Calculating life with variable operating conditions

In some applications, like industrial gearboxes, the operating conditions, such as the magnitude and direction of loads, speeds, temperatures and lubrication conditions are continually changing. In these types of applications, bearing life cannot be calculated without first reducing the load spectrum or duty cycle of the application to a limited number of simplified load cases (diagram 1).
In case of continuously changing loads, each different load level can be accumulated and the load spectrum reduced to a histogram of constant load blocks. Each block should characterize a given percentage or time-fraction during operation. Heavy and normal loads consume bearing life at a faster rate than light 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, the bearing load and operating conditions can be averaged to some constant value. The number of operating hours or revolutions expected from each duty interval showing the life fraction required by that particular load condition should also be included. Therefore, if N1 equals the number of revolutions required under the load condition P1, and N is the expected number of revolutions for the completion of all variable loading cycles, then the cycle fraction U1 = N1/N is used by the load condition P1, which has a calculated life of L10m1. Under variable operating conditions, bearing life can be rated using the equation:

Bearing life

where
L10m=SKF rating life (at 90% reliability) [million revolutions]
L10m1, L10m2, ...=fraction SKF rating lives (at 90% reliability) under constant conditions 1, 2, ... [million revolutions]
U1, U2, ...=life cycle fraction under the conditions 1, 2, ...
U1 + U2 + ... Un = 1
The use of this calculation method depends very much on the availability of representative load diagrams for the application. This type of load history can also be derived from a similar type of application.
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