ROLLING-CONTACT

BEARINGS

Main Sources: Shigley, J.E., Mischke, C.R., Budynas, R.C., Mechanical Engineering Design

Hamrock, B.J., Jacobson, B., Schmid, S. R., Fundamentals of Machine Elements

Khonsari, M.M., Booser, E. R., Applied Tribology

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

http://iec.skf.com/

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

http://www.cwbearing.com/

Introduction

• Rolling-contact bearings are used to minimize the friction associated with

relative motion performed under load. To achieve this, the main load is

transferred through elements in rolling contact rather than in sliding contact.

Sliding Versus Rolling Bearings

Bearing Types

Ball Bearings

Angular ball bearings have higher thrust load

capacity in one direction than due radial ball

bearings.

Bearing Types

Roller Bearings • Roller bearings have higher load capacity than ball bearings.

• Needle bearings have very high load ratings and require less space.

Tapered

Spherical

Straight roller Spherical roller, thrust Tapered roller, thrust

Needle Tapered roller Steep-angle tapered roller

Bearing Types

Roller Bearings

Radial cylindrical Radial tapered Thrust

Needle – drawn cup Needle – heavy duty

Needle - thrust Needle - cage

Bearing Life

• The bearing life 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, spalling) occurs on one of its rings or rolling elements.

• The rating life, 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 life is the 50th percentile life of a group of bearings corresponding to between 4 and 5 times the L10 life.

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

0

00

P

Cs

Equivalent Static Bearing Load

• The equivalent static radial load does the same damage as the

combined radial and thrust loads together.

a0r00 PYPXP

Bearing Load Life Relationship

• Typical bearing load-life log-log curve

• This function can be expressed as

with p = 3 for ball bearings

p = 10/3 for roller bearings

p

2

1

1

2

P

P

L

L

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

pPLC1

pnLPC h

1

610

60

p

P

CL

10

p

hP

C

nL

60

106

10

Equivalent Dynamic Bearing Load

• A rotation factor V is defined as V = 1 when the inner ring rotates

and V = 1.2 when the outer ring rotates.

airi PYVPXP

Variable Loading

• For a piecewise constant loading in a cyclic pattern

where

Pe,i = equivalent radial load for the ith event

ni = speed of the ith event

Ti = time period of the ith event

• Using the linear damage theory the equivalent constant load is

p1

j

1i

ii

j

1i

p

i,eii

nT

PnT

P

Guidelines on Bearing Life

Bearing Ratings

Example from SKF catalogue

Bearing Ratings

SKF 6308 NR:

Adjusted Rating Life

• Recent experimental and analytical results indicate much longer

fatigue life under ideal conditions than predicted by basic life

calculations.

• ABMA revised life equation

or

• where

Lna = adjusted rating life, millions of revolutions

a1 = life adjustment factor for reliability.

a2 = life adjustment factor for material.

a3 = life adjustment factor for operating conditions.

p

321naP

CaaaL

10321na LaaaL

Reliability versus Life

• The reliability given by the three-parameter Weibull distribution is

where R = reliability

x = life measure dimensionless variate, L/L10

x0 = guaranteed, or “minimum”, value of the variate

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

b = shape parameter that controls the skewness

• The cumulative distribution function is

• The reliability of a group of N independent bearings with identical reliability R is

b

x

xxR

0

0exp

b

x

xxRF

0

0exp11

N

N RR

Life Adjustment Factor for

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

giving a life adjustment factor a1 = L/L10 equal to

that can be presented in a table, like this one

5.1

1048.4exp

L

LR

32

10

1

100ln48.4

RL

La

Constant Reliability Contours

• A – Catalog rating C10 at x = L/L10 = 1

• B – Load C10 at R = RD

• D – Design load PD and life xD = LD/L10 with the desired reliability RD

Manufacturers own Life Factors

• Most manufacturers have detailed programs to help select bearings.

• SKF revised life equation

where aSKF is the life adjustment factor for lubricant film thickness,

for loading relative to fatigue load limit (infinite life) and for

contamination. This replaces a2a3 in estimating fatigue life in

operating conditions from severe to ideal.

10SKF1na LaaL

Manufacturers own Life Factors

• CW revised life equation

• where aISO is the adjustment factor for operating conditions and

takes account of the bearing load, the lubrication condition (type

and viscosity of the lubricant, additives, speed, bearing size), the

fatigue limit of the material, the type of bearing, the environmental

conditions (contamination of the lubricant).

10ISO1nm LaaL

Manufacturers own Life Factors

• FAG revised life equation

• where aDIN is the adjustment factor

for operating conditions and takes

account of the bearing load, the

lubrication condition (type and

viscosity of the lubricant, additives,

speed, bearing size), the fatigue limit

of the material, the type of bearing,

the environmental conditions

(contamination of the lubricant).

10DIN1nm LaaL

Variation of lubricant viscosity as a

function of temperature (SKF)

Reference Viscosity (SKF)

SKF

Lubricant Contamination Factor

Factor aSKF for Radial Ball Bearings

(SKF)

Factor aSKF for Radial Roller

Bearings (SKF)

Variation of lubricant viscosity as a

function of temperature (CW)

Reference Viscosity (CW)

CW

Lubricant Contamination Factor

Factor aISO for Radial Ball Bearings

(CW)