Answer
Bending Stress, Sigma = 7.63 kpsi
Work Step by Step
Pitch Diameter, $d = N/P$ = 22/6 = 3.667 inches
where, N = number of teeth
P = diametral pitch
Lewis form factor, $Y = 0.331$ ; for 22 teeth with 20degree pressure
angle
Pitch line velocity, $V = ( pi * d * n)/12$ ; where; n = speed in rpm
therefore V = ( 3.14 * 3.667 * 1200 )/12 = 1152 ft/min
Velocity Factor, $K = (1200+V)/1200$ ; for cut or milled profile
therefore K = (1200+1152)/1200 = 1.96
Tangential laod, $W = (33000 * hp)/V$ ; where hp is horse power
therefore W = (33000 * 15 )/ 1152 = 429.7 lbf
$Bending Stress = ( K * W * P ) / ( F * Y )$ ; where F is facewidth
Bending Stress = ( 1.96 * 429.7 * 6 ) / ( 2* 0.331 ) = 7633 psi
Bending Stress = 7.63 kpsi
