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Drgania okresowe, prawie okresowe i chaotyczne w procesach toczenia

Łuczko J.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2008

z. 74 [258]

221-232

The paper is concerned with qualitative analysis of a non-linear model describing the vibrations in cutting processes. The model of the regenerative turning process is described by two delay differential equations. The influence of selected parameters such as the rotational velocity and the frequency of the kinematic excitations as well as the cutting speed and the cutting resistance on the character and level of vibrations is studied. The possibility of the excitation of quasi-periodic or chaotic oscillations for some values of the parameters has been shown. Zones of the sub-harmonic, quasi-periodic and chaotic vibrations were estimated by the methods of numerical integration. Bifurcation diagrams have been used to explain the phenomenon of vibration synchronization. Different types of vibration are illustrated by plots of time histories, phase and stroboscopic portraits.

Drgania chaotyczne belki wymuszone nadkrytyczną siłą osiową

Łuczko J.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2002

z. 60 [197]

397-404

In the paper the qualitative analysis of the geometrically non-linear beam model subjected to super critical axial force was presented. The Melnikov and Galerkin methods coupled with the methods of bifurcation analysis were applied. The regions of periodical and chaotical vibrations were determined. The results obtained were verified by methods of numerical integration.

Almost periodic vibration excited by dry friction

Bogacz R., Ryczek B.

Mechanics and Mechanical Engineering

2000

Vol. 4, nr 2

197--212

This paper attends to the problem of a self-excited system with dry friction. The system is composed of mass that interact viscoelasticly with the drive, and by means of dry friction with a foundation The objective of the experimental research on the system was to formulate a dry friction model that would describe the case of stick-slip vibration as well as almost-periodic vibration of steel-polyester pair The model allows for the impact of the following parameters: velocity of motion, acceleration sign, time of adhesion and force rate. The paper includes computer simulation of the vibration of the considered system and comparison between the results of experimental and theoretical analysis.