ABSTRACT
M Bearing moment load N mm (in. lb) P Applied load at a N (lb)
Q Rolling element load N (lb)
< Radius from bearing centerline to raceway groove center mm (in.) T Applied moment load at a N mm (in. lb) w Load per unit length N/mm (lb/in.)
x Distance along the shaft mm (in.)
y Deflection in the y direction mm (in.)
z Deflection in the z direction mm (in.)
a8 Free contact angle rad, 8 g D cos
dm d Bearing radial deflection mm (in.) u Bearing angular misalignment rad, 8 Sr Curvature sum mm1 (in.1) c Rolling element azimuth angle rad, 8
Subscripts
1, 2, 3 Bearing location
a Axial direction
h Bearing location
j Rolling element location
y y Direction
z z Direction
xy xy Plane
xz xz Plane
Superscript
k Applied load or moment
In some modern engineering applications of rolling bearings, such as high-speed gas turbines,
machine tool spindles, and gyroscopes, the bearings must often be treated as integral to the
system to be able to accurately determine shaft deflections and dynamic shaft loading as well
as to ascertain the performance of the bearings. Chapter 1 and Chapter 3 detail methods of
calculation of rolling element load distribution for bearings subjected to combinations of
radial, axial, and moment loadings. These load distributions are affected by the shaft radial
and angular deflections at the bearing. In this chapter, equations for the analysis of bearing
loading as influenced by shaft deflections will be developed.
