Interplay of Nonsmoothness, Time Delay, and Stochasticity in Turning Dynamics

Abstract: The stochastic dynamics of orthogonal metal cutting with both regenerative and nonsmooth frictional effects are investigated numerically in this paper. The shortcomings of neglecting nonsmoothness in frictional and stochastic effects in modeling the dynamics of such a machining process are demonstrated. Dynamics of the tool motion is observed to exhibit rich nonlinear phenomena such as stick-slip during chatter, with stochastic perturbations in cutting forces adding further complexity, leading to the occurrence of stochastic P and D bifurcations. Measures of entropy are found to be effective in quantifying the dynamical transitions occurring in the dynamics of the tool. Subsequently, basin stability analyses, modified to account for stochasticity and time-delays, are carried out to systematically investigate the dynamics of the cutting tool across multiple surface roughness profiles of the workpiece. Basin stability analyses indicate that chatter can be controlled by restricting initial tool displacement and controlling initial workpiece surface roughness, suggesting practical strategies to improve machining outcomes for precision manufacturing.