toroidal vortex flow

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Toroidal Vortex Flow

Figure 7.1 Toroidal vortex flow in a journal bearing.

Conditions for vortex flow:

Taylor Number:

Reynolds Number:


Mass Flow

Figure 7.1 Mass flow through rectangular-section control volume. (a) x-y plane; (b) y-z plane; (c) x-y plane. [From Hamrock and Dowson (1981).]


Reynolds Equation


Reynolds Equation Terms

Figure 7.3 Density wedge. Figure 7.4 Stretch mechanism.



Figure 7.5 Physical wedge mechanism.Figure 7.6 Normal squeeze mechanism.



Figure 7.7 Translation squeeze mechanism.

Figure 7.8 Local expansion mechanism.


Possible Motion in Bearings

Figure 7.9 Normal squeeze and sliding velocities.


Parallel-Surface Slider Bearing

Figure 8.1 Velocity profiles in a parallel-surface slider bearing.


Flow in Inclined Slider

Figure 8.2 Flow within a fixed-incline slider bearing (a) Couette flow; (b)

Poiseuille flow; (c) resulting velocity profile.


Thrust Bearing

Figure 8.3 Thrust bearing geometry.Figure 8.3 Force components and oil film geometry in a hydrodynamically lubricated thrust sector.


Parallel-Surface Bearing

Figure 8.5 Parallel-surface slider bearing.


Fixed-Incline Slider Bearing

Figure 8.6 Fixed-incline slider bearing.

Figure 8.7 Pressure distributions of fixed-incline slider bearing.


Fixed-Incline Bearing Results

Figure 8.8 Effect of film thickness ratio on normal load-carrying capacity.

Figure 8.9 Effect of film thickness ratio on force components.



Figure 8.10 Effect of film thickness ratio on friction coefficient parameter.

Figure 8.11 Effect of film thickness ratio on dimensionless volume flow rate.



Figure 8.12 Effect of film thickness ratio on dimensionless adiabatic temperature rise.

Figure 8.13 Effect of film thickness ratio on dimensionless center of pressure.


Streamlines in Fixed-Incline Slider Bearing

Figure 8.14 Streamlines in fixed-incline bearing at four film thickness ratios Ho. (a) Ho =2; (b) Ho =1 (critical value).


Streamlines in Fixed-Incline Slider Bearing

(cont.)

Figure 8.14 Concluded. (c) Ho = 0.5; (d) Ho = 0.25.


Parallel-Step Bearing

Figure 8.15 Parallel-step slider bearing.


Parallel-Step Pad Slider Bearing

Figure 9.1 Finite parallel-step-pad slider bearing.


Parallel-Step-Pad Bearing Results


Parallel-Step-Pad Bearing Results

Figure 9.3 Shrouded-step slider bearings. (a) Semicircular step; (b) truncated triangular step.


Fixed-Incline-Pad Slider Bearing

Figure 9.4 Side view of fixed-incline-pad bearing. [From Raimondi and Boyd (1955).]

Figure 9.5 Configurations of multiple fixed-incline-pad thrust bearing. [From Raimondi and Boyd (1955).]


Film Thickness for Given Surface Finish


Fixed-Incline Slider Results

Figure 9.6 Chart for determining minimum film thickness corresponding to

maximum load or minimum power loss for various pad proportions - fixed-incline-pad

bearings. [From Raimondi and Boyd (1955).]



Figure 9.7 Chart for determining minimum film thickness for fixed-incline-pad thrust bearings. [From Raimondi and Boyd (1955).]



Figure 9.8 Chart for determining dimensionless temperature rise due to viscous shear heating of lubricant in fixed-incline-pad thrust bearings. [From Raimondi and Boyd (1955)]



Figure 9.9 Chart for determining performance parameters of fixed-incline-pad thrust bearings. (a) Friction coefficient; (b) power loss. [From Raimondi and Boyd (1955)].



Figure 9.9 Concluded. (c) Lubricant flow; (d) lubricant side flow.


Pivoted-Pad Slider Bearing

Figure 9.10 Side view of pivoted-pad thrust bearing. [From Raimondi and Boyd (1955).]

Figure 9.11 Configuration of multiple pivoted-pad thrust bearing. [From Raimondi and Boyd (1955).]


Pivoted-Pad Slider Results

Figure 9.12 Chart for determining pivot location corresponding to maximum load or minimum power loss for various pad proportions - pivoted-pad bearings. [From Raimondi and Boyd (1955).]



Figure 9.13 Chart for determining outlet film thickness for pivoted-pad thrust bearings. [From Raimondi and Boyd (1955).]

Figure 9.14 Chart for determining dimensionless temperature rise due to viscous shear heating of lubricant for pivoted-pad thrust bearing. [From Raimondi and Boyd (1955).]



Figure 9.15 Chart for determining performance parameters for pivoted-pad thrust bearings. (a) Dimensionless load; (b) friction coefficient. [From Raimondi and Boyd (1955).]



Figure 9.15 Concluded. (c) Lubricant flow; (d) lubricant side flow; (e) power loss.


Journal Bearing

Figure 10.1 Hydrodynamic journal bearing geometry.

Figure 10.2 Unwrapped film shape in a journal bearing.


Sommerfeld Angle


Full Sommerfeld Solution

Figure 10.3 Pressure distribution for full Sommerfeld solution.

Sommerfeld substitution:

Pressure distribution:

Maximum pressure:


Forces for Sommerfeld Solution

Figure 10.4 Coordinate system and force components in a journal bearing.

Figure 10.5 Vector forces acting on a journal.


Reynolds Boundary Condition

Figure 10.6 Location of shaft center for full and half Sommerfeld journal bearing solutions.

Figure 10.7 Pressure profile for a journal bearing using Reynolds boundary condition.


Hydrodynamic Journal Bearings

Figure 11.1 Pressure distribution around a journal bearing.

Sommerfeld number:

Diameter-to-width ratio:


Film Thickness and Eccentricity

Figure 11.2 Effect of bearing number on minimum film thickness for four diameter-to-width ratios. [From Raimondi and Boyd (1958)].


Attitude Angle

Figure 11.3 Effect of bearing number on attitude angle for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]


Friction Coefficient

Figure 11.4 Effect of bearing number on friction coefficient for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]


Fluid Flow

Figure 11.6 Effect of bearing number on volume side flow ratio for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]

Figure 11.5 Effect of bearing number on dimensionless flow rate for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]


Maximum Pressure & Location

Figure 11.8 Effect of bearing number on location of terminating and maximum pressures for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]

Figure 11.7 Effect of bearing number on dimensionless maximum film pressure for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]


Effect of Radial Clearance

Figure 11.9 Effect of radial clearance on some performance parameters for a particular case.


Fixed-Incline Pad Journal Bearings


Effect of Preload

Figure 11.11 Effect of preload factor mp on two-lobe bearings. (a) Largest shaft that fits in bearing. (b) mp =0; largest shaft, ra; bearing clearance cb = c. (c) mp =1.0; largest shaft, rb; bearing clearance cb =0. [From Allaire and Flack (1980).]


Hydrodynamic Squeeze Film Bearings

Figure 12.2 Journal bearing with normal squeeze film action. Rotational velocities are all zero.

Figure 12.1 Parallel-surface squeeze film bearing.


Parallel Circular Plate

Figure 12.3 Parallel circular plate approaching a plane surface.

Load support:

Time of approach:


Rigid Cylinder

Figure 12.4 Rigid cylinder approaching a plane surface.

Load support:

Time of approach:

toroidal vortex flow

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