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).

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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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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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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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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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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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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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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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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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 3150C as compared to 1200C 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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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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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/m2/0C

A = Projected area of the bearing in m2 (A=length x diameter)

tb = Temperature of the bearing surface in 0C

ta = Temperature of surrounding air in 0C

The value of C depends upon the type of bearing, its ventilation and the temperature difference. The

average values for C (in W/m2/0C) for journal bearings can be taken as follows.

For unventilated bearings (still air)

C = 140 to 420 W/m2/0C

For well ventilated bearings

C = 490 to 1400 W/m2/0C

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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Note

For a well designed bearing, the temperature of the oil film should not be more than 600C,

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/0C

t = Difference between outlet and inlet temperature of oil in oC

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 55oC

Ambient temperature of oil = 15.5oC

Maximum bearing pressure = 1.5N/mm2 for the pump

Heat dissipation coefficient of bearing = 1232 W/m2/oC

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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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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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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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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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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Taper roller bearing

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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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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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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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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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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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