Journal ArticleDOI
Updated semi‐discretization method for periodic delay‐differential equations with discrete delay
Tamás Insperger,Gabor Stepan +1 more
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TLDR
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.Abstract:
An updated version of the semi-discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time-period/time-delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.read more
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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
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
Chatter stability of milling in frequency and discrete time domain
TL;DR: In this article, the frequency and discrete time domain chatter stability laws for milling operations are presented in a unified manner. And the time periodic dynamics of the milling process are modelled by averaging time varying directional factors at cutter pitch intervals.
Journal ArticleDOI
On stability prediction for milling
Janez Gradišek,Martin Kalveram,Tamás Insperger,Klaus Weinert,Gabor Stepan,Edvard Govekar,Igor Grabec +6 more
TL;DR: In this article, the authors investigated the stability of 2-dof milling by using the zeroth order approximation (ZOA) and semi-discretization (SD) methods.
References
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Book
Introduction to Functional Differential Equations
TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.
Book
Introduction to Robotics mechanics and Control
TL;DR: This chapter discusses Jacobians: Velocities and Static Forces, Robot Programming Languages and Systems, and Manipulator Dynamics, which focuses on the role of Jacobians in the control of Manipulators.