1. University of Vocational Technology
(Established by the Act of Parliament No.31 of 2008)
Bachelor of Technology (B. Tech.) in
Manufacturing/Mechatronics Technology
2014/2015 Semester 3
Module Code: MF30501
Module: Machine Design
Lecture notes on Bearings
Eng. K.G.S.Bandara BSc. (Eng) C.Eng., MIE(SL).

2. Bearings for rotary motion
A bearing is a machine part which supports a moving part and confines its motion. Bearings can be divided
into two groups depending upon the direction of load to be supported or depending upon the nature of
contact.
1. Depending upon the direction of load to be supported.
The bearings under this group are classified as
(a) Radial bearings (b) Thrust bearings
In radial bearings, the load acts perpendicular to the direction of motion of the moving element. In thrust
bearings, the load acts along the axis of rotation.
2. Depending upon the nature of contact.
The bearings under this group are classifies as
(a) Sliding contact bearings (b) Rolling contact bearings
In sliding contact bearings, the sliding takes place along the surfaces of the contact between the moving
element and the fixed element. The sliding contact bearings are also known as plain bearings. In rolling
contact bearings the steel balls or rollers, are interposed between the moving and fixed elements. The balls
offer rolling friction at two points for each ball or roller.
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3. Sliding contact bearings
Sliding contact bearings ae commonly used for low-modest speed applications.
Advantages and disadvantages sliding contact bearings
These bearings have certain advantages over the rolling contact bearings.
They are:
1. The design of the bearing and housing is simple.
2. They occupy less radial space and are more compact.
3. They cost less.
4. The design of shaft is simple.
5. They operate more silently.
6. They have good shock load capacity.
7. They are ideally suited for medium and high speed operation provided that there is proper
hydrodynamic lubrication and cooling.
The disadvantages are:
1. The frictional power loss is more.
2. They required good attention to lubrication.
3. They are normally designed to carry radial load or axial load only.
Sliding contact bearings are classified in three ways.
1.0 Based on type of load carried
2.0 Based on type of lubrication
3.0 Based on lubrication mechanism
1.0 Bearing classification based on type of load carried
1.1 Radial bearings
1.2 Thrust bearings or axial bearings
1.3 Radial – thrust bearings
1.1 Radial bearings
These bearings carry only radial loads. Radial bearings are also called journal bearings. Radial load is
transferred through lubricant film between journal and bearing.
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4. 1.2 Thrust bearings or axial bearings
The thrust load is transferred through lubricant film between thrust collar on rotor and thrust collar on
housing.
1.3 Radial thrust bearings
Radial thrust bearings are subjected to combined radial and thrust loads. These bearings carry both radial
and thrust loads.
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5. 2.0 Bearing classification based on type of lubrication
The type of lubrication means the extent to which the contacting surfaces are separated in a shaft bearing
combination. This classification includes
2.1 Boundary lubrication
2.2 Thin film lubrication (Mixed lubrication)
2.3 Thick film lubrication (Hydrodynamic lubrication)
2.1 Boundary lubrication
Here the surface contact is continuous and extensive. The lubricant is continuously smeared over the
surfaces and provides a continuously renewed adsorbed surface film which reduces the friction and wear.
The typical coefficient of friction is 0.05 to 0.20.
2.2 Thin film lubrication (Mixed lubrication)
Here even though the surfaces are separated by thin film of lubricant, at some high spots Metal-to-metal
contact does exist. Because of this intermittent contacts, it also known as mixed film lubrication. Surface
wear is mild. The coefficient of friction commonly ranges from 0.004 to 0.10.
2.3 Thick film lubrication (Hydrodynamic lubrication)
The surfaces are separated by thick film of lubricant and there will not be any metal-to-metal contact. The
film thickness is anywhere from 8 to 20 μm. Typical values of coefficient of friction are 0.002 to 0.010.
Hydrodynamic lubrication is coming under this category. Wear is the minimum in this case.
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6. 3.0 Bearing classification based on lubrication mechanism
3.1 Hydrodynamic lubricated bearings
3.2 Hydrostatic lubricated bearings
3.3 Elasto-hydrodynamic lubricated bearings
3.4 Boundary lubricated bearings
3.5 Solid film lubricated bearings
Material used for sliding contact bearings
3.1 Hydrodynamic lubricated bearings
In these bearings the load-carrying surfaces are separated by a stable thick film of lubricant that prevents
the metal-to-metal contact. The film pressure generated by the moving surfaces that force the lubricant
through a wedge shaped zone. At sufficiently high speed the pressure developed around the journal
sustains the load.
3.2 Hydrostatic lubricated bearings
In these bearings, externally pressurized lubricant is fed into the bearings to separate the surfaces with
thick film of lubricant. These types of bearings do not require the motion of the surfaces to generate the
lubricant film. Hence they can operate from very low speed to high speed.
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7. 3.3 Elasto hydrodynamic lubricated bearings
Rolling contact bearings come under this category. The oil film thickness is very small. The contact
pressures are going to be very high. Hence to prevent the metal-to-metal contact, surface finishes are to be
of high quality. Such a type of lubrication can be seen in gears, rolling contact bearings, cams etc.
3.4 Boundary lubricated bearings
When the speed of the bearing is inadequate, less quantity of lubricant is delivered to the bearing, an
increase in the bearing load, or an increase in the lubricant temperature resulting in drop in viscosity – any
one of these may prevent the formation of thick film lubrication and establish continuous metal-to-metal
contact extensively. Often bearings operating in such situations are called boundary lubricated bearings.
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8. Solid film lubricated bearings
For extreme temperature operations ordinary mineral oils are not satisfactory. Solid film lubricants such as
graphite, molybdenum disulfide or their combinations which withstand high operating temperature are
used. These types of bearings are common in furnace applications, or trunnion bearings of liquid metal
handling systems, hot drawing mills etc.
Materials Used for sliding contact bearings
1.0 Metallic bearings
2.0 Non metallic bearings
1.0 Metallic bearings
1.1 Babbitt metal
1.2 Bronze – Alloy of copper, tin and zinc
1.3 Cast iron
1.4 Silver
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9. 1.1 Babbit metal
Tin base Babbit and lead base babbits are widely used as bearing materials. The babbits are recommended
where maximum pressure on projected area of the journal is not over 7-14 N/mm2
. The babbit is generally
used as a thin layer of 0.05mm to 0.15mm thick bonded to an insert or steel shell.
Tin based babbits – Tin 90% , Copper 4.5%, Antimony 5%, Lead 0.5%
Lead based babbits – Lead 84%, Tin 6%, Antimony 9.5%, Copper 5%
1.2 Bronze – Alloy of copper, tin and zinc
The bronzes (alloy on copper, tin and zinc) are generally use in the form of machined bushes pressed into
the shell. The bush may be in one or two pieces. The bronzes commonly used for bearing material are gun
metal and phosphor bronzes.
The gun metal (Copper 88%, Tin 10%, Zinc 2%) is used for high grade bearings subjected to high pressures
(not more than 10N/mm2
on projected area of the journal) and high speeds.
The phosphor bronze (Copper 80%, Tin 10%, Lead 9%, phosphorus 1%) is used for bearings subjected to
high pressures (14N/mm2
on projected area of journal) and high speeds.
1.3 Cast iron
The cast iron bearings are usually used with steel journals. Such types of bearings are fairly successful
where lubrication is poor and pressure is limited to 3.5N/mm2
and speed is limited to 40m/min
1.4 Silver
The silver and silver lead bearings are mostly used in aircraft engines where the fatigue strength is the
most important consideration.
2.0 Non metallic bearings
2.1 Carbon (Graphite)
2.2 Rubber
2.3 Wood
2.4 Plastic
2.1 Carbon (Graphite)
The carbon-graphite bearings are self lubricating, dimensionally stable over a wide range of operating
conditions, chemically inert and can operate at higher temperatures than other bearings. Such types of
bearings are used in food processing and other equipment where grease or oil contamination is not
allowed. These bearings are also used in applications where the shaft speed is too low to maintain a
hydrodynamic oil film.
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10. 2.2 Rubber
The soft rubber bearings are used with water or other low viscosity lubricants, particularly where sand or
other large particles are present. Rubber bearings are excellent for absorbing shock loads and vibrations.
The rubber bearings are mainly used on marine propeller shafts, hydraulic turbines and pumps.
2.3 Wood
Wood bearings are used in many applications where low cost, cleanliness, inadequate lubrication, and anti-
seizing are important.
2.4 Plastic
The commonly used plastic materials for bearings are Nylon and Teflon. These materials have many
characteristics desirable in bearing materials. Nylon and Teflon can be used without a lubricant film. (Dry
bearings). The nylon is stronger, harder and more resistant to abrasive wear. It is used for applications such
as elevator bearings, side bearers in railway vehicles etc.
Teflon is rapidly replacing Nylon as a wear surface or liner for journal and other sliding bearings because of
the following properties.
 It has lower coefficient of friction, about 0.04 (dry) as compared to 0.15 for Nylon.
 It can be used at higher temperatures up to about 3150
C as compared to 1200
C for Nylon.
 It is dimensionally stable because it does not absorb moisture.
 It is chemically inert.
Design of journal bearings
1.1 Dimensions
 Determine the bearing internal diameter (A) according to shaft diameter.
 Refer the following table to decide the length of the bearing and check whether the bearing
dimensions can bear the maximum bearing pressure.
Bearing material
Bearing Shell
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11. 10

12. 1.2 Decide lubricant for the bearing and find bearing modulus.
 Calculate bearing modulus K (K = The critical value of ZN/p that gives minimum value for friction
coefficient)
Where Z - Absolute viscosity of lubricant , in kg/m-s
N - Speed of the journal in r.p.m.
p - Bearing pressure on the projected bearing area in N/mm2
In order to achieve more stable lubricant film thickness ZN/p is taken as 3 times the bearing
modulus.
I.e. ZN/p = 3K
ZN/p = 15K may be used if the bearing is subjected to large fluctuations of load and heavy impacts.
From the value of bearing modulus we can decide whether the bearing works under boundary
lubrication (Thin film lubrication) or Hydrodynamic lubrication (Thick film lubrication).
1.3 Determine the coefficient of friction (μ) of the journal bearing by using the
relation μ= 33/10(ZN/p)(d/c) +k
Where,
Z = Absolute viscosity of the lubricant, in kg/ms
N = Speed of the journal in r.p.m.
p = Bearing pressure on the projected area of journal in N/mm2
d = Diameter of the journal
c = Diametric clearance of the bearing
k = Factor to correct for end leakage. It depends upon the ratio of length to
Diameter of the bearing (k = 0.002 for all values of l/d between 0.7 to 2.8)
Value of d/c for various types of bearings can be taken from the table.
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13. 1.4 Calculate the heat generated in the bearing
Heat is generated in a bearing due to fluid friction and friction of the parts having relative motion. Heat
generated in bearing (Qg )is given by
Qg = μ.W.V (watts)
Where,
μ = Coefficient of friction
W = Load on the bearing in N
V = Rubbing velocity in m/s
1.5 Calculate the heat dissipated by the bearing
The amount of heat dissipated depends upon the temperature difference, size and mass of the radiating
surface and on the amount of air flow around the bearing. But in designing of journal bearings, the actual
heat dissipating area is expressed in terms of the projected area of the journal.
Heat dissipated by the bearing (Qd) is given by the following equation
Qd = C.A(tb-ta) (watts)
Where,
C = Heat dissipation coefficient in W/m2
/0
C
A = Projected area of the bearing in m2
(A=length x diameter)
tb = Temperature of the bearing surface in 0
C
ta = Temperature of surrounding air in 0
C
The value of C depends upon the type of bearing, its ventilation and the temperature difference. The
average values for C (in W/m2
/0
C) for journal bearings can be taken as follows.
For unventilated bearings (still air)
C = 140 to 420 W/m2
/0
C
For well ventilated bearings
C = 490 to 1400 W/m2
/0
C
It has been shown by experiments that the temperature of the bearing (tb) is approximately mid-way
between the temperature of the oil film (to) and the temperature of the outside air (ta).
i.e. tb-ta = ½(to-ta)
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14. Note
 For a well designed bearing, the temperature of the oil film should not be more than 600
C,
otherwise the viscosity of oil decreases rapidly and the bearing loses its performance and life of the
bearing is reduced.
 In case the temperature of the oil film is higher, then the bearing is cooled by circulating water
through the bearing.
 The mass of the oil to remove the heat generated at the may be obtained by equating the heat
generated to the heat taken away by oil. Heat taken by the oil is given by
Qt = m.S.t (in watts)
Where,
m = Mass flow rate of oil in kg/s
S = Specific heat of oil. Its value may be taken as 1840 to 2100 J/kg/0
C
t = Difference between outlet and inlet temperature of oil in o
C
Example:
Design a journal bearing for a centrifugal pump from the following data.
Load on the journal = 20000N
Speed of the journal = 900 r.p.m.
Type of lubricant oil = SAE 10
Viscosity of oil SAE10 = 0.017kg/ms at 55o
C
Ambient temperature of oil = 15.5o
C
Maximum bearing pressure = 1.5N/mm2
for the pump
Heat dissipation coefficient of bearing = 1232 W/m2
/o
C
Diameter of the journal = 100mm
Calculate also mass of the lubricating oil required for artificial cooling, if the rise of temperature of oil be
limited to 10 o
C
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15. 1. Dimensions
Journal diameter = 100mm
Since l/d = 1 to 2 from the table for centrifugal pumps let’s take l/d =1.6
Length of the bearing = 1.6 x 100 mm
= 160mm
Bearing pressure = W/ld
= 20000/0.1x0.16
= 1.25 x 106
N/m2
= 1.25 N/mm2
Allowable bearing pressure = 1.5 x106
N/m2
Since the allowable bearing pressure is greater than the actual bearing pressure the assumed dimensions
of the journal bearing are correct.
2. Bearing modulus
Operating value of ZN/p = 28 (for centrifugal pumps from the table)
Critical value of ZN/p for minimum friction = K
For a stable oil film 3 x K = 28
K = 9.33
Value of ZN/p for this bearing = 0.017 x 900/1.25
= 12.24
Since this value is greater than critical value of ZN/p (K) , the bearing will operate under hydrodynamic
conditions.
3. Coefficient of friction of the bearing
μ = 33/108
(ZN/p)(d/c) +k
= 33/108 (12.24) (1/0.0013) + 0.002
= 0.0051
4. Heat generated in the bearing
Qg = μ.W.V
= μ.W.( ΠdN/60)
= 0.0051 x 20000 (Π x 0.1 x 900/60)
= 480.7 W
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16. 5. Heat dissipated by the bearing
Qd = C.A(tb-ta)
= C.l.d (tb-ta)
= 1232 x0.16 x 0.1 x ½(to –ta)
= 19.712 x ½ (55 -15.5)
= 389.3 W
Heat generated is greater than the heat dissipated. Therefore the bearing is warming up and artificial
cooling is required.
Amount of artificial cooling = Qg - Qd
= 480.7-389.3
= 91.4 W
Mass flow rate of lubricating oil = M
Amount of heat taken away by oil (Qt) = M. S.t
= M x 1900 x (10)
= 1900M
Amount of artificial cooling should be equal to the amount of heat taken away by oil
1900M = 91.4
M = 0.0048kg/s
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17. Bearing Classification
Rolling contact bearings
Rolling contact bearings are also called anti-friction bearing due to its low friction characteristics. These
bearings are used for radial load, thrust load and combination of thrust and radial load. These bearings are
extensively used due to its relatively lower price, being almost maintenance free and for its operational
ease. However, friction increases at high speeds for rolling contact bearings and it may be noisy while
running.
Designation of rolling bearings
(As per DIN 623 standard)
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18. Each rolling bearing is designed by a code that clearly indicates construction, dimensions, tolerances
and bearing clearance. Bearings codes comprising only the basic code without prefixes and suffixes
indicate normal bearings. Deviations from the normal construction are indicated by prefixes or
suffixes.
Basic code consisits of "Series Code". Series code contains number (i.e, 0,1,2.....) or combination of
letter(i.e, BK, HK, .....) & numbers. Following table illustrates first part of "Series Code", which
indicates the type of bearing.
Rolling bearing nomenclature
Ball Bearing
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19. Taper roller bearing
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20. Thrust ball bearing
Thrust roller bearing
Mounting of bearings
Specialized experience is required for bearing installation. It needs to follow the bearing manufacturer’s
instructions as well as the requirements of the client and application environment.
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21. Rolling contact bearing sizes
It is interesting to note that for same bore diameter, load capacity of rolling bearings can be increased by
increasing diameter of rolling elements.
Rolling contact bearing selection
Selection of rolling bearing is a complicated process. It needs some experience and understanding about
the application, static and dynamic loads acting on the bearing, environment, maintenance, assembly and
disassembly etc.
Following parameters are defined and they are used for rolling bearing selection for simplicity. The
parameters used for bearing selection are rating life, bearing load, basic load rating, and Equivalent radial
load.
Rating life
Rating life is defined as the life of a group of apparently identical ball or roller bearings, in number of
revolutions or hours, rotating at a given speed, so that 90% of the bearings will complete or exceed before
any indication of failure occur.
Suppose we consider 100 apparently identical bearings. All the 100 bearings are put onto a shaft rotating
at a given speed while it is also acted upon by a load. After some time, one after another, failure of
bearings will be observed. When in this process, the tenth bearing fails, then the number of revolutions or
hours lapsed is recorded. These recorded numbers of revolutions give the rating life of the bearings or
simply L10 life (10 % failure). Similarly, L50 means, 50 % of the bearings are operational. It is known as
median life.
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22. Bearing load
If two groups of identical bearings are tested under loads P1 and P2 for respective lives of L1 and L2, then,
Where,
L1/L2 = ( P2/P1)a
L: life in millions of revolution or life in hours
a: constant which is 3 for ball bearings and 10/3 for roller bearings
Basic load rating
It is the load which a group of apparently identical bearings can withstand for a rating life of one million
revolutions.
The basic or dynamic load rating (C) is given by
C = P(L)1/a
The value of C represents the load carrying capacity of the bearing for one million revolutions for a given
load and a given life.
This value of C, for the purpose of bearing selection, should be lower than that given in the manufacturer’s
catalogue. Normally the basic or the dynamic load rating as prescribed in the manufacturer’s catalogue is a
conservative value, therefore the chances of failure of bearing is very less.
Equivalent radial load
The load rating of a bearing is given for radial loads only. Therefore, if a bearing is subjected to both axial
and radial load, then an equivalent radial load is estimated as,
Pe = XVPr
Pe = XVPr + YPa
Where,
Pe : Equivalent radial load
Pr : Given radial load
Pa : Given axial load
V : Rotation factor (1.0, inner race rotating; 1.2, outer race rotating)
X : A radial factor
Y : An axial factor
The values of X and Y are found from the chart whose typical format and few representative values are
given below.
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23. Bearing selection procedure
Depending on the shaft diameter and magnitude of radial and axial load a suitable type of bearing is to be
chosen from the manufacturer’s catalogue, either a ball bearing or a roller bearing. The equivalent radial
load is to be determined from the equation Pe = XVPr + YPa
If it is a tapered bearing then manufacturer’s catalogue is to be consulted for the equation given for
equivalent radial load. The value of dynamic load rating C is calculated for the given bearing life and
equivalent radial load. From the known value of C, a suitable bearing of size that conforms to the shaft is to
be chosen. However, some augmentation in the shaft size may be required after a proper bearing is
chosen.
Ex:
A simply supported shaft, diameter 50mm, on bearing supports carries a load of 10kN at its center. The
axial load on the bearings is 3kN. The shaft speed is 1440 rpm. Select a bearing for 1000 hours of
operation.
Solution
The radial load Pr = 5 kN and axial load Pa = 3 kN. Hence, a single row deep groove ball bearing may be
chosen as radial load is predominant. This choice has wide scope, considering need, cost, future changes
etc.
Bearing life, in millions of revolution for the bearing L10 = 1440 x 60 x1000/106
= 86.4
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24. The equivalent radial load on the bearing is given by,
Pe = XVPr+ YPa Here, V = 1.0 (assuming inner race rotating)
From the catalogue, Co = 19.6 kN for 50mm inner diameter.
Therefore, Pa/Co = 3/19.6
= 0.153
From the table given above value of e = 0.329 (by interpolation)
Pa/Pr = 3/5 =0.6> e
From the table, X= 0.56, Y= 1.35
Pe = XVPr+ YPa
= 0.56 x 1.0 x 5.0+1.35 x 3.0 = 6.85 kN
Therefore basic load rating,
C = P(L)1/3
= 6.85(86.4)1/3
= 30.3 kN
Now, the table for single row deep groove ball bearing of series- 02 shows that for a 50mm inner
diameter, the value of C = 35.1 kN. Therefore, this bearing may be selected safely for the given
requirement without augmenting the shaft size. A possible bearing could be SKF 6210. (Please refer SKF
bearing catalog)
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