### 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 language | English |
---|---|

Pages (from-to) | 1697-1704 |

Number of pages | 8 |

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), 1697-1704. https://doi.org/10.1299/kikaic.67.1697

**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.** / 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. 1697-1704. https://doi.org/10.1299/kikaic.67.1697

}

TY - JOUR

T1 - Self-excited and Forced Oscillations with Solid Friction

T2 - 1st Report, Solutions and Stabilities by Averaging Method in Case of Combined Friction-Velocity Characteristics of Linear and Hyperbolic Curves

AU - Takano, Eisuke

AU - Kawaguti, Hidenobu

AU - Zhang, Xiang Yong

AU - Saeki, Masato

PY - 2001

Y1 - 2001

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

UR - http://www.scopus.com/inward/record.url?scp=85024453738&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024453738&partnerID=8YFLogxK

U2 - 10.1299/kikaic.67.1697

DO - 10.1299/kikaic.67.1697

M3 - Article

VL - 67

SP - 1697

EP - 1704

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 -