Toroidal Vortex Flow

1
Toroidal Vortex Flow
Conditions for vortex flow
Taylor Number
Reynolds Number
Figure 7.1 Toroidal vortex flow in a journal
bearing.
2
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).
3
Reynolds Equation
4
Reynolds Equation Terms
Figure 7.3 Density wedge.
Figure 7.4 Stretch mechanism.
5
Reynolds Equation Terms
Figure 7.5 Physical wedge mechanism.
Figure 7.6 Normal squeeze mechanism.
6
Reynolds Equation Terms
Figure 7.7 Translation squeeze mechanism.
Figure 7.8 Local expansion mechanism.
7
Possible Motion in Bearings
Figure 7.9 Normal squeeze and sliding
velocities.
8
Possible Motion in Bearings
Figure 7.9 Normal squeeze and sliding
velocities.
9
Parallel-Surface Slider Bearing
Figure 8.1 Velocity profiles in a
parallel-surface slider bearing.
10
Flow in Inclined Slider
Figure 8.2 Flow within a fixed-incline slider
bearing (a) Couette flow (b) Poiseuille flow
(c) resulting velocity profile.
11
Thrust Bearing
Figure 8.3 Force components and oil film
geometry in a hydrodynamically lubricated thrust
sector.
Figure 8.3 Thrust bearing geometry.
12
Parallel-Surface Bearing
Figure 8.5 Parallel-surface slider bearing.
13
Fixed-Incline Slider Bearing
Figure 8.6 Fixed-incline slider bearing.
Figure 8.7 Pressure distributions of
fixed-incline slider bearing.
14
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.
15
Fixed-Incline Bearing Results
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.
16
Fixed-Incline Bearing Results
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.
17
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).
18
Streamlines in Fixed-Incline Slider Bearing
(cont.)
Figure 8.14 Concluded. (c) Ho 0.5 (d) Ho
0.25.
19
Parallel-Step Bearing
Figure 8.15 Parallel-step slider bearing.
20
Parallel-Step Pad Slider Bearing
Figure 9.1 Finite parallel-step-pad slider
bearing.
21
Parallel-Step-Pad Bearing Results
22
Parallel-Step-Pad Bearing Results
23
Parallel-Step-Pad Bearing Results
Figure 9.3 Shrouded-step slider bearings. (a)
Semicircular step (b) truncated triangular step.
24
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).
25
Film Thickness for Given Surface Finish
26
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).
27
Fixed-Incline Slider Results
Figure 9.7 Chart for determining minimum film
thickness for fixed-incline-pad thrust bearings.
From Raimondi and Boyd (1955).
28
Fixed-Incline Slider Results
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)
29
Fixed-Incline Slider Results
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).
30
Fixed-Incline Slider Results
Figure 9.9 Concluded. (c) Lubricant flow (d)
lubricant side flow.
31
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).
32
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).
33
Pivoted-Pad Slider Results
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 9.13 Chart for determining outlet film
thickness for pivoted-pad thrust bearings. From
Raimondi and Boyd (1955).
34
Pivoted-Pad Slider Results
Figure 9.15 Chart for determining performance
parameters for pivoted-pad thrust bearings. (a)
Dimensionless load (b) friction coefficient.
From Raimondi and Boyd (1955).
35
Pivoted-Pad Slider Results
Figure 9.15 Concluded. (c) Lubricant flow (d)
lubricant side flow (e) power loss.
36
Journal Bearing
Figure 10.2 Unwrapped film shape in a journal
bearing.
Figure 10.1 Hydrodynamic journal bearing
geometry.
37
Sommerfeld Angle
38
Full Sommerfeld Solution
Sommerfeld substitution
Pressure distribution
Maximum pressure
Figure 10.3 Pressure distribution for full
Sommerfeld solution.
39
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.
40
Reynolds Boundary Condition
Figure 10.7 Pressure profile for a journal
bearing using Reynolds boundary condition.
Figure 10.6 Location of shaft center for full
and half Sommerfeld journal bearing solutions.
41
Hydrodynamic Journal Bearings
Sommerfeld number
Diameter-to-width ratio
Figure 11.1 Pressure distribution around a
journal bearing.
42
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).
43
Attitude Angle
Figure 11.3 Effect of bearing number on
attitude angle for four diameter-to-width ratios.
From Raimondi and Boyd (1958).
44
Friction Coefficient
Figure 11.4 Effect of bearing number on
friction coefficient for four diameter-to-width
ratios. From Raimondi and Boyd (1958).
45
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).
46
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).
47
Effect of Radial Clearance
Figure 11.9 Effect of radial clearance on some
performance parameters for a particular case.
48
Fixed-Incline Pad Journal Bearings
49
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).
50
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.
51
Parallel Circular Plate
Load support
Time of approach
Figure 12.3 Parallel circular plate approaching
a plane surface.
52
Rigid Cylinder
Load support
Time of approach
Figure 12.4 Rigid cylinder approaching a plane
surface.