Palmgren-Miner equation derivation

k.udhay · Nov 14, 2019

Summary: This equation is used in ISO standard ISO 6336-6. I want to understand how it is derived.

This equation helps to consolidate damage caused by multiple torque, cycle bins. A bin means a torque applied for a given number of cycle. As an outcome of the equation, a single equivalent torque that produces the total damage caused by multiple bins for the total number of cycles as original bins.

The equation is:

Equation (A.2) for equivalent torque: Teq = ( (n1 T1^p + n2 T2^p + ....) / (n1 + n2 + ....) )^(1/p), with definitions: ni is cycles for bin i, Ti is torque for bin i, p is the slope of the Woehler-damage line.

Pl. note that coordinates n1,T1; n2,T2 and n3,T3 do not need to be on the same line.

My objective is to derive the above equation. While I attempted to do that, I could progress to this level:

Handwritten-style typed derivation: straight line slope formula, log form, and steps to T_j^p × n_j = T_i^p × n_i, beside a log-log plot of torque T against cycles n with points j and i marked and slope m = -1/p.

Can someone help to proceed further to reach until the equivalent torque formula given in the ISO standard? Many thanks in advance!

pbuk · Nov 29, 2019

Hi, I was about to answer this and suggest it would be better in the Engineering topic here (as this is all about engineering approximation rather than scientific derivation), but while searching for refs I realized that you have posted this on another forum where it has been answered: https://www.eng-tips.com/viewthread.cfm?qid=460402

berkeman · Nov 29, 2019

(and thread title corrected: "Palgmer-Miner" --> "Palmgren-Miner")

https://en.wikipedia.org/wiki/Fatigue_(material)#Miner's_rule

Palmgren-Miner equation derivation

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