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.

Figures (14)

• Figure 1: Schematic of the turning process representing the orientation of the tool and workpiece and their relative directions of motion.
• Figure 2: Schematic of the turning process modeled as a spring-mass-damper system representing various cutting forces.
• Figure 3: Stribeck friction coefficient $\mu(V_\gamma)$ with parameters $\mu_d=0.23$, $\mu_s=0.54$, $V_s=0.65\;\mathrm{ms^{-1}}$. The antisymmetric curve shows an exponential transition from static to dynamic friction regimes around the Stribeck velocity.
• Figure 4: The stability lobe diagram shows the numerically computed stable region in green and the chatter region in magenta. The blue curve depicts the stability lobes for the model with both frictional and regenerative effects, whereas the orange curve shows the lobes for the regenerative and static-friction model. The red crosses denote chatter and the green stars indicate stable cutting as observed experimentally by Altintas et al.altintas2008identification.
• Figure 5: Bifurcation diagram using depth of cut $a_p$ as the bifurcation parameter. Figure (a) shows the maximum and minimum values of chip thickness $H$, and (b) shows the corresponding maximum and minimum values of frictional velocity $V_\gamma$.