ABSTRACT
J Mass moment of inertia kg mm2 (in. lb sec2) K Load-deflection constant N=mmx (lb=in.x) l Roller length mm (in.)
m Ball or roller mass kg (lb sec2=in.) M Moment N mm (lb in.) Mg Gyroscopic moment N mm (lb in.) M Applied moment N mm (lb in.) n Rotational speed rpm
nm Ball or roller orbital speed, cage speed rpm
nR Ball or roller speed about its own axis rpm
Pd Radial or diametral clearance N (lb.)
q Roller-raceway load per unit length N=mm (lb=in.) Q Ball or roller normal load N (lb)
Qa Axial direction load on ball or roller N (lb)
Qr Radial direction load on ball or roller N (lb)
R Radius to locus of raceway groove curvature centers mm (in.)
s Distance between inner and outer groove
curvature center loci mm (in.)
X1 Axial projection of distance between ball center and
outer raceway groove curvature center mm (in.)
X2 Radial projection of distance between ball center and
outer raceway groove curvature center mm (in.)
a Contact angle 8, rad b Ball attitude angle 8, rad g (D cos a)=dm d Deflection or contact deformation mm (in.) u Bearing misalignment or angular deflection 8, rad r Mass density kg=mm3 (lb z sec2=in.4) f Angle in WV plane 8, rad c Angle in yz plane 8, rad v Rotational speed rad=sec vm Orbital speed of ball or roller rad=sec vR Speed of ball or roller about its own axis rad=sec Dc Angular distance between rolling elements rad
Subscripts
a Axial direction
e Rotation about an eccentric axis
f Roller guide flange
i Inner raceway
j Rolling element at angular location
m Cage motion and orbital motion
o Outer raceway
r Radial direction
R Rolling element
x x direction
z z direction
Dynamic (inertial) loading occurs between rolling elements and bearing raceways because of
rolling element orbital speeds and speeds about their own axes. At slow-to-moderate operat-
ing speeds, these dynamic loads are very small compared with the ball or roller loads caused
by the loading applied to the bearing. At high operating speeds, however, these rolling
element dynamic loads, centrifugal forces, and gyroscopic moments will alter the distribution
of the applied loading among the balls or rollers. In roller bearings, the increase in loading on
the outer raceway due to roller centrifugal forces causes larger contact deformations in that
member; this effect is similar to that of increasing clearance. Increase of clearance, as
demonstrated in Chapter 7 of the first volume of this handbook, causes increased maximum
roller load due to a decrease in the extent of the load zone. For relatively thin section bearings
supported at only a few points on the outer ring, for example, an aircraft gas turbine
mainshaft bearing, the centrifugal forces cause bending of the outer ring, also affecting the
distribution of loading among the rollers.
