Summary
A theoretical analysis of finite slider bearings with the Bingham rheological model is presented which includes a full consideration for thermal effects. Full thermohydrodynamic (THD) as well as simplified ISOADI solutions are presented for a wide range of operating conditions. Results are authenticated with a number of published one-dimensional isoviscous solutions. An extensive set of parametric studies of the Bingham model together with an illustrative example is presented.
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Abbreviations
- a :
-
Clearance ratio
- B :
-
Pad length in the direction of motion (m)
- c o :
-
Lubricant specific heat (J/Kg K)
- f :
-
Friction coefficient
- F :
-
Frictional force (Pa)
- H b :
-
Thickness of the stationary component (m)
- h :
-
Film thickness (m)
- h 1,h 2 :
-
Maximum and minimum film thickness (m)
- h a,h b :
-
Height of the lower and upper boundary of core (m)
- h L,h H :
-
Height of the lower and upper boundary of fluid film (m)
- h conv :
-
Convective heat transfer coefficient (W/m2 K)
- K f :
-
Bearing characteristic number
- k o :
-
Thermal conductivity of the lubricant (W/m K)
- L :
-
Bearing length in the axial direction (m)
- m :
-
Slope of the slider bearing
- P :
-
Pressure (Pa)
- P a :
-
Ambient pressure (Pa)
- P L :
-
Average unit load (Pa)
- P max :
-
Maximum pressure (Pa)
- P s :
-
Supply pressure (Pa)
- Q in :
-
Inlet flow rate (m3/sec)
- Q leakage :
-
Leakage flow rate (m3/sec)
- S h :
-
Difference between the maximum and minimum film thickness (m)
- T :
-
Temperature (oC)
- T a :
-
Ambient temperature (oC)
- T b :
-
Stationary component temperature (oC)
- T max :
-
Maximum temperature (oC)
- T mean :
-
Mean temperature (oC)
- T s :
-
Lubricant temperature supplied (oC)
- T exit :
-
Exit temperature (oC)
- U 1,U 2 :
-
Velocity of the lower and upper surface along the film (m/sec)
- U L,U H :
-
Velocity of the lower and upper boundary of fluid film along the film (m/sec)
- U c,W c :
-
Velocity of core along the film and in the axial direction (m/sec)
- u, v, w :
-
Velocity component along, across the film and in the axial direction (m/sec)
- W :
-
Bearing load-carrying capacity (N)
- W L,W H :
-
Velocity of the lower and upper boundary of fluid film in the axial direction (m/sec)
- x, y, z :
-
Coordinate system (m)
- x b,y b :
-
Coordinate system used in the stationary component (m)
- β:
-
Temperature-viscosity coefficient (1/K)
- βτ :
-
Yield stress-temperature coefficient (1/K)
- \(\dot \gamma \) :
-
Shear rate (1/sec)
- ν:
-
Non-Newtonian viscosity (Pa·sec)
- ℵ1, ℵ2 :
-
Temperature-rise parameters
- Λ s :
-
Aspect ratio of the slider bearing
- μ:
-
Viscosity (Pa·sec)
- μ i :
-
Inlet viscosity (Pa·sec)
- μ eff :
-
Effective viscosity (Pa·sec)
- ρ o :
-
Density of the lubricant (Kg/m3)
- τ:
-
Shear stress (Pa)
- τ0 :
-
Critical shear stress (Pa)
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Jang, J.Y., Khonsari, M.M. On the thermohydrodynamic analysis of a Bingham fluid in slider bearings. Acta Mechanica 148, 165–185 (2001). https://doi.org/10.1007/BF01183676
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DOI: https://doi.org/10.1007/BF01183676