Technical Briefs

Uncertainty Considerations in the Dynamic Loading and Failure of Spur Gear Pairs1

[+] Author and Article Information
Fisseha M. Alemayehu

e-mail: fisseha.alemayehu@ttu.edu

Stephen Ekwaro-Osire

e-mail: stephen.ekwaro-osire@ttu.edu
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409

1Part of this paper was presented at the ASME 2012 International Mechanical Engineering Congress and Exposition, Nov. 9–15, Houston, TX.

2Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received September 7, 2012; final manuscript received February 13, 2013; published online June 20, 2013. Assoc. Editor: Qi Fan.

J. Mech. Des 135(8), 084501 (Jul 20, 2013) (7 pages) Paper No: MD-12-1439; doi: 10.1115/1.4023870 History: Received September 07, 2012; Revised February 13, 2013

Gears and gear systems, like any other mechanical system, are subjected to design parameter, and loading uncertainties emanating from inherent randomness, manufacturing, and assembly errors. The traditional deterministic approach to the design of such systems overlooks these uncertainties. This work presents a novel probabilistic multibody dynamic analysis (PMBDA) that enhances the deterministic design practice of gears and gear systems. A contact based, rigid multibody spur gear pair model with random loading, and design parameters has been developed. An advanced mean based on fast probability integration method was implemented to perform a reliability analysis of performance measurements: dynamic factor, root bending stress, and fatigue life of gears. Probabilistic sensitivity analysis of these performance functions to several random variables was also determined. In addition to revealing system reliability or probability of failure, the PMBDA approach also helps designers to consider certain variables critically.

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Fig. 1

Dynamic Gear-Pair Model with random loading and design parameters

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Fig. 6

Probabilistic sensitivity factors with respect to the mean values of each random variable evaluated at different p-levels of surface contact stress

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Fig. 2

CDF of the probability of occurrence of different values of the root bending stress

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Fig. 3

Probabilistic importance factors of each random variable evaluated at different p-levels of root bending stress

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Fig. 4

Sensitivity plots: (a) percentage probabilistic importance factor, and (b) sensitivity levels, evaluated at a probability of failure value of p = 0.4

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Fig. 5

CDF of the probability of occurrence of different values of surface contact stress

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Fig. 7

CDF of the probability of occurrence of different values of the fatigue life

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Fig. 8

Probabilistic sensitivity factors with respect to the variation of the mean of each random variable evaluated at different p-levels of fatigue life

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Fig. 9

Probabilistic sensitivity factors with respect to the variation of the SD of each random variable evaluated at different p-levels of fatigue life

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Fig. 10

Sensitivity levels of all random variables to the probability of failure in terms of respective mean and SD, using AIS2 (red and yellow bars) and MC (blue and cyan bars)



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