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:

n_{i} | = | number of cycles at the i^{th} stress level. |

N_{i} | = | number of cycles to failure correspontiing to the i^{th} stress level. |

n_{i}∕N_{i} | = | damage ratio at the i^{th} stress level. |

Instead of load cycles we can alo use lifetimes:

where:

l_{i} | = | time at a the i^{th} stress level. |

L_{i} | = | permissible lifetime at the i^{th} stress level. |

l_{i}∕L_{i} | = | damage ratio at the i^{th} stress level. |

Assuming the fraction of time at each stress level is known rather than the actual number of cycles or times, then:

where:

α_{i} | = | fraction of time at the i^{th} 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, α_{i}, and the load ratio, β_{i} and
additionally a speed ratio ω_{i} is needed for the calculation of the permissible
lifetimes L_{i}.

where:

β_{i} | = | instantaneous load/baseline load |

ω_{i} | = | 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: