Answer
Bending Stress = 9.34 kpsi
Work Step by Step
Pitch Diameter, $d=N/P$ = 18/10 = 1.8 inches
where, N = number of teeth
P = diametral pitch
Lewis form factor, $Y=0.309$ ; for 18 teeth with 20degree pressure angle
Pitch line velocity, $V=(pi ∗ d ∗ n)/12$ ; where; n = speed in rpm
therefore V = ( 3.14 * 1.8 * 600 )/12 = 282.7 ft/min
Velocity Factor, $K=(1200+V)/1200$ ; for cut or milled profile
therefore K = (1200+282.7)/1200 = 1.236
Tangential load, $W=(33000∗hp)/V$ ; where hp is horse power
therefore W = (33000 * 2 )/ 282.7 = 233.5 lbf
$BendingStress=(K∗W∗P)/(F∗Y)$ ; where F is facewidth
Bending Stress = ( 1.236 * 233.5 * 10 ) / ( 1* 0.309 ) = 9340 psi
Bending Stress = 9.34 kpsi
