An Analytical Model of Cutting Dynamics. Part 1: Model Building

Abstract

A mathematical model of machining chatter has been developed through an analytical approach in order to predict dynamic cutting force from steady-state cutting tests. The model is derived from a pseudo-static geometric configuration of the cutting process by taking into account the fact that the mean friction coefficient fluctuates dynamically responding to variation of the relative speed on the chip-tool interface. The force functions through this derivation can be used to explain all three basic mechanics associated with chatter vibration, namely, velocity dependent, regenerative, and mode coupling effects.

Prospects for chaos control of machine tool chatter

“…Early two-dimensional modeling by Tlusty and Ismail [ 191 found that the tool can lose contact with the workpiece at large chatter amplitude, thus improving chatter stability for turning and milling. The nonlinear delayed differential equation (DDE) model of Wu and Liu [25] included fluctuations in the mean friction coefficient due to chip removal, and yielded results that are consistent with experimental chatter dynamics [26]. Berger et al [2] used the model of Ref.…”

“…Berger et al [2] used the model of Ref. 25 and found chaotic dynamics for certain parameter regimes, with limit cycle behavior in heavy chatter and more complex dynamics in mild chatter. Chaotic dynamics has also been found in related models [5,22].…”

Complex dynamics in metal cutting

“…In the following, F is given by the Wu-Liu model [4], in which regenerative effects are included. The resulting coupled system of dissipative nonlinear differential delay equations was found to have unbounded solutions, contrary to experimental evidence.…”

“…The continuous system consisting of cutting tool and supporting structure is modeled in [4] by a set of o.d.e. of the form my + by + ky = F…”

Improvement of chatter stability in boring operations with passive vibration absorbers

“…Wu and Liu [9,10] derived a mathematical model taking into account the effect of dry friction at the tool-chip interface, which was identified as a source of chatter due to its velocity-dependent nature.…”