Designing Coaxial Output Shafts: Fatigue Analysis

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Part of my design project requires that I design two coaxial output shafts. I've gone through and calculated the inner shaft based on deflection and Goodman fatigue criterion. The problem now is this: the other output shaft must be a hollow shaft that shares its axis with the interior shaft. All of the fatigue analysis I've done to estimate shaft sizing thus far is based on solid shaft design where solid dimension 'd' is the parameter being solved for. I can determine an approximate sizing based on bearing deflections but that's it for now. Any suggestions?

Thanks,
 
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There's not a whole lot of difference between the two cases. You have a cross sectional moment of inertia that drives your stresses in either case.

Have you had the opportunity to take a look at ASME B106.1M, Design of Transmission Shafting? In it there is a specified approach that uses past testing to provide an approach that takes into account both alternating bending moments and torsional moments.
 
I think I am going to chase down the derivation of the goodman equation and find where they insert the diameter cross section and then plug in my hollow shaft cross sectional area and find it that way. thanks