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10. Selection of bearings by dynamical loads

Bearings are selected from catalogs, before referring to

catalogs you should know the followings:

• Bearing load – radial, thrust (axial) or both

• Bearing life and reliability
• Bearing speed (rpm)
• Space limitation
• Accuracy

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Example of table in catalog:

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Load factor
There are many instances where the actual operational shaft load is much
greater than the theoretically calculated load, due to machine vibration
and/or shock. This actual shaft load can be found by using formula (4.1).

K ＝ fw・Kc （4.1）
：
where,

：
K Actual shaft load N

：
fw Load factor (Table 4.1)
Kc Theoretically calculated value N

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Bearing life

Even in bearings operating under normal conditions, the surfaces of the raceway and
rolling elements are constantly being subjected to repeated compressive stresses which
cause flaking of these surfaces to occur. This flaking is due to material fatigue and will
eventually cause the bearings to fail. The effective life of a bearing is usually defined in
terms of the total number of revolutions a bearing can undergo before flaking of either the
raceway surface or the rolling element surfaces occurs.

A group of seemingly identical bearings when subjected to identical load and operating
conditions will exhibit a wide diversity in their durability. The basic rating life is based
on a 90% statistical model which is expressed as the total number of revolutions 90% of
the bearings in an identical group of bearings subjected to identical operating conditions
will attain or surpass before flaking due to material fatigue occurs. For bearings operating
at fixed constant speeds, the basic rating life (90% reliability) is expressed in the total
number of hours of operation.

 ＝(/) （3.1）

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where,
p= 3 For ball bearings
p= 10/3 For roller bearings

 : Basic rating life 10 revolutions
C : Basic dynamic rating load, N (Cr: radial bearings, Ca: thrust bearings)
P : Equivalent dynamic load, N (Pr: radial bearings, Pa: thrust bearings)

Equation (3.1) can be expressed and

 ＝ 

(/)

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Bearing Load Calculation

Allowable static equivalent load

Generally the static equivalent load which can be permitted is limited by the basic static
rating load. However, depending on requirements regarding friction and smooth operation,
these limits may be greater or lesser than the basic static rating load. In the following
formula (3.9) and Table 3.4 the safety factor So can be determined considering the
maximum static equivalent load.

So =Co/Po （3.9）
where, So : Safety factor
Co : Basic static rating load, N (radial bearings: Cor, thrust bearings: Coa)
Po max : Maximum static equivalent load, N (radial: Por max, thrust: Coa max)

Note 1: For spherical thrust roller bearings,

min.  value=4.
2: For shell needle roller bearings, min. 
value=3.
3: When vibration and/or shock loads are
present, a load factor based on the shock load
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needs to be included in the  max value

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Equivalent load - Dynamic equivalent load

When both dynamic radial loads and dynamic axial loads act on a bearing at the same
time, the hypothetical load acting on the center of the bearing which gives the bearings the
same life as if they had only a radial load or only an axial load is called the dynamic
equivalent load. For radial bearings, this load is expressed as pure radial load and is called
the dynamic equivalent radial load. For thrust bearings, it is expressed as pure axial load,
and is called the dynamic equivalent axial load.

The dynamic equivalent radial load is expressed by formula (4.17).

Pr ＝V X Fr＋Y Fa (4.17)

：
where,

：
Pr Dynamic equivalent radial load, N

：
Fr Actual radial load, N

：
Fa Actual axial load, N

：
X Radial load factor
Y Axial load factor
The values for X and Y are listed in the bearing tables.
V = 1.0 for inner race rotating
V = 1.2 for outer race rotating
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11. Selection of bearing tolerances

Bearing arrangement
In order to guide and support a rotating shaft, at least two bearings are required which are
arranged at a certain distance from each other. Depending on the application, a bearing
arrangement with locating and floating bearings, with adjusted bearings or with floating
bearings can be selected.

Locating-floating bearing arrangement

Due to machining tolerances the center distances between the shaft seats and the housing
seats are often not exactly the same with a shaft which is supported by two radial bearings.
Warming- up during operation also causes the distances to change.
These differences in distance are compensated for in the floating bearing. Cylindrical roller
bearings of N and NU designs are ideal floating bearings. These bearings allow the roller
and cage assembly to shift on the raceway of the lipless bearing ring. Both rings can be
fitted tightly.

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All other bearing types, e.g. deep groove ball bearings and spherical roller bearings, only
function as floating bearings when one bearing ring is provided with a loose fit. The ring
under point load is therefore given a loose fit; this is generally the outer ring.
The locating bearing, on the other hand, guides the shaft axially and transmits external axial
forces. For shafts with more than two radial bearings, only one bearing is designed as a
locating bearing in order to avoid detrimental axial preload. The bearing to be designed as a
locating bearing depends on how high the axial load is and how accurately the shaft must be
axially guided.

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12. Selection and control calculations of key and spline joints, other fasteners

Some possible failures of key joints:

The working face of the weaker element may be crushed;
The elements are worn excessively;
Keys are snipped.

The first and the second one are the common cases of key failure. The last
form seldom takes place unless serious overload happens.
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The key joint design steps

(The design configuration - materials and sizes of the joined parts, the
transmitted loads are known)
1. Selecting the type of the keys
According to the configurations, working condition, centering quantity, fixing
and location to select key type.

（ ）
2. Choose the configuration and size of the keys
According to the diameter of the shaft, get the section b × h and length L of
the key.
(Table presents keys dimension in accordance with BS 4235-1:1972:
Specification for metric keys and keyways - Parallel and taper keys)

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3. Check the strength of keys

Strength calculations of straight key joints:
For plain flat key joints:
The shearing stress is


 =  /  = 2/ (
) or
≥
 

 for steel key can be taken 20 … 25 MPa

If to take = !" /N
Then the compressive stress is
  4
= = =
#  $ 
$

( )
2 2

Letting this stress equal the design compressive stress allows the computation of the
required length of the key for this mode of failure:
&
L≥
'(

In typical industrial applications, N = 3 is adequate.

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：
If the strength is insufficient, do like following

① Use two keys. These two keys install at an angle of 180.0, the
strength calculation will be carried out for 1.5 keys

② Make the hub longer. But it should not be beyond 2.25d

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