Timken Super Precision Bearings for Machine Tool Applications

ENGINEERING
A
DETERMINATION OF APPLIED LOADS AND BEARING ANALYSIS
This key is not intended to be comprehensive, but serves as a useful reference for symbols found in this catalog.
Symbol Description Units
a 1 Reliability Life Factor
a 2 Material Life Factor
a 3 Operating Condition Life Factor
a 3d Debris Life Factor
a 3h Hardness Life Factor
a 3k Load Zone Life Factor
a 3l Lubrication Life Factor
a 3m Misalignment Life Factor
a 3p Low Load Life Factor
a e Effective Bearing Spread mm, in.
b Tooth Length mm, in.
c 1, c 2 Linear Distance (positive or negative) mm, in.
C Dynamic Radial Load Rating N, lbf
C 0 Static Load Rating N, lbf
C 90 Single-Row Basic Dynamic Load Rating N, lbf
C e Extended Dynamic Capacity N, lbf
C p Specific Heat of Lubricant J/(kg -˚C),
BTU/(lb x ˚F)
d Bearing Bore Diameter mm, in.
d c Distance Between Gear Centers mm, in.
d m Mean Bearing Diameter mm, in.
dN Bore in mm • RPM
D Bearing Outside Diameter mm, in.
D m Mean Diameter or Effective Working
Diameter of a Sprocket, Pulley, Wheel or Tire
Also, Tapered Roller Bearing Mean
Large Rib Diameter
mm, in.
D mG Mean or Effective Working Diameter of the Gear mm, in.
D mP Effective Working Diameter of the Pinion mm, in.
D mW Effective Working Diameter of the Worm mm, in.
D pG Pitch Diameter of the Gear mm, in.
D pP Pitch Diameter of the Pinion mm, in.
D pW Pitch Diameter of the Worm mm, in.
e Life Exponent
Lubricant Flow Rate
L/min, U.S. pt/min
B Belt or Chain Pull Factor
F General Term for Force N, lbf
F a Applied Axial Load N, lbf
F ae External Axial Load N, lbf
F aG Axial Force on Gear N, lbf
F aP Axial Force on Pinion N, lbf
F aW Axial Force on Worm N, lbf
F c Centrifugal Force N, lbf
F r Applied Radial Load N, lbf
F sG Separating Force on Gear N, lbf
F sP Separating Force on Pinion N, lbf
F sW Separating Force on Worm N, lbf
F tG Tangential Force on Gear N, lbf
F tP Tangential Force on Pinion N, lbf
F tW Tangential Force on Worm N, lbf
F W Force of Unbalance N, lbf
F P Axial Force on Pinion N, lbf
H Power kW, HP
HF s Static Load Rating Adjustment Factor for
Raceway Hardness
k Centrifugal Force Constant lbf/RPM 2
k 1 Bearing Torque Constant N-m, lbf-in.
k 4, k 5, k 6 Dimensional Factor to Calculate Heat Generation
SUMMARY OF SYMBOLS USED IN THIS CATALOG
Symbol Description Units
K Tapered Roller Bearing Radial-to-Axial Dynamic
Load Rating Factor
K T Relative Axial Load Factor (Ball Bearings)
L H Lead Axial Advance of a Helix for
One Complete Revolution
mm, in.
L Distance Between Bearing Geometric
Center Lines
mm, in.
m Gearing Ratio
M Bearing Operating Torque or Moment N-m, N-mm, lbf-in.
n Bearing Operating Speed or
General Term for Speed
rot/min, RPM
n G Gear Operating Speed (RPM) rot/min, RPM
n P Pinion Operating Speed (RPM) rot/min, RPM
n W Worm Operating Speed (RPM) rot/min, RPM
N G Number of Teeth in the Gear
N P Number of Teeth in the Pinion
N S Number of Teeth in the Sprocket
P a Dynamic Equivalent Axial Load N, lbf
P 0 Static Equivalent Load N, lbf
P 0a Static Equivalent Axial Load N, lbf
P 0r Static Equivalent Radial Load N, lbf
P r Dynamic Equivalent Radial Load N, lbf
Q Generated Heat or Heat Dissipation Rate W, BTU/min
r Radius
R Percent Reliability Used in the Calculation
of the a 1 Factor
T Torque N-m, lbf-in.
v Vertical (used as subscript)
V Linear Velocity or Speed km/h, mph
V r Rubbing, Surface or Tapered Roller
Bearing Rib Velocity
m/s, fpm
X Dynamic Radial Load Factor
Y Dynamic Axial Load Factor
Y 1, Y 2, Y 3 Axial Load Factors
G Bevel Gearing – Gear Pitch Angle deg.
Hypoid Gearing – Gear Root Angle
deg.
P Bevel Gearing – Pinion Pitch Angle deg.
Hypoid Gearing – Pinion Face Angle
deg.
Half Included Cup Angle
deg.
A, B... Bearing Position (used as a subscript) cSt
Efficiency, Decimal Fraction
ambt Ambient Temperature ˚C, ˚F
1, 2, 3 Gear Mesh Angles Relative to the
Reference Plane
deg.
i, o Oil Inlet or Outlet Temperature ˚C, ˚F
Worm Gear Lead Angle deg.
μ Coefficient of Friction
v Lubricant Kinematic Viscosity cSt
0 Approximate Maximum Contact Stress MPa, psi
Normal Tooth Pressure for the Worm (Gearing) deg.
G Normal Tooth Pressure Angle for the Gear deg.
P Normal Tooth Pressure Angle for the Pinion deg.
G Helix (Helical) or Spiral Angle for the Gear deg.
P Helix (Helical) or Spiral Angle for the Pinion deg.
Lubricant Density kg/m 3 , lb/ft 3
1, 2, ...n Conditions (used as subscript)
36 TIMKEN MACHINE TOOL CATALOG