An analytical model for micro-endmill dynamics

This article presents an analytical model of the transverse vibration of rotating micro-endmills in the presence of three-dimensional tilt and rotary axis misalignment. To accurately capture the rotary inertia and shear deformations of non-slender micro-endmills, the Timoshenko beam model is used. The boundary-value problem is derived using the extended Hamilton's principle. The numerical solution of the problem is obtained through a spectral Tchebychev technique. Non-smooth diameter variations along the length are handled by considering the micro-endmill as a sectioned beam and using a component mode synthesis method. The mode shapes and natural frequencies from the model are compared to those from a commercial finite element solver. The effectiveness of the model is illustrated by applying it to analyze (1) the effect of the rotational speed on the micro-endmill dynamics, (2) the effect of geometry on mode shapes and natural frequencies, (3) the influence of three-dimensional tilt and eccentricity on vibrations, and (4) the dynamic response of the micro-endmills to harmonic forcing. It was shown that the derived model and associated spectral Tchebychev technique effectively and efficiently capture the dynamic behavior of rotating micro-endmills. The model can be used for designing micro-tools with specified dynamic characteristics, as well as for modeling and stability analysis of the micromilling process.