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Originally Posted by Matt Adams
Using this number, and the standard AGMA gear equation
Lewis Form Factor (Y) for a 14.5 degree PA gear = 0.223
Radius = 13/20 / 2 inches = 0.325 inches
Force on Tooth (Wt) = 53.25 / .325 = 163.85 lbs.
Face Width (F) = .375
Pitch (P) = 20
Matt
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The Lewis form factors are very very conservative for an intermittent duty or short life application (such as a FIRST robot). I have designed many production actuators for automotive applications (power liftgate actuators, power sliding door actuators, power lock/unlock actuators, power cinching latches, power cinching strikers, power unlatch actuators, power window actuators, etc.) I have never had a case where the Lewis forumulas gave me useful data.
I have had good success approximating a gear tooth as a uniform beam with its cross section equal to the cross section of the base of the tooth and its length equal to the height of the tooth with a load applied at the end of the beam.
Pcircular = 2 Pi/P = .31"
Circular Tooth Thickness = Pcircular/2 = .16
Tooth Height = 2.25/P = .11
This can be approximated as a beam
L = .11 in
H = Circ Tooth Thickness = .16 in (this is conservative but a first order approx)
T = .375 in
F = 164 lbsf
I = (1/12) T * H^3 = (1/12) * (.375) * (.16)^3 = .000128 in^4
c = H/2 = .08
Going to the efunda.com site I linked to above, I get the
Stress = 11,000 psi
Unless your gear is plastic, I don't think you have to worry about 11,000psi stress levels.
Joe J.