ABSTRACT
J Polar moment of inertia per unit length N sec2 (lb sec2) J J/E’<i mm sec2 (in sec2) kb Lubricant thermal conductivity W/m 8C
(Btu/hr in. 8F) K0 Bulk modulus parameter Pa 8K K1 Bulk modulus parameter Pa l Roller effective length mm (in.)
L Factor for calculating film thickness reduction due to
thermal effects
M Moment N mm (in. lb) n Speed rpm
p Pressure MPa (psi)
Q Force acting on roller or ball N (lb)
Q Q/E’<
r relative occupied volume
expansion factor
R relative occupied volume m3
Ro relative occupied volume at 208C m 3
R Cylinder radius mm (in.)
< Equivalent radius mm (in.) s rms surface finish (height) mm (in.)
SSU Saybolt university viscosity sec
t Time sec
T Lubricant temperature 8C,8K (8F, 8R) u Fluid velocity mm/sec (in./sec)
U Entrainment velocity (U1U1) mm/sec (in./sec) U h0U/2E’< v Fluid velocity, displacement in y direction mm/sec, mm (in./
sec, in.)
V Volume mm3
Vo Volume at 208C mm 3
V Sliding velocity (U1U1) mm/sec (in./sec) V h0V/E’< w Deformation in z direction mm (in.)
y Distance in y direction mm (in.)
z Distance in z direction mm (in.)
b’ Coefficient for calculating viscosity as a function of temperature g (D cos a)/dm _ Lubricant shear rate sec1
« Strain mm/mm (in./in.) e occupied volume expansivity 8C1
h Lubricant viscosity cp (lb sec/in.2) hb Base oil viscosity (grease) cp (lb sec/in.2) heff Effective viscosity (grease) cp (lb sec/in.2) h0 Fluid viscosity at atmospheric pressure cp (lb sec/in.2) k Ellipticity ratio a/b l Pressure coefficient of viscosity mm2/N (in.2/lb) L Lubricant film parameter vb Kinematic viscosity stokes (cm
j Poisson’s ratio r Weight density g/mm3/(lb/in.3) s Normal stress MPa (psi) t Shear stress MPa (psi) u Angle rad Y Factor to calculate wTS w Film thickness reduction factor F Factor to calculate wS c Angular location of roller rad v Rotational speed rad/sec
Subscripts
b Entrance to contact zone
e Exit from contact zone
G Grease
i Inner raceway film
j Roller location
m Orbital motion
NN Non-Newtonian lubricant
o Outer raceway film
R Roller
S Lubricant starvation
SF Surface roughness (finish)
T Temperature
TS Temperature and lubricant starvation
x x Direction, that is, transverse to rolling
y y Direction, that is, direction of rolling
z z Direction
m Rotating raceway v Nonrotating raceway
0 Minimum lubricant film
1, 2 Contacting bodies
Ball and roller bearings require fluid lubrication if they are to perform satisfactorily for long
periods of time. Although modern rolling bearings in extreme temperature, pressure, and
vacuum environment aerospace applications have been adequately protected by dry film
lubricants, such as molybdenum disulfide among many others, these bearings have not been
subjected to severe demands regarding heavy load and longevity of operation without fatigue.
It is further recognized that in the absence of a high-temperature environment only a small
amount of lubricant is required for excellent performance. Thus, many rolling bearings can be
packed with greases containing only small amounts of oil and then be mechanically sealed to
retain the lubricant. Such rolling bearings usually perform their required functions for
indefinitely long periods of time. Bearings that are lubricated with excessive quantities of
oil or grease tend to overheat and burn up.
