Dynamic analysis of micro-endmill by Chebyshev spectral method

A Chebyshev spectral method for studying the dynamic characteristics of micro-endmill was presented. Considering the shear deformation and rotary inertia of micro-endmill, the uniform and tapered Timoshenko beam models were used in the dynamic analysis of the segments of endmill. The discrete forms of the dynamic models were gained by Chebyshev spectral method and synthesized by dynamic substructure technique to get the equation of motion of the whole system. A software package for solving the natural frequencies and modal shapes was developed. To validate the method, the impacts of structural parameters on dynamic characteristics were analysed. The simulation results were compared with those obtained by the stepped beam method and finite element method. It is shown that the calculated result converges into a range of 0.04% when the order of polynomials is larger than 16. The method is of good precision and can be applied to optimize structural parameters of micro-endmill.