Bearings
What is a Bearing?
It is a mechanical element that is needed to allow
relative motion between two machine elements
with minimum friction.
Bearings perform the following functions:
– bearings support rotating shafts and / or sliding elements
and hold them in position.
– bearings transmit forces from rotating or sliding elements
to the machine frame or foundations.
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Bearings: Classification based on
contact
Rolling Contact Bearings – load is transferred
through rolling elements such as balls, straight and
tapered cylinders and spherical rollers.
Sliding Contact Bearings – load is transferred
through a thin film of lubricant (oil).
Hydrostatic Bearings – load is supported on an
externally pressurized fluid film
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Bearings:
Classification based on the direction of load:
– Radial bearings support loads which are perpendicular
to the axis of the shaft.
– Thrust bearings support axial loads.
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Rolling Contact Bearings
Load is transferred through elements in rolling contact rather
than sliding contact.
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Sliding Contact Bearings
Journal (Sleeve) Bearings
Load is transferred through a lubricant in sliding contact
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Sliding Contact Bearings :Journal (Sleeve) Bearings
Thick-film lubrication (hydrodynamic), pressure distribution, and
film thickness.
hmin = minimum film thickness, c = radial clearance,
e = eccentricity
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Rolling Contact Bearings: Design
Considerations
Bearings are selected from catalogs, before referring to
catalogs you should know the following:
Thrust load
Radial load
•
•
•
•
•
Radial load
Bearing load – radial, thrust (axial) or both
Desired life and reliability
Bearing speed (rpm)
Space limitation
Accuracy
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Rolling Contact Bearings: Types
1. Ball bearings
• Deep groove bearing
• Filling notch ball bearing or maximum capacity
bearing
• Angular contact bearings
2. Roller bearings
• Cylindrical bearings
• Needle bearings
• Tapered bearings
• Spherical bearings
3. Thrust bearings
4. Linear bearings
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Ball Bearings
1. Deep groove bearing
•
Load capacity is limited by the number of balls
•
Primarily designed to support radial loads, the thrust
capacity is about 70% of radial load capacity
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Deep Groove-Ball Bearings
2. Filling notch or maximum capacity ball bearings
Bearings have the same basic radial construction as Deep
Groove. However, a filling notch (loading groove) permits more
balls to be used.
Notch
•
•
Dr B K Gupta
Radial load capacity is 20 – 40% higher than deep-groove
type
Thrust load capacity drops to 20% (2 directions) of
radial load capacity.
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Ball Bearings
3. Angular contact bearings (AC)
The centerline of contact between the balls and the raceway
is at an angle to the plane perpendicular to the axis of
rotation.
Extra support
in the back
Direction
of thrust
•
Dr B K Gupta
Used for high radial and thrust load applications
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Roller Bearings
Roller bearings have higher load capacity than ball bearings, load
is transmitted through line contact instead of point contact.
Straight cylindrical roller
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Needle type
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Roller Bearings
Tapered bearings
Designed to withstand high radial loads, high thrust loads, and
combined loads at moderate to high speeds. They can also
withstand repeated shock loads.
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Roller Bearings
Spherical bearings
Bearing design uses barrel shaped rollers. Spherical roller bearings
combine very high radial load capacity with modest thrust load
capacity and excellent tolerance to misalignment.
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Thrust Bearings
Roller thrust bearing
Ball thrust bearing
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Roller Thrust Bearings
Spherical Thrust Bearings
Cylindrical
Thrust
Bearings
Tapered
Thrust
Bearings
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Linear Bearings (Recirculation ball bearings)
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Linear Bearings
Ball or Roller bearing
Dr B K Gupta
Recirculation ball bearing
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Bearings (special purpose)
Roller bearing cam follower
Spherical rod end
Flanged
V-Grooved
Load runners (idler-rollers)
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Bearings (special purpose)
Split Ball or Roller Bearing
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Bearing Failure
If a bearing is clean, properly lubricated and mounted
and is operating at reasonable temp., failure is due to
fatigue caused by repeated contact stresses (Hertzian
stress)
Fatigue failure consists of a spalling or pitting of the curved
surfaces
Spalling – crack initiates below the curved surface at the
location of maximum shear stress, propagates to the
surface causing surface damage.
Failure criterion – spalling or pitting of an area of 6
mm2, Timken company (Depth and size depends on other parameters
such as permissible noise and vibrations)
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Bearing Life and Basic Dynamic Load Rating
Life – number of revolution or hours of operation, at constant speed,
required for the failure criterion to develop.
Rating Life – defines the number of revolution or hours of
operation, at constant speed, in such a way that 90% of the bearings
tested (from the same group) will complete or exceed before the first
evidence of failure develops. This is known as L10 life.
For ball bearings and spherical bearings:
L10 = 500 (hours) x 33.33 (rpm) x 60 = 106 = 1 million revolutions
For tapered bearings manufactured by Timken:
L10 = 3000 (hours) x 500 (rpm) x 60 = 90 x 106 = 90 million
revolutions
Basic Dynamic Load Rating, Cr – constant radial load that a
group of bearings can carry for L10 life for one million revolutions.
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Basic rating life, L10
Cr = basic dynamic radial load rating, (N)
Ca = basic dynamic axial load rating, (N)
Pr = dynamic equivalent radial load, (N)
Pa = dynamic equivalent axial load, (N)
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Dynamic Equivalent Radial Load
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Dr B K Gupta
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Static Load Capacity of Rolling
Contact Bearings
Static load is defined as the load acting on the bearing
when the shaft is stationary.
As there is either a point contact (ball bearings) or line
contact (roller bearing), the contact stresses are high
and leads to permanent deformation even for small
loads.
The permissible static load is dependent on the
magnitude of permanent deformation acceptable-so
that the bearing can still be used. The deformation is
largely limited to the rolling elements and as such the
limit of deformation is also based on the rolling
element.
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Static Load Capacity of Rolling
Contact Bearings (Contd.)
Based on experience, total permanent deformation
should be limited to 0.0001 times the ball or roller
diameter. Static load capacity (Co) based on this
permanent deformation are available in the Data
Books. However, where the requirements of low
friction, noise and smoothness are not critical, a
static loads upto 4Co may be allowed. On the other
hand, where extreme smoothness is required, a
smaller permanent deformation, i.e., a bearing with
higher value of Co may selected.
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Dynamic Equivalent Radial Load
Basic Static Load Rating, Co in Newton’s
Co = fo i z D2 cos α
fo a constant, 12.258 for radial contact and angular
contact grooved ball bearing made of hardened steel
i = no. of rows of balls
z = no. of balls / row
D = diameter of balls, mm
α = angle of contact
(Similar formulae are available for other types
rolling bearings)
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Equivalent Radial Load for single and double-row
Deep Groove Ball Bearings
Dynamic Equivalent Radial Load is given by the following
equation:
Pr = XVFr + YFa
Pr = dynamic equivalent radial load
Fr = applied radial load (constant)
Fa = applied thrust load
X = radial factor
Y = thrust factor
V = rotational factor
Values of X and Y are given in Table 1 & 2 for Deep Groove Ball Bearings
and Angular Contact Ball Bearings, respectively.
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Table-1
Sl. No.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Fa/Co
0.014
0.028
0.056
0.084
0.110
0.170
0.280
0.420
0.560
X
0.56
0.56
0.56
0.56
0.56
0.56
0.56
0.56
0.56
Fa / (VFr) > e
Y
2.30
1.99
1.71
1.55
1.45
1.31
1.15
1.04
1.00
e*
0.19
0.22
0.26
0.28
0.30
0.34
0.38
0.42
0.44
* limiting value of Fa / (VFr)
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Table-2
S.No
.
1.
2.
3.
4.
5.
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Single
Row
20
25
30
35
40
X
0.43
0.41
0.39
0.37
0.35
Y
1.00
0.87
0.76
0.66
0.57
Double Row
e
X
1
1
1
1
1
Y
1.09
0.92
0.78
0.66
0.55
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X
0.70
0.67
0.63
0.60
0.57
Y
1.63
1.41
1.24
1.07
0.93
0.57
0.68
0.80
0.95
1.14
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Cylindrical or Straight and Taper Roller
Bearings
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(in relation to load, inner ring is : rotating V= 1, stationary V = 1.2)
X
Y
Single – Row Roller Double – Row Single
– Row Double – Row
Bearing
Roller Bearing
Roller Bearing
Roller Bearing
1.0
0.4
1.0
0.67
0.0
0.4 cot α
0.45 cot α
e
1.5
0.67 cot α tan α
(α is the nominal angle of contact, i.e., nominal angle between the axis of
rolling elements and plane perpendicular to the bearing axis)
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Dynamic Equivalent Radial Load
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Bearing Reliability
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Bearing Reliability (Weibull Distribution)
In applications where there is risk to human life, it is necessary
to select a bearing of a reliability of more than 90%
Relationship is given by Weibull distribution:
(1)
(2)
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Life Adjustment Factor
Dividing equation (1) by (2)
L50 = 5L10 (based on experimental evidence)
Solving equations (1) and (2)
a = 6.84, b = 1.17
IS 3824:2002 recommends the value of exponent b as 1.5 in
place of 1.17; i.e.
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Table 4- Life adjustment factor for
reliability, a1
Reliability (R) a1 = L / L10 for b = a1 = L / L10 for b = 1.5
1.17
90
1
1
95
0.54
0.62
96
0.44
0.53
97
0.35
0.44
98
0.19
0.33
99
0.13
0.21
99.5
0.07
0.13
Thus LR = a1L90. Value of a1 for the desired reliability R
may be taken from the above table or may be calculated
from equation (b).
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System Reliability
(i)
System Reliability with N identical
bearings in the system.
System Reliability, SR = (R)N
where R = reliability of each bearing.
(ii)
SR = R1 R2 R3 ………..
where R1, R2 etc. is the reliability of
individual bearing in the system.
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Selection of Bearing Life and Load
Factor
Selection of the size of a bearing depends on the
expected life of the bearing for the given
application. Most of the manufactures’ data
books contain data on bearing life for many
classes of machinery, as well as information on
load factors. These factors are based on
experience and may be used in selecting the
rolling element bearing for a given application.
Tables 5 and 6 provide recommendations for
Load Factor and Life, respectively.
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Table 5- Load Factors or Service
Factors Load Factor
Sl. Type of Application
No.
1.
2.
3.
4.
Constant Load
Precision Gearing
Commercial Gearing
Machinery with light impacts or
shock
5. Machinery with medium
impacts: reciprocating
compressors, internal
combustion engines V-Belt
drives, etc
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1.0
1 – 1.1
1.1 – 1.3
1.2 – 1.5
1.5 – 3.0
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Table 6- Bearing-Life Recommendations for Various
Classes of Appliances and Machines.
Sl. Type of Application
No
.
1. Instruments, Kitchen appliances, bearings used in automobiles
Life L1OH
Upto- 500
500 – 2000
4000 – 8000
2.
3.
Aircraft engines, railway wagons, etc
Machines for short or intermittent duration and where breakdown will
not have serious consequences: hand tools, lifting tackles in
workshops, domestic machines, agriculture machines, etc
4.
Machines working intermittently but their breakdown would have 8000 – 12000
serious consequences: auxiliary machinery in power stations,
conveyors, lifts, machine tools used infrequently.
Machines used for 8 hours per day service and not fully utilized such 12000 – 20000
as electric motors gear drives
Machines used for 8 hours per day fully utilized – machine for the 20000 – 30000
engineering industry generally, ventilating fans, electric motor, etc
5.
6.
7.
8.
Machines for continuous 24 hours service – pumps, mine hoists, 40000 – 60000
electric motors, etc
Machines required to work continuously 24 hours with high degree of
100000 reliability- public power plants, mine pumps, pulp and paper industry,
200000
etc
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Design for Variable Loads and Speeds
Many rolling element bearings are subjected to loads
and speeds that vary in magnitude and / or direction,
for example, bearings used in transport vehicles.
There is not much information available if the load
change in direction; but it is reasonable to assume
that, if anything, the changing direction will be
beneficial because it will result in more uniform
distribution of wear in the non-rotating member.
For the situation when the magnitudes of load and
speed change over a period of time the load-life
relationship derived earlier can be used. The equation
for a ball bearing
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Design for Variable Loads and Speeds (Contd.)
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Design for Variable Loads and Speeds (Contd.)
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Design for Variable Loads and Speeds (Contd.)
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