What is Miner's Rule?

Author: Frank C Uherek

Category: Gear

Article Tags:

cumulative damage

Cumulative damage model

inverse power law

inverse power law model

linear damage accumulation model

miner’s rule

SN-Curve

The power capacity of a Gear Drive is an important factor in ensuring successful operation of driven equipment with minimum downtime. Making sure that the unit is correct for the application can be difficult when presented with the options from various manufacturers, especially if the specifications are unknown. However, if the amount of load and its time duration are known for an application, a cumulative fatigue analysis such as Miner’s rule can be used to precisely determine the life of a gear drive.

Coined by M.A. Miner in 1945, Miners Rule is one of the most commonly used cumulative damage equations for failures caused by fatigue. As seen in the equation, Miner's Rule states that there are p different stress levels and the number of cycles to failure at the ith stress, Si, is Nfi. The number of cycles at stress Si, is ni. The ratio of n to N is the damage fraction, the amount of life that is used up by stress Si. When the sum of damage fractions are greater than 1.0, failure is said to occur.

Miner's rule assumes that the damage done by each stress repetition at a given stress level is equal, meaning the first stress cycle at a uniform stress level is as damaging as the last. Miner's rule operates on the hypothesis that the portion of useful fatigue life used up by a number of repeated stress cycles at a particular stress is proportional to the total number of cycles in the fatigue life, if that were the only stress level applied to the part. For example, if a part is stressed for 3,000 cycles at a stress level which would cause failure in 100,000 cycles, 3 percent of the fatigue life would be expended. Repeated stress at another stress level would consume another similarly calculated portion of the fatigue life. When 100 percent of the fatigue life is expended in this manner, the part could be expected to fail. The order in which each of these individual stress cycles is applied is not considered significant in Miner's analysis. The above graph illustrates a complete load spectrum made up of bins of a given stress magnitude for a fixed number of cycles.

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Frank C Uherek

Frank has been a Principal Engineer for the Rexnord Gear Group for over 10 years. Before his tenure at Rexnord, he spent time at Regal Beloit, Flender Corporation and Winergy Drive Systems Corporation. In addition to his responsibilities at Rexnord, Frank is an active committee chair on both AGMA and ISO rating committees. Frank holds a Bachelor of Science in Mechanical Engineering and a Masters of Business Administration in Production and Accounting from the Illinois Institute of Technology.