1.2 bearing life

Bearing Life

Bearing Life

Even when bearings are properly applied and maintained,Eventual failure occurs in the form of Material Fatigue.

Fatigue is a result of sub-surface shear stresses cyclically applied with initiation immediately below the load carryingSurface.

Failure begins in the subsurface material and propagates tothe surface as a small undetectable crack. The conditionGradually matures to Flaking or Spalling of the surface, the rate dependent upon Load, Speed and Lubrication conditionAnd worsens as it spreads circumferentially around the ringSurface.

Bearing Life

Failure mode - Spalling

Bearing Life

Bearing life is defined as the Number of revolutions

that a bearing undergoes under a constant load

( Equivalent Dynamic Bearing Load ) before

the first sign of fatigue failure occurs.

Bearing Life

Locating Non-locating

Fr Load

Fa

Fr

Equivalent Dynamic Bearing Load

Calculating Dynamic Bearing Load

G

Kr

Ka

G1

Kr1

I

II

l

a1

FrII

FrI

l

a1a2

Kr

Ka

III

FrI FrII

Kr1

Stationary Electrical Machine

a2

The following symbols have been used :

W = Power , kW (Output for motors, input for generators)n = Speed, rpmG = Weight of armature and shaft , KgG1 = Weight of any load on shaft end , KgA = Projected air gap surface = length x diameter of armature, mm2

Kp = Peripheral Force, KgKm= Magnetic pull, Kg


The following symbols have been used :

Kr = Radial force at CG of armature , KgKr1 = Radial force at shaft end , Kg Ka = Axial Force , Kgfk,fd,fb = factors for additional dynamic forcesFrI, = Radial bearing load at position I , KgFrII = Radial bearing load at position II, Kg Fa = Axial bearing load , Kga1, a2 = distance from line of action of force to bearing centre line, mml = Bearing span, mm


Radial force at the centre of gravity of the armature:

Kr = Km + fb x G

Where

Km = 0.002 A



Machine Partfb

Horizontal shaft Vertical shaft

Armature Direct coupled Flexible coupling 1.05 – 1.2 0.2 – 0.5

Solid coupling 1.2 0.5

Belt / Gear / chain drive 1 0

Fly wheel etc, solid coupling 1.05 – 1.2 0.2 – 0.5

The loads acting on the bearing can be calculated according to the laws of mechanics if the externalforces (e.g. forces from power transmission, work forces or inertia forces) are known or can becalculated. When calculating the load components for a single bearing, the shaft is considered as being a beam resting on rigid, moment-free supports for the sake of simplification.



Elastic deformations in the bearing, the housing or the machine frame are not considered, nor are the moments produced inthe bearing as a result of shaft deflection.

These simplifications are necessary if a bearing arrangement is to be calculated using readily available aids such as pocket calculators.

The standardized methods for calculating basic load ratings and equivalent bearing loads are based on similar assumptions.


It is possible to calculate bearing loads based on the theory of elasticity without making the above assumptions, but this requires the use of a powerful computer and lengthy complex programs.

The bearings, shaft and housing are considered as resilient components of a system.


Those external forces which arise, for example, from the inherent weight of the shaft and thecomponents which it carries, or from the weight of a vehicle, and the other inertia forces are either known or can be calculated. However, when determining the work forces (rolling forces, cutting forces in machine tools etc.), shock forces and additional dynamic forces, e.g. as a result of unbalance, it is often necessary to rely on estimations based on experience gained with similar machines or bearing arrangements.


Gear trains :

With a gear train, the theoretical tooth forces can be calculated from the power transmitted and thedesign characteristics of the gear teeth. However, there are additional dynamic forces, produced either in the gear itself or by the input drive or power take-off.

Additional dynamic forces in gears result fromerrors of form of the teeth and from unbalance of the rotating components.


Gear trains :

Because of the requirements for quiet running, gears are made to high standards of accuracy and these forces are generally so small that they can be neglected when making bearing calculations.

Additional forces arising from the type and mode of operation of the machines coupled to the gear can only be determined when the operating conditions are known.


Gear trains :

Their influence on the rating lives of the bearings is considered using an "operation" factor which takes into account shock loads and the efficiency of the gear.

Values of this factor for different operating conditions can usually be found in information published by the gear manufacturer.


For a quick estimation, one can use the formula:

Kr1 = fk * fd * Kp + G1 for Horizontal shafts

= fk * fd * Kp for Vertical shaftsWhereKr1 = Radial force on shaft end, Kgfk , fd = factors for additional dynamic forcesKp = Peripheral force, Kg


No.of engagement

Quality of gear wheel fk

1

Precision teeth ( error < 25µm) 1.05 – 1.1

Commercial planed or milled teeth, also sprockets

( error 25 – 125 µm)

1.1 – 1.3

Cast teeth ( error > 125 µm) 1.5 – 2.2

2Precision teeth 0.6 – 0.7

Commercial planed or milled teeth 0.7 – 0.8

Factor fk for additional dynamic forces for calculating the actual tooth force

The lower value applies to low tooth speeds v 1.85M/sec


Factor fd for additional dynamic forces arising from mechanisms coupled to gearing

Types of Machines fd

Electric Machines ,Turbines 1.0 – 1.1

Traction Motors 1.1 – 1.5

Conveying Equipment 1.0 – 2.5

Mining & Construction Eqpt 1.1 - 2.2

Agricultural & Food Processing Machineries 1.1 – 2.0

Paper making Machines 1.0 – 1.1

Chippers 1.5 – 2.0

Shaking Equipment 1.5 – 2.5

Drilling / Milling / Grinding Machines 1.1 – 1.3

Frame Saws 1.2 – 1.3

Machine Tools with reciprocating motions 1.4 – 1.6


Belt drives :

For belt drives it is necessary to take into account the effective belt pull (circumferential force) which is dependent on the transmitted torque, when calculating bearing loads.

The belt pull must be multiplied by a factor which is dependent on type of belt, its preload, belt tension and any additional dynamic forces.


For a quick estimation, one can use the formula:

Kr1 = f * Kp + G1 for Horizontal shafts

= f * Kp for Vertical shaftsWhereKr1 = Radial force on shaft end, Kgf = factor for belt pullKp = Peripheral force, Kg


Values of factor f are usually published by belt manufacturers. However, should information not be available, the following values can be used:

Type of belt f

Toothed belts 1,1 to 1,3

Vee belts 1,2 to 2,5

Plain belts 1,5 to 4,5

Larger values apply when distance between shafts is short, for heavy or shock-type duty, orwhere belt tension is high.


Direct drive through Flexible coupling :

For a quick estimation, one can use the formula: Kr1 = 8.17 * \ ( W / n ) + G1

WhereKr1 = Radial force on shaft end, KgW = Power , Wattsn = Speed, rpmG1 = Weight of half coupling , Kg


Thrust Forces :

The thrust load on the locating bearing is : Fa = Ka in Horizontal machines And Fa = G + G1 +Ka in Vertical machines WhereKa = External thrust load, KgG = Weight of rotor , KgG1 = Weight at shaft end e.g.,coupling etc, Kg


Ka could be the Axial component of gear tooth forces Pressure from a pump Pressure from a turbine Thrust load from certain types of flexible couplings, brakes etc.

For Vertical direct coupled turbines, Ka = weight of impeller etc. + water load.

Thrust force arising out of magnetic unbalance in an electrical machine may be ignored.

Bearing Life

Equivalent Dynamic Bearing Load

P = X Fr + Y Fa

Where :

X = Radial Load Factor

Y = Axial Load Factor

General Catalogue – Page 49

Bearing Life

Radial & Axial Load Factors

DGBB : General Catalogue Pages 184 - 185

P = Fr if Fa/Fr </= e

P = X Fr + Y Fa if Fa/Fr > e

C0 is given in Pages 186 – 253e is given in Page 185

Bearing Life


SABB : General Catalogue Page 261

P = Fr + Y1 Fa if Fa/Fr </= e

P = 0.65 Fr + Y2 Fa if Fa/Fr > e

Y1, Y2 & e are given in Pages 264 – 283

Bearing Life


ACBB : General Catalogue Page 292Single Bearing / Tandem :P = Fr if Fa/Fr </= 1.14P = 0.35 Fr + 0.57 Fa if Fa/Fr > 1.14

Paired X or O :P = Fr + 0.55 Fa if Fa/Fr </= 1.14P = 0.57 Fr + 0.93 Fa if Fa/Fr > 1.14

Bearing Life


DRACBB : General Catalogue Page 311

P = Fr + 0.73 Fa if Fa/Fr </= 0.86P = 0.62 Fr + 1.17 Fa if Fa/Fr > 0.86

Bearing Life


CRB : General Catalogue Page 336

P = Fr

For Flanged CRB,P = Fr if Fa/Fr </= eP = 0.92 Fr + Y Fa if Fa/Fr > e

Y & e are given in Page 336

Bearing Life


SRB : General Catalogue Page 467




Bearing Life


SRTRB : General Catalogue Page 520 - 521

P = Fr if Fa/Fr </= e

P = 0.4 Fr + Y Fa if Fa/Fr > e

Y & e are given in Pages 526 – 585

Bearing Life


Paired TRB : General Catalogue Page 589




Bearing Life


ThBB / CRThB : General Catalogue Page 597/622

P = Fa

Bearing Life


SRThB : General Catalogue Page 646

P = Fa + 1.2 Fr if Fr </= 0.55Fa

P = 0.88(Fa + 1.2 Fr ) if adjustable assembly & Fr </= 0.55Fa

Bearing Life

( )C pL = 10 P Lundberg Palmgren Equation 1947



Bearing Life


( )C pL = na

Pa1a 23 Adjusted Rating Life Equation 1977


Bearing Life


( )C pL = na

Pa1a 23 Adjusted Rating Life Equation 1977

New SKF Life Equation 1989L = naaa1a SKF( )C p

P


Bearing Selection

Bearings are selected based on:

Load

Speed

Temperature

Environment

Life expectancy

Selection of bearingsSome aspects to be considered

Available space Misalignment

Speed Life

Load/Direction Operating conditions

L = 10 ( )C

P

p

Load carrying capacity

Load carrying capacity is expressed as the basic dynamic load rating

of different bearing types having the same bore and outside diameters

Speed ratings speed limit

0 r/min

Oil lubricationspeed rating

Grease lubricationspeed rating

Bearing speed limit

=

Factors influencing speed capability

Increases speed

Low loads

High accuracy

Good sliding properties

of cage guiding surface

Correct clearance

Optimised lubrication

Effective cooling

Reduces speed

High loads

Poor accuracy

Excess of lubricant

Lack of lubricant

Excessive lubricant viscosity

Poor cooling

Basic Terminologies :

1. Static Load

1. Dynamic Load

1. Life Requirement


Basic dynamic load rating

ISO dynamic load rating C = Load that gives a basic ratinglife of 1 000 000 revolutions

C

Basic Dynamic Load Rating

Basic Dynamic Load Rating of a Radial Ball Bearing is :

C = fc (i cos α)0.7 z 2/3 F (Dw)

Where C = Basic Dynamic Load Rating , Kgfc = Factor for calculating Ci = Number of rows of ballsz = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the balls, mmF (Dw) = Dw

1.8 when Dw 25.4 mm = 3.647 Dw

1.4 when Dw >25.4 mm


Basic Dynamic Load Rating of Single Row Thrust Ball Bearing (α900) is :

C = fc (cos α)0.7 tan α z 2/3 F (Dw)

Where C = Basic Dynamic Load Rating , Kgfc = Factor for calculating Cz = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the balls, mmF (Dw) = Dw

1.8 when Dw 25.4 mm = 3.647 Dw



Basic Dynamic Load Rating of Single Row Thrust Ball Bearing (α = 900) is :

C = fc z 2/3 F (Dw)

Where C = Basic Dynamic Load Rating , Kgfc = Factor for calculating Cz = Number of rolling elements per rowDw = Diameter of the balls, mmF (Dw) = Dw

1.8 when Dw 25.4 mm = 3.647 Dw



Basic Dynamic Load Rating of a Radial Roller Bearing is :

C = fc (i la cos α) 7/9 z 3/4 Dw 29/27

Where C = Basic Dynamic Load Rating , Kgi = Number of rows of rollersla = Effective length of rollers, mmDw = Diameter of the rollers, mmz = Number of rolling elements per rowα = Contact angle, Degrees


Basic Dynamic Load Rating of Single Row Thrust Roller Bearing (α900) is :

C = fc (la cos α)7/9 tan α z 3/4 Dw 29/27

Where C = Basic Dynamic Load Rating , Kgfc = Factor for calculating Cla = Effective length of rollers, mmz = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the rollers, mm


Basic Dynamic Load Rating of Single Row Thrust Roller Bearing (α = 900) is :

C = fc la 7/9 z 3/4 Dw 29/27

Where C = Basic Dynamic Load Rating , Kgfc = Factor for calculating Cla = Effective length of rollers, mmz = Number of rolling elements per rowDw = Diameter of the rollers, mm

Basic static load rating

ISO basic load rating Co corresponds to a stress that gives permanent deformationof 0,0001 of the rollingelement diameter

Basic Static Load Rating

Basic Static Load Rating of a Radial Ball Bearing is :

C0 = 0.22 ko i z Dw2

Cos α

Where C0 = Basic Static Load Rating , Kgk0 = Factor for calculating C0 i = Number of rows of ballsz = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the balls, mm


Basic Static Load Rating of a Radial Roller Bearing is :

C0 = 0.22 ko i z Dw la Cos α

Where C0 = Basic Static Load Rating , Kgk0 = Factor for calculating C0 i = Number of rows of rollersz = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the rollers, mmla = Effective length of rollers, mm


Basic Static Load Rating of Single row thrust Ball Bearing is :

C0 = ko z Dw 2

Sin α

Where C0 = Basic Static Load Rating , Kgk0 = Factor for calculating C0 z = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the balls, mm


Basic Static Load Rating of Multi row thrust Ball Bearing (α = 900) is :

C0 = ko Σ z Dw 2

Where C0 = Basic Static Load Rating , Kgk0 = Factor for calculating C0 z = Number of rolling elements per rowDw = Diameter of the balls, mm


Basic Static Load Rating of Single row thrust roller bearing is :

C0 = ko z Dw la Sin α

Where C0 = Basic Static Load Rating , Kgk0 = Factor for calculating C0 z = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the rollers, mmla = Effective length of rollers, mm


Basic Static Load Rating of Multi row thrust roller bearing (α = 900) is :

C0 = ko Σ z Dw la

Where C0 = Basic Static Load Rating , Kgk0 = Factor for calculating C0 z = Number of rolling elements per rowα = Contact angle, DegreesDw = Diameter of the rollers, mmla = Effective length of rollers, mm

Bearing Life considerations varydepending on :

Type of Rolling Element

1. Ball2. Roller

a. Cylindricalb. Needlec. Taperedd. Spherical

I SymmetricalII Asymmetrical

Different Applications require different Life:

1. Hand Tool2. Elevator3. Machine Tools4. Industrial Fans5. Pumps6. Water Circulating Pumps

Load carrying capacityBasic dynamic load rating C

L10 = basic rating life, millions of

revolutions

C = basic dynamic load rating, N

P = equivalent dynamic bearing load, N

p = exponent of the life equation

With the load P = C

the L life will be 1 million revolutions 10

Basic static load rating C 0

P 0

P 0

P

P

The ISO life equation

s0 = static safety factor

P0 = equivalent static bearing load, N

C0 = basic static load rating, N

With the load P = C0

the static safety factor s0 will be 1

The static safety factor

s = 0

C 0P 0

( )CL = 10 P

p


Equivalent Static Bearing Load

P0 = X0 Fr + Y0 Fa

Where :

X0 = Static Radial Load Factor

Y0 = Static Axial Load Factor



Bearing Life

L10 = Basic Rating Life, Millions of Revolutions

C = Basic Dynamic Load Rating , NP = Equivalent Dynamic Bearing Load, Np = Exponent of the life equation = 3 for ball bearings = 10/3 for roller bearings

L = 10h

( )C p P Lundberg Palmgren Equation 1947

Bearing Life

L10h = Basic Rating Life, Operating Hours

C = Basic Dynamic Load Rating , NP = Equivalent Dynamic Bearing Load, Np = Exponent of the life equation = 3 for ball bearings = 10/3 for roller bearingsn = Rotational Speed rpm

1 000 00060 n



Adjusted Rating Life Equation

( )C pL =

na

Pa1a 23

Lna = Adjusted Rating Life, Millions of Revolutions

a1 = Life Adjustment Factor for Reliabilitya23 = Life Adjustment Factor for Material and Lubrication

Reliability Factor a1


Material & Lubrication Factor a23


New SKF Life Equation 1989

L = naa a1a SKF ( )C p

P

Lnaa = Adjusted Rating Life to new life theory, Millions of Revolutions

a1 = Life Adjustment Factor for ReliabilityaSKF = Life Adjustment Factor for Material,

Lubrication, Minimum load and Contamination





General Catalogue : Page 24 - 25

General Catalogue : Page 24 - 25

Bearing Life

CPL = 10

( )p

L = a a naa 1 SKF( )C

Pp

ISO

Finite life

Load P

Life

The SKF New Life Theory

Infinite life

Load P

Life

Service life:This is the actual life achieved by the bearing before it fails.

P U

Bearing calculationsCatalogue methods

Advanced methods

Manual calculations Computer calculationsCADalog is acomputerisedversion of theGeneral Catalogue

L = 10( )pC

P

L = a a na 1 23( )pC

P

L = a a naa 1 SKF( )pC

P

SKF application engineers have a comprehensive library ofsophisticated computer programs at their disposal. These programscan be used to determine more accurately the bearing size and life.

GeneralCatalogue

CADalog

Friction Under certain conditions the frictionalmoment can be calculated with sufficientaccuracy

M = 0,5 . µ . F . d

M = frictional moment (Nmm)µ = coefficient of frictionF = bearing load (N)d = bearing bore diameter (mm)

General Catalogue : Page 56

Speeds

The speed limit is relatedto the permitted operatingtemperature

Speed ratings are givenunder a load correspondingto L10h 150.000

General Catalogue : Page 65

Engineering

1.2 bearing life