Chapter 11: Rolling Element Bearings

ME/MF F241:

Machine Design and Drawing

Dr. Regalla Srinivasa Prakash

Scope

• Bearing types

• Bearing life

• Bearing load(F)-life(L) trade off at constant reliability

• Bearing survival: the reliability(R)-life(L) trade-off

• Load(F)-life(L) –reliability(R) trade-off

• Combined radial (Fr) and thrust (Fa) loading

• Variable loading

• Selection of ball and roller bearings

• Selection of tapered roller bearings

• Adequacy assessment for selected rolling contact bearings

• Lubrication in rolling element bearings

• Mounting and enclosure in rolling element bearings

ROLLING ELEMENTS BEARINGS – THE TWO TYPES:

• Rolling element bearings are two types:

– Ball bearings (balls are the rolling elements)

– Roller bearings (cylinders are the rolling elements)

Ball Bearing Nomenclature:

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 load (F) - Life (L) trade-off at constant (rated, 90%) reliability (R):

1/ aFL =constant

a=3 for ball bearings

a=10/3 for roller bearings

Experimentally

obtained data

plotted, for 90%

reliability

Rating Life

Rating life

Rating life for different manufacturers:

• SKF: 106 revolutions

• Timken: 90(10)6 revolutions

•The rating life is a term sanctioned by the Anti-friction

Bearing Manufacturers Association (AFBMA)

• “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.”

•For Timken company, the criterion is a wear area of 6.5

mm2.

Contd.

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, we can write,

a

DD

aLFLC

/1/1

1010

Here FD and LD refer to the design quantities for the bearing to be selected.

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

What the different terms in the above equation mean?

Rating

Life=L10

Desired

Life=LD

Desired Load=FD

Rating Load=C10

Contd.

1/

10

60( )

60

aD DD

R R

L nC F

L n

Inverting the equation,

Catalogue load rating=

a

DDD

a

RR nLFnLC/1/1

10 6060

Catalog rating, kN

Rating life in hours

Rating speed in RPM Desired radial load, kN

Desired life in hours

Desired speed in RPM

Example:

The SKF rates its rolling contact bearings as 106 revolutions whereas Timken rates as 90*(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 90% from the SKF catalogue.

Solution:

kNN

nL

nLFC

a

RR

DDD 43.2476.24429

10

60180050003000

60

603/1

6

/1

10

From the table 11-2, 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).

0

0

1 1 exp[ ( ) ]bx xF R

x

0

0

exp[ ( ) ]bx xR

x

R=reliability

x=life measure dimensionless variate,

L/L10

x0=guaranteed, or minimum value of

the variate

Using the Weibull distribution, along

any constant load line (horizontal

line in the graph on the right):

=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 if more or less than 90% reliability is desired?):

Failure (not force)

probability =

Contd.

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

Revisit to the previous example:

• The SKF rates its rolling contact bearings as 106 revolutions whereas Timken rates as 90*(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, now with a reliability of 95% from the SKF catalogue. 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 (-x0)=4.439 and the shape parameter as b=1.483.

Solution: desired value of the dimensionless variate

xD=L/L10=(60*LD*nD)/(60*LR*nR) = (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.

Exercise Problem:

An angular-contact, inner ring rotating, 02-series ball bearing is required for an

application in which the life requirement is 50000 h at 480 rev/min. The design

radial load is 2745. The application factor is 1.4. The reliability goal is 0.90. Find the

multiple of rating life xD required and the catalog rating C10 with which to enter

Table 11–2. Choose a bearing and write down all of its specifications. Also

estimate, the actually chosen ball bearing, the actual existing reliability in service.

Two different applications having and not having a thrust load:

No thrust load

Thrust load present

Accounting for thrust force:

1e

r

F

VF when

e

r

Fe

VF

e a

r r

F FX Y

VF VF when e

r

Fe

VF

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.

THE ITERATIVE SOLUTION METHOD WITH BOTH Fr AND Fa

• Calculate xD.

• Ignore Fa, and for FD=Fr, find the C10 as well as C0 from catalogue for given reliability. C0 is the bearing’s static load catalog rating. Assign (C10)old = C10.

• Find Fa/C0.

• Find “e” from Table 11-1 using interpolation for this Fa/C0.

• For this Fa/C0, is Fa/(VFr) greater than “e”?, if Yes note down the X2 and Y2 values. Interpolation may be needed. If No, ignore Fa, solution ends.

• Estimate the equivalent load Fe. Apply V only to Fr. Calculate the desired load FD=af(Fe). The af 1 is the load application factor accounting for unsteady nature of loading.

• Calculate the new (C10)new value. Compare with the earlier (C10)old value. If (C10)new < (C10)old, then (C10)old is the final desired rating of the bearing to be selected. The solution ends. If (C10)new > (C10)old we need to go for another iteration.

• Assign (C10)old = (C10)new . Find the new C0 for the (C10)new .

• Continue the iterations until the (C10)new is less than preceding (C10)old.

RELIABILITY GOAL OF THE MECHANICAL SYSTEM

• The combined reliability goal is normally specified, say, Rt. It is the for the shaft mounted on those bearings.

• 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

,

9746.095.0

,95.0.,.

, 2

Example problem:

The worm shaft shown in part a of

the figure transmits 1.35 hp at 600

rpm. A static force analysis gave the

results shown in part b of the figure.

Bearing A is to be an angular contact

ball bearing mounted to take the

555-lbf thrust load. The bearing at B

is to take only the radial load, so a

straight roller bearing will be

employed. Use an application factor

of 1.3, a desired life of 25 kh, and a

reliability goal, combined of 0.99.

Specify each bearing.

The coding method for standard bearings:

02 bearings means…

Shoulder dimensions:

What ds and dH in the

catalogues mean…