# Probabilistic approach in fatigue of crankshaft by using Markov chain model

Nik Abdullah Nik Mohamed, Salvinder Singh Karam Singh, Shakib Sharifian, Mohd. Salmi Md. Noorani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

### 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 (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.

Original language English Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012 National Committee on Applied Mechanics 604-611 8 9781922107619 Published - 2012 7th Australasian Congress on Applied Mechanics, ACAM 2012 - Adelaide, SADuration: 9 Dec 2012 → 12 Dec 2012

### Other

Other 7th Australasian Congress on Applied Mechanics, ACAM 2012 Adelaide, SA 9/12/12 → 12/12/12

### Fingerprint

Crankshafts
Markov processes
Fatigue of materials
Torsional stress
Statistical methods
Bending (deformation)
Pistons
Connecting rods
Seals
Crack propagation

• Bending
• Markov chain
• Probability
• Stochastic
• Torsion

### ASJC Scopus subject areas

• Mechanics of Materials

### Cite this

Nik Mohamed, N. A., Singh, S. S. K., Sharifian, S., & Md. Noorani, M. S. (2012). Probabilistic approach in fatigue of crankshaft by using Markov chain model. In 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nik Mohamed, NA, Singh, SSK, Sharifian, S & Md. Noorani, MS 2012, Probabilistic approach in fatigue of crankshaft by using Markov chain model. in 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.
Nik Mohamed NA, Singh SSK, Sharifian S, Md. Noorani MS. Probabilistic approach in fatigue of crankshaft by using Markov chain model. In Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012. National Committee on Applied Mechanics. 2012. p. 604-611
Nik Mohamed, Nik Abdullah ; Singh, Salvinder Singh Karam ; Sharifian, Shakib ; Md. Noorani, Mohd. Salmi. / Probabilistic approach in fatigue of crankshaft by using Markov chain model. Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012. National Committee on Applied Mechanics, 2012. pp. 604-611
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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.

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