Vibration of a rotating tapered composite shaft and applications to high speed cutting

A mechanical model is developed of a tapered, filament-wound composite shaft which is rotating at constant speed about its axis. The model represents an extended length cutting tool intended for use in high speed operations. Deflection dependent cutting forces are included. The effects of shaft tapering and the use of composite materials on the structure's response are studied. The spatial solutions to the equations of motion are carried out using the general Galerkin method. For free vibrations it is found that by tapering, bending natural frequencies and stiffness can be significantly increased over those of uniform shafts having the same volume and made of the same material. Various graphite fiber composite laminate cases are treated and it is found that improvements of performance are possible over equivalent steel shafts. Cutting stability diagrams and forced responses during a cutting process are determined using the monodromy matrix method and numerical integration, respectively. It is shown that increasing the static bending stiffness by tapering and the higher damping of the composites increase the stable-cutting regions. Also, use of composites and shaft tapering, with the attendant increase in bending natural frequencies, can be beneficial from a forced motion viewpoint, provided the forcing frequency is below the first bending natural frequency.