Buckling loads and natural frequencies of drill bits and fluted cutters

The buckling loads, natural frequencies and mode shapes of twist-drill bits and certain fluted cutters under a variety of combinations of twist angle, cross-section geometry, and axial loading have been obtained. The drill bit is modelled as a twisted Euler beam under axial loading that is clamped at both ends. The governing system of differential equations is solved by the Galerkin procedure. Explicit forms for the basis functions used to generate the Galerkin coefficients are presented in general form in an appendix. They may be used for obtaining numerical results for that class of problems which use the Rayleigh-Ritz-Galerkin methods with beamtype functions as the basis functions. The representative set of modes obtained exhibit a complex out-of-plane twisting-type motion that suggests a possible explanation for the out-of-roundness of certain drilled holes.