**
12.19 FAILURE OF
ROLLING-ELEMENT BEARINGS
**

If
sufficient, clean lubricant is provided, failure in rolling bearings will be by
surface fatigue. Failure is considered to occur when either raceway or balls (rollers)
exhibit the first pit. Typically the raceway will fail first. The bearing will
give an audible indication that pitting has begun by emitting noise and
vibration. It can be run beyond this point, but as the surface continues to
deteriorate, the noise and vibration will increase, eventually resulting in
spalling or fracture of the rolling elements and possible jamming and damage to
other connected elements.

Any
large sample of bearings will exhibit wide variations in life among its
members. The failures do not distribute statistically in a symmetrical Gaussian
manner, but rather according to a Weibull distribution, which is skewed.
Bearings are typically rated based on the life, stated in revolutions (or in
hours of operation at the design speed), that 90% of a random sample of
bearings of that size can be expected to reach or exceed at their design load.
In other words, 10% of the batch can be expected to fail at that load before
the design life is reached. This is called the
*
L
*
10
life.* For critical applications, a smaller failure percentage can be designed
for, but most manufacturers have standardized on the
*
L
*
10
life as a means of defining the load-life characteristic of a bearing. The
rolling-bearing selection process largely involves using this parameter to
obtain whatever life is desired under the anticipated loading or overloading
conditions expected in service.

* Some bearing manufacturers refer to this as the
*
B
*
90 or
*
C
*
90 life, referring to the
survival of 90% of the bearings rather than the failure of 10%.

Figure
12-28 shows a curve of bearing failure and survival percentages as a function
of relative fatigue life. The
*
L
*
10 life is taken as the reference. The curve is
relatively linear to 50% failure, which occurs at a life 5 times that of the
reference. In other words, it should take 5 times as long for 50% of the
bearings to fail as it does for 10% to do so. After that point the curve
becomes quite nonlinear, showing that it will take about 10 times as long to
fail 80% of the bearings as to fail 10%. At 20 times the
*
L
*
10
life, there are still a few percent of the original bearings running.

**
**

**
12.20 SELECTION OF
ROLLING-ELEMENT BEARINGS
**

Once
a bearing type suited to the application is chosen based on considerations discussed
above, selection of an appropriate-size bearing depends on the magnitudes of
applied static and dynamic loads and the desired fatigue life.

**
**

**
Basic Dynamic Load Rating C
**

Extensive
testing by bearing manufacturers, based on well-established theory, has shown
that the fatigue life
*
L
*
of rolling bearings is inversely proportional
to the third power of the load for ball bearings, and to the 10/3 power for
roller bearings. These relationships can be expressed as

ball
bearings :
*
L
*
(12.27a)

*
*

roller
bearings :
*
L
*
(12.27b)

*
*

where
*
L
*
is fatigue life expressed in millions of revolutions,
*
P
*
is the applied load,* and
*
C
*
is
the
*
basic dynamic load rating
*
for the particular bearing that is defined by
the manufacturer and published for each bearing in the bearing catalogs. The
**
***
basic dynamic load rating
*
*
C
*
is
defined as
*
the load that will
give a life of 1 million revolutions of the inner race
*
. This load
*
C
*
is typically
larger than any practical load that one would subject the particular bearing
to, because the desired life is usually much higher than 1 million revolutions.
In fact, some bearings will fail statically if actually subjected to a load
equal to
*
C
*
. It is simply a reference value that allows
bearing life to be predicted at any level of actual applied load. Figure 12-29
shows a page from a cam-follower bearing manufacturer’s catalog that specifies
the value of
*
C
*
for each bearing.

* Note that even a constant external load applied to a
rotating bearing creates dynamic loads in the bearing elements in the same
manner that a constant moment on a rotating shaft causes dynamic stresses,
because any one point on a ball, roller, or raceway sees the load come and go
as the bearing rotates.

**
**

**
FIGURE 12-29
**

Dimensions and load ratings for CCFH-SB series
Camrol cam follower bearings
(
Courtesy
of McGill Precision Bearings, Valparaiso, IN.)

**
Basic Static Load Rating
**
**
***
C
*
**
0
**

Permanent
deformations on rollers or balls can occur at even light loads because of the
very high stresses within the small contact area. The limit on static loading
in a bearing is defined as the load that will produce a total permanent
deformation in the raceway and rolling element at any contact point of 0.0001
times the diameter
*
d
*
of the rolling element. Larger deformations
will cause increased vibration and noise, and can lead to premature fatigue
failure. The stresses required to cause this 0.0001
*
d
*
static
deformation in bearing steel are quite high, ranging from about 4 GPa (580
kpsi) in roller bearings to 4.6 GPa (667 kpsi) in ball bearings. Bearing
manufacturers publish a basic static load rating
*
C
*
0
for each bearing, calculated according to AFBMA standards. This loading can
sometimes be exceeded without failure, especially if rotating speeds are low,
which avoids vibration problems. It usually takes a load of 8
*
C
*
0
or larger to fracture a bearing. Figure 12-29 shows a page from a bearing
manufacturer’s catalog that specifies the value of
*
C
*
0
for each bearing.

**
**

**
Calculation Procedures
**

Equations
12.27 can be solved for any situation in which either the applied load or a
desired fatigue life is known. Usually, the radial loads acting on the follower
bearing will be known from a load analysis of the design. A bearing
manufacturer’s catalog should then be consulted, a trial bearing (or bearings)
selected, and the values of
*
C
*
, and
*
C
*
0 extracted. The load
*
P
*
and
basic dynamic load rating
*
C
*
are used in equations 12.27 to find the
predicted fatigue life
*
L
*
.

Alternatively,
equations 12.27 can be solved for the value of dynamic load factor
*
C
*
required
to achieve a desired life
*
L
*
. The bearing catalogs can then be consulted to
find a suitably sized bearing with the necessary
*
C
*
value.
In either case, the static load should also be compared to the static load
factor
*
C
*
0 for the chosen bearing to guard against
excessive deformations.

**
**