Page 331 - Analysis and Design of Machine Elements

Substitute Eq. (11.20), (11.22) and (11.25) to Eq. (11.21), we have Rolling Contact Bearings 309
k k
∑ a n H ∑ P a n
i i
i i i
( ) = = 1 (11.26)
P P n
i=1 m L i=1 m m
P i m
The average equivalent dynamic load P is
m
1
k
⎛ ∑ ⎞ √
a n P

⎜ i i i ⎟ a n P + a n P +···+ a n P
i=1 1 1 1 2 2 2 k k k
P = ⎜ ⎟ = (11.27)
m
⎜ n m ⎟ n m
⎜ ⎟
⎝ ⎠
Then the expected life of the bearing in hours would be [13]
( ) 6
6
10 C 10 C
L = = × (11.28)
h
60n P 60 a n P + a n P +···+ a n P
m m 1 1 1 2 2 2 k k k
11.3.3 Static Strength Analysis
When a bearing carries a static load exceeding its load capacity, rolling elements will
slightly indent the raceway and cause plastic deformation. Large deformation will easily
cause increased vibration and noise, leading to premature fatigue failure. The allowable
permanent deformation decides the permissible static load or basic static load rating.
Basic static load rating C is the maximum static load that will produce a permanent
0
deformation of approximately 0.0001 times the diameter of the rolling element at the
most heavily loaded element contact site [11, 14]. For radial bearings, the basic static
load ratings are radial loads, and for thrust bearings these are axial loads.
Similar to the definition of equivalent dynamic load, when a bearing rotates at
extremely low speed carrying a combined static radial and axial load, under an imagi-
nary load the maximum contact stress between rolling elements and raceway groove
is the same as that under the actual load. The imaginary load is called the equivalent
static load, given by
P = X R + Y A (11.29)
0 0 0
The static radial and axial load factor X and Y can be found in bearing catalogues or
0 0
design handbooks [6].
The basic static load rating C is used for selecting a bearing when bearings rotate at
0
slow speeds, or when heavy shock loads act on bearings, evaluated by
C ≥ S P (11.30)
0
0 0
where S is a static safety factor, which depends on the requirements of application and
0
loading conditions. For high requirements of operation precision and stability, select a
large static safety factor within 1.2–2.5; otherwise, select a static safety factor less than
1.0. More detailed data can be found in the design handbook [4].