Rolling Element Bearings

BITS PilaniPilani Campus

VINAYAK KALLURI

BITS PilaniPilani Campus

BITS Pilani, Pilani Campus

ROLLING ELEMENT BEARINGS

• Also called as rolling-contact bearing, antifriction bearing, and

rolling bearing

• Class of bearing in which the main load is transferred through

elements in rolling contact rather than in sliding contact

• Bearings are manufactured to take pure radial loads, pure thrust

loads, or a combination of the two kinds of loads

• The starting friction is about twice the running friction, but still it is

negligible in comparison with the starting friction of a sleeve

(journal) bearing


Rolling element bearings –Two types:

–Ball bearings (balls are the rolling elements)

–Roller bearings (cylinders are the rolling elements)


Ball Bearing Nomenclature:

Fa

Fa

Fr

Fr


Different types of ball bearings:


Deep Groove Ball Bearing

• Radial load as well as some thrust load

Single- row Deep

Groove Ball Bearing

Double-row Deep

Groove Ball Bearing


Filling notch Deep Groove Ball Bearing

• Use of filling notch in the inner and outer rings enables agreater number of balls to be inserted, thus increasing theradial load capacity compared with deep groove.

• Thrust capacity decrease because of bumping of ballsagainst the edge of the notch when thrust loads are present.

Single- row Filling

notch Ball Bearing


Angular Contact Ball Bearing

• Provides a greater thrust capacity along with the radial load

• Single row bearing takes axial thrust in one direction only, whereas double row bearing accommodate axial thrust in bothdirections

Single- row Angular

contact Ball Bearing

Double- row Angular

contact Ball Bearing


Self Aligning Ball Bearing

• shaft misalignment of deflection is severe, self-aligning

bearings may be used

Double- row Self

aligning Ball Bearing


• Must not be subjected to any radial load

• Single direction thrust ball bearings can accommodate axial loads inone direction and thus locate a shaft axially in one direction.

• In general, thrust ball bearings consist of a shaft washer, a housingwasher and a ball and cage thrust assembly.

• The bearings are separable so that mounting is simple as the washersand the ball and cage assembly can be mounted separately.

Thrust Ball Bearing

Single direction thrust ball bearings


Shielded and sealed bearings

• All the above discussed bearings may be obtained with shields on oneor both sides to protect against dirt (not a complete closure ).

• A variety of bearings are manufactured with seals on one or bothsides. When the seals are on both sides, the bearings are lubricated atthe factory and to be lubricated for life.

• Usually a shielded bearing has a thin "shield" that helps keep debrisout of the bearing surfaces whereas a sealed bearing has "seals" that

attempt to keep out debris and moisture.

Shielded bearing Sealed bearing


Different types of roller bearings

a) Straight roller

b) Tapered roller, thrust

c) Spherical roller, thrust

d) Needle

e) Tapered roller (both radial and thrust)

f) Steep-angle tapered roller


Straight roller Bearing

• Straight roller bearings will carry a greater radial load than

ball bearings of the same size because of the greater contact

area

• They have the disadvantage of requiring almost perfect

geometry of the raceways and rollers. A slight misalignment

will cause the rollers to skew and get out of line. For this

reason, the retainer must be heavy. Straight roller bearings

will not, of course, take thrust loads.


Tapered roller (Thrust) Bearing

• Tapered roller thrust bearings enable axially verycompact bearing arrangements to be produced which cancarry very heavy axial loads, are insensitive to shockloads and are stiff.


Spherical roller ( Thrust) Bearing

• The spherical-roller thrust bearing is useful where heavy loads

and misalignment occur. The spherical elements have the advantage

of increasing their contact area as the load is increased

• In spherical roller thrust bearings the load is transmitted from one

raceway to the other at an angle to the bearing axis. The bearings are

therefore suitable to accommodate radial loads in addition to

simultaneously acting axial loads.


Needle roller Bearing

• Needle bearings are very useful where radial space is limited.

They have a high load capacity when separators are used, but may

be obtained without separators. They are furnished both with and

without races.


• Tapered roller bearings have tapered inner and outer ring

raceways between which tapered rollers are arranged.

• Tapered roller bearings can take either radial or thrust loads

or any combination of the two, and in addition, they have

the high load-carrying capacity of straight roller bearings.

• The tapered roller bearing is designed so that all elements

in the roller surface and the raceways intersect at a common

point on the bearing axis.

Tapered roller (both radial and thrust) Bearing


Tapered roller (both radial and thrust) Bearing

The axial load carrying capacity of the bearings is largely

determined by the contact angle ‘α’


Bearing life• If a bearing is maintained in condition of clean and

properly lubricated, is mounted and sealed against the

entrance of dust and dirt and is operated at reasonable

temperatures, then metal fatigue will be the only cause of

failure.

• Bearing life of an individual bearing is defined as the total

number of revolutions (or hours at a constant speed) of

bearing operation until the failure criterion is developed.

• ABMA (American Bearing Manufacturers Association) standard states

that the failure criterion is the first evidence of fatigue.

• For Timken company, the criterion is a wear area of 6.45

mm2.


Rating life

•The rating life is used by AFBMA (Anti-friction Bearing

Manufacturers Association)

• “the rating life of a group of nominally identical ball or

roller bearings is defined as the number of revolutions (or

hours at a constant speed) that 90% of the group of bearings

will achieve or exceed before the failure criterion develops.”

• Rating life for different manufacturers:

SKF : 106 revolutions

Timken : 90(10)6 revolutions


Bearing load (F) - Life (L) trade-off at

constant (rated, 90%) reliability (R):

Rating Life

Fig: Typical bearing load-life log-log curve.

Using a regression equation of the form

Experimentally

obtained data

plotted, for 90%

reliability


( ) ( ) a

DDD

a

RR nLFnLC/1/1

10 6060 =

aa LFLF1

22

1

11 =

Associating the load F1 with C10, the catalogue rating that you need to look at, and

the life measure in revolutions L1 with the L10, which is the manufacturer specific

quantity, FD and LD refer to the design quantities for the bearing to be selected, we

can write,

( ) ( ) a

DD

aLFLC

/1/1

1010 =Here If we want to specify in the life hours, then we can write, rpm (nR & nD) values:

Different terms in the above equation? →→→→

Rating

Life=L10

Desired

Life=LD

Desired Load=FD

Rating Load=C10

1

2




( ) ( ) a

DDD

a

RR nLFnLC/1/1

10 6060 =

Catalog rating, kN

Rating life in hours

Rating speed in RPM Desired load, kN

Desired life in hours

Desired speed in RPM

Solving for C10 gives

a

DDD

a

RR

DDD

liferating

nLF

nL

nLF

/1/1

10

60

60

60 Crating, load Catalogue

=

=




The Desired load (FD) is not steady then Load application factor

(A.F) is used

For all problems in this chapter,

�If A.F is not given , Don’t use it

�If it is given, then directly multiply with FD to get Desired load

Table 11–5

Effect of load application factor


Problem:

The rating life of rolling contact bearings as 106

revolutions. Select a ball bearing for a motorcycle

for a life of 5000 hours to work at a speed of

1800 RPM under a radial load of 3000 N.


Solution:

( )kNN

nL

nLFC

a

RR

DDD 43.2476.24429

10

60180050003000

60

603/1

6

/1

10 ≅=

=

=

From the table 11-2 (next slide), for the above load

rating, the nearest ball bearing is 35 mm bore, 72 mm

OD, 17 mm width, 1 mm fillet radius, 41 mm shaft

diameter and 65 mm housing shoulder diameter (it has

C10 of 25.5 kN).

Assumed reliability is 90%


Table 11–2:

Dimensions and Load Ratings for Single-Row 02-Series

Deep-Groove and Angular-Contact Ball Bearings


Table 11–3

Dimensions and Basic Load Ratings for

Cylindrical Roller Bearings


The coding method for standard bearings:

02 bearings means…

�As per ABMA, the bearings are identified by a two-digit number

called the dimension-series code.

�The first number is from the width series, 0, 1, 2, 3, 4, 5, & 6.

�The second number is from the diameter series (outside), 8, 9, 0, 1, 2,

3, & 4.


Shoulder dimensions:

What ds and dH in the catalogues

mean…

The housing and shaft shoulder diameters

listed in the tables should be used whenever

possible to secure adequate support for the

bearing and to resist the maximum thrust

loads


Example


Reliability goal of the mechanical system

• The combined reliability goal is normally specified, say, Rt.

• Then each of the two bearings, if both of them are same type, mustpossess a reliability of:

t

t

t

tBA

BAt

RRThus

R

Rge

RRor

RRRRRRRIf

RRR

>

==

=

=

=×=⇒==

×=

,

948.090.0

,90.0.,.

, 2

When dissimilar bearings are to be chosen at the two ends, the more

critical of the two will be designed for Rt. RB=Rt/RA=Rt/Rt=1. Thus

automatically the second bearing will have 100% reliability.


0

0

exp[ ( ) ]bx x

Rxθ

−= −

−

Using the Weibull distribution, along any

constant load line (horizontal line in the

graph):

θ=characteristic parameter corresponding to the 63.2121 percentile value of the

variate; b= shape parameter that controls the skewness

Bearing load (F) - Life (L) - reliability (R)

three-way relationship

(What to do, if more than 90% reliability is desired?):

R=reliability

x=life measure dimensionless variate, L/L10

x0=guaranteed, or minimum value of the variate


1 /

1 0 1 /

0 0

( ) , 0 .9 0( ) (1 )

aDD b

D

xC F R

x x Rθ= ≥

+ − −

aDD

aBB xFxF

11

=a

B

aD

DB

x

xFF

1

1

=⇒Along a constant load line (AB),

( )

ngsubstituti

Rxxx

xSolving

x

xxR

b

D

B

B

b

BD

/1

00

0

0

1ln

exp

−+=

−−

−=

θ

θ

( ) ( )( )

a

b

D

DD

aB

aD

DBRxx

xF

x

xFCF

/1

/1

00

1

1

10/1ln

−+===

θ

The natural logarithmic function can be series-expanded and simplified to yield

Bearing load (F) - Life (L) - reliability (R)

three-way relationship


• The rating life of rolling contact bearings as 106 revolutions.

Select a ball bearing for a motorcycle for a life of 5000 hours to

work at a speed of 1800 RPM under a radial load of 3000 N, with

a reliability of 95%. The pure radial load is not steady and hence

use an application factor (AF) of 1.5. Use Weibull distribution and

Weibull parameters, guaranteed or minimum value of the

dimensionless variate x as x0=0.02, characteristic parameter minus

the minimum guaranteed value as (θ-x0)=4.439 and the shape

parameter as b=1.483.

Example


Solution: desired value of the dimensionless variate

xD=L/L10=(60 LD nD)/(rating life)

= (60*5000*1800)/(106)=540

This means that the design life is to be 540 times the L10 life.

Hence the necessary C10 is

( )kNNC 24.4343236

95.01439.402.0

540)3000)(5.1(

31

483.1110 ==

−+=

From the table 11-2, for the above load rating, the nearest ball bearing

is 55 mm bore, 100 mm OD, 21 mm width, 1.5 mm fillet radius, 63

mm shaft diameter and 605 mm housing shoulder diameter. The C10

itself is 43.6 kN.

Solution


No thrust load

Thrust load present

Combined Radial and Thrust Loading

Two different applications having and not having a thrust load:


Accounting for thrust force:

1e

r

F

VF= when

e a

r r

F FX Y

VF VF= + when

e i r i aF X VF Y F= +

Purpose is to find the equivalent radial load Fe, that

would do the same damage as that done by the

existing radial and thrust loads together. V is the

rotation factor. V=1 for inner ring rotation, V=1.2

for outer ring rotation.

e

Generalizing for both zones,

For horizontal line zone, i=1 and for

inclined line zone, i=2.

Table 11-1 gives the values of Xi and Yi.

a

a


THE ITERATIVE SOLUTION METHOD

(BOTH FrAND FaACTING)

1) Calculate Fa/(VFr) , Assume this is greater than “e” in table 11-1

and note down the X2 and Y2 values.

2) Estimate the equivalent load Fe. Calculate the desired load

FD=A.F(Fe). Calculate C10 for the given reliability.

3) Find the C10 as well as C0 from catalogue for given reliability. C0

is the bearing’s static load catalog rating.

4) Find Fa/C0 and for this Fa/C0, is Fa/(VFr) greater than “e”?, if Yes

note down the X2 and Y2 values.

5) Estimate the equivalent load Fe. Calculate the desired load

FD=A.F(Fe). Calculate the new C10 value for the given reliability.

6) If the same bearing is obtained, stop. (calculated C10 is less than old

C10)

7) If not, take next bearing for new C10 value and repeat from step 4


The SKF rates its rolling contact bearings as 107 revolutions.

Select a 2-series angular contact ball bearing for a life of

10000 hours to work at a speed of 200 RPM under a radial

load of 2.5kN and a axial load of 1kN having a reliability of

99% from SKF catalogue. The load is not steady and use an

application factor of 1.5. Use Weibull distribution and

Weibull parameters are: guaranteed or minimum value of the

dimensionless variate X as X0=0.02, characteristic parameter

minus the minimum guaranteed value as (Ѳ-X0)=4.439 and

the shape parameter as b= 1.483.

Problem





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Rolling Element Bearings