### Abstract

Above a certain critical speed, sliding systems with frictional heating such as brakes and clutches can exhibit thermoelastic instability in which non-uniform perturbations develop in the pressure and temperature fields. A method is described in which the transient thermomechanical behaviour of such systems is approximated by a reduced order model, describing one or more dominant perturbations or eigenfunctions. The goal is to construct a mathematical model of the system with a modest number of degrees of freedom. If a single dominant perturbation is used, an integral expression can be written for the evolution of the perturbation with time. A more accurate description involving several terms requires that the transient behaviour be generated by a sequence of operations in which the sliding speed is piecewise constant. Both models are evaluated by comparison with a direct numerical simulation and prove to give good accuracy with a dramatic reduction in computing time.

Original language | English |
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Pages (from-to) | 451-464 |

Number of pages | 14 |

Journal | International Journal of Mechanical Sciences |

Volume | 44 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2002 |

### Fingerprint

### Keywords

- Brake
- Clutch
- Eigenfunction series
- Reduced order model
- TEI
- Thermoelastic instability

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

**Transient solution of a thermoelastic instability problem using a reduced order model.** / Al-Shabibi, Abdullah M.; Barber, J. R.

Research output: Contribution to journal › Article

*International Journal of Mechanical Sciences*, vol. 44, no. 3, pp. 451-464. https://doi.org/10.1016/S0020-7403(01)00110-2

}

TY - JOUR

T1 - Transient solution of a thermoelastic instability problem using a reduced order model

AU - Al-Shabibi, Abdullah M.

AU - Barber, J. R.

PY - 2002/3

Y1 - 2002/3

N2 - Above a certain critical speed, sliding systems with frictional heating such as brakes and clutches can exhibit thermoelastic instability in which non-uniform perturbations develop in the pressure and temperature fields. A method is described in which the transient thermomechanical behaviour of such systems is approximated by a reduced order model, describing one or more dominant perturbations or eigenfunctions. The goal is to construct a mathematical model of the system with a modest number of degrees of freedom. If a single dominant perturbation is used, an integral expression can be written for the evolution of the perturbation with time. A more accurate description involving several terms requires that the transient behaviour be generated by a sequence of operations in which the sliding speed is piecewise constant. Both models are evaluated by comparison with a direct numerical simulation and prove to give good accuracy with a dramatic reduction in computing time.

AB - Above a certain critical speed, sliding systems with frictional heating such as brakes and clutches can exhibit thermoelastic instability in which non-uniform perturbations develop in the pressure and temperature fields. A method is described in which the transient thermomechanical behaviour of such systems is approximated by a reduced order model, describing one or more dominant perturbations or eigenfunctions. The goal is to construct a mathematical model of the system with a modest number of degrees of freedom. If a single dominant perturbation is used, an integral expression can be written for the evolution of the perturbation with time. A more accurate description involving several terms requires that the transient behaviour be generated by a sequence of operations in which the sliding speed is piecewise constant. Both models are evaluated by comparison with a direct numerical simulation and prove to give good accuracy with a dramatic reduction in computing time.

KW - Brake

KW - Clutch

KW - Eigenfunction series

KW - Reduced order model

KW - TEI

KW - Thermoelastic instability

UR - http://www.scopus.com/inward/record.url?scp=0036501647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036501647&partnerID=8YFLogxK

U2 - 10.1016/S0020-7403(01)00110-2

DO - 10.1016/S0020-7403(01)00110-2

M3 - Article

VL - 44

SP - 451

EP - 464

JO - International Journal of Mechanical Sciences

JF - International Journal of Mechanical Sciences

SN - 0020-7403

IS - 3

ER -