Self-excited and Forced Oscillations with Solid Friction

2nd Report, Occurrence of Limit Cycles and Evaluation of Solutions in Case of Combined Friction-Velocity Characteristics

Eisuke Takano, Hidenobu Kawaguti, Xiang Yong Zhang, Masato Saeki

Research output: Contribution to journalArticle

Abstract

Forced frictional oscillations in a self-excited system occurred when the maximum static friction force did not become an isolation point and the kinetic friction force was given as a combined function of the relative sliding velocity composed of linear and hyperbolic functions. This process of oscillation was reviewed by the averaging method in continuation of the previous report. The properties of the limit cycle occurring where there was only one unstable first approximation solution of the harmonic oscillation with the values of the oscillation force circular frequency and the moving surface velocity are explained in this report. Various characteristics of the resultant stable, nonharmonic oscillations are also reviewed. By comparing results of the previous report with highly accurate, piecewise linear approximation solution, it was determined that this averaging method workes quite well and therefore is an effective method for judging the stability of the solution. It was learned that the highly accurate solution of the sliding motion could be estimated quantitatively by the stable first approximation solution using the averaging method. The unstable region in the first approximation solution corresponded with the occurrence region of the non-harmonic oscillations in the highly accurate solution. The solution by the averaging method showed the qualitative change of the amplitude.

Original languageEnglish
Pages (from-to)1705-1711
Number of pages7
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume67
Issue number658
DOIs
Publication statusPublished - 2001 Jan 1
Externally publishedYes

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Friction
Hyperbolic functions
Kinetics

Keywords

  • Averaging Method
  • Forced Vibration
  • Frictional Vibration
  • Limit Cycle
  • Mechanical Driving System
  • Nonlinear Vibration
  • Piecewise Linear System
  • Self-excited Oscillation
  • Sliding Friction
  • Sliding Surface
  • Vibration

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

Cite this

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title = "Self-excited and Forced Oscillations with Solid Friction: 2nd Report, Occurrence of Limit Cycles and Evaluation of Solutions in Case of Combined Friction-Velocity Characteristics",
abstract = "Forced frictional oscillations in a self-excited system occurred when the maximum static friction force did not become an isolation point and the kinetic friction force was given as a combined function of the relative sliding velocity composed of linear and hyperbolic functions. This process of oscillation was reviewed by the averaging method in continuation of the previous report. The properties of the limit cycle occurring where there was only one unstable first approximation solution of the harmonic oscillation with the values of the oscillation force circular frequency and the moving surface velocity are explained in this report. Various characteristics of the resultant stable, nonharmonic oscillations are also reviewed. By comparing results of the previous report with highly accurate, piecewise linear approximation solution, it was determined that this averaging method workes quite well and therefore is an effective method for judging the stability of the solution. It was learned that the highly accurate solution of the sliding motion could be estimated quantitatively by the stable first approximation solution using the averaging method. The unstable region in the first approximation solution corresponded with the occurrence region of the non-harmonic oscillations in the highly accurate solution. The solution by the averaging method showed the qualitative change of the amplitude.",
keywords = "Averaging Method, Forced Vibration, Frictional Vibration, Limit Cycle, Mechanical Driving System, Nonlinear Vibration, Piecewise Linear System, Self-excited Oscillation, Sliding Friction, Sliding Surface, Vibration",
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AB - Forced frictional oscillations in a self-excited system occurred when the maximum static friction force did not become an isolation point and the kinetic friction force was given as a combined function of the relative sliding velocity composed of linear and hyperbolic functions. This process of oscillation was reviewed by the averaging method in continuation of the previous report. The properties of the limit cycle occurring where there was only one unstable first approximation solution of the harmonic oscillation with the values of the oscillation force circular frequency and the moving surface velocity are explained in this report. Various characteristics of the resultant stable, nonharmonic oscillations are also reviewed. By comparing results of the previous report with highly accurate, piecewise linear approximation solution, it was determined that this averaging method workes quite well and therefore is an effective method for judging the stability of the solution. It was learned that the highly accurate solution of the sliding motion could be estimated quantitatively by the stable first approximation solution using the averaging method. The unstable region in the first approximation solution corresponded with the occurrence region of the non-harmonic oscillations in the highly accurate solution. The solution by the averaging method showed the qualitative change of the amplitude.

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