load carrying capacity and life

Load carrying capacity and life Fatigue theory as a principle Dimensioning of rolling bearings Dynamic load carrying capacity and life Calculation of the rating life Equivalent operating values Required rating life Operating life Axial load carrying capacity of cylindrical roller bearings Static load carrying capacity Top

SchaefflerKG introduced the Expanded calculation of the adjusted rating life in 1997. This method was standardised for the first time in DINISO281Appendix1 and has been a constituent part of the international standard ISO281 since 2007.

As part of the international standardisation work, the life adjustment factor aDIN was renamed as aISO but without any change to the calculation method.

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Fatigue theory as a principle

The basis of the rating life calculation in accordance with ISO281 is Lundberg and Palmgren's fatigue theory which always gives a final rating life.

However, modern, high quality bearings can exceed by a considerable margin the values calculated for the basic rating life under favourable operating conditions. Ioannides and Harris have developed a further model of fatigue in rolling contact that expands on the Lundberg/Palmgren theory and gives a better description of the performance capability of modern bearings.

The method Expanded calculation of the adjusted rating life takes account of the following influences:

the bearing load the fatigue limit of the material the extent to which the surfaces are separated by the lubricant the cleanliness in the lubrication gap additives in the lubricant the internal load distribution and frictional conditions in the bearing.

The influencing factors, especially those relating to contamination, are extremely complex. A great deal of experience is essential for an accurate assessment. As a result the Engineering Service of Schaeffler Group Industrial should be consulted for further advice.

The tables and diagrams can only give guide values.

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Dimensioning ofrolling bearings

The required size of a rolling bearing is dependent on the demands made on its:

rating life load carrying capacity operational reliability.

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Dynamic loadcarrying capacity and life

The dynamic load carrying capacity is described in terms of the basic dynamic load ratings. The basic dynamic load ratings are based on DINISO281.

The basic dynamic load ratings for rolling bearings are matched to empirically proven performance standards and those published in previous FAG and INA catalogues.

The fatigue behaviour of the material determines the dynamic load carrying capacity of the rolling bearing.

The dynamic load carrying capacity is described in terms of the basic dynamic load rating and the basic rating life.

The fatigue life is dependent on:

the load the operating speed the statistical probability of the first appearance of failure.

The basic dynamic load rating C applies to rotating rolling bearings. It is:

a constant radial load Cr for radial bearings a constant, concentrically acting axial load Ca for axial bearings.

The basic dynamic load rating C is that load of constant magnitude and direction which a sufficiently large number of apparently identical bearings can endure for a basic rating life of one million revolutions.

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Calculation of the rating life

The methods for calculating the rating life are:

basic rating life L10 and L10h to ISO281, see link adjusted rating lifeLna to DINISO281:1990 (no longer a constituent part of ISO281), see link expanded adjusted rating lifeLnm to ISO281, see link.

Basic rating life

The basic rating life L10 and L10h is calculated as follows:

L10106 revolutions

The basic rating life in millions of revolutions is the life reached or exceeded by 90% of a sufficiently large group of apparently identical bearings before the first evidence of material fatigue develops

L10hh

The basic rating life as defined for L10 but expressed in operating hours

CN

Basic dynamic load rating

PN

Equivalent dynamic bearing load for radial and axial bearings

p

Life exponent; for roller bearings: p=10/3 for ball bearings: p=3

nmin1

Operating speed.

Equivalent dynamic load

The equivalent dynamic load P is a calculated value. This value is constant in size and direction; it is a radial load for radial bearings and an axial load for axial bearings.

The load value P gives the same rating life as the combined load occurring in practice.

PN

Equivalent dynamic bearing load

FrN

Radial dynamic bearing load

FaN

Axial dynamic bearing load

X

Radial factor given in the dimension tables or product description

Y

Axial factor given in the dimension tables or product description.

This calculation cannot be applied to radial needle roller bearings, axial needle roller bearings and axial cylindrical roller bearings. Combined loads are not permissible with these bearings.

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Adjusted rating life

The adjusted rating life Lna can be calculated if, in addition to the load and speed, other influences are known such as:

special material characteristics lubrication

or

if a requisite reliability other than 90% is specified.

This calculation method was replaced in ISO281:2007 by the calculation of the expanded adjusted rating life Lnm, see link.

Lna106 revolutions

Adjusted rating life for special material characteristics and operating conditions with a requisite reliability of (100n)%

L10106 revolutions

Basic rating life

a1

Life adjustment factor for a requisite reliability other than 90%. In ISO281:2007, the values for the life adjustment factora1 have been redefined, see table

a2

Life adjustment factor for special material characteristics. For standard rolling bearing steels: a2=1

a3

Life adjustment factor for special operating conditions; in particular lubrication, Figure 1.

The viscosity ratio is determined according to the formula on link.

Good cleanliness and suitable additivesVery high cleanliness and low loadContamination in the lubricanta3=life adjustment factor=viscosity ratioFigure 1Life adjustment factor a3

Viscosity ratio

The viscosity ratio is an indication of the quality of lubricant film formation:

mm2s1

Kinematic viscosity of the lubricant at operating temperature

1mm2s1

Reference viscosity of the lubricant at operating temperature.

The reference viscosity 1 is determined from the mean bearing diameter dM=(D+d)/2 and the operating speed n, Figure 2.

The nominal viscosity of the oil at +40C is determined from the required operating viscosity and the operating temperature , Figure 3. In the case of greases, is the operating viscosity of the base oil.

In the case of heavily loaded bearings with a high proportion of sliding contact, the temperature in the contact area of the rolling elements may be up to 20K higher than the temperature measured on the stationary ring (without the influence of any external heat).

Taking account of EP additives in calculation of the expanded adjusted rating life Lnm: see link.

1=reference viscositydM=mean bearing diametern = speedFigure 2Reference viscosity 1

=operating viscosity=operating temperature40=viscosity at +40CFigure 3V/T diagram for mineral oils

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Expanded adjusted rating life

The calculation of the expanded adjusted rating life Lnm was standardised in DINISO281Appendix 1. Since 2007, it has been standardised in the worldwide standard ISO281. Computer-aided calculation in accordance with DINISO281Appendix 4 has been specified since 2008 in ISO/TS16281.

Lnm is calculated as follows:

Lnm106 revolutions

Expanded adjusted rating life to ISO281

a1

Life adjustment factor for a requisite reliability other than 90%, see table

aISO

Life adjustment factor for operating conditions

L10106 revolutions

Basic rating life, see link.

The values for the life adjustment factor a1 were redefined in ISO281:2007 and differ from the previous data.

Life adjustment factor a1

Requisite reliabilityExpanded adjusted rating lifeLife adjustment factor

%Lnma1

90L10m1

95L5m0,64

96L4m0,55

97L3m0,47

98L2m0,37

99L1m0,25

99,2L0,8m0,22

99,4L0,6m0,19

99,6L0,4m0,16

99,8L0,2m0,12

99,9L0,1m0,093

99,92L0,08m0,087

99,94L0,06m0,08

99,95L0,05m0,077

Life adjustment factoraISO

The standardised method for calculating the life adjustment factor aISO essentially takes account of:

the load on the bearing the lubrication conditions (viscosity and type of lubricant, speed, bearing size, additives) the fatigue limit of the material the type of bearing the residual stress in the material the environmental conditions contamination in the lubricant.

aISO

Life adjustment factor for operating conditions,Figure 4 to Figure 7

eC

Life adjustment factor for contamination, see table

CuN

Fatigue limit load

PN

Equivalent dynamic bearing load

Viscosity ratio, see linkFor 4, calculation should be carried out using =4.For 0,1, this calculation method cannot be used.

Taking account of EP additives in the lubricant

In accordance with ISO281, EP additives can be taken into consideration in the following way:

For a viscosity ratio 1 and a contamination factor eC0,2, calculation can be carried out using the value =1 for lubricants with EP additives that have proven effective. With severe contamination (contamination factor eC0,2), the effectiveness of the additives under these contamination conditions must be proven. The effectiveness of the EP additives can be demonstrated in the actual application or on a rolling bearing test rigFE8 to DIN51819-1.If the EP additives are proven effective and calculation is carried out using the value =1, the life adjustment factor must be restricted to aISO3. If the value aISO calculated for the actual is greater than 3, this value can be used in calculation.

Figure 4Life adjustment factor aISOfor radial roller bearings

Figure 5Life adjustment factor aISOfor axial roller bearings

Figure 6Life adjustment factor aISOfor radial ball bearings

Figure 7Life adjustment factor aISOfor axial ball bearings

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Fatigue limit load

The fatigue limit load Cu in accordance with ISO281 is defined as the load below which, under laboratory conditions, no fatigue occurs in the material.

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Life adjustment factorfor contamination

The life adjustment factor for contamination ec takes into consideration the influence of contamination in the lubrication gap on the rating life, see table.

The rating life is reduced by solid particles in the lubrication gap and is dependent on:

the type, size, hardness and number of particles the relative lubrication film thickness the bearing size.

Due to the complex nature of the interaction between these influencing factors, only an approximate guide value can be attained. The values in the tables are valid for contamination by solid particles (factoreC). They do not take account of other contamination such as that caused by water or other fluids.

Under severe contamination (eC0) the bearings may fail due to wear. In this case, the operating life is substantially less than the calculated life.

FactoreC

ContaminationFactor eC

dM 100mm1) dM 100mm1)

Extreme cleanliness Particle size within lubricant film thickness Laboratory conditions 11

High cleanliness Oil filtered through extremely fine filter Sealed, greased bearings 0,8 to 0,60,9 to 0,8

Standard cleanliness Oil filtered through fine filter 0,6 to 0,50,8 to 0,6

Slight contamination Slight contamination of oil 0,5 to 0,30,6 to 0,4

Typical contamination Bearing contaminated with abraded material from other machine elements 0,3 to 0,10,4 to 0,2

Heavy contamination Bearing environment is heavily contaminated Bearing arrangement is insufficiently sealed 0,1 to 00,1 to 0

Very heavy contamination00

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1dM=mean bearing diameter (d+D)/2.

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Equivalent operating values

The rating life formulae assume a constant bearing load P and constant bearing speed n. If the load and speed are not constant, equivalent operating values can be determined that induce the same fatigue as the actual conditions.

The equivalent operating values calculated here already take account of the life adjustment factors a3 or aISO. They must not be applied again when calculating the adjusted rating life.

Variable load and speed

If the load and speed vary over a time period T, the speed n and equivalent bearing load P are calculated as follows:

Variation in steps

If the load and speed vary in steps over a time period T, n and P are calculated as follows:

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Variable load at constant speed

If the functionF describes the variation in the load over a time periodT and the speed is constant, P is calculated as follows:

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Load varying in steps andconstant speed

If the load varies in steps over a time period T and the speed is constant, P is calculated as follows:

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Constant load at variable speed

If the speed varies but the load remains constant, the following applies:

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Constant load withspeed varying in steps

If the speed varies in steps, the following applies:

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Under oscillating bearing motion

The equivalent speed is calculated as follows:

The formula is valid only if the angle of oscillation is greater than twice the angular pitch of the rolling elements. If the angle of oscillation is smaller, there is a risk of false brinelling.

Figure 8Angle of oscillation

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Symbols, units and definitionsnmin1

Mean speed

Tmin

Time period under consideration

PN

Equivalent bearing load

p

Life exponent;for roller bearings: p=10/3for ball bearings: p=3

ai, a(t)

Life adjustment factoraISO for current operating condition,see link

ni, n(t)min1

Bearing speed for current operating condition

qi%

Duration of operating condition as a proportion of the total operating period;qi = (ti/T) 100

Fi, F(t)N

Bearing load during the current operating condition

noscmin1

Frequency of oscillating motion

Angle of oscillation, Figure 8.

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Required rating life

If no information is available on the rating life, the guide values from the following tables may be used.

Do not overspecify the bearing. If the calculated life is 60000h, this normally means that the bearing arrangement is overspecified. Pay attention to the minimum load for the bearings; see the design and safety guidelines in the product sections.

Motor vehicles

Mounting locationRecommended rating life in h

Ball bearingsRoller bearings

fromtofromto

Motorcycles40020004002400

Passenger car powertrains50011005001200

Passenger car gearboxes protected against contamination200500200500

Passenger car wheel bearings1400530015007000

Light commercial vehicles2000400024005000

Medium commercial vehicles2900530036007000

Heavy commercial vehicles40008800500012000

Buses290011000360016000

Internal combustion engines90040009005000

Rail vehicles



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Wheelset bearings for freight wagons780021000--

Tram carriages--3500050000

Passenger carriages--2000035000

Goods wagons--2000035000

Tipper wagons--2000035000

Powered units--3500050000

Locomotives, external bearings--3500050000

Locomotives, internal bearings--75000110000

Gearboxes for rail vehicles14000460002000075000

Shipbuilding



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Marine thrust blocks--2000050000

Marine shaft bearings--50000200000

Large marine gearboxes14000460002000075000

Small marine gearboxes400014000500020000

Boat propulsion systems17007800200010000

Agricultural machinery



fromtofromto

Tractors1700400020005000

Self-propelled machinery1700400020005000

Seasonal machinery50017005002000

Construction machinery



fromtofromto

Dozers, loaders40007800500010000

Excavators, travelling gear50017005002000

Excavators, slewing gear1700400020005000

Vibratory road rollers, imbalance generators1700400020005000

Vibrator bodies50017005002000

Electric motors



fromtofromto

Electric motors for household appliances17004000--

Series motors21000320003500050000

Large motors320006300050000110000

Electric traction motors14000210002000035000

Rolling mills, steelworks equipment



fromtofromto

Roll stands5001400050020000

Rolling mill gearboxes14000320002000050000

Roller tables7800210001000035000

Centrifugal casting machines21000460003500075000

Machine tools



fromtofromto

Headstock spindles, milling spindles14000460002000075000

Drilling spindles14000320002000050000

Grinding spindles7800210001000035000

Workpiece spindles in grinding machines210006300035000110000

Machine tool gearboxes14000320002000050000

Presses, flywheels21000320003500050000

Presses, eccentric shafts14000210002000035000

Electric tools and compressed air tools400014000500020000

Woodworking machinery



fromtofromto

Milling spindles and cutter blocks14000320002000050000

Saw frames, main bearings--3500050000

Saw frames, connecting rod bearings--1000020000

Circular saws400014000500020000

Gearboxes ingeneral machine building



fromtofromto

Universal gearboxes400014000500020000

Geared motors400014000500020000

Large gearboxes, stationary14000460002000075000

Conveying equipment



fromtofromto

Belt drives, mining--75000150000

Conveyor belt rollers, mining460006300075000110000

Conveyor belt rollers, general7800210001000035000

Belt drums--5000075000

Bucket wheel excavators, travel drive7800210001000035000

Bucket wheel excavators, bucket wheel--75000200000

Bucket wheel excavators, bucket wheel drive460008300075000150000

Winding cable sheaves32000460005000075000

Sheaves7800210001000035000

Pumps, fans, compressors



fromtofromto

Ventilators, fans21000460003500075000

Large fans320006300050000110000

Piston pumps21000460003500075000

Centrifugal pumps14000460002000075000

Hydraulic axial and radial piston engines500780050010000

Gear pumps500780050010000

Compressors400021000500035000

Centrifuges, stirrers



fromtofromto

Centrifuges7800140001000020000

Large stirrers21000320003500050000

Textile machinery



fromtofromto

Spinning machines, spinning spindles21000460003500075000

Weaving and knitting machines14000320002000050000

Plastics processing



fromtofromto

Plastics worm extruders14000210002000035000

Rubber and plastics calenders21000460003500075000

Crushers, mills, screens



fromtofromto

Jaw crushers--2000035000

Gyratory crushers, roll crushers--2000035000

Rigid hammer mills, hammer mills, impact crushers50000110000

Tube mills--50000100000

Vibration grinding mills--500020000

Grinding track mills--50000110000

Vibrating screens--1000020000

Briquette presses--3500050000

Rotary furnace track rollers--50000110000

Paper and printing machinery



fromtofromto

Paper machinery, wet section--110000150000

Paper machinery, dry section--150000250000

Paper machinery, refiners--80000120000

Paper machinery, calenders--80000110000

Printing machinery32000460005000075000

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Operating life

The operating life is defined as the life actually achieved by the bearing. It may differ significantly from the calculated value.

This may be due to wear or fatigue as a result of:

deviations in operating conditions misalignment between the shaft and housing insufficient or excessive operating clearance contamination insufficient lubrication excessive operating temperature oscillating bearing motion with very small angles of oscillation (false brinelling) high vibration and false brinelling very high shock loads (static overloading) prior damage during installation.

Due to the wide variety of possible installation and operating conditions, it is not possible to precisely predetermine the operating life. The most reliable way of arriving at a close estimate is by comparison with similar applications.

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Axial load carrying capacityof cylindrical roller bearings

Radial cylindrical roller bearings used as semi-locating and locating bearings can support axial forces in one or both directions in addition to radial forces.

The axial load carrying capacity is dependent on:

the size of the sliding surfaces between the ribs and the end faces of the rolling elements the sliding velocity at the ribs the lubrication on the contact surfaces the tilting of the bearing.

Ribs subjected to load must be supported across their entire height.

The permissible axial loadFaper must not be exceeded, in order to avoid unacceptably high temperatures.

The limiting load Famax must not be exceeded, in order to avoid unacceptable pressure at the contact surfaces.

The ratio Fa/Fr must not exceed a value of 0,4. For bearings of TB design, the value0,6 is permissible.

Continuous axial loading without simultaneous radial loading is not permissible.

Bearings of TB design

In the case of bearings of TB design, the axial load carrying capacity has been significantly improved through the use of new calculation and manufacturing methods.

Optimum contact conditions between the roller and rib are ensured by means of a special curvature of the roller end faces. As a result, axial surface pressures on the rib are significantly reduced and a lubricant film with improved load-carrying capabilities is achieved. Under normal operating conditions, wear and fatigue at the rib contact running and roller end faces is completely eliminated. The axial frictional torque is reduced by up to 50%. The bearing temperature during operation is therefore significantly lower.

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Permissible andmaximum axial load

Faper and Famax are calculated as follows:

Bearings of standard design

Bearings of TB design

Bearings of standard and TB design

Fa perN

Permissible axial load

Fa maxN

Axial limiting load

kS

Factor dependent on the lubrication method,see table

kB

Factor dependent on the bearing series,see table

dMmm

Mean bearing diameter (d+D)/2

nmin1

Operating speed.

Misalignment of the bearing

Misalignment caused by shaft deflection for example, may lead to alternating stresses on the inner ring ribs. In this instance, the axial load must be restricted to Fas in accordance with the formula where the bearing is tilted up to a maximum of 2angular minutes.

For more severe tilting, a separate strength analysis is required.

Factor kSfor lubrication method

Lubrication methods1) FactorkS

Minimal heat dissipation, drip feed oil lubrication, oil mist lubrication, low operating viscosity (0,51)7,5to 10

Little heat dissipation, oil sump lubrication, oil spray lubrication, low oil flow10to 15

Good heat dissipation, recirculating oil lubrication (pressure oil lubrication)12to 18

Very good heat dissipation,recirculating oil lubrication with oil cooling,high operating viscosity (21)16to 24

______

1The precondition for these kS values is the reference viscosity 1 according to the section Oil lubrication. Doped oils should be used such as CLP(DIN51517) and HLP(DIN51524) of ISO-VG classes 32 to 460 and ATF oils(DIN51502) and gearbox oils (DIN51512) of SAE viscosity classes 75W to 140W.

Bearing factorkB

SeriesFactorkB

SL1818, SL01484,5

SL1829, SL014911

SL1830, SL185017

SL182220

LSL1923, ZSL192328

SL192330

NJ2..-E, NJ22..-E, NUP2..-E, NUP22..-E15

NJ3..-E, NJ23..-E, NUP3..-E, NUP23..-E20

NJ422

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Static load carrying capacity

Very high static loads or shock loads can cause plastic deformation on the raceways and rolling elements. This deformation limits the static load carrying capacity of the rolling bearing with respect to the permissible noise level during operation of the bearing.

If a rolling bearing operates with only infrequent rotary motion or completely without rotary motion, its size is determined in accordance with the basic static load rating C0.

According to DINISO76, this is:

a constant radial load C0r for radial bearings a constant, concentrically acting axial load C0a for axial bearings.

The basic static load rating C0 is that load under which the Hertzian pressure at the most heavily loaded point between the rolling elements and raceways reaches the following values:

for roller bearings, 4000N/mm2 for ball bearings, 4200N/mm2 for self-aligning ball bearings, 4600N/mm2.

Under normal contact conditions, this load causes a permanent deformation at the contact points of approx.1/10000 of the rolling element diameter.

Static load safety factor

In addition to dimensioning on the basis of the fatigue limit life, it is advisable to check the static load safety factor. The guide values and shock loads occurring in operation to table must be taken into consideration, see table, link.

The static load safety factor S0 is the ratio between the basic static load rating C0 and the equivalent static load P0:

S0

Static load safety factor

C0 (C0r, C0a)N

Basic static load rating

P0 (P0r, P0a)N

Equivalent static load on the radial or axial bearing, see link.

Guide values for axial spherical roller bearings and high precision bearings: see corresponding product description.

For drawn cup needle roller bearings, S03 is necessary.

Guide valuesfor static load safety factor

Operating conditionsStatic load safety factorS0

for roller bearingsfor ball bearings

Smooth, low-vibration, normal operation with minimal demands for smooth running;bearings with slight rotary motion10,5

Normal operation with higher requirements for smooth running21

Operation with pronounced shock loads32

Bearing arrangement with high requirements for running accuracy and smooth running43

Equivalent static load

The equivalent static load P0 is a calculated value. It corresponds to a radial load in radial bearings and a concentric axial load in axial bearings.

P0 induces the same load at the centre point of the most heavily loaded contact point between the rolling element and raceway as the combined load occurring in practice.

P0N

Equivalent static bearing load

F0rN

Radial static bearing load

F0aN

Axial static bearing load

X0

Radial factor given in the dimension tables or product description

Y0

Axial factor given in the dimension tables or product description.

This calculation cannot be applied to radial needle roller bearings, axial needle roller bearings and axial cylindrical roller bearings. Combined loads are not permissible with these bearings.

For radial needle roller bearings and all radial cylindrical roller bearings, P0=F0r.

load carrying capacity and life

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