ABSTRACT
M Moment Nmm (lb in.) n Load-deflection exponent
Pd Diametral clearance mm (in.)
q Load per unit length N/mm (lb/in.)
Q Ball or roller-raceway normal load N (lb)
Qa Roller end-ring flange load in cylindrical roller bearing N (lb)
Qf Roller end-ring flange load in tapered roller bearing N (lb)
r Raceway groove curvature radius mm (in.)
r Radius to raceway contact in tapered roller bearing mm (in.)
rf Radius from inner-ring axis to roller end-flange contact in
tapered roller bearing mm (in.)
Rf Radius from tapered roller axis to roller end-flange contact mm (in.)
< Ring radius to neutral axis mm (in.) < Radius of locus of raceway groove curvature centers mm (in.) s Distance between loci of inner and outer raceway groove
curvature centers mm (in.)
u Ring radial deflection mm (in.)
U Strain energy Nmm (lb in.) Z Number of balls or rollers per bearing row
a Mounted contact angle rad, 8 ao Free contact angle rad, 8 b tan1 l=ðdm DÞ rad, 8 g D cosa=dm d Deflection or contact deformation mm (in.) d1 Distance between inner and outer rings mm (in.) D Contact deformation due to ideal normal loading mm (in.) Dc Angular spacing between rolling elements rad, 8 z Roller tilt angle rad, 8 h tan1l=D rad, 8 u Bearing misalignment angle rad, 8 l Lamina position m Coefficient of sliding friction between roller end and
ring flange
s Normal contact stress or pressure MPa (psi) j Poisson’s ratio j Roller skewing angle rad, 8
In most bearing applications, only applied radial, axial, or combined radial and axial loadings
are considered. However, under very heavy applied loading or if shafting is hollow to
minimize weight, the shaft on which the bearing is mounted may bend, causing a significant
moment load on the bearing. Also, the bearing housing may be nonrigid due to design
targeted at minimizing both size and weight, causing it to bend while accommodating
moment loading. Such combined radial, axial, and moment loadings result in altered distri-
bution of load among the bearing’s rolling element complement. This may cause significant
changes in bearing deflections, contact stresses, and fatigue endurance compared to these
operating parameters associated with the simpler load distributions considered in Chapter 7
of the first volume of this handbook.
