A statistical index for monitoring tooth cracks in a gearbox

Fathy Ismail; Hugh R. Martin; Farag Omar

doi:10.1115/DETC1995-0389

A statistical index for monitoring tooth cracks in a gearbox

Fathy Ismail, Hugh R. Martin, Farag Omar

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

1 Citation (Scopus)

Abstract

This paper is concerned with detecting and monitoring the growth of a tooth root crack in a gearbox. It uses the reciprocal of the Kurtosis of the beta distribution 1/k for each tooth period, as the damage indicator. A general equation to generate the statistical moments strictly in terms of the a and P parameters of the beta function is developed. To monitor the growth of the crack, a new index, called the "Kurtosis Index", is formulated from 1/k's of all the teeth. This index correlates well with the size of the crack, and it shows that small cracks can be detected.

Original language	English
Title of host publication	15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems
Publisher	American Society of Mechanical Engineers (ASME)
Pages	1413-1418
Number of pages	6
ISBN (Electronic)	9780791817186
DOIs	https://doi.org/10.1115/DETC1995-0389
Publication status	Published - 1995
Externally published	Yes
Event	ASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium - Boston, United States Duration: Sept 17 1995 → Sept 20 1995

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	3A-1995

Conference

Conference	ASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium
Country/Territory	United States
City	Boston
Period	9/17/95 → 9/20/95

ASJC Scopus subject areas

Mechanical Engineering
Computer Graphics and Computer-Aided Design
Computer Science Applications
Modelling and Simulation

Access to Document

10.1115/DETC1995-0389

Cite this

Ismail, F., Martin, H. R., & Omar, F. (1995). A statistical index for monitoring tooth cracks in a gearbox. In 15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems (pp. 1413-1418). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 3A-1995). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC1995-0389

A statistical index for monitoring tooth cracks in a gearbox. / Ismail, Fathy; Martin, Hugh R.; Omar, Farag.
15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems. American Society of Mechanical Engineers (ASME), 1995. p. 1413-1418 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 3A-1995).

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

Ismail, F, Martin, HR & Omar, F 1995, A statistical index for monitoring tooth cracks in a gearbox. in 15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems. Proceedings of the ASME Design Engineering Technical Conference, vol. 3A-1995, American Society of Mechanical Engineers (ASME), pp. 1413-1418, ASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium, Boston, United States, 9/17/95. https://doi.org/10.1115/DETC1995-0389

Ismail F, Martin HR, Omar F. A statistical index for monitoring tooth cracks in a gearbox. In 15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems. American Society of Mechanical Engineers (ASME). 1995. p. 1413-1418. (Proceedings of the ASME Design Engineering Technical Conference). doi: 10.1115/DETC1995-0389

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abstract = "This paper is concerned with detecting and monitoring the growth of a tooth root crack in a gearbox. It uses the reciprocal of the Kurtosis of the beta distribution 1/k for each tooth period, as the damage indicator. A general equation to generate the statistical moments strictly in terms of the a and P parameters of the beta function is developed. To monitor the growth of the crack, a new index, called the {"}Kurtosis Index{"}, is formulated from 1/k's of all the teeth. This index correlates well with the size of the crack, and it shows that small cracks can be detected.",

author = "Fathy Ismail and Martin, {Hugh R.} and Farag Omar",

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AB - This paper is concerned with detecting and monitoring the growth of a tooth root crack in a gearbox. It uses the reciprocal of the Kurtosis of the beta distribution 1/k for each tooth period, as the damage indicator. A general equation to generate the statistical moments strictly in terms of the a and P parameters of the beta function is developed. To monitor the growth of the crack, a new index, called the "Kurtosis Index", is formulated from 1/k's of all the teeth. This index correlates well with the size of the crack, and it shows that small cracks can be detected.

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A statistical index for monitoring tooth cracks in a gearbox

Abstract

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ASJC Scopus subject areas

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