Complex dynamics in metal cutting

Abstract

Abstract. The attractor associated with a system of nonlinear differential-delay equations, arising from the Wu-Liu metal cutting model, is shown to have a noninteger pointwise dimension and positive metric entropy. Projections of the attractor onto a two-dimensional plane substantiate the existence of complex dynamics. The result suggests that certain regenerative chatter states may be chaotic.Introduction. In [1-3] a system of coupled discontinuous ordinary differential equations, identical in form to Eq. (1), model an orthogonal metal-cutting process. The cutting force, F, is assumed to be a discontinuous function of the depth of cut and the relative velocity between tool and cutting surface. Regenerative effects are omitted. For certain parametric ranges, the response of the system is shown to be

Stability Modeling and Analysis of Orthogonal Turn-Milling with Variable Cutting Depth and Cutting Thickness

“…Merrit [3] was the first one who used chatter stability lobes to analyze regenerative chatter stability of orthogonal cutting. In terms of stability modeling for milling, Minis et al [4] used analytical method to forecast the stability limit of 2-DOF milling system. Considering the changeable direction coefficients of cutting force, Altintas and Budak [5] established a 2-DOF milling stability model and used Zero-order solution to solve the dynamic equations.…”

Stability analysis in a second-order differential equation with delays

“…The second-order delay differential equations arise in many areas, such as [1,[3][4][5][6]. In [7], typically these equations take the form…”

Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity

“…[5][6][7][8][9][10][11] The linear stability and Hopf bifurcation of Eq. Equation ͑1.1͒ also arises in a variety of mechanical, or neuromechanical, system in which inertia plays an important role.…”