DETERMINATION OF APPLIED LOADS AND BEARING ANALYSIS
ENGINEERING
TIMKEN TAPERED ROLLER BEARING CATALOG 15
Determination of applied loads and Bearing Analysis
SUMMARY OF SYMBOLS USED TO DETERMINE APPLIED LOADS AND BEARING ANALYSIS
Symbol Description U nits (Metric/Inch System)
a Axial Distance from Inner Ring Backface to
Effective Load Center mm, in.
a
1 Reliability Life Factor unitless
a
2 Material Life Factor unitless
a
3 Operating Condition Life Factor unitless
a
3d Debris Life Factor unitless
a
3k Load Zone Life Factor unitless
a
3l Lubrication Life Factor unitless
a
3p Low-Load Life Factor unitless
a
e Effective Bearing Spread mm, in.
A, B, … Bearing Position (used as subscripts) unitless
B Outer Ring Width mm, in.
B
1 Inner Ring Width mm, in.
b Tooth Length mm, in.
c
1, c2 Linear Distance (positive or negative). mm, in.
C Basic Dynamic Radial Load Rating of a Double-Row N, lbf
Bearing for an L
10 of One Million Revolutions
C
a90 Basic Dynamic Thrust Load Rating of a Single-Row
Bearing for an L
10 of 90 Million Revolutions or
3000 Hours at 500 RPM N , lbf
C
o Basic Static Radial Load Rating N , lbf
C
oa Basic Static Axial Load Rating N , lbf
C
90 Basic Dynamic Radial Load Rating of a Single-Row
Bearing for an L
10 of 90 Million Revolutions N , lbf
C
90(2) Basic Dynamic Radial Load Rating of a Double-Row
Bearing for an L
10 of 90 Million Revolutions N , lbf
C
a Basic Dynamic Axial Load Rating N , lbf
C
g Geometry Factor (used in a 3l equation) unitless
C
l Load Factor (used in a 3l equation) unitless
C
j Load Zone Factor (used in a 3l equation) unitless
C
s Speed Factor (used in a 3l equation) unitless
C
v Viscosity Factor (used in a 3l equation) unitless
C
gr Grease Lubrication Factor (used in a 3l equation) unitless
Cp Specific Heat of Lubricant J/(Kg - °C), BTU/(lbf - °F)
C
t Basic Thrust Dynamic Load Rating N , lbf
d Bearing Bore Diameter mm, in.
d Ball Diameter mm, in.
d
1 Spherical Diameter mm, in.
d
a Shaft Shoulder Diameter mm, in.
d
0 Mean Inner Ring Diameter mm, in.
dc Distance Between Gear Centers mm, in.
dm Mean Bearing Diameter mm, in.
d
si Shaft Inside Diameter mm, in.
D Bearing Outside Diameter mm, in.
D
0 Tapered Roller Bearing Outer Ring
Mean Raceway Diameter mm, in.
Dh Housing Outside Diameter mm, in.
Dm Mean Diameter or Effective W orking Diameter
of a Sprocket, Pulley, Wheel or Tire mm, in.
Dm Tapered Roller Mean Large Rib Diameter mm, in.
Symbol Description U nits (Metric/Inch System)
Dm
G Mean or Effective W orking Diameter of the Gear mm, in.
Dm
P Effective W orking Diameter of the Pinion mm, in.
Dm
W Effective W orking Diameter of the W orm mm, in.
Dp
G Pitch Diameter of the Gear mm, in.
Dp
P Pitch Diameter of the Pinion mm, in.
Dp
W Pitch Diameter of the W orm mm, in.
e Life Exponent unitless
e Limiting V alue of F
a/Fr for the Applicability of
Different V alues of Factors X and Y unitless
E Free Endplay mm, in.
f Lubricant Flow Rate L /min, U.S. pt/min
f
0 Viscous Dependent Torque Coefficient unitless
f
1 Load Dependent Torque Coefficient unitless
f
b Belt or Chain Pull N, lbf
f
n Speed Factor unitless
f
2 Combined Load Factor unitless
f
3 Combined Load Factor unitless
F General Term for Force N, lbf
F
1, F2, …, F n Magnitudes of Applied Force During a Loading Cycle N, lbf
F
a Applied Thrust (Axial) Load N, lbf
F
ai Induced Thrust (Axial) Load Due to Radial Loading N, lbf
F
ac Induced Thrust (Axial) Load Due to Centrifugal Loading N, lbf
F
aG Thrust Force on Gear N, lbf
F
aP Thrust Force on Pinion N, lbf
F
aW Thrust Force on W orm N, lbf
F
az Allowable Axial Load N , lbf
F
b Belt or Chain Pull N, lbf
F
β Load Term for Torque Equation N, lbf
Fc Centrifugal Force N, lbf
F
r Applied Radial Load N, lbf
F
rh Resultant Horizontal Force N, lbf
F
rs Resultant Separating Force N, lbf
F
rv Resultant V ertical Force N, lbf
F
s Separating Force on Gear N, lbf
Fs
G Separating Force on Gear N, lbf
Fs
P Separating Force on Pinion N, lbf
Fs
W Separating Force on W orm N, lbf
F
t Tangential Force N, lbf
F
te Tractive Effort on V ehicle Wheels N, lbf
F
tG Tangential Force on Gear N, lbf
F
tP Tangential Force on Pinion N, lbf
F
tW Tangential Force on W orm N, lbf
F
W Force of Unbalance N, lbf
F
wb W eighted Average Load N , lbf
G Gear (used as subscript) unitless
G
1 Geometry Factor from Bearing Data Tables unitless
G
2 Geometry Factor from Bearing Data Tables unitless
H Power kW, hp
H
s Housing Shoulder Inner Diameter mm, in.