Thread: Gear Woes
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Unread 17-01-2002, 22:10
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This is a big topic...

I found a lecture online that is not too bad:

Beam Stress Lecture with example problems



The bottom line is that you need to use the formula

S = Mc/I

S=stress
M is moment on the section of the beam in our case the height of the tooth times the stall torque of the motor (with a safety factor if you want -- I calculate the stress first and put in the safety factor afterwards)
c is 1/2 the thickness of the tooth at its weakest point near the base
I is the standard I (moment of inertia) for a rectangular cross section 1/12 b h^3 where b = width and h is the height (in our case the thickness of the tooth).

Solving you get:

Stress = 6 * Ftooth * ToothHeight / (ToothFaceWidth * ToothThicknessMin ^ 2)

Look on a table to see what material you are using and what stress it can take. I would not go above 30,000psi for unheated steel if I an help it (this is where I have my safety factor).

You can either assume your max stress and calculate your required facewidth or you can assume your facewidth and calculate your stress.

This is a very crude approximation but it is good enough for most of what I do in my daily job.

That is about as simple as I have time for right now.

Good luck.

Joe J.