








Modified Rating Life
The modified rating life is calculated by considering lubrication, contaminations and fatigue limit (according to ISO 281:2007(E).
The life L_{nm} for special bearing properties and for special operating conditions is derived from the following formula for ball
bearings:
L_{nm} 
modified rating life [10^{6} revolutions] (the index n
represents the difference between the requisite reliability and 100 %)^{ } 
a_{1} 
reliability factor for a requisite reliability other than 90 % 
a_{ISO} 
life modification factor for operating conditions 
For a reliability of 90 %, equation 4 takes the following form:
Given a constant bearing rotation speed, it is very often so that the bearing life in operating hours is of particular interest.
For ball bearings:
L_{nmh} 
modified rating life [in operating hours] 
Reliability factor a_{1}
The a_{1} factor for reliability is used to determine lives other
than the L_{10m} life, i.e. lives which are attained or exceeded with a greater probability than 90 %. Values of
a_{1} are set out in the Table 3.
Table 3: Reliability factor a_{1}
Variable Bearing Loads and Variable Rotation Speeds
If the load and/or rotation speed for dynamically stressed ball bearings changes in time, this has to be considered when calculating the bearing lifetime. The bearing
lifetime is typically composed of a series of individual loads
[P_{1,2,...t}] and rotation speeds [n_{1,2,...t}] of a certain duration
[q_{1,2,...t}]. This means the bearing is loaded during Period 1 with an dynamic equivalent load P_{1}
and has a rotation speed n_{1}, and so on. For these composite operating conditions, the enhanced adjusted rating life can be calculated
as follows:
L_{10m1}, L_{10m2}, L_{10m3} ..... can be calculated for ball bearings using Formula 5.
n_{1,2,...t} 
rotational speed for a particular operation condition [rpm] 
n_{m} 
mean rotation speed [rpm] 
q_{1,2,...t} 
duration of a particular operation condition (as a ratio relative to the full period in percent) 
D_{PW} 
pitch diameter [mm]; 
d 
bearing bore diameter taken from our product tables 
D 
bearing bore diameter taken from our product tables 
Life Modification Factor a_{ISO}
Among other things, the life adjustment factor a_{ISO} considers the influence of:
 fatigue limit of the bearing components’ material by the fatigue load limit C_{u}
 grade of contaminations by the factor e_{c} and
 lubrication conditions by the viscosity ratio
Fatigue Load Limit C_{u}
The stress of the raceway fatigue depends primarily on the internal stress distribution at the highly loaded rolling contact point of the bearing. In order to simplify
the calculation, the fatigue load limit C_{u} was introduced. The fatigue load limit is defined as the load below which no material
fatigue will occur under laboratory conditions.
This factor takes into consideration:
 bearing type, size and internal geometry
 profile of balls and raceways
 manufacturing quality of the bearing
 fatigue limit load of the bearing raceway material
The fatigue load limit C_{u} for single and double row deep groove ball bearings as well as
single and double row angular contact ball bearings, are listed in the product tables
for all our bearing types.
Lubricant Contamination Factor e_{c}
The factor e_{c} considers the influence of contaminants, e.g. solid particles in the lubrication gaps, on the rating life. The lifetime
reduction caused by solid particles depends on their size in comparison to the lubricant film, their hardness and quantity.
Table 4: Lubricant contamination factor e_{c}
More detailed information about the contamination factor e_{c} depending on
and the bearing size is available in ISO 281:2007(E).
Figure 1: Variation of lubricant viscosity as a function of temperature for various mineral oils
Figure 2: Reference viscosity
Viscosity Ratio
The viscosity ratio acts as an indicator for the quality of the
lubricant film. is the ratio of lubricant viscosity
at operating temperature in relation to the reference viscosity
and it can be calculated using the following equation:

viscosity ratio 

kinematic viscosity of lubricant at operating temperature taken from Figure 1 for different mineral
oils [mm^{2}/s] 

reference viscosity [mm^{2}/s] 
The base oil viscosity is relevant for greases. Depending on rotation speed n and pitch diameter D_{PW}
of the ball bearing, the reference viscosity can set off Figure 2.
Life Modification Factor a_{ISO}
As a function of the life modification factor a_{ISO}
for ball bearings can be read from the Figure 3.
Figure 3: Life modification factor a_{ISO} for radial ball bearings according to ISO 281:2007(E)
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