Question 14.1: A stock spur gear is available having a diametral pitch of 8...

The term moderate applications seems to imply that the gear can be rated by using the yield strength as a criterion of failure. From Table A–20, we find S_{ut} = 55 kpsi and S_{y} = 30 kpsi. A design factor of 3 means that the allowable bending stress is 30/3 = 10 kpsi. The pitch diameter is N/P = 16/8 = 2 in, so the pitch-line velocity is

V =\frac{πdn}{12} =\frac{π(2)1200}{12} = 628  ft/min

The velocity factor from Eq. (14–4b) is found to be

K_{v} =\frac{1200 + V}{1200}    (cut or milled profile)               (14–4b)

K_{v} =\frac{1200 + V}{1200}=\frac{1200 + 628}{1200} = 1.52

Table 14–2 gives the form factor as Y = 0.296 for 16 teeth. We now arrange and substitute in Eq. (14–7) as follows:

σ =\frac{K_{v}W^{t} P}{FY}                        (14–7)

W^{t} =\frac{FYσ_{all}}{K_{v} P} =\frac{1.5(0.296)10 000}{1.52(8)} = 365  lbf

Table 14–2
Values of the Lewis Form Factor Y (These Values Are for a Normal Pressure Angle of 20°, Full-Depth Teeth, and a Diametral Pitch of Unity
in the Plane of Rotation)

The horsepower that can be transmitted is

hp =\frac{W^{t}V}{33 000} =\frac{365(628)}{33 000} = 6.95  hp

It is important to emphasize that this is a rough estimate, and that this approach must not be used for important applications. The example is intended to help you understand some of the fundamentals that will be involved in the AGMA approach.