Nonlinear behaviour of the regenerative chatter in turning process with a worn tool: Forced oscillation and stability analysis

Self-excited and forced vibrations are important topics in machining processes because their occurrence results in poor surface finish, increase in tool wear and reduction of material removal rate. In this paper, turning process is modeled as a single degree of freedom (SDOF) dynamic system including quadratic and cubic structural nonlinearities. The effect of tool flank wear, as a contact force between the workpiece and tool, is addressed vigorously. Multiple scale method is used to find the solution of the nonlinear delay-differential equation including regenerative chatter, forced excitation and tool wear. During the stability analysis, it is shown that width of cut can be considered as the bifurcation parameter of the system. Finding frequency-response function, behaviour of the system under primary, sub-harmonic and super-harmonic resonances is explained. Specifically, under sub-harmonic and super-harmonic resonances, turning process shows interesting behaviour. The existence of jump phenomenon and its relationship with the machining parameters and structural nonlinearity is discussed in each resonance cases. Finally, stability of the steady state motion is investigated in terms of tool wear length, width of cut and spindle speed. Results are compared for two distinct cases: system with fresh and worn tools.