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Journal Bearings
Chapter Outline
5.1 Introduction 169
5.2 Sliding bearings 171
5.2.1 Lubricants 175
5.3 Design of boundary-lubricated bearings 176
5.4 Design of full film hydrodynamic bearings 179
5.4.1 Reynolds equation derivation 184
5.4.2 Design charts for full-film hydrodynamic bearings 199
5.4.3 Alternative method for the design of full film hydrodynamic bearings 219
5.5 Conclusions 227
References 227
Websites 228
Standards 228
Further reading 230
Nomenclature
Generally, preferred SI units have been stated.
a radius (m)
b outer radius (m)
b
o characteristic length (m)
c radial clearance (m)
D journal diameter (m)
e eccentricity
Eu Euler number (dimensionless)
f coefficient of friction
F
g geometrical factor
Fr Froude number (dimensionless)
F
x body force component in the x direction (N/m3)
F
y body force component in the y direction (N/m3)
F
z body force component in the z direction (N/m3)
g acceleration due to gravity (m/s2)
h film thickness (m)
h
o minimum film thickness (m)
Ic
cosine load integral
Is
sine load integral
L characteristic length, length (m), bearing length (m)
lo
characteristic length (m)
N speed (normally in rpm)
Mechanical Design Engineering Handbook. https://doi.org/10.1016/B978-0-08-102367-9.00005-6
© 2019 Elsevier Ltd. All rights reserved.Ns
journal speed (revolutions per second)
p static pressure (Pa)
pmax maximum annulus static pressure (N/m2)
P load capacity (N/m2), load (N)
qx volumetric flow rate per unit width in the x direction (m2/s)
qy volumetric flow rate per unit width in the y direction (m2/s)
Q lubricant flow rate (m3/s)
Qπ flow through the minimum film thickness (m3/s)
Qs side flow rate (m3/s)
r radius (m)
rm
mean radius (m)
R specific gas constant (J/kgK)
Re Reynolds number (dimensionless)
Re
x Reynolds number based on x component of velocity (dimensionless)
Re
y Reynolds number based on y component of velocity (dimensionless)
Re
z Reynolds number based on z component of velocity (dimensionless)
S geometrical factor, bearing characteristic number
SAE Society of Automotive Engineers
t time (s)
t
o characteristic time scale (s)
t* dimensionless time ratio (dimensionless)
T temperature (°C, K)
T
av average temperature (°C)
T1 temperature of the lubricant supply (°C)
T2 temperature of the lubricant leaving the bearing (°C)
Ta Taylor number (dimensionless)
Ta
m Taylor number based on mean radius (dimensionless)
Ta
m,cr critical Taylor number based on mean annulus radius (dimensionless)
u
r velocity component in the r direction (m/s)
u
x velocity component in the x direction (m/s)
u
x,o characteristic velocity component in the x direction (m/s)
u
y velocity component in the y direction (m/s)
u
y,o characteristic velocity component in the y direction (m/s)
u
z velocity component in the z direction (m/s)
u
z,o characteristic velocity component in the z direction (m/s)
uϕ velocity component in the tangential direction (m/s)
u average velocity (m/s)
Uo
characteristic velocity (m/s), reference velocity (m/s)
V journal velocity (m/s); velocity (m/s)
W applied load (N)
x distance along the x axis (m),
x* dimensionless location (dimensionless)
y* dimensionless location (dimensionless)
z distance along the z axis (m)
z* dimensionless axial location (dimensionless)
α angle (degree or rad)
ε eccentricity ratio
ϕpmax angular position of maximum pressure (degree)
ϕh
o
angular position of minimum film thickness (degree)
168 Mechanical Design Engineering Handbookϕpo film termination angle (degree)
ϕ position of the minimum film thickness (degree), attitude angle (degree),
azimuth angle (rad)
ϕ0 relative azimuth angle (rad)
ϕ* nondimensional circumferential location (dimensionless)
μ viscosity (Pas)
μo reference viscosity (Pas)
μ* dimensionless viscosity (dimensionless)
ν kinematic viscosity (m2/s)
ρ density (kg/m3)
ρ* dimensionless density (dimensionless)
ρo reference density (kg/m3)
σ
s squeeze number (dimensionless)
τ
zx viscous shear stress acting in the x direction, on a plane normal to the z direction
(N/m2)
τ
zy viscous shear stress acting in the y direction, on a plane normal to the z direction
(N/m2)
ω angular velocity (rad/s)
Ω angular velocity magnitude (rad/s)
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