Analysis of Hydrodynamic Plain Journal Bearing

Ravindra M. Mane*1, Sandeep Soni1

1
Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat, India
India-395007
*
Corresponding Author: At/Po: Varkute
Varkute-Mhaswad,
Mhaswad, Tal: Man, Dist: Satara, MH, India-415509,
India
ravimmane@gmail.com

Abstract: This paper presents the 3D model of comparison is made between simulation results and
hydrodynamic plain journal bearing using COMSOL analytical results.
Multiphysics 4.3a software.. Using 3D Model,
pressure distribution in plain journal bearing is
obtained by steady state analysis of plain journal
bearing. Generalized Reynoldslds equation is used for
analyzing hydrodynamic journal bearing by
COMSOL as well as by analytical method by
applying Sommerfeld boundary conditions. This
Reynolds equation is solved for two theories of
hydrodynamic journal bearing called infinitely short
journal bearing and infinitely long journal bearing.
Results obtained for pressure distribution by
simulation are compared with analytical results and
shows that the solutions are approximately similar to
the analytical solutions. The comparison is quite
decent
ecent for both version of the plain journal bearing,
because
cause the analytical and simulation results
correspond to each other. Only the magnitude of the
pressure build-up/drop
up/drop differs, but this can be caused Figure 1. Hydrodynamic long journal bearing.
bearing
by the analytical assumptions and the software 2. Reynolds Governing Equation
approximation.
The hydrodynamic theory applied to the
Keywords - hydrodynamic plain journal bearing, hydrodynamic lubricated bearing is mathematically
COMSOL MultiphysicsTM, Reynolds equation, explained by Reynolds’s Equation. The classical
infinitely short journal bearing, infinitely long journal theory of Reynolds is based on several assumptions
bearing, Sommerfeld boundary conditions. that were adopted to simplify the mathematical
1. Introduction derivations. The following
owing are the basic assumptions
of classical hydrodynamic lubrication theory:
theory i) the
Hydrodynamic type journal bearings are flow is laminar, ii) the
he fluid lubricant is continuous,
continuous
considered to be a vital component of all rotating Newtonian, and incompressible, iii) iii there is no fluid
machinery. A journal bearing consists of a stationary slip at the boundary, iv) the
he velocity component in y
cylindrical body (sleeve) separated from a rotating direction is negligible in comparison to the other two
tw
shaft by a layer of lubricant. Load carrying capacity velocity components nts in the x and z directions, v) v
of journal bearing is dependent on pressure ggenerated velocity gradients along the thin fluid film, in the x
in layer of lubricant during rotation of shaft or and z directions, are small and negligible relative to
journal. Hence, it is necessary to analyze the fluid the velocity gradients across the film,
film vi) the effect of
film of lubricant using latest simulation software like the curvature can be ignored,, vii) the pressure
COMSOL Multiphysics. This paper represents the variations in the y direction are very small and their
simulation of fluid film of lubricant in hydrodynamic effect is negligible
le in the equations of motion, viii)
vii
plain journal bearing using COMSOL software. the
he force of gravity on the fluid is negligible,
negligible ix) the
Generalized Reynolds equation is used to obtain the fluid viscosity, m, is constant.
pressure distribution using Sommerfeld boundary
conditions.. This Reynold equation is solved for Hydrodynamic lubrication can be expressed
infinitely short journal bearing and infinitely lolong mathematically in the form of an equation which was
journal bearing theoretically and implemented in originally derived by Reynolds and is commonly
COMSOL to get the simulation results and known as the ‘Reynolds equation’. There are several
ways of deriving this equation. Since it is a

Excerpt from the Proceedings of the 2013 COMSOL Conference in Bangalore

simplification of the Navier-Stokes
Stokes momentum and
continuity equation it can be derived from this basis.
It is, however, more often derived by considering the
equilibrium of an element of liquid subjected to
viscous shear and applying the continuity of flow
principle.

Figure 3. Shows typical configuration for thin-film

thin flow.

4. Results and Discussion

The steady state analysis of plain journal bearings has
been carried out for the case of infinitely long journal
bearing and infinitely short journal bearing at
eccentricity ratios of 0.5 with constant length to
diameter ratio. Following data is selected for
infinitely short and infinitely long journal bearing.
Figure 2. Fluid element from hydrodynamic film
film. Table 1: Plain journal bearing dimensions and oil
properties.
The Reynolds equation for Newtonian
incompressible and constant-viscosity
viscosity fluid in a thin Parameters Short Bearing Long Bearing
clearance between two rigid surfaces of relative Length 0.025[m] 0.125[m]
motion is given by; Diameter of
0.05[m] 0.05[m]
∂ h ∂p ∂ h ∂p ∂h
h
 
journal
    6U 1 L/D ratio 0.5 2.5
∂x µ ∂x ∂z µ ∂z ∂xx Radial Clearance 2.5 x 10-5[m] 2.5 x 10-5 [m]
Eccentricity 1.25 x 10-5[m] 1.25 x 10-5 [m]
This is the common Reynolds equation is widely used
for solving the pressure distribution of hydrodynamic Eccentricity ratio 0.5 0.5
bearings. By applying boundary conditions of short Speed of journal 1000[rpm] 1000[rpm]
and long journal bearing above equation reduced Dynamic
0.19[Pa.s] 0.19[Pa.s]
following two equations; Viscosity of Oil
Inlet Temperature 315[K] 315[K]
∂ h ∂p ∂
∂h
  6U 2
∂x µ ∂x ∂
∂x
Pressure distribution have been determined by using
COMSOL software and compared with analytical
This is the equation for long journal bearing. results. The results obtained have plotted for
∂ h ∂p ∂
∂h
comparisons for eccentricity ratio of 0.5 with full
  6U 3 Sommerfeld boundary conditions. After simulation
∂z µ ∂z ∂
∂x pressure distribution on journal surface has been
found out as contour representation. The maximum
This is the equation for short journal bearing.
pressure is reached in a region closer to the minimum
Where, h is the variable film thickness is due to the fluid film thickness and negative pressure results due
journal eccentricity; to appropriate boundary conditions. The pressure
h θ c 1  ε cos θθ 4
distribution and pressure contours
rs are shown in figure
fig
4 & 5 respectively for long and short journal bearing.
3. Use of COMSOL At the boundary pressure is zero and maximum at
The models described in this paper were midline in axial direction. Therefore the pressure
constructed using COMSOL Multiphysics v4.1 v4.1a distribution is plotted along the midline of the plain
running on a computer with CAD LAB of Chemical journal bearing and compared ared with the analytical
Engineering Department, SVNIT Surat, Gujarat, solutions.
India on windows 7.. For this analysis thin film flow
physics with CFD model of journal bearing is used.

Excerpt from the Proceedings of the 2013 COMSOL Conference in Bangalore

Figure 4. 3D pressure distribution for LJB using full Figure 5. 3D pressure distribution for SJB using full
Sommerfeld condition at eccentricity ratio, ε = 0.5. Sommerfeld condition at eccentricity ratio, ε = 0.5.

Figure 6. Comparison of analytical and simulated pressure Figure 7. Comparison of analytical and simulated pressure
distribution for LJB using full Sommerfeld condition at distribution for SJB using full Sommerfeld condition at
eccentricity ratio, ε = 0.5. eccentricity ratio, ε = 0.5.

The plain journal bearing has only one high point respectively for long and short journal bearing and
pressure along the circumference of the journal found that they are approximately matching. The
bearing. This is due to geometry of bearing and how solutions of these simulations are approximately
the fluid gap expands and contracts once around the similar to the analytical solutions of the plain journal
circumference of the journal shaft. A typical pressure bearing. The comparison is quite decent for both
distribution along the circumference of the journal version of the plain journal bearing, because the
shaft of the journal bearing is shown in figure 4 & 5, analytical and software solutions correspond to each
respectively for long and short journal bearing. other. Only the magnitude of the pressure build-
Results for pressure distribution obtained by up/drop differs, but this can be caused by the
simulation are compared with analytical solution and analytical assumptions and the software
using graph of pressure vs. angle along approximation. Hence solution obtained by
circumferential direction shown in figure 6 & 7, simulation gets validated.

Figure 8. Polar plot for LJB showing comparison of Figure 9. Polar plot for SJB showing comparison of
pressure by analytical and simulation around the journal pressure by analytical and simulation around the journal
bearing using full Sommerfeld condition at eccentricity bearing using full Sommerfeld condition at eccentricity
ratio ε = 0.5. ratio ε = 0.5.

Excerpt from the Proceedings of the 2013 COMSOL Conference in Bangalore

Figure 10. Comparison of pressure distribution for LJB Figure 11. Comparison of pressure distribution for SJB
using full Sommerfeld condition at eccentricity ratio, ε = 0 using full Sommerfeld condition at eccentricity ratio, ε = 0
to 0.9. to 0.9.

5. Conclusion 6. References
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Excerpt from the Proceedings of the 2013 COMSOL Conference in Bangalore

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Excerpt from the Proceedings of the 2013 COMSOL Conference in Bangalore