39975060 a Brief History About Bearings

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2010

Hasan ERBAY 66784

Sevde Dilruba ŞAHIN 66817

Medine KESKIN 66807

Introduction to Mechanical

DesignA study on

Roller and Ball

Bearings



Index

1. A BRIEF HISTORY ABOUT BEARINGS .................................................................................... 4

2. WHAT ARE TYPES OF THE BEARINGS? ................................................................................. 4

2.1. BALL BEARINGS ................................................................................................................................... 4 2.1.1. Shielded Ball bearing ................................................................................................................................ 5 2.1.2. Sealed ball bearing .................................................................................................................................... 5 2.1.3. Load Carrying Capability ........................................................................................................................... 5 2.1.4.THRUST BALL BEARINGS ............................................................................................................................ 6

2.2. ROLLER BEARINGS ............................................................................................................................. 6 2.2.1. Roller Thrust Bearing ................................................................................................................................ 7 2.2.2. Taper Roller Bearing ................................................................................................................................. 7

3. OTHER BEARING TYPES ............................................................................................................. 7

4. BEARİNG MATERIALS ................................................................................................................. 8

4.1. High/mid carbon alloy steel ...................................................................................................................... 8

4.2. Case hardened (carburizing) steel ........................................................................................................... 8

4.3. Heat resistant bearing steel .................................................................................................................. 8

4.4. Corrosion resistant bearing steel ........................................................................................................ 9

4.5. Induction hardened steel ...................................................................................................................... 9

4.6. Other bearing materials ........................................................................................................................ 9

5. CAGE MATERIALS ......................................................................................................................... 9

6. THE USAGE PLACE FOR BALL AND ROLLER BEARINGS ................................................... 9

6.1. The Examples from Industries that are Using Bearings .................................................................. 11

7. COMPARISON OF BALL AND ROLLER BEARINGS ............................................................ 11

8. CALCULATIONS FOR BEARINGS ............................................................................................ 13

8.1. Bearing Life ........................................................................................................................................... 13

8.2. Static Load Rating ................................................................................................................................ 13

8.3. Equivalent Static Bearing Load .......................................................................................................... 14



8.4. Bearing Load Life Relationship .......................................................................................................... 14

8.5. Basic Dynamic Load Rating ................................................................................................................. 15

8.6. Equivalent Dynamic Bearing Load ..................................................................................................... 16

8.7. Variable Loading .................................................................................................................................. 16

8.8. Guidelines on Bearing Life .................................................................................................................. 17

8.9. Adjusted Rating Life ............................................................................................................................. 18

8.10. Reliability versus Life ........................................................................................................................ 18

8.11. Life Adjustment Factor for Reliability ............................................................................................. 19

8.12. Constant Reliability Contour ............................................................................................................ 19

8.13. Manufacturers own Life Factors ...................................................................................................... 20

8.14. The steps should be followed when we choose the bearing ......................................................... 21

9. STANDARTS FOR BALL AND ROLLER BEARINGS ............................................................ 21

10. PROBLEMS & SOLUTIONS .................................................................................................... 23

Exercise – 1 .................................................................................................................................................. 23

Solution - 1 ................................................................................................................................................... 24

Exercise – 2 .................................................................................................................................................. 26

Solution-2 ..................................................................................................................................................... 27

Exercise – 3 .................................................................................................................................................. 29

Solution - 3 ................................................................................................................................................... 29

BIBLIOGRAPHY ............................................................................................................................... 30



1. A BRIEF HISTORY ABOUT BEARINGS

Ancient Egyptian hieroglyphics have been discovered that show large blocks, presumably

used to build monuments for the Pharaohs, being pulled across tree trunks acting as roller

bearings. Later, in the 15th century, Leonardo Da Vinci described and designed a type of ball

bearing, according to the American Bearing Manufacturers Association. The turning point in

the development of the bearing was the industrial revolution, when a variety of types of

bearings were designed to fill different needs.

Ball bearings are one major invention that was done during the industrial revolution which

has galvanized the whole manufacturing and other related industries. Before the ball bearings

were invented a big part of the effort went in making sure that machines were able to take the

load using some primitive load bearing methods. These methods then generated so much heat

and effort went in cooling off the machine as well as in replacing the damaged parts.

2. WHAT ARE TYPES OF THE BEARINGS?

There are many types of bearings, each used for different purposes either singularly or in

combinations. All bearings are very unique in their construction and have special capabilities

to carry loads. These include ball bearings, roller bearings, ball thrust bearings, roller thrust

bearings and tapered roller thrust bearings.

2.1. BALL BEARINGS

Ball bearings, as shown to the left, are the most common type by

far. They are found in everything from skate boards to washing

machines to PC hard drives. These bearings are capable of

taking both radial and thrust loads, and are usually found in

applications where the load is light to medium and is constant in

nature (ie not shock loading). The bearing shown here has the

outer ring cut away revealing the balls and ball retainer.

Ball bearings are also called as “Deep grove Ball bearing”

because of their constructional aspects. The balls are made to

run in deep grooves formed in the inner race and outer race of

the bearing. The basic parts of a ball bearing include:

http://www.botebearings.com/





Inner Race – This is the part that is mounted on the rotating shaft and tends to rotate

the shaft.

Outer Race – This is the part that is mounted to the housing and is stationary. This also

serves as a means for transferring the loads from the bearing to the housing.

Rolling Element “Balls” – These are the elements that carry the load distributing it

throughout the raceways. They tend to rotate about the inner race, but not at the speed

the inner race rotates. It is something like the relation between the earth and the moon.

Cage – This is an important element in the bearing. This acts as a barrier between the

balls preventing them from bumping into each other .

Apart from this the ball bearings are available with certain special constructional features like

shielded bearings and sealed bearings.

2.1.1. Shielded Ball bearing

The main difference between them is that in the case of a shielded bearing, it shields

the rolling elements from the external dirt and the shield is normally made up of

plastic or special rubber.

2.1.2. Sealed ball bearing The sealed ball bearing is one which is completely sealed with lubricant inside. It

prevents the flow of other lubricants into the rolling element area and also prevents the

lubricant inside i.e. grease from getting out of the rolling element area.

2.1.3. Load Carrying Capability

Ball bearing has a good capability to run at high speeds but average in carrying loads.

They are able to carry only medium loads and hence find use in almost all the

household items such as ceiling fans, Mixes, Grinders, etc.

Ball bearings are capable of carrying good amount of radial loads but axial loads can

be carried only to an extent. Hence these bearings are not used in applications that

require heavy axial load to be carried.





bearing. However, this type of bearing cannot handle thrust loads to any significant degree. A

variation of this bearing design is called the needle bearing. The needle roller bearing uses

cylindrical rollers like those above but with a very small diameter. This allows the bearing to

fit into tight places such as gear boxes that rotate at higher speeds .

2.2.1. Roller Thrust Bearing

Roller thrust bearings like the one

illustrated to the left can support very large

thrust loads. They are often found in

gearsets like car transmissions between

gear sprockets, and between the housing

and the rotating shafts. The helical gears used in most transmissions have angled teeth; this

can causes a high thrust load that must be supported by this type of bearing.

2.2.2. Taper Roller Bearing

Tapered roller bearings are designed to support large

radial and large thrust loads. These loads can take the

form of constant loads or shock loads. Tapered roller

bearings are used in many car hubs, where they are

usually mounted in pairs facing opposite directions.

This gives them the ability to take thrust loads in both

directions. The cutaway taper roller on the left shows

the specially designed tapered rollers and demonstrates

their angular mounting which gives their dual load

ability.

3. OTHER BEARING TYPES

The above bearing types are some of the most common. There are thousands of other designs,

some standard and some specific applications but all perform the same basic function.

Essentially further types of bearings usually take all or some of the characteristics of the

above bearings and blend them into one design. Through the use of careful material selection



and applying the correct degree of machining precision, a successful bearing solution can

usually be found.

4. BEARİNG MATERIALS While the contact surfaces of a bearing's raceways and rolling elements are subjected to

repeated heavy stress, they still must maintain high precision and rotational accuracy. To

accomplish this, the raceways and rolling elements must be made of a material that has high

hardness, is resistant to rolling fatigue, is wear resistant, and has good dimensional stability.

The most common cause of fatigue in bearings is the inclusion of non-metallic impurities in

the steel. Non-metallic inclusion includes hard oxides that can cause fatigue crack. Clean steel

with minimal non-metallic inclusion must therefore be used. For bearings requiring especially

high reliability and long life, steels of even higher in purity, such as vacuum melted steel

(VIM, VAR) and electro-slag melted steel (ESR), are used.

4.1. High/mid carbon alloy steelIn general, steel varieties which can be hardened not just on the surface but also deep

hardened by the so-called "through hardening method" are used for the raceways and rolling

elements of bearings. Foremost among these is high carbon chromium bearing steel, which is

widely used. For large type bearings and bearings with large cross sectional dimensions,induction hardened bearing steel incorporating manganese or molybdenum is used. Also in

use is midcarbon chromium steel incorporating silicone and manganese, which gives it

hardening properties comparable to high carbon chromium steel.

4.2. Case hardened (carburizing) steelCarburizing hardens the steel from the surface to the proper depth, forming a relatively soft

core. This provides hardness and toughness, making the material suitable for impact loads.

4.3. Heat resistant bearing steelWhen bearings made of ordinary high carbon chromium steel which have undergone standard

heat treatment are used at temperatures above 120°C for long durations, unacceptably large

dimensional changes can occur. For this reason, a dimension stabilizing treatment (TS

treatment) has been devised for very high temperature applications. This treatment however

reduces hardness of the material, thereby reducing rolling fatigue life.



4.4. Corrosion resistant bearing steelFor applications requiring high corrosion resistance, stainless steel is used. To achieve this

corrosion resistance a large proportion of the alloying element chrome is added to martensite

stainless steel.

4.5. Induction hardened steelBesides the use of surface hardening steel, induction hardening is also utilized for bearing

raceway surfaces, and for this purpose mid-carbon steel is used for its lower carbon content

instead of through hardened steel. For induction hardening of the deep layers required for

larger bearings and bearings with large surface dimensions, mid-carbon steel is fortified with

chrome and molybdenum.

4.6. Other bearing materialsFor ultra high speed applications and applications requiring very high level corrosion

resistance, ceramic bearing materials such as Si3N4 are also available.

5. Cage materialsBearing cage materials must have the strength to withstand rotational vibrations and shock

loads. These materials must also have a low friction coefficient, be light weight, and be able

to withstand bearing operation temperatures.

For small and medium sized bearings, pressed cages of cold or hot rolled steel with a low

carbon content of approx. 0.1% are used. However, depending on the application, austenitic

stainless steel is also used.

Machined cages are generally used for large bearings. Carbon steel for machine structures or

high-strength cast brass is frequently used for the cages, but other materials such as

aluminium alloy are also used.

6. THE USAGE PLACE FOR BALL AND ROLLER BEARINGS

Today the ball bearing is used in numerous everyday applications. Ball bearings are used for

dental and medical instruments. In dental and medical hand pieces, it is necessary for the

medical hand pieces are made from 440C stainless steel, which allows smooth rotations at fast

speeds. Because of this requirement, dental and medical hand pieces are made from 440C

stainless steel, which allows smooth rotations at fast speeds.



Hard drive bearings used to be highly spherical, and were said to be the best spherical

manufactured shapes, but this is no longer true, and more and more are being replaced

with fluid bearing

German ball bearing factories were often a target of allied aerial bombings during

World War II; such was the importance of the ball bearing to the German war

industry.

In horology, the company Jean Lassale designed a watch movement that used ball

bearings to reduce the thickness of the movement. Using 0.20 mm balls, the Calibre

1200 was only 1.2 mm thick, which still is the thinnest mechanical watch movement.

Aerospace bearings are used in many applications on commercial, private and military

aircraft including pulleys, gearboxes and jet engine shafts. Materials include M50 tool

steel (AMS6491), Carbon chrome steel (AMS6444), the corosion resistant AMS5930,

440C stainless steel, silicon nitride (ceramic) and titanium carbide- coated 440C.

Following the early use of ball bearings in drive shafts, factory engineers found other

applications in the manufacturing arena. Individual parts could be moved easily over ramps

equipped with ball bearings. Motor-driven machines became more efficient as ball bearings

reduced friction between parts. Unlike other types of bearings, ball bearings allow for both

rotary and axial movement, which added versatility to machine design.One of the most common examples of ball bearings in action is the roller skate. Four wheels

are attached to two axles on the bottom of a boot. A closer inspection of these wheels reveals

a collection of small metal balls which surround the axle. As the skater places his or her full

weight on the wheels, each ball bearing absorbs the load temporarily. As the skater pushes

forward, the ball bearings roll in a track around the axle.

Because the ball bearings are perfectly round and smooth, there is very little friction generated

between them. The ball bearings allow the skater to move in a straight line with littleresistance.

Ball bearings is an integral part of any machinery nowadays but that said choose the right

kind of ball bearings keeping mind the factors like the heat generated and the amount of

pressure that will be generated. Plus each manufacturer has its own.

Common uses of these are in car's wheels, also known as wheel bearings. This would be a

perfect implementation since a car has radial and axial forces from the car moving forward on

a road, and a car moving up and down (from the car's suspension caused by bumps in the

road).

http://en.wikipedia.org/wiki/Strategic_bombing_during_World_War_II


http://en.wikipedia.org/wiki/Jean_Lassale

http://en.wikipedia.org/wiki/Aerospace_bearings

http://en.wikipedia.org/wiki/Jet_engine

http://en.wikipedia.org/wiki/Silicon_nitride

http://en.wikipedia.org/wiki/Titanium_carbide

http://en.wikipedia.org/wiki/Titanium_carbide

http://en.wikipedia.org/wiki/Silicon_nitride

http://en.wikipedia.org/wiki/Jet_engine

http://en.wikipedia.org/wiki/Aerospace_bearings

http://en.wikipedia.org/wiki/Jean_Lassale





Thrust bearings are used to take on large thrust loads and are used mainly in the car

transmissions and gears.

Bearings are truly a wonder of nature! They make life much easier for almost all human

beings living on this planet. They can be found in the smallest electric motors to the largest

pieces of mining equipment. Bearings operate so efficiently that they are sometimes referred

to as being “anti -friction” devices. Life would be much harder without them. Like most other

highly engineered products, bearings have a very sophisticated and scientific side.

6.1. The Examples from Industries that are Using Bearings

Cranes

Excavators

Offshore industry

Wind Turbines

Solar Energy

Port Equipment

Mining

Tunneling

Robotics

Machine Tools

Medical

Radar

Transport and Handling

Railway Industry

Packaging

Military Industry

7. COMPARISON OF BALL AND ROLLER BEARINGSRolling-element bearings have the advantage of a good trade-off between cost, size, weight,

carrying capacity, durability, accuracy, friction, and so on. Other bearing designs are often

better on one specific attribute, but worse in most other attributes, although fluid bearings can

sometimes simultaneously outperform on carrying capacity, durability, accuracy, friction,

rotation rate and sometimes cost. Only plain bearings have as wide use as rolling-element bearings .

http://en.wikipedia.org/wiki/Fluid_bearing

http://en.wikipedia.org/wiki/Plain_bearing

http://en.wikipedia.org/wiki/Plain_bearing

http://en.wikipedia.org/wiki/Fluid_bearing



Both ball bearings and roller bearings work by rolling between two surfaces to reduce friction.

The concept is based on the fact that things roll more easily and with less effort than if you

slide them. Imagine attaching a rope to a concrete block and pulling it across a sidewalk. Now

imagine pulling that same block across marbles that have been scattered on the sidewalk. The

block would move much more easily because the marbles have acted as ball bearings.

Ball bearings reduced the damage to the machinery as the load bearing was shifted from the

actual parts to small steel balls encloses in two sleeves which are the outer and the inner

sleeves. These sleeves shield the ball from direct pressure and the pressure is transferred by

the balls from the outer sleeves to the inner sleeve.

The basics behind the roller bearings is the simple principle that easier to roll than to slide

because the two surfaces in contact have a lesser area of contact and that helps in reducing the

friction as opposed to sliding which has larger area in contact and which means that there will

be more friction.

Ball bearings are by far the most common type of bearing and are used in everything from

dishwashers and washing machines to blenders and computer hard drives. They provide the

ability to spin and a small to medium amount of weight-bearing support. Because their design

does not allow large amounts of weight to be supported, they are most commonly used in

household appliances and tools.Roller bearings are shaped like cylinders and are most commonly used in heavy machinery or

industrial applications. Conveyor belt rollers in factories use this type of bearing because,

unlike the ball bearing, where any weight pushing down on it is focused on one point, weight

is spread out in a line along the surface of the bearing. This allows the roller bearing to handle

much more weight and makes it ideal for heavy-duty applications.

Also there is a figure that shows us differences between rolling bearings and sliding bearings

in the next page.

http://www.botebearings.com/Bearings/Nonstandard-bearing.htm

http://www.botebearings.com/Bearings/Nonstandard-bearing.htm



8. CALCULATIONS for BEARINGS

8.1. Bearing Life

• The bearing l if e is defined as:

- The number of revolutions or,

- The number of operating hours at a given speed which the bearing is capable of

enduring before the first sign of metal fatigue (flaking, spilling) occurs on one of its rings

or rolling elements.

• The rating lif e , L10, of a group of identical bearings is defined as the life that 90

percent of them will at least achieve before the failure criterion develops.

• The median lif e is the 50th percentile life of a group of bearings corresponding to

between 4 and 5 times the L 10 life.

8.2. Static Load Rating

• The basic static load rating C0 is used in calculations when the bearings are to rotate

at very slow speeds (n < 10 r/min),

• Perform very slow oscillating movements,



• Be stationary under load for certain extended periods.

• Verification of the static bearing loads is performed checking the static safety factor of

the application, which is defined as:

Where:

C0 = basic static load rating, kN

P0 = equivalent static bearing load, kN

s0 = static safety factor

8.3. Equivalent Static Bearing Load

The equivalent static radial load does the same damage as the combined radial and

thrust loads together.

8.4. Bearing Load Life Relationship

• Typical bearing load-life log-log curve:

0

00 P

C s

ar P Y P X P 000



• This function can be expressed as

With p = 3 for ball bearings, p = 10/3 for roller bearings.

8.5. Basic Dynamic Load Rating

• The basic dynamic load rating is that load which will cause 10% of a sample of

bearings to fail at or before 1 million revolutions and the others 90% to survive.

or

The Basic Rating Life is:

or

Where :

L10 = basic rating life (at 90 % reliability), millions of revolutions

L10h = basic rating life (at 90 % reliability), operating hours

C = basic dynamic load rating, kN

P = equivalent dynamic bearing load, kN

n = rotational speed, r/min

p

P P

L L

2

1

1

2

p PLC 1

pn L P C h

1

61060

p

P C

L

10

p

h P C

n L

6010 6

10



8.6. Equivalent Dynamic Bearing Load

A rotation factor V is defined as V = 1 when the inner ring rotates and V = 1.2 when theouter ring rotates.

8.7. Variable Loading

• For a piecewise constant loading in a cyclic pattern:

Where:

Pe,i = equivalent radial load for the it event

ni = speed of the it event

T i = time period of the it event

• Using the linear damage theory the equivalent constant load is:

air i P Y VP X P

p

j

iii

j

i

pieii

nT

P nT P

1

1

1,



8.8. Guidelines on Bearing Life





8.11. Life Adjustment Factor for Reliability

• In the manufacturer’s catalogs, reliability is estimated using this

giving a life adjustment factor a 1 = L/L 10 equal to:

that can be presented in a table, like this one:

8.12. Constant Reliability Contour

s

• A – Catalog rating C 10 at x = L/L 10 = 1

5.1

1048.4exp

L L

R

32

101

100ln48.4

R L L

a





8.14. The steps should be followed when we choose the bearing

9. STANDARTS for BALL and ROLLER BEARINGS





10. Problems & Solutions

Exercise – 1The second shaft on a parallel-shaft 25-hp foundry crane speed reducer contains a helical

gear with a pitch diameter of 8.08 in. Helical gears transmit components of force in the

tangential, radial, and axial directions. The components of the gear force transmitted to the

second shaft are shown in the figure below. The bearing reactions at C and D, assuming

simple-supports, are also shown. A ball bearing is to be selected for location C to accept the

thrust, and a cylindrical roller bearing is to be utilized at location D. The life goal of the speed

reducer is 10 kh, with a reliability factor for the ensemble of all four bearings (both shafts) to

equal or exceed 0.96 for the Weibull parameters. The application factor is to be 1.2.

(a) Select the roller bearing for location D.

(b) Select the ball bearing (angular contact) for location C , assuming the inner ring rotates



Solution - 1The torque transmitted is T = 595(4.04) = 2404 lbf · in. The speed at the rated horsepower is

=63 025

=63 025(25)

2404= 655.4 rev/min

=

The radial load at D is 106.6 2 + 297.5 2 = 316.00

The radial load at C is 356.6 2 + 297.5 2 = 464.4

The individual bearing reliabilities, if equal, must be at least 0.964 = 0.98985 0.99.

The dimensionless design life for both bearings is

=10

= 6060

= 60 10000 655.410 6 = 393.2

(a) Application factor of 1.2, and a = 10/3 for the roller bearing at D. the catalog rating

should be equal to or greater than

10 = 0 + −0 1 −

= 1.2 316 393.20.02 + 4.439 1 −0.991.483

10

3 = 3591 = 16.0

The absence of a thrust component makes the selection procedure simple. We choose a

02-25 mm series, or a 03-25 mm series cylindrical roller bearing from the table.

(b) The ball bearing at C involves a thrust component. This selection procedure requires

an iterative procedure. Assuming /( ) > ,

1. Choose Y 2 from Table (Equivalent Radial Load Factors for Ball Bearings).

2. Find C 10.3. Tentatively identify a suitable bearing from Table, note C 0.

4. Using F a/C 0 enter Table (Equivalent Radial Load Factors for Ball Bearings) to obtain

a new value of Y 2.

5. Find C 10.

6. If the same bearing is obtained, stop.

7. If not, take next bearing and go to step 4.

As a first approximation, take the middle entry from Table (Equivalent Radial Load Factors for Ball Bearings)

Where

H = power, hp, T = torque, lbf · in, n = shaft



X 2 = 0.56, Y 2 = 1.63.

From the equation as in below, with V =1,

= 0.56 + 1.63344

1(464.4)= 1.77 = 1.77 = 1.77 1 464.4=822 lbf or 3.66 kN

From equation as in below (11 – 7), with a = 3,

10 = 1.2 3.66 393.2

0.02+4.439 1−0.991

1.483

13

= 53.4

From Table 11 – 2, angular-contact bearing 02-60 mm has C 10 = 55.9 kN, C 0 is 35.5 kN

Step 4 becomes, with F a in kN,

0=

344(4.45)10 −3

35.5= 0.0431 Which makes e from Table approximately 0.24.

Now F a/ [V F r ] = 344/ [(1)464.4] = 0.74, which is greater than 0.24, so we find Y 2 by

interpolation:

From the equation as in below

= 0.56 + 1.84 344464.4

= 1.92

= 1.92 = 1.92 1 464.4 = 892 3.97

The prior calculation for C 10 changes only in F e, so

10 =3.973.66

53.4 = 57.9

From Table, an angular contact bearing 02-65 mm has C 10 = 63.7 kN and C 0 of 41.5 kN.

Again,



0=

344(4.45)10 −3

41.5= 0.0369

Making e approximately 0.23. Now from before, F a/ (V F r ) = 0.74, which is greater than0.23. We find Y 2 again by interpolation:

= 0.56 + 1.90344

464.4= 1.967

= 1.967 = 1.967 1 464.4 = 913.5 4.065

The prior calculation for C 10 changes only in F e, so

10 =4.073.66

53.4 = 59.4

From Table an angular-contact 02-65 mm is still selected, so the iteration is complete.

Exercise – 2The shaft depicted in below carries a helical gear with a tangential force of 3980 N, a

separating force of 1770 N, and a thrust force of 1690 N at the pitch cylinder with directions

shown. The pitch diameter of the gear is 200 mm. The shaft runs at a speed of 1050 rev/min,

and the span (effective spread) between the direct-mount bearings is 150 mm. The design life

is to be 5000 h and an application factor of 1 is appropriate. The lubricant will be ISO VG 68

(68 cSt at 40 ◦C) oil with an estimated operating temperature of 55 ◦C. If the reliability of the

bearing set is to be 0.99, select suitable single-row tapered-roller Timken bearings.



Solution-2The reactions in the xy plane from the figure are

=1770(50)

150+

169000150

= 1716.7 = 1717

=1770(100)

150 −169000150

= 53.3

The radial loads F r A and F r B are the vector additions of R yA and R zA, and R yB and

R zB, respectively:

= ( 2 + 2 )1/2 = (1327 2 + 1717 2 )1/2 = 2170

= (2

+2

)1/2

= (26532

+ 53.3)1/2

= 2654 Tri al 1: We will use K A = K B = 1.5 to start. From Table, noting that m = +1 for directmounting and F ae to the right is positive, we write

0.47

<? >0.47 −

0.471.5

<? >0.47(2654)

1.5 −+1 (−1690) 680 < 2522

We use the upper set of equations in to find the thrust loads:



=0.47 − =

0.47(2654)1.5 −(+1)( −1690) = 2522

=0.47

=0.47(2654)

1.5= 832

The dynamic equivalent loads P A and P B are

P A = 0.4 F rA + K A F aA = 0.4(2170) + 1.5(2522) = 4651 N

P B = F rB = 2654 N

From the figure 1050 rev/min at 55 ◦C, f T = 1.31, f v = 1.01.

Estimate 099 = 0.995 .

For bearing A, the catalog entry C 10 should equal or exceed

10 = 1 46515000 1050 60

4.48 1.32 1 –0.99523 90 10 6

310

= 11.446

From the figure, tentatively select type TS 15100 cone and 15245 cup, which will work: K A =1.67, C 10 = 12 100 N.

For bearing B, the catalog entry C 10 should equal or exceed

10 = 1 26545000 1050 60

4.48 1.32 1 –0.99523 90 10 6

310

= 6543

Tentatively select the bearing identical to bearing A, which will work: K B = 1.67,

C 10 = 12 100 N.

Tri al 2: Use K A = K B = 1.67 from tentative bearing selection. The sense of the previous

inequality 680 < 2521 is still the same, so the same equations apply:

=0.47 − =

0.47(2654)1.67 −(+1)( −1690) = 2437

=0.47

=0.47(2654)

1.67= 747

P A = 0.4 F rA + K A F aA = 0.4(2170) + 1.67(2437) = 4938 N

P B = F rB = 2654 N

For bearing A, the corrected catalog entry C 10 should equal or exceed



10 = 1 49385000 1050 60

4.48 1.32 1 –0.99523 90 10 6

310

= 12174

Although this catalog entry exceeds slightly the tentative selection for bearing A, we will keep

it since the reliability of bearing B exceeds 0.995. In the next section we will quantitatively

show that the combined reliability of bearing A and B will exceed the reliability goal of 0.99.

For bearing B, P B = F rB = 2654 N

10 = 1 26545000 1050 60

4.48 1.32 1 –0.99523 90 10 6

310

= 6543

Select cone and cup 15100 and 15245, respectively, for both bearing A and B.

The computational effort can be simplified only after this is understood, and not until then.

Exercise – 3A certain application requires ball bearing with an inner ring rotating with a design life of

30000 h, at the speed of 300 rev/min. The radial load is 1.898 kN and application factor is 1.2,

the reliability goal is 90%.

(a) Find the multiple x D and the catalog C 10 with which enter a bearing table.

(b) Chose 02-series deep-grove ball bearing and the estimated in use R=?

Solution - 3(a) Lh = 30000 hours.

L (in revolution) = 310 4 60 300 = 540 10 6 revolutions.

=10

= 540(106

)10 6 = 540 ( )

( ) = = 1.2 1.898 = 2.2776

10 = 1/ = 2.2776 540 1/3 = 18.547 3

From the table, for 02-30 mm series, C 10 =19.5 kN.

(b) = 10 =19.5

2.2776

3= 627.6

= 1 1= = 540627.6

= 0.860



Now, let’s estimate the reliability in use:

1 =10

= 4.48100

23

=

1001

4.481.5

BIBLIOGRAPHY www.google.pt

http://www.utm.edu/departments/engin/lemaster/ http://www.fag.com/content.fag.de/en/index.jsp Shigley, J.E., Mischke, C.R., Budynas, R.C., Mechanical Engineering Design Hamrock, B.J., Jacobson, B., Schmid, S. R., Fundamentals of Machine Elements IPM course lecture notes.

=100

0.8604.48

1.5 = 91.91

http://www.google.pt/

http://www.utm.edu/departments/engin/lemaster/

http://www.fag.com/content.fag.de/en/index.jsp

http://www.fag.com/content.fag.de/en/index.jsp

http://www.utm.edu/departments/engin/lemaster/

http://www.google.pt/

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