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EME 2016 Engineering Design I - Ball Bearings Chapter 7

EME 2016- Engineering Design I

TRIMESTER II, 2008 / 2009 SESSIONPrepared by: Dr. B F YOUSIF

Introduction rolling-contact bearings

It can be called as rolling-contact bearing, antifriction bearing, or rolling bearing. Load, speed and

operating viscosity of the lubricant do affect the frictional property of a rolling bearing. So, it is a mistake

to call it as antifriction. However, in industries, the term is used.

7.1 Bearing NomenclatureIn general, the main loads subjected to a bearing are radial loads, pure thrust loads or a combination of

the two kinds of loads. Figure 7.1 shows the main four essential parts of a bearing as outer ring, inner

ring, balls/rolling element and the separator. Sometimes, the separator is omitted. Some of the commontypes of bearing are listed in figure 7.2.

Fig. 7.1Nomenclature of a ball bearing

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Radial and

some thrustRadial and less

thrust

Some Radial

and high thrustJust offer protection

against dirtOffer good

lubrication

For shaft

misalignment

Very heavy radial

and thrust loadsSeef andg For very heavy

thrustFor very heavy

thrust and seef

Fig. 7.2Some of the common types of ball bearing.

For heavier radial loads, roller bearings offer that which is due to the bigger contact area compared to the

ball bearing ones. There are many types as well of roller bearing. Some of the common types available in

the market are listed in figure 7.3.

Straight Spherical Tapered

Needle Tapered angular Steep-angle tapered

Fig. 7.3Some of the common types of roller bearing.

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Bearing life

The life measure of bearing is defined as the total number of revolution of bearing operation until the

failure took place. In general, the failure criterion is the first evidence of fatigue assuming the bearing

working in ideal condition, i.e. no dust or dirt, suitable temperature.. etc. The life of the bearing is

influenced by load and reliability.

Load life at rated reliability

If we assumed the reliability is constant (0.9). The relation between the load and the life of the bearing

can be shown as in figure below:

Force,

ibf,orkN

Rating life

Fig. 7.4bearing load-life

Using a regression equation of the form

FL 1/a = constant

From the empirical tests,

a = 3 for bal l bear ings

a= 10/3 for r oller bear ings

In Timken company, the use the revolution by 90 106

to calculate the suitable load. This can be called ascatalog load ratingas C10. Then the above equation can be as

C10L101/a= FL 1/a (7-1)

C10 (LRnR60)1/a= FD (LDnD60)

1/aa

RR

DDD

nL

nLFC

/1

1060

60

= (7-2)

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Example 7-1

Consider SKF, which rates in bearings for 1 million revolutions, so that L 10life is 60LRnR=106

revolutions. TheLRnR60product produces a familiar number. Timken, for example, uses 90(106)

revolutions. If you desire a life of 5000 h at 1725 rev/min with a load of 2 kN with a reliability of 90

percent, for which catalog rating would you search in an SKF catalog?

Solution

kNnL

nLFC

a

RR

DDD 06.16

10

60)1725(50002

60

603/1

6

/1

10 =

=

=

Load, Life and Reliability

Figure 7.5 shows the relation between the load, reliability and the life. The life is expressed in a

dimensionless value (x). x= L/L10Here is the designer problem; the designer can not use the load, speed and/or the reliability from the

catalogue provided by the supplier. The figure below shows that. Let use assume that the designer wantsto use desired force (FD) and life (xD) at a reliability of RD. The catalog load rating can be determined

form the following equation

a

b

Do

DD

Rxx

xFC

/1

/1

0

10)1)((

+=

(7-3)

where:

R= reliability

x= life measure dimensionless = L/L10x0= guarantee value of variety = characteristic parameter

b= Sharpe parameter that control the skewness

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Fig. 7.5 Relation between reliability, load and life

The Weibull parameters (http://www.barringer1.com/apr01prb.htm) are x0= 0.02, 439.4)( 0 =x and

b = 1.483.

So equation 7-3 can rewritten asa

D

DD

R

xFC

/1

483.1/110 )1(439.402.0

+= (7-3)

Example 7-2

The design load on a ball bearing is 1840 N and an application factor of 1.2 is appropriate. The speed

of the shaft is to be 300 rev/min, the life to be 30 kh with reliability of 0.99. what is the C10catalog entry

to be sought (or exceeded) when searching for a deep-groove bearing in a manufacturers catalog on the

basis of 106revolutions for rating life? The weibull parameters are 439.4)(,02.0 00 == xx , and

.483.1=b

Solution

54010

300)00030(60

60

606

10

====RR

DDD

nL

nL

L

Lx

Thus, the design life is 540 times thanL10life . For a ball bearing, a=3(check page3) . Then, from the

equation below:

kNC

RRxx

xFC

a

b

D

DD

7.29)99.01(439.402.0

540)84.1)(2.1(

90.0)1)((

3/1

483.1110

/1

/1

00

.

10

=

+=

+=

Dr. B F YOUSIF 5
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