# FAG bearing calculator

Schaeffler Group introduced the "Expanded calculation of the adjusted rating life" in 1997. This method was standardised for the first time in DIN ISO 281 Appendix 1 and has been a constituent part of the international standard ISO 281 since 2007.

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 FAG 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 for fatigue in rolling contact that expands on the Lundberg and 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 fatigue limit of the material
• the extent to which the surfaces are separated by the lubricant
• the cleanliness in the lubrication gap
• the internal load distribution and frictional conditions in the bearing.

## Calculating dimensioning of FAG rolling bearings

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

• rating life
• operational reliability.

## Dynamic load carrying capacity and life calculator

The dynamic load carrying capacity is described in terms of the basic dynamic load ratings. The basic dynamic load ratings are based on DIN ISO 281.

The term dynamic indicates that the operating condition is with the bearing rotating. This is not a variable 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 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, concentrically acting axial load Ca for axial bearings.

## The rating life of FAG bearing calculator

### Basic rating life

Rating life in revolutions

Rating life in operating hours

 L10 106 The basic rating life in millions of revolutions, that is reached or exceeded by 90% of a sufficiently large number of apparently identical bearings before the first indications of material fatigue appear L10h h The basic rating life in operating hours, that is reached or exceeded by 90% of a sufficiently large number of apparently identical bearings before the first indications of material fatigue appear C N Basic dynamic load rating, see FAG bearing size chart P N Equivalent dynamic bearing load p Life exponent; for roller bearings: p = 10/3 for ball bearings: p = 3 n min-1 Operating speed (nominal speed).

The equivalent dynamic load P on a FAG bearing subjected to combined load (with a radial and axial load) is calculated in accordance with

The calculation in accordance 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.

Lna = a1 * a2 * a3 * L10

 Lna 106 Adjusted rating life for special material characteristics and operating conditions with a requisite reliability of (100 – n) % L10 106 Basic rating life a1 Life adjustment factor for a requisite reliability other than 90%. In ISO 281:2007, the values for the life adjustment factor a1 have been redefined a2 Life adjustment factor for special material characteristics. For standard FAG rolling bearing steels: a2 = 1 a3 Life adjustment factor for special operating conditions; in particular lubrication, Figure below.

1, Good cleanliness and suitable additives
2, Very high cleanliness and low load
3, Contamination in the lubricant
k = viscosity ratio

Lnm = a1 * aISO * L10

 Lnm 106 Expanded adjusted rating life to ISO 281 L10 106 Basic rating life a1 Life adjustment factor for a requisite reliability other than 90%. In ISO 281:2007, the values for the life adjustment factor a1 have been redefined aISO Life adjustment factor for operating conditions

rating life
% Lnm a1
90 L10m 1
95 L5m 0,64
96 L4m 0,55
97 L3m 0,47
98 L2m 0,37
99 L1m 0,25
99,2 L0,8m 0,22
99,4 L0,6m 0,19
99,6 L0,4m 0,16
99,8 L0,2m 0,12
99,9 L0,1m 0,093
99,92 L0,08m 0,087
99,94 L0,06m 0,08
99,95 L0,05m 0,077

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 of the lubricant

 aISO Life adjustment factor for operating conditions ec Life adjustment factor for contamination Cu N Fatigue limit load P N Equivalent dynamic bearing load k Viscosity ratio

Guide values for the contamination ec

Contamination Contamination factor eC
dM ＜ 100 mm dM ≧ 100 mm
from to from to
Very high cleanliness:
• Particle size within the order of magnitude
of the lubricant filmthickness
• Laboratory conditions.
1 1
High cleanliness:
• Oil filtered through extremely fine filter
• Sealed, greased bearings.
0,8 0,6 0,9 0,8
Standard cleanliness:
• Oil filtered through fine filter.
0,6 0,5 0,8 0,6
Slight contamination:
• Slight contamination of oil.
0,5 0,3 0,6 0,4
Typical contamination:
• Bearing contaminated by wear debris
from other machine elements.
0,3 0,1 0,4 0,2
Heavy contamination:
• Bearing environment is heavily contaminated
0,1 0 0,1 0
Very heavy contamination 0 0

## Guide values for dimensioning

The values for the recommended rating life are guide values for normal operating conditions. In addition, the tables give the operating life values that are usually achieved in practice at various mounting locations.

Motor vehicles

Mounting location Recommended rating life
h
Ball bearings Roller bearings
from to from to
Motorcycles 400 2 000 400 2 400
Passenger car powertrains 500 1 100 500 1 200
Passenger car gearboxes protected against contamination 200 500 200 500
Passenger car wheel bearings 1 400 5 300 1 500 7 000
Light commercial vehicles 2 000 4 000 2 400 5 000
Medium commercial vehicles 2 900 5 300 3 600 7 000
Heavy commercial vehicles 4 000 8 800 5 000 12 000
Buses 2 900 11 000 3 600 16 000
Internal combustion engines 900 4 000 900 5 000

Rail vehicles

Mounting location Operating life
Millions of kilometres
from to
Wheelset bearings for freight wagons 0,1 0,1
Urban transport vehicles 1 2
Passenger carriages 2 3
Goods wagons 1 2
Tipper wagons 1 2
Powered units 2 3
Locomotives, external bearings 2 4
Locomotives, internal bearings 2 4
Shunting and industrial locomotives 0,5 1
Gearboxes for rail vehicles 0,5 2

Shipbuilding

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Marine thrust bearings - - 20 000 50 000 30 000 80 000
Marine shaft bearings - - 50 000 200 000 30 000 80 000
Large marine gearboxes 14 000 46 000 20 000 75 000 30 000 80 000
Small marine gearboxes 4 000 14 000 5 000 20 000 5 000 20 000
Boat propulsion systems 1 700 7 800 2 000 10 000 2 000 10 000

Agricultural machinery

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Tractors 1 700 4 000 2 000 5 000 5 000 10 000
Self-propelled machinery 1 700 4 000 2 000 5 000 2 000 6 000
Seasonal machinery 500 1 700 500 2 000 500 2 000

Construction machinery

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Dozers, loaders 4 000 7 800 5 000 10 000 5 000 10 000
Excavators,
travelling gear
500 1 700 500 2 000 500 2 000
Excavators, slewing gear 1 700 4 000 2 000 5 000 2 000 5 000
Vibratory road rollers, unbalance generators 1 700 4 000 2 000 5 000 5 000 30 000
Vibrator bodies 500 1 700 500 2 000 500 2 000

Electric motors

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Electric motors
for household appliances
1 700 4 000 - - 500 1000
Series motors 21 000 32 000 35 000 50 000 20 000 30 000
Large motors 32 000 63 000 50 000 110 000 40 000 50 000
Wind energy generators - - - - 100 000 200 000
Generators - - - - 40 000 50 000

Rolling mills, steelworks equipment

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Rolling mill frames 500 14 000 500 20 000 2 000 10 000
Rolling mill gearboxes 14 000 32 000 20 000 50 000 20 000 40 000
Roller tables 7 800 21 000 10 000 35 000 20 000 40 000
Centrifugal casting machines 21 000 46 000 35 000 75 000 30 000 60 000

Machine tools

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Headstock spindles, milling spindles 14 000 46 000 20 000 75 000 10 000 30 000
Drilling spindles 14 000 32 000 20 000 50 000 1 000 20 000
External grinding spindles 7 800 21 000 10 000 35 000 10 000 20 000
Hole grinding spindles - 500 2 000
Workpiece spindles
in grinding machines
21 000 63 000 35 000 110 000 20 000 30 000
Machine tool gearboxes 14 000 32 000 20 000 50 000 10 000 20 000
Presses, flywheels 21 000 32 000 35 000 50 000 20 000 30 000
Presses, eccentric shafts 14 000 21 000 20 000 35 000 10 000 20 000
Electric tools and compressed air tools 4 000 14 000 5 000 20 000 100 200

Woodworking machinery

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Milling spindles and cutter blocks 14 000 32 000 20 000 50 000 10 000 20 000
Saw frames,
main bearings
- - 35 000 50 000 -
Saw frames,
connecting rod bearings
- - 10 000 20 000 -
Circular saws 4 000 14 000 5 000 20 000 10 000 20 000

Gearboxes in general machine building

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Universal gearboxes 4 000 14 000 5 000 20 000 5 000 20 000
Geared motors 4 000 14 000 5 000 20 000 5 000 20 000
Large gearboxes, stationary 14 000 46 000 20 000 75 000 20 000 80 000

Conveying equipment

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Belt drives, mining - - 75 000 150 000 10 000 30 000
Conveyor belt rollers, mining 46 000 63 000 75 000 110 000 10 000 30 000
Conveyor belt rollers, general 7 800 21 000 10 000 35 000 10 000 30 000
Belt drums - - 50 000 75 000 10 000 30 000
Bucket wheel excavators, travel drive 7 800 21 000 10 000 35 000 5 000 15 000
Bucket wheel excavators, bucket wheel - - 75 000 200 000 30 000 50 000
Bucket wheel excavators, bucket wheel drive 46 000 83 000 75 000 150 000 30 000 50 000
Winding cable sheaves 32 000 46 000 50 000 75 000 50 000 80 000
Sheaves 7 800 21 000 10 000 35 000 8 000 30 000
Tunnel-boring machines: drill head main bearings - - - - 5 000 10 000

Pumps, fans, compressors

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Ventilators, fans 21 000 46 000 35 000 75 000 20 000 100 000
Large fans 32 000 63 000 50 000 110 000 10 000 -
Piston pumps 21 000 46 000 35 000 75 000 20 000 50 000
Centrifugal pumps 14 000 46 000 20 000 75 000 20 000 50 000
Hydraulic axial and
500 7 800 500 10 000 1 000 20 000
Gear pumps 500 7 800 500 10 000 1 000 20 000
Compressors 4 000 21 000 5 000 35 000 30 000 80 000

Centrifuges, stirrers

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Centrifuges 7 800 14 000 10 000 20 000 40 000 60 000
Large stirrers 21 000 32 000 35 000 50 000 40 000 50 000

Textile machinery

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Spinning machines, spinning spindles 21 000 46 000 35 000 75 000 10 000 50 000
Weaving and
knitting machines
14 000 32 000 20 000 50 000

Plastics processing

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Plastics worm extruders 14 000 21 000 20 000 35 000 20 000 100 000
Rubber and
plastics calenders
21 000 46 000 35 000 75 000

Crushers, mills, screens

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Jaw crushers - - 20 000 35 000 25 000 40 000
Gyratory crushers,
roll crushers
- - 20 000 35 000
Rigid hammer mills, hammer mills,
impact crushers
50 000 110 000 40 000 40 000
Tube mills - - 50 000 100 000 100 000 100 000
Vibration grinding mills - - 5 000 20 000 30 000 60 000
Grinding track mills - - 50 000 110 000 60 000 100 000
Vibrating screens - - 10 000 20 000 10 000 30 000
Briquette presses - - 35 000 50 000 40 000 40 000
support rollers
- - 50 000 110 000 100 000 -
Roller presses - - - - 40 000 40 000

Paper and printing machinery

Mounting location Recommended rating life Operating life
h h
Ball bearings Roller bearings
from to from to from to
Paper machinery,
wet section
- - 110 000 150 000 50 000 100 000
Paper machinery,
dry section
- - 150 000 250 000 -
Guide rolls 50 000 120 000
Dryer rolls 50 000 150 000
M.G. cylinders 50 000 200 000
Paper machinery,
refiners
- - 80 000 120 000 50 000 100 000
Paper machinery, calenders - - 80 000 110 000 50 000 100 000
Printing machinery 32 000 46 000 50 000 75 000 30 000 60 000

## Static load carrying capacity calculator

If high, static or shock loads occur, the raceways and rolling elements may undergo plastic deformation. This deformation limits the static load carrying capacity of the FAG 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.

In accordance with DIN ISO 76, this is:

• 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, 4 000 N/mm2
• for ball bearings, 4 200 N/mm2
• for self-aligning ball bearings, 4 600 N/mm2.

Under normal contact conditions, this load causes a permanent deformation at the contact points of approx. 1/10 000 of the rolling element diameter.

S0 = C0 / P0

Static load safety factor S0 for ball and roller beraings

Operating conditions and application Static load safety factor
S0
min.
Ball bearings Roller bearings
Low-noise, smooth running, free from vibrations, high rotational accuracy 2 3
Normal, smooth running, free from vibrations, normal rotational accuracy 1 1,5