### Abstract

Frictional oscillations occurring in a forced self-excited system were treated when the kinetic friction force was shown as a combined characteristic curve of linear and hyperbolic functions of the relative sliding velocity. The authors studied the characteristics and stabilities of the oscillations in the first approximate solution for harmonic oscillation form (among the steady-state oscillation solutions which can be obtained by the averaging method). The study results of various properties of the solution for non-harmonic oscillation solution accompanying the occurrence of limit cycles have been reported previously. Highly accurate, steady-state oscillation solutions (with consideration given to the two motions of slipping and sticking) are obtained with a computer by approximating the characteristic curve of the frictional force and slipping velocity with n broken lines and connecting the successive solution curves on the phase plane in the velocity boundaries of each broken line. The piecewise linear approximation method for obtaining a highly accurate solution which is very similar to the exact solution is explained first. The occurrence forms and the distribution conditions of various steady-state oscillation solutions unobtainable by the averaging method, including the maximum static friction force becoming an isolated point, are described. The resonance characteristics of the system and the effect of the velocity of the moving surface on the characteristics of the steady-state oscillation solutions are reported.

Original language | English |
---|---|

Pages (from-to) | 1712-1718 |

Number of pages | 7 |

Journal | Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C |

Volume | 67 |

Issue number | 658 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### 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

*Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C*,

*67*(658), 1712-1718. https://doi.org/10.1299/kikaic.67.1712

**Self-excited and Forced Oscillations with Solid Friction : 3rd Report, Piecewise Linear Approximate Solutions in Case of Combined Friction-Velocity Characteristics.** / Takano, Eisuke; Kawaguti, Hidenobu; Zhang, Xiang Yong; Saeki, Masato.

Research output: Contribution to journal › Article

*Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C*, vol. 67, no. 658, pp. 1712-1718. https://doi.org/10.1299/kikaic.67.1712

}

TY - JOUR

T1 - Self-excited and Forced Oscillations with Solid Friction

T2 - 3rd Report, Piecewise Linear Approximate Solutions in Case of Combined Friction-Velocity Characteristics

AU - Takano, Eisuke

AU - Kawaguti, Hidenobu

AU - Zhang, Xiang Yong

AU - Saeki, Masato

PY - 2001

Y1 - 2001

N2 - Frictional oscillations occurring in a forced self-excited system were treated when the kinetic friction force was shown as a combined characteristic curve of linear and hyperbolic functions of the relative sliding velocity. The authors studied the characteristics and stabilities of the oscillations in the first approximate solution for harmonic oscillation form (among the steady-state oscillation solutions which can be obtained by the averaging method). The study results of various properties of the solution for non-harmonic oscillation solution accompanying the occurrence of limit cycles have been reported previously. Highly accurate, steady-state oscillation solutions (with consideration given to the two motions of slipping and sticking) are obtained with a computer by approximating the characteristic curve of the frictional force and slipping velocity with n broken lines and connecting the successive solution curves on the phase plane in the velocity boundaries of each broken line. The piecewise linear approximation method for obtaining a highly accurate solution which is very similar to the exact solution is explained first. The occurrence forms and the distribution conditions of various steady-state oscillation solutions unobtainable by the averaging method, including the maximum static friction force becoming an isolated point, are described. The resonance characteristics of the system and the effect of the velocity of the moving surface on the characteristics of the steady-state oscillation solutions are reported.

AB - Frictional oscillations occurring in a forced self-excited system were treated when the kinetic friction force was shown as a combined characteristic curve of linear and hyperbolic functions of the relative sliding velocity. The authors studied the characteristics and stabilities of the oscillations in the first approximate solution for harmonic oscillation form (among the steady-state oscillation solutions which can be obtained by the averaging method). The study results of various properties of the solution for non-harmonic oscillation solution accompanying the occurrence of limit cycles have been reported previously. Highly accurate, steady-state oscillation solutions (with consideration given to the two motions of slipping and sticking) are obtained with a computer by approximating the characteristic curve of the frictional force and slipping velocity with n broken lines and connecting the successive solution curves on the phase plane in the velocity boundaries of each broken line. The piecewise linear approximation method for obtaining a highly accurate solution which is very similar to the exact solution is explained first. The occurrence forms and the distribution conditions of various steady-state oscillation solutions unobtainable by the averaging method, including the maximum static friction force becoming an isolated point, are described. The resonance characteristics of the system and the effect of the velocity of the moving surface on the characteristics of the steady-state oscillation solutions are reported.

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

UR - http://www.scopus.com/inward/record.url?scp=85024469983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024469983&partnerID=8YFLogxK

U2 - 10.1299/kikaic.67.1712

DO - 10.1299/kikaic.67.1712

M3 - Article

AN - SCOPUS:85024469983

VL - 67

SP - 1712

EP - 1718

JO - Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

JF - Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

SN - 0387-5024

IS - 658

ER -