The overall analytical model incorporates a number of nonclassical structural effects that range from rotary inertia, shear deformation, taper ratio, to the rate of twist. For detailed frequency analyses, systematic solution of the elastodynamics governing equations is provided with the spectral finite element method. To assess the accuracy of the presented method, the frequency values of each of the spatial sub-structure are validated through available results in the literature. In the same vein, the solution of the entire ensemble of the distributed parameter system compares well with ANSYS® simulation. The investigation reveals the spinning rate to have the most significant effect on the frequency value of the micro tool followed by the taper ratio and the complex geometry of the micro flute.