Nonlinear dynamics of a regenerative cutting process

TL;DR

This paper investigates the nonlinear dynamics of a regenerative cutting process using a non-smooth model with friction and delay, introducing a statistical 0-1 test for chaos detection and analyzing the transition from chaos to regularity with increasing cutting speed.

Contribution

It proposes a novel application of the 0-1 chaos test to a regenerative cutting model and demonstrates its effectiveness in identifying dynamic transitions.

Findings

Transition from chaotic to regular motion with increasing cutting speed

Validation of chaos detection using spectral density and multiscaled entropy

Application of the 0-1 test as an alternative to Lyapunov exponents

Abstract

We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test analysis for chaos detection. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. For the investigated deterministic model we are able to show a transition from chaotic to regular motion with increasing cutting speed. For two values of time delay showing the different response the results have been confirmed by the means of the spectral density and the multiscaled entropy.