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Fatigue Life Reduction in Mixed Lubricated Elliptical Contacts

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Highly loaded ball and rolling element bearings are often required to operate in the mixed elastohydrodynamic lubrication regime in which surface asperity contact occurs simultaneously during the lubrication process. Predicting performance of components operating in this regime is important as the high asperity contact pressures can significantly reduce the fatigue life of the interacting components. Rolling contact fatigue is one of the most dominant causes of failure of components operating in mixed lubrication regime. Contact fatigue begins with the initiation of microscopic fatigue cracks in the rolling contact surfaces or within the sub-surface regions due to cyclic shear stresses. Investigation of mixed lubrication effects on performance of machine components is of significant importance in order to understand and enhance their load carrying capacity. This article investigates the effects of mixed lubrication and surface roughness on machine components performance. Results from a mixed lubrication model are utilized to investigate the effects of different operating conditions on fatigue life of the components. Simple rough surfaces consisting of single hemispherical bump as well as complex rough surfaces consisting of a numerically generated 3D rough surface operating under mixed lubrication conditions are studied and results presented. The stress-based Ioannides and Harris model incorporating the fatigue limit is used to evaluate the fatigue life variation. Fast Fourier Transform (FFT) technique is used to significantly reduce the time required for the computation of internal stresses.

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a :

Half width of Hertzian contact across rolling direction (m)

A r :

Radius ratio (R y /R x )

b :

Half width of Hertzian contact along rolling direction (m)

E1, E2:

Modulus of elasticity of surface 1 and 2, respectively (Pa)


Equivalent elastic modulus (2/E′ =  (1−ν 1 2 )/E1 + (1−ν 2 2 )/E2)(Pa)

f :

Dimensionless complementary energy

G :

Material parameter (G =  αE′)(Pa)

h :

Film thickness (m)

H :

Dimensionless film thickness (hRx/b2)

h l :

Film thickness due to lubricant pressure

H l :

Dimensionless film thickness only due to the lubricant pressure (h l Rx/b2)

h o :

Constant in the film thickness equation

H o :

Dimensionless constant (h o Rx/b2)

h min :

Minimum film thickness (m)

H min :

Dimensionless minimum film thickness (hminRx/b2)

H s :

Dimensionless elastic deformation only due to the solid contact pressure

p :

Dimensional pressure (Pa)

P :

Dimensionless pressure (p/P H )

P H :

Maximum Hertzian pressure (Pa)

q x :

Volume flow rate per unit width in the rolling direction (m 2/s)

q :

Heat flux (W/m 2)

R x :

Reduced radius of curvature in x-direction (m)

R y :

Reduced radius of curvature in y-direction (m)

R q :

R.m.s roughness

S :

Slide-to-roll ratio S = 2(u1−u2)/(u1 + u2)

t :

Time (s)


Velocities of surface 1 and 2, respectively, along rolling direction (m/s)

u s :

Sliding velocity (m/s)

U :

Dimensionless speed parameter

W :

Dimensionless total load

w :

External load (N)

zR :

Roelands viscosity coefficient

x, y, z:

Dimensional cartesian coordinates

X, Y, Z:

Dimensionless cartesian coordinates for mixed lubrication calculations


Absolute viscosity of the lubricant (Pa· s)

η0 :

Absolute viscosity of the lubricant at p = 0 and constant temperature (Pa· s)

\(\bar{\eta}\) :

Dimensionless absolute viscosity of the lubricant (η/η0)


Dimensionless time ((u1 + u2)t/2/b)


Ellipticity parameter (a/b)


Poisson’s ratio


Density of lubricant (kg/m3)

ρ0 :

Density of lubricant at p = 0 (kg/m3)

ρ s :

density of solid (kg/m3)


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The Authors would like to provide their deepest appreciations to the Sentient Corporation for their support of this project.

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Correspondence to Farshid Sadeghi.

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Deolalikar, N., Sadeghi, F. Fatigue Life Reduction in Mixed Lubricated Elliptical Contacts. Tribol Lett 27, 197–209 (2007).

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  • Partial-EHL
  • Roughness Effects
  • Rolling-contact fatigue