An Analytical Model of Micro-Endmill Dynamics in the Presence of Tool Setup Errors

This paper presents an analytical model of micro-endmill dynamics in the presence of the setup errors. To accurately capture the rotary inertia and shear deformations of non-slender micro-endmills, Timoshenko-beam equations are used to derive the boundary-value problem for transverse vibrations of rotating micro-endmills with setup errors. The numerical solution of the boundary-value problem is obtained through a spectral-Tchebychev method. The model and the spectral-Tchebychev method are validated by comparing the mode shapes and natural frequencies to those from a commercial finite-elements code. The effectiveness of the model is illustrated by applying it to investigate (1) rotational stability of micro-endmills, (2) the effect of tool geometry on mode shapes and natural frequencies, (3) the influence of setup errors, and (4) the dynamic response of the micro-endmills to harmonic forcing. The model can be used for designing micro tools with preferred dynamic characteristics, as well as for modeling and stability analysis of the micromilling process.