Complex dynamics in metal cutting
Open Access
- 1 December 1993
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 51 (4) , 601-612
- https://doi.org/10.1090/qam/1247430
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.Keywords
This publication has 13 references indexed in Scilit:
- Improved Methods for the Prediction of Chatter in Turning, Part 1: Determination of Structural Response ParametersJournal of Engineering for Industry, 1990
- Practical considerations in estimating dimension from time series dataPhysica Scripta, 1989
- Explanation of random vibrations in cutting on grounds of deterministic chaosRobotics and Computer-Integrated Manufacturing, 1988
- Chaotic dynamics of the cutting processInternational Journal of Machine Tools and Manufacture, 1988
- Evaluation of dimensions and entropies of chaotic systemsJournal of the Optical Society of America B, 1988
- Chaos generated by the cutting processPhysics Letters A, 1986
- An Approach to Error-Estimation in the Application of Dimension AlgorithmsPublished by Springer Nature ,1986
- Ergodic theory of chaos and strange attractorsReviews of Modern Physics, 1985
- Stability in linear multistep methods for pure delay equationsJournal of Computational and Applied Mathematics, 1984
- The dimension of chaotic attractorsPhysica D: Nonlinear Phenomena, 1983