Analityczna metoda określania amplitudy drgań ciernych (typu stick-slip)

Translated title of the contribution: Analytical approach to estimate amplitude of stick-slip oscillations

Jamil Abdo, Ahmed A. Abouelsoud

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The objective of the present work is to evaluate alternative approximate techniques to determine the amplitudes of the limit cycles that evolve from stick-slip vibrations based on a mass-on-moving-belt model. The control of self-excited systems is a very interesting problem because of friction-induced self sustained oscillations which result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using the Liapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition, an estimate of the amplitude of the velocity of the limit cycle of stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are indistinguishable.

Original languageUndefined/Unknown
Pages (from-to)971-986
Number of pages16
JournalJournal of Theoretical and Applied Mechanics
Volume49
Issue number4
Publication statusPublished - 2011

Fingerprint

Stick-slip
Oscillation
Limit Cycle
Estimate
Motion
Zero of a function
Positive Definite Functions
Coulomb Friction
Damper
Friction
Vibration
Derivative
Evaluate
Alternatives
Model
Simulation

Keywords

  • Liapunov second method
  • Limit cycles
  • Stick-slip oscillations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Analityczna metoda określania amplitudy drgań ciernych (typu stick-slip). / Abdo, Jamil; Abouelsoud, Ahmed A.

In: Journal of Theoretical and Applied Mechanics, Vol. 49, No. 4, 2011, p. 971-986.

Research output: Contribution to journalArticle

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N2 - The objective of the present work is to evaluate alternative approximate techniques to determine the amplitudes of the limit cycles that evolve from stick-slip vibrations based on a mass-on-moving-belt model. The control of self-excited systems is a very interesting problem because of friction-induced self sustained oscillations which result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using the Liapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition, an estimate of the amplitude of the velocity of the limit cycle of stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are indistinguishable.

AB - The objective of the present work is to evaluate alternative approximate techniques to determine the amplitudes of the limit cycles that evolve from stick-slip vibrations based on a mass-on-moving-belt model. The control of self-excited systems is a very interesting problem because of friction-induced self sustained oscillations which result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using the Liapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition, an estimate of the amplitude of the velocity of the limit cycle of stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are indistinguishable.

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