A stock spur gear is available having a diametral pitch of 8 teeth/in, a 1 1/2-in face, 16 teeth, and a pressure angle of 20° with full-depth teeth. The material is AISI 1020 steel in as-rolled condition. Use a design factor of nd = 3 to rate the horsepower output of the gear corresponding

Question

A stock spur gear is available having a diametral pitch of 8 teeth/in, a [latex]1 \frac{1}{2}[/latex]-in face, 16 teeth, and a pressure angle of 20° with full-depth teeth. The material is AISI 1020 steel in as-rolled condition. Use a design factor of [latex]n_{d}=3[/latex] to rate the horsepower output of the gear corresponding to a speed of 1200 rev/m and moderate applications.

Accepted Answer

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 [latex]S_{u t}=55[/latex] kpsi and [latex]S_{y}=30[/latex] kpsi. A design factor of 3 means that the allowable bending stress is [latex]30 / 3=[/latex] 10 kpsi. The pitch diameter is [latex]d=N / P=16 / 8=2[/latex] in, so the pitch-line velocity is

[latex]V=\frac{\pi d n}{12}=\frac{\pi(2) 1200}{12}=628 ft / min[/latex]

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

[latex]K_{v}=\frac{1200+V}{1200} \quad ext { (cut or milled profile) }[/latex] (14–4b)

[latex]K_{v}=\frac{1200+V}{1200}=\frac{1200+628}{1200}=1.52[/latex]

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:

[latex]\sigma=\frac{K_{v} W^{t} P}{F Y}[/latex] (14–7)

[latex]W^{t}=\frac{F Y \sigma_{ all }}{K_{v} P}=\frac{1.5(0.296) 10000}{1.52(8)}=365 lbf[/latex]

The horsepower that can be transmitted is

[latex]h p=\frac{W^{t} V}{33000}=\frac{365(628)}{33000}=6.95 hp[/latex]

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.

Question 14–1: A stock spur gear is available having a diametral pitch of 8...

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