Exploration of the chaotic phenomena induced by fast plastic deformation of metals

We developed a nonlinear mathematical model for chip formation during cutting, comprising four autonomous differential equations and a constitutive equation describing the characteristics of metals. We used a continuation and bifurcation software to find the possible solutions of the differential equations. Certain solutions were determined using numerical simulation and the obtained times series were examined. The seven-dimensional parameter-space of the solutions was partially explored. We found that periodic solutions typically undergo a sequence of period doubling bifurcations as the model parameters are varied. We pointed out during the analysis of the set of equations that chaotic phenomena may also occur besides the formation of continuous chips reflecting a stable equilibrium state and lamellar chips that can be characterised by a periodic solution. Our model was verified by experimental results.