Journal ArticleDOI
Semi‐discretization method for delayed systems
Tamás Insperger,Gabor Stepan +1 more
TLDR
In this article, the authors present a numerical method for the stability analysis of linear delayed systems based on a special kind of discretization technique with respect to the past effect only.Abstract:
SUMMARY The paper presents an ecient numerical method for the stability analysis of linear delayed systems. The method is based on a special kind of discretization technique with respect to the past eect only. The resulting approximate system is delayed and also time periodic, but still, it can be transformed analytically into a high-dimensional linear discrete system. The method is applied to determine the stability charts of the Mathieu equation with continuous time delay. Copyright ? 2002 John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
Chatter in machining processes: A review
Guillem Quintana,Joaquim Ciurana +1 more
TL;DR: A review of the state of research on the chatter problem and classifications the existing methods developed to ensure stable cutting into those that use the lobbing effect, out-of-process or in-process, and those that, passively or actively, modify the system behavior as mentioned in this paper.
Journal ArticleDOI
Updated semi‐discretization method for periodic delay‐differential equations with discrete delay
Tamás Insperger,Gabor Stepan +1 more
TL;DR: In this paper, an updated version of the semi-discretization method is presented for periodic systems with a single discrete time delay, where the delayed term is approximated as a weighted sum of two neighboring discrete delayed state values and the transition matrix over a single period is determined.
Journal ArticleDOI
Chatter suppression techniques in metal cutting
Jokin Munoa,Xavier Beudaert,Zoltan Dombovari,Yusuf Altintas,Erhan Budak,Christian Brecher,Gabor Stepan +6 more
TL;DR: A critical review of the different chatter suppression techniques can be found in this paper, where the evolution of each technique is described remarking the most important milestones in research and the corresponding industrial application.
Journal ArticleDOI
A full-discretization method for prediction of milling stability
TL;DR: A full-discretization method based on the direct integration scheme for prediction of milling stability based on Floquet theory that has high computational efficiency without loss of any numerical precision is presented.
Journal ArticleDOI
Stability of up-milling and down-milling, part 1: alternative analytical methods
TL;DR: In this paper, the dynamic stability of the milling process is investigated through a single degree of freedom mechanical model and two alternative analytical methods are introduced, both based on finite dimensional discrete map representations of the governing time periodic delay differential equation.
References
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Book
Theory of Functional Differential Equations
TL;DR: In this paper, Liapunov functional for autonomous systems is used to define the saddle point property near equilibrium and periodic orbits for linear systems, which is a generalization of the notion of stable D operators.
Journal ArticleDOI
Sur les équations différentielles linéaires à coefficients périodiques
TL;DR: In this paper, Gauthier-Villars implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
Journal ArticleDOI
Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt
TL;DR: Auf Veranlassung meines verehrten Kollegen, Herrn A. Stodola, beschaftigte ich mich vor einiger Zeit mit der Frage, wann eine Gleichung n ten Grades with reelle Koeffizienten ist negativ sind as discussed by the authors.
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Updated semi‐discretization method for periodic delay‐differential equations with discrete delay
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