Analysis of tool oscillation and hole roundness error in a quasi-static model of reaming

A quasi-static model of reaming is developed to explain oscillation of the tool during cutting and the resulting roundness errors in reamed holes. A t ool with N evenly-spaced teeth often produces holes with N + 1 or N - 1 "lo bes." These profiles correspond, respectively to forward or backward whirl of the tool at N cycles/rev. Other whirl harmonics (2N cycles/rev, e.g.) ar e occasionally seen as well. The quasi-static model is motivated by the obs ervations that relatively large oscillations occur at frequencies well belo w the natural frequency of the tool, and that in this regime the wavelength of the hole profile is largely independent of both cutting speed and tool natural frequency. In the quasi-static approach, inertial and viscous dampi ng forces are neglected, but the system remains dynamic because regenerativ e (time-delayed) cutting and rubbing forces are included. The model leads t o an eigenvalue problem with forward and backward whirl solutions that clos ely resemble the tool behavior seen in practice.