Modeling of chatter vibrations in gun drilling process

The dynamics of the gun drilling process is analyzed in this paper. The tool shank is modeled as long straight beam vibrating in transverse direction under action of cutting forces. Axial force component is expressed as proportional to cutting thickness, which is determined as nonlinear function of beam transverse deflection with time delay. Nonlinear equations of motion of the drilling shank are derived. The stability diagram of the system dynamics was determined. The bifurcation analysis of nonlinear differential delay equations by means of multiple scale method was performed. The obtained results were verified by numerical integration of nonlinear equations. The influence of cutting conditions on system stability and chatter amplitude was observed.