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Palgmer - Miner equation derivation 5

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namelessudhay

Mechanical
May 24, 2010
20
Palgmer-Miner equation is used in ISO standard ISO 6336-6. I want to understand how it is derived. It 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:

Equivalent_torque_from_ISO_standard_ihq29c.png


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:

SN_curve_fundamental_equation_nmhz99.png


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