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Calculate the Torque capacity of a spline

Calculate the Torque capacity of a spline

Calculate the Torque capacity of a spline

I need to calculate the torque capacity of an involute spline where the internal and external spline are shrink fitted together. Referencing the Machinery's Handbook (25th Ed) the major diameter of the external spline cannot exceed Ø25". I was using three formulas:
Shear stress under roots of external spline (equation 1 for a solid shaft) pg 2058, Shear stress at the pitch diameter of teeth (equation 3)pg 2059, and Compressive stresses on sides of spline teeth (equation 5 for fixed spline) pg 2059. The trouble I am having is determining the maximum effective length (Le) of the fixed spline with a pitch diameter of Ø24.833" (6/12 pitch 149 teeth - is one idea that gave me that diameter). I am using allowable shear stress of 40,000 psi shear, and 3,000 psi compressive for straight sided teeth - not crowned (no hardening). I need the splines to handle 2850 kNm (~25,224,632 lbin). If I can determine the Le, I think I can get a handle on this. Another thing, the handbook mentions fixed splines with helix modifications and without helix modification...what does that mean? Which do I use?

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