Page 329 - Analysis and Design of Machine Elements

Rolling Contact Bearings
The values of X and Y vary with specific bearings and with the ratio of axial load to 307
radial load. To evaluate the effect of axial loads on the load carrying capacity of a bearing,
manufacturers specify a factor e for different types of bearing and define a ratio of axial
and radial loads for comparison [1]. That is, for relatively small axial loads or a ratio
A/R ≤ e,select X = 1and Y = 0, that is, the equivalent load is pure radial load and the
effect of axial load can be ignored. If A/R > e, the effect of axial load on the load carrying
capacity of bearing must be considered and Eq. (11.14) is used to compute equivalent
dynamic load P. For deep-groove ball bearings, both e and Y depend on the ratio of A/C ,
0
where C is the static load rating of a particularly selected bearing. Therefore, a simple
0
trial-and-error method is used [1]. Table 11.1 gives dynamic radial and axial load factors
for selected bearing types. Values of X, Y and e for loads or contact angles other than
those shown are obtained by linear interpolation. Designers can refer to manufacturer’s
catalogue for detailed data for different types of bearings.
In summary, for bearings such as cylindrical roller bearings, which are subject to radial
loads only, the equivalent load is a radial load, that is, P = R. For bearings such as thrust
bearings, which are subject to axial loads only, the equivalent load is an axial load, that
is, P = A. For other bearings that are subject to the combination of radial and axial loads,
the equivalent load follows P = XR + YA. For a pair of bearings supporting a shaft, values
forbothbearings X , Y and X , Y should be calculated and whichever combination
1 1 2 2
gives a larger equivalent dynamic load P is used for life calculation.
The bearing rated capacity is for stable loading. Shock or impact loads may reduce
bearing life and load factor f is introduced to consider the severity of shock. The load
p
factor f varies from light impact (f = 1.0–1.2), through moderate impact (f = 1.2–1.8)
p
p
p
to heavy impact (f = 1.8–3.0) loading. The equivalent dynamic load is thus modified
p
as f P.
p
∘
When a bearing operates at a temperature higher than 120 C, the basic dynamic load
rating will decrease. The effect of temperature on load carrying capacity is considered
by multiplying the basic dynamic load rating C by a temperature factor of f .Thetem-
t
∘
perature factor f is selected as 1.0 for temperatures less than 120 C, andas0.9,0.8,0.7,
t
∘
∘
∘
∘
∘
0.6 and 0.5 for temperatures at 150 C, 200 C, 250 C, 300 C and 350 C, respectively [5].
Temperature factors at other temperatures can be decided by linear interpolation. The
design life can be computed by a modified formula as,
( )
10 6 f C
t
L = ≥ [L ] (11.15)
10h h
60n f P
p
If the design life L and design load P areknown,weuse thefollowing design formula
10h
to compute the required basic dynamic load rating C for bearing size selection,
f P ( 60nL 10h ) 1
p
C = (11.16)
f 10 6
t
11.3.1.3 Rated Life at Different Reliability
The basic dynamic load rating listed in the manufacturer’s catalogue has a reliability
of 90%. When a higher reliability is desired by designers, a life-adjustment factor for
reliability is incorporated in bearing life calculation. Thus, the rated bearing life, L ,
1 10
may be adjusted to a higher reliability using
L = L (11.17)
n
1 10