# Life calculation with variable operating conditions

In applications where bearing load varies over time both in magnitude and direction with changes of speed, temperature, lubrication conditions and level of contamination, the bearing life cannot be calculated directly without the need of the intermediate calculation step of an equivalent load related to the variable load conditions. Given the complexity of the system, however, this intermediate parameter would not be easy to determine and would not simplify the calculation.
Therefore, in the case of fluctuating operating conditions it is necessary to reduce the load spectrum or duty cycle of the application to a limited number of simpler load cases (diagram 1). In case of continuously variable load, each different load level can be accumulated and the load spectrum reduced to a histogram of constant load blocks, each characterizing a given percentage or time-fraction of the operation of the application. Note that heavy and medium loads consume bearing life at a faster rate than lighter loads. Therefore it is important to have shock and peak loads well represented in the load diagram even if the occurrence of these loads is relatively rare and limited to a few revolutions.
Within each duty interval or "bin", the bearing load and operating conditions can be averaged to some constant value. Furthermore the number of operating hours or revolutions expected from each duty interval shows the life fraction required by that particular load condition. Thus for instance denoting with N1 the number of revolutions required under the load condition P1, and with N the total life cycle of the application, then life cycle fraction U1 = N1/N will be used by the load condition P1, which has a calculated life of L10m1. Under variable operating conditions bearing life can be predicted using the equation:

where

 L10m = SKF rating life (at 90% reliability) [millions of revolutions] L10m1, L10m2, ... = fraction SKF rating lives (at 90% reliability) under constant conditions 1, 2,... [millions of revolutions] U1, U2, ... = life cycle fraction under the conditions 1, 2,... Note: U1+ U2 +...... Un=1
The use of this calculation method is very much dependent on the availability of representative load diagrams for the application. Note that such load history can also be derived from typical operating conditions or standard duty cycles required from that type of application.
For calculation of the bearing life considering a load cycle, see the program SKF Bearing Select.