ABSTRACT
J Conversion factor, 103 N mm¼ 1 W sec k Thermal conductivity W/m 8C (Btu/hr ft 8F) L Length of heat conduction path m (ft) M Friction torque N mm (in. lb) n Rotational speed rpm
Pr Prandtl number
q Error function
Re Reynolds number
< Radius m (ft) s Surface roughness mm (min.) S Area normal to heat flow m2 (ft2)
T Temperature 8C (8F) us Fluid velocity m/sec (ft/sec)
v Velocity m/sec (ft/sec)
w Weight flow rate g/sec (lb/sec)
W Width m (ft) x Distance in x direction m (ft)
z Number of rolling elements
« Error h Absolute viscosity cp (lb sec/in.2) n Fluid kinematic viscosity m2/sec (ft2/sec) s Rolling element-raceway contact normal stress MPa (psi)
t Surface friction shear stress MPa (psi) v Rotational velocity rad/sec V Rotational velocity rad/sec
Subscripts
a Air or ambient condition
BRC Ball-raceway contact
c Heat conduction
CRL Contact between the cage rail and ring land
CPR Contact between the cage pocket and rolling element
f Friction
fdrag Viscous drag on the rolling elements
i Inner raceway
j Rolling element position
n raceway
o Oil or outer raceway
r Heat radiation
REF Roller end-flange contact
RRC Roller-raceway contact
tot Bearing total friction heat generation
v Heat convection
x x direction, transverse to rolling direction
y y direction, rolling direction
1 Temperature node 1
2 Temperature node 2, and so on
The overall temperature level at which a rolling bearing operates depends on many variables
among which are:
. Applied load
. Operating speeds
. Lubricant type and its rheological properties
. Bearing mounting arrangement and housing design
. Operational environment
In the steady-state operation of a rolling bearing, the friction heat generated must be
dissipated. Therefore, the steady-state temperature level of one bearing system compared
with that of another using identical sizes and number of bearings is a measure of that system’s
efficiency of heat dissipation.
