# Thread: Shear stress on spline teeth

1. ## Shear stress on spline teeth

Hi, I'm checking the shear stress on B100x94 (DIN 5482) spline teeth and am a little confused now after attempting to cross check my results.

When using the method described in "When splines need Stress control", I get a Shear stress of 216MPa (note: this calc assumes 50% tooth engagement)

splines.pdf

but when I use the calc found on this site I get, I get roughly 191MPa, with only 25% tooth engagement and a much shorter spline length.
https://www.engineersedge.com/gears/...ear-design.htm

Can somebody share the referenced pages of "Machine Design: Theory & practice", or perhaps explain how this calc works? I found an excel version of it and I still don't understand it. The formula in the excel spreadsheet I found is 16*\$Torque/(PI()*DiametralPitch^2*EffectiveLength)

My input data is:
No teeth: 44
PCD: 99mm (3.89 in)
Torque: 32143Nm (284489.5 lbf.in)
tooth thickness: 2.008mm (0.079055 in)
Spline length: 68mm (2.677 in)
Km factor: 1

Any help would be greatly appreciated   Reply With Quote

2. Originally Posted by maksimb_93 When using the method described in "When splines need Stress control", I get a Shear stress of 216MPa (note: this calc assumes 50% tooth engagement)
I don't think the EE calculator assumes 50% engagement but full.  Reply With Quote

3. Originally Posted by Kelly Bramble I don't think the EE calculator assumes 50% engagement but full.
At the bottom under the "Shear Stress" result it says "*Shear stress and spline length are calculated based on the assumption that only 25% of the teeth make contact at any given moment." *Shear stress and spline length are calculated based on the assumption that only 25% of the teeth make contact at any given moment.  Reply With Quote

4. Well for anyone thats interested, I found the textbook in a library and I believe the EE calc I linked is wrong.
Below is a basic explanation from the book.

So first, we know allowable torque that can be transmitted through a shaft is (T) = (pi * RootDia^3 * ShearAllow)/16

Next, Shear area of the teeth at the PCD is A = pi*PCD*Length/2 (this is wrong as it assumes male and female teeth are the same width).

The force acting on the teeth at the PCD is F = T/(PCD/2)

Stress = F/A and when you sub all that in get ShearStress = 4*T/(pi*PCD^2*L)

If we decide that Shear stress at the PCD is to be equal to the torsional stress of the shaft, we can combine the last formula with the first torque one and get the spline length required to transmit the torque;

L = (RootDia^3)/(4*PCD^2)

then it says "actual practice has shown that due to inaccuracies in spacing and tooth form, the equivalent of about 25% of teeth are in contact"

Therefore Le (Effective Length) = 4*L

Le = RootDia^3/PCD^2

Hope this helps someone in future.  Reply With Quote

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