Involute Splines Factor

[umatrix]

Hello Eng-Tips,
The Machinery's Handbook 27th edition on P. 2173 gives the equation for calculating the shear stress at the pitch diameter of teeth.

Which is given as :
Ss=(4*T*Ka*Km)/(DN*Le*t*Kf)
where T= torque, nmm
Ka= spline application factor
Km= spline misaligment factor
D= pitch dia, mm
Le= effective spline length, mm
t= actual tooth thickness, mm
Kf= fatigue factor.

The factor of 4 assumes that only 1/2 of the teeth will carry the load. I am confused how to arive at the value of 4.
a search on the subject points to SAE, but I could not find the original source deravation. Anyone help me clarify ?

 

[chez311]

jmatrix,

Since nobody else has answered I'll take a stab at it.

The same equation can be expressed in the below form - with Ks as an additional "tooth factor". If only half the teeth are assumed to take the load as in the Machinery's Handbook equation, then this factor is 0.5 and the shear stress will be twice as much and the original factor of 2 is effectively doubled - and the equation is in the same form as the one you have shown.