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Text version of the page
ENGINEERING
Spherical Roller Bearings - 4918 A A
DETERMINATION OF APPLIED LOADS AND BEARING REACTIONS
The following equations are used to determine the forces developed by machine elements commonly encountered in bearing applications.
SUMMARY OF SYMBOLS USED TO DETERMINE APPLIED BEARING LOADS AND BEARING ANALYSIS
Symbol Description Units Symbol Description Units a2 1 Reliability Life Factor a k Centrifugal Force Constant lbf/RPM
2 Material Life Factor a k
1 Bearing Torque Constant k
3 Operating Condition Life Factor a
4 , k
5 , k
6 Dimensional Factor to calculate heat generation L 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, lb-in.n Bearing Operating Speed or General Term for Speed rot/min, RPM n
3d Debris Life Factora
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
G Gear Operating Speed (RPM) rot/min, RPMn
Static Load Rating N, lbfC
P Pinion Operating Speed (RPM) rot/min, RPMn
p Specifi c Heat of Lubricant J/(kg x ˚C), BTU/(lb x ˚F) d Bearing bore diameter mm, in.d
W Worm Operating Speed (RPM) rot/min, RPMN
G Number of Teeth in the Gear N
P Number of Teeth in the Pinion N
Mean inner race diameter mm, in.d
S Number of Teeth in the Sprocket P
c Distance Between Gear Centers mm, in.d
Static Equivalent Load N, lbfP
m Mean Bearing Diameter mm, in.d
0a Static Equivalent Thrust (Axial) Load N, lbfP
s Shaft inside diameter mm, in.D Bearing outside diameter mm, in.D
0r Static Equivalent Radial Load N, lbfP
r Dynamic Equivalent Radial Load N, lbfQ Generated Heat or Heat Dissipation Rate W, BTU/minT Torque N-m, lb.-in.v Vertical (used as subscript) V Linear Velocity or Speed km/h, mph V
Mean outer race diameter mm, in.D
h Housing outside diameter mm, in.D
m Mean Diameter or Effective Working Diameter of a Sprocket, Pulley, Wheel or Tire Also, Tapered Roller Mean Large Rib Diameter mm, in.D
r Rubbing or Surface Velocity m/s, fpmX Dynamic Radial Load Factor X
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
Static Radial Load Factor Y Dynamic Thrust (Axial) Load Factor Y
pG Pitch Diameter of the Gear mm, in.D
pP Pitch Diameter of the Pinion mm, in.D
Static Thrust (Axial) Load Factor
pW Pitch Diameter of the Worm mm, in.e Life Exponent ˍ
G Bevel Gearing Gear Pitch Angle deg. Hypoid Gearing Gear Root Angle deg. Lubricant Flow Rate L/min, U.S. pt/min ˍ
P Bevel Gearing Pinion Pitch Angle deg. Hypoid Gearing Pinion Face Angle deg. Coeffi cient of linear expansion mm/mm/ ˚C, in./in./˚Fs Interference fi t of inner race on shaft mm, in. h Interference fi t of outer race in housing mm, in.
Viscous Dependent Torque Coeffi cient
1 Load Dependent Torque Coeffi cient
B Belt or Chain Pull Factor F General Term for Force N, lbfF
a Applied Thrust (Axial) Load N, lbfF
aG Thrust Force on Gear N, lbfF
˟ Effi ciency, Decimal Fraction
aP Thrust Force on Pinion N, lbfF
Ƨ 1,
Ƨ 2,
Ƨ 3 Gear Mesh Angles Relative to the Reference Plane deg.
aW Thrust Force on Worm N, lbfF
b Belt or Chain Pull N, lbfF
Ƨ i,
Ƨ o Oil inlet or outlet temperature ˚C, ˚F
c Centrifugal Force N, lbfF
ƪ Worm Gear Lead Angle deg. Coeffi cient of Friction v Lubricant Kinematic Viscosity cSt
r Applied Radial Load N, lbfF
sG Separating Force on Gear N, lbfF
sP Separating Force on Pinion N, lbfF Ʊ
Approximate Maximum Contact Stress MPa, psi
sW Separating Force on Worm N, lbfF
G Normal Tooth Pressure Angle for the Gear deg.
te Tractive Effort on Vehicle Wheels N, lbfF
P Normal Tooth Pressure Angle for the Pinion deg.
tG Tangential Force on Gear N, lbfF
G Helix (Helical) or Spiral Angle for the Gear deg.
tP Tangential Force on Pinion N, lbfF
P Helix (Helical) or Spiral Angle for the Pinion deg. T Temperature difference between shaft/inner race + rollers and housing/bearing outer race ˚C, ˚F Lubricant Density kg/m
tW Tangential Force on Worm N, lbfF
W Force of Unbalance N, lbfh Horizontal (used as subscript) H Power (kW or hp) kW, hp
3 , lb/ft
3 Table 2.