### Abstract

This paper describes the probabilistic method of using Markov chain model in determining the statistical relationship between bending and torsion on the effects of fatigue on the crankshaft. The crankshaft is subjected to cyclic loading which will tend to display the effects of fatigue which is stochastic in nature. This is because of the bending stresses due to self-weight of the piston, connecting rod and other components or misalignment of the piston and torsion stress. The Markov Chain was modelled to represent the probability for bending and torsion that would be acting on the crankshaft. It was observed from the model, that the loading on the crankshaft would be in a recurrent state where the loading would be returning or happening over time. Each probability was tested over a given time interval and the statistical analysis of the expected results were calculated and shown. Based from the statistical analysis, the coefficient of determination (R^{2}) was calculated to be 81% where it is significant to conclude that the fatigue of a crankshaft is due to bending and supported by torsion. The effects of the statistical analysis can also be observed through the path of the crack propagation on the journal of the crankshaft which starts from the fillet region and propagates to the oil seal at a 45 degree angle.

Original language | English |
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Title of host publication | Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012 |

Publisher | National Committee on Applied Mechanics |

Pages | 604-611 |

Number of pages | 8 |

ISBN (Print) | 9781922107619 |

Publication status | Published - 2012 |

Event | 7th Australasian Congress on Applied Mechanics, ACAM 2012 - Adelaide, SA Duration: 9 Dec 2012 → 12 Dec 2012 |

### Other

Other | 7th Australasian Congress on Applied Mechanics, ACAM 2012 |
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City | Adelaide, SA |

Period | 9/12/12 → 12/12/12 |

### Fingerprint

### Keywords

- Bending
- Markov chain
- Probability
- Stochastic
- Torsion

### ASJC Scopus subject areas

- Mechanics of Materials

### Cite this

*Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012*(pp. 604-611). National Committee on Applied Mechanics.

**Probabilistic approach in fatigue of crankshaft by using Markov chain model.** / Nik Mohamed, Nik Abdullah; Singh, Salvinder Singh Karam; Sharifian, Shakib; Md. Noorani, Mohd. Salmi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012.*National Committee on Applied Mechanics, pp. 604-611, 7th Australasian Congress on Applied Mechanics, ACAM 2012, Adelaide, SA, 9/12/12.

}

TY - GEN

T1 - Probabilistic approach in fatigue of crankshaft by using Markov chain model

AU - Nik Mohamed, Nik Abdullah

AU - Singh, Salvinder Singh Karam

AU - Sharifian, Shakib

AU - Md. Noorani, Mohd. Salmi

PY - 2012

Y1 - 2012

N2 - This paper describes the probabilistic method of using Markov chain model in determining the statistical relationship between bending and torsion on the effects of fatigue on the crankshaft. The crankshaft is subjected to cyclic loading which will tend to display the effects of fatigue which is stochastic in nature. This is because of the bending stresses due to self-weight of the piston, connecting rod and other components or misalignment of the piston and torsion stress. The Markov Chain was modelled to represent the probability for bending and torsion that would be acting on the crankshaft. It was observed from the model, that the loading on the crankshaft would be in a recurrent state where the loading would be returning or happening over time. Each probability was tested over a given time interval and the statistical analysis of the expected results were calculated and shown. Based from the statistical analysis, the coefficient of determination (R2) was calculated to be 81% where it is significant to conclude that the fatigue of a crankshaft is due to bending and supported by torsion. The effects of the statistical analysis can also be observed through the path of the crack propagation on the journal of the crankshaft which starts from the fillet region and propagates to the oil seal at a 45 degree angle.

AB - This paper describes the probabilistic method of using Markov chain model in determining the statistical relationship between bending and torsion on the effects of fatigue on the crankshaft. The crankshaft is subjected to cyclic loading which will tend to display the effects of fatigue which is stochastic in nature. This is because of the bending stresses due to self-weight of the piston, connecting rod and other components or misalignment of the piston and torsion stress. The Markov Chain was modelled to represent the probability for bending and torsion that would be acting on the crankshaft. It was observed from the model, that the loading on the crankshaft would be in a recurrent state where the loading would be returning or happening over time. Each probability was tested over a given time interval and the statistical analysis of the expected results were calculated and shown. Based from the statistical analysis, the coefficient of determination (R2) was calculated to be 81% where it is significant to conclude that the fatigue of a crankshaft is due to bending and supported by torsion. The effects of the statistical analysis can also be observed through the path of the crack propagation on the journal of the crankshaft which starts from the fillet region and propagates to the oil seal at a 45 degree angle.

KW - Bending

KW - Markov chain

KW - Probability

KW - Stochastic

KW - Torsion

UR - http://www.scopus.com/inward/record.url?scp=84907382108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907382108&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781922107619

SP - 604

EP - 611

BT - Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012

PB - National Committee on Applied Mechanics

ER -