An analytical study of the effect of process damping on reamer vibrations

A frequency-domain approach is used to study the effects of a velocity-dependent force caused by the rubbing between the reamer margins and the hole wall. The solution method determines tool stability and hole form. The velocity-dependent force, colloquially known as process damping, has been used in turning and milling, where it has been shown to stabilize the system at low spindle speeds. The addition of the process-damping model in the reamer model stabilizes self-excited chatter near the first fundamental tool bending frequency, but destabilizes low-frequency vibration. The method yields combinations of cutting speed and depth of cut that bind stable cutting regions. The boundaries for reaming with no process damping closely resemble the shape of milling stability diagrams, but the small radial depth of cut is unrealistic. The addition of process damping changes the shape of the stability regions and also increases the stable depth of cut. Notably, eigenvalue solutions are found with increased process damping that lead to low-frequency whirling modes, which resemble those found in practice. A simulation using a numerical Euler integration technique will be used to match the analytical model. The simulation will allow for future research using nonlinear models, uneven tooth spacing, and arbitrary initial hole profile data.