The Palmgren-Miner Linear-cumulative-fatigue-damage-theory (Miner’s Rule) is used to calculate the resultant pitting or bending fatigue lives for gears that are subjected to loads which are not of constant magnitude but vary over a wide range. According to Miner’s Rule, failure occurs when:
where:
| ni | = | number of cycles at the ith stress level. |
| Ni | = | number of cycles to failure correspontiing to the ith stress level. |
| ni∕Ni | = | damage ratio at the ith stress level. |
Instead of load cycles we can alo use lifetimes:
where:
| li | = | time at a the ith stress level. |
| Li | = | permissible lifetime at the ith stress level. |
| li∕Li | = | damage ratio at the ith stress level. |
Assuming the fraction of time at each stress level is known rather than the actual number of cycles or times, then:
where:
| αi | = | fraction of time at the ith stress level. |
| L | = | Resultant number of cycles to failure under the applied load spectrum. |
Defining the time ratio as:
Miner’s Rule may be rewritten as:
Which may be solved for the resultant life:
The load spectrum is defined by the time ratio, αi, and the load ratio, βi and additionally a speed ratio ωi is needed for the calculation of the permissible lifetimes Li.
where:
| βi | = | instantaneous load/baseline load |
| ωi | = | instantaneous speed/nominal load |
The baseline load is entered with the Load Data input screen by specifying the transmitted horsepower and speed of the pinion. The load spectrum is entered on the page Lifetime: