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Research Papers

A Numerical Model for Life Scatter in Rolling Element Bearings

[+] Author and Article Information
Nihar Raje

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906

Farshid Sadeghi1

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906

Richard G. Rateick

Engines, Systems and Services, Honeywell Aerospace, South Bend, IN 46620

Michael R. Hoeprich

 Timken Research, Canton, OH 44706

1

Corresponding author.

J. Tribol 130(1), 011011 (Dec 26, 2007) (10 pages) doi:10.1115/1.2806163 History: Received June 06, 2007; Revised August 13, 2007; Published December 26, 2007

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the mechanisms responsible for the bearing failure process. Life models that account for this dispersion are empirical in nature and do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the inhomogeneous nature of the bearing material. Here, a new approach based on a discrete material representation is presented that simulates this inherent material randomness. In this investigation, two levels of randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress field in Hertzian line contacts is studied. Fatigue life is formulated as a function of a critical stress quantity and its corresponding depth, following a similar approach to the Lundberg–Palmgren theory. However, instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. A new critical stress quantity is introduced that considers shear stress acting along internal material planes of weakness. It is found that there is a scatter in the magnitude as well as depth of occurrence of this critical stress quantity, which leads to a scatter in computed fatigue lives. Further, the range of depths within which the critical stress quantity occurs is found to be consistent with experimental observations of fatigue cracks. The life distributions obtained from the numerical simulations are found to follow a two-parameter Weibull distribution closely. The L10 life and the Weibull slope decrease when a nonuniform distribution of elastic modulus is assumed throughout the material. The introduction of internal flaws in the material significantly reduces the L10 life and the Weibull slope. However, it is found that the Weibull slope reaches a limiting value beyond a certain concentration of flaws. This limiting value is close to that predicted by the Lundberg–Palmgren theory. Weibull slopes obtained through the numerical simulations range from 1.29 to 3.36 and are within experimentally observed values for bearing steels.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 7

Orthogonal shear stress variation along depth for four randomly generated material domains

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Figure 6

Loading histories for two interelement Joints A (θ=67.53deg) and B (θ=11.57deg)

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Figure 5

The rolling contact cycle and the RVE

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Figure 4

The Voronoi tessellation process (19)

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Figure 3

(a) Partially broken joint and (b) material domain with broken joints

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Figure 2

(a) Interelement contact in the discrete model and (b) fiber model

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Figure 1

(a) Discrete representation of the semi-infinite domain forming the bearing line contact and (b) zoomed view

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Figure 14

Locations of five internal flaws for a sample material domain

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Figure 9

Variation of critical depth and stress quantities due to topological disorder (a) critical depth and (b) critical stress

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Figure 8

Joint shear stress range variation along depth for the four randomly generated material domains

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Figure 18

Effect of internal flaws on (a) L10 life and (b) Weibull slope e

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Figure 17

Life distributions in the presence of variable number of flaws

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Figure 16

Life distribution in the presence of five internal flaws

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Figure 13

Life distribution with nonuniform elastic properties

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Figure 15

Variation of critical depth and stress quantities with introduction of flaws (a) critical depth and (b) critical stress

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Figure 12

Joint stiffness frequency distribution for a randomly selected material domain

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Figure 11

Two-parameter Weibull life plot for the 44 randomly generated material domains

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Figure 10

Two-parameter Weibull plot for critical depth locations in the 44 randomly generated material domains

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