Modelling the tuned criticality in stick-slip friction during metal cutting
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Cutting is a ubiquitous process in nature and man-made systems. Here we demonstrate that, based on morphological patterns observed in experiments, the friction behaviour of metal cutting exhibits a criticality with cutting speed as a tuned parameter. The corresponding stick-slip events can be described by a power law distribution. A dynamic thermo-mechanical model is developed to investigate how such a tuned criticality occurs. It is shown that, in terms of the linear stability analysis, stick-slip friction is due to the thermo-mechanical instability and dynamical interaction between shear dissipation and nonlinear friction. Moreover, there is a secondary transition from a criticality state to a limit cycle that is dominated by the inertia effect, which is similar to the frequency lock phenomenon in a forced Duffing oscillator.
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