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Static Performance of Finite Hydrodynamic Journal Bearings Lubricated by Magnetic Fluids with Couple Stresses

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Abstract

Based upon the Stokes micro-continuum theory, the problem of lubrication of finite hydrodynamic journal bearing lubricated by magnetic fluids with couple stresses is investigated. By taking into account the couple stresses due to the microstructure additives and the magnetic effects due to the magnetization of the magnetic fluid, modified Reynolds equation is obtained. The effects of couple stresses are studied by defining the couple stress parameter L that can be considered as a measure of the chain length of the additive molecule. The magnetic effects of the magnetic fluid are investigated by the magnetic coefficient γ. Using the finite-difference technique and for different values of couple stress parameter and magnetic coefficient, the Reynolds equation is solved, and pressure distributions are obtained. The bearing static characteristics namely load carrying capacity, attitude angle, friction coefficient, and side leakage flow are determined. The results indicate that the influence of couple stresses and magnetic effects on the bearing characteristics are significantly apparent. It is concluded that fluids with couple stresses are better than Newtonian fluids. The improvement of the bearing characteristics is enhanced if the magnetic effects are present.

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Abbreviations

C :

Bearing clearance

e :

Eccentricity of the journal center

F j :

Friction force at the journal surface

F :

Dimensionless friction force   \({F=\frac{F_{j}(C/R)^{2}}{\mu \omega L_b C}}\)

f :

Friction coefficient   \({f=\frac{F_{j}}{w}=(C/R)\frac{F}{W}}\)

F m :

Unit volume value of the induced magnetic force

F mx :

Magnetic force in x direction (circumferential direction)

F mz :

Magnetic force in z direction (axial direction)

h :

Lubricant film thickness

H :

Dimensionless film thickness   H = h/C

h m :

Magnetic field intensity

h mo :

Characteristic value of magnetic field intensity

H m :

Dimensionless magnetic field intensity   H m  = h m /h mo

I :

Strength of the current passing through the wire

K :

Distance ratio parameter   K = R o /R = 1.2

l :

Couple stress parameter   \({l=\left({\frac{\eta}{\mu}}\right)^{1/2}}\)

L :

Dimensionless couple stress parameter   L = l/C

L b :

Bearing length

p :

Lubricant pressure

P :

Dimensionless pressure   \({P=\frac{p(C/R)^{2}}{\mu\omega}}\)

q :

Bearing side leakage

Q :

Dimensionless side leakage   \({Q=\frac{2q}{L_{b}RC\omega}}\)

R :

Bearing or journal radius

R o :

Distance from the wire position to the bearing center

u:

Circumferential velocity component

v:

Radial velocity component

w:

Axial velocity component

w :

Load carrying capacity

W :

Dimensionless load carrying capacity   \({W=\frac{w(C/R)^{2}}{\mu\omega L_{b}R}}\)

W ɛ :

Dimensionless load capacity component in the eccentricity direction

W φ :

Dimensionless load capacity component in the direction normal to the eccentricity

X m :

Susceptibility of magnetic fluid

x, y, z:

Cartesian coordinates

Z :

Dimensionless axial distance   Z = z/L b

γ:

Magnetic coefficient   \({\gamma =\frac{(h_{mo})^{2}\mu _{o}X_{m}C^{2}}{\mu \omega L_{b} ^{2}}}\)

ɛ:

Eccentricity ratio   ɛ =  e / C

φ:

Attitude angle

λ:

Length to diameter ratio   λ = L b /2R

η:

Material constant responsible for the couple stress property

μ:

Fluid viscosity

θ:

Angular coordinate   θ =  x / R

μ o :

Permeability of free space of air   μ o  = 4π.10−7 AT/m

ρ:

Lubricant density

ψ:

Position angle of the displaced wire magnetic models   ψ = π/2

τ:

Shear stress

ω:

Angular speed

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Authors and Affiliations

  1. Department of Mechanical Engineering, Higher Technological Institute, Tenth of Ramadan city, Egypt

    G. S. Nada

  2. Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, Cairo, Egypt

    T. A. Osman

Authors
  1. G. S. Nada
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  2. T. A. Osman
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Correspondence to G. S. Nada.

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Nada, G.S., Osman, T.A. Static Performance of Finite Hydrodynamic Journal Bearings Lubricated by Magnetic Fluids with Couple Stresses. Tribol Lett 27, 261–268 (2007). https://doi.org/10.1007/s11249-007-9222-0

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