ROLLING ELEMENT

BEARING

Antifriction Bearing

ABMA (American Bearing

Manufacturers Association) AFBMA (Anti-friction Bearing

Manufacturers Association)

TIMKEN, SKF

Is a precision item and can not be “Designed” but only “Selected” out of available ones!

M S Dasgupta, BITS Pilani

Unlike coefficient of sliding friction, the coefficient of rolling friction varies with conditions and has a dimension as unit of length. The rolling resistance can be expressed as Fr = c W (1) where Fr = rolling friction (N) c = rolling resistance coefficient - dimensionless (coefficient of rolling friction - CRF) W = m g = normal force or weight of body (N) m = mass of body (kg) g = accelaration of gravity (9.81 m/s2) The rolling resistance can alternatively be expressed as Fr = cl W / r (2) where cl = rolling resistance coefficient with dimension length (coefficient of rolling friction) (mm) r = radius of wheel (mm)

M S Dasgupta, BITS Pilani

Size?

Advantage?

Although the starting friction is about twice the

running friction, but still it is negligible in

comparison with the starting friction of a journal

bearing

Working

M S Dasgupta, BITS Pilani

Rolling elements

Single use item

M S Dasgupta, BITS Pilani

Ball Bearing Nomenclature:

Conrad type

Filling Notch type

How the balls go inside the races?

M S Dasgupta, BITS Pilani

Balls / Rollers as rolling element

One piece cage retainer

Different types of ball bearings:

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

Bearing life

•Virtually infinite!

• If 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.

•For example Timken company takes the failure criterion as

a wear area of 6.45 mm2.

•Wear debris, vibration etc. may be other criteria.

•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.

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 nFnC/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:

Rating

Life=L10

Desired

Life=LD

Desired Load=FD

Rating Load=C10

1

2

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

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

a

DDD

a

RR nFnC/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

nF

nL

nF

/1/1

10

60

60

60 Crating, load Catalogue

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

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

M S Dasgupta, BITS Pilani

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

(A.F) is used

Table 11–5

Effect of load application factor

Table 11–3

Dimensions and Basic Load Ratings for

Cylindrical Roller Bearings

The coding method for standard bearings:

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.

Table 11–2:

Dimensions and Load Ratings for Single-Row 02-Series

Deep-Groove and Angular-Contact Ball Bearings

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

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, must possess 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 xR

x

Using the Weibull distribution, along any

constant load line (horizontal line in the

graph):

=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/

10 1/

0 0

( ) , 0.90( )(1 )

aDD b

D

xC F R

x x R

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

a

b

D

DD

aB

aD

DBRxx

xF

x

xFCF

/1

/1

00

1

1

10/1ln

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

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

three-way relationship

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

Fe may separately be multiplied by ‘service factor’ if load is not steady

Table 11–1

Equivalent Radial Load Factors for Ball Bearings

Variable loading:

= Constant = K a

F L

F may be already be an equivalent

steady radial load for radial-thrust load

combination If load level of F1 is selected and run to failure

criteria, the area under the F1- L1 trace is

numerically equal to K

Three types of variable loading are possible:

1) Piecewise constant loading in a cycle pattern

2) Continuously variable loading in a repeatable cyclic pattern

3) Random variation

The damage done by loads Fe1, Fe2, and Fe3 is

D = Fae1 l1 + Fa

e2 l2 + Fae3 l3

The loads Fei are equivalent steady radial loads for combined radial–thrust loads.

The equivalent steady load Feq

when run for l1 + l2 + l3 revolutions

does the same damage D.

Thus

D = Faeq (l1 + l2 + l3)

Equating above equations and solving for Feq

Piece-wise continuous cycle:

Piece-wise continuous cycle:

1/{ [( ) ] }a a

eq i i eiF f AF F

li can be expressed as ni ti , where ni is the rotational speed at load Fei and ti is the duration of that speed,

1/ 1/1 1 2 2 3 3

1 2 3

[ ] [ ]a a a

a a a

eq i i

F l F l f lF f F

l l l

1/[ ]

a

i i ei a

eq

i i

n t FF

n t

where fi is the fraction of revolution run up under load Fei .