Self-excited and Forced Oscillations with Solid Friction

1st Report, Solutions and Stabilities by Averaging Method in Case of Combined Friction-Velocity Characteristics of Linear and Hyperbolic Curves

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

Research output: Contribution to journalArticle

Abstract

In the present paper, the frictional oscillations in a mechanical driving system are studied theoretically on the self-excited and forced oscillations, when the friction-velocity characteristic curves are given as the combined curves of linear and hyperbolic functions and maximum static friction force is not an isolated point. Bodies acted upon by sinusoidal external force while sliding along a surface at a fixed velocity exhibit regular oscillations. We have analyzed these motions using an averaging method, without distinguishing between slipping and sticking. We have also examined the amplitude characteristic of motions found in the obtainable first approximations of the form of harmonic vibrations. Finally, we made a detailed investigation of the stability of these first approximations. Also, we have assembled the results of a comparison of the precise solutions for motions over a wide range of velocities where the kinetic velocity of the body exceeding the surface motion velocity, and we propose a usable theoretical analysis method, aimed at understanding the important aspects of regular harmonic solutions.

Original languageEnglish
Pages (from-to)1697-1704
Number of pages8
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume67
Issue number658
DOIs
Publication statusPublished - 2001
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: 1st Report, Solutions and Stabilities by Averaging Method in Case of Combined Friction-Velocity Characteristics of Linear and Hyperbolic Curves",
abstract = "In the present paper, the frictional oscillations in a mechanical driving system are studied theoretically on the self-excited and forced oscillations, when the friction-velocity characteristic curves are given as the combined curves of linear and hyperbolic functions and maximum static friction force is not an isolated point. Bodies acted upon by sinusoidal external force while sliding along a surface at a fixed velocity exhibit regular oscillations. We have analyzed these motions using an averaging method, without distinguishing between slipping and sticking. We have also examined the amplitude characteristic of motions found in the obtainable first approximations of the form of harmonic vibrations. Finally, we made a detailed investigation of the stability of these first approximations. Also, we have assembled the results of a comparison of the precise solutions for motions over a wide range of velocities where the kinetic velocity of the body exceeding the surface motion velocity, and we propose a usable theoretical analysis method, aimed at understanding the important aspects of regular harmonic solutions.",
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",
author = "Eisuke Takano and Hidenobu Kawaguti and Zhang, {Xiang Yong} and Masato Saeki",
year = "2001",
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journal = "Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C",
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AU - Takano, Eisuke

AU - Kawaguti, Hidenobu

AU - Zhang, Xiang Yong

AU - Saeki, Masato

PY - 2001

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N2 - In the present paper, the frictional oscillations in a mechanical driving system are studied theoretically on the self-excited and forced oscillations, when the friction-velocity characteristic curves are given as the combined curves of linear and hyperbolic functions and maximum static friction force is not an isolated point. Bodies acted upon by sinusoidal external force while sliding along a surface at a fixed velocity exhibit regular oscillations. We have analyzed these motions using an averaging method, without distinguishing between slipping and sticking. We have also examined the amplitude characteristic of motions found in the obtainable first approximations of the form of harmonic vibrations. Finally, we made a detailed investigation of the stability of these first approximations. Also, we have assembled the results of a comparison of the precise solutions for motions over a wide range of velocities where the kinetic velocity of the body exceeding the surface motion velocity, and we propose a usable theoretical analysis method, aimed at understanding the important aspects of regular harmonic solutions.

AB - In the present paper, the frictional oscillations in a mechanical driving system are studied theoretically on the self-excited and forced oscillations, when the friction-velocity characteristic curves are given as the combined curves of linear and hyperbolic functions and maximum static friction force is not an isolated point. Bodies acted upon by sinusoidal external force while sliding along a surface at a fixed velocity exhibit regular oscillations. We have analyzed these motions using an averaging method, without distinguishing between slipping and sticking. We have also examined the amplitude characteristic of motions found in the obtainable first approximations of the form of harmonic vibrations. Finally, we made a detailed investigation of the stability of these first approximations. Also, we have assembled the results of a comparison of the precise solutions for motions over a wide range of velocities where the kinetic velocity of the body exceeding the surface motion velocity, and we propose a usable theoretical analysis method, aimed at understanding the important aspects of regular harmonic solutions.

KW - Averaging Method

KW - Forced Vibration

KW - Frictional Vibration

KW - Limit Cycle

KW - Mechanical Driving System

KW - Nonlinear Vibration

KW - Piecewise Linear System

KW - Self-excited Oscillation

KW - Sliding Friction

KW - Sliding Surface

KW - Vibration

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