In a set of spur gears, a 300-Brinell 18-tooth 16-pitch 20° full-depth pinion meshes with a 64-tooth gear. Both gear and pinion are of grade 1 through-hardened steel. Using β =−0.023, what hardness can the gear have for the same factor of safety?

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Accepted Answer

For through-hardened grade 1 steel the pinion strength ([latex]S_{t} )_{P}[/latex] is given in Fig. 14–2:

[latex](S_{t} )_{P} = 77.3(300) + 12 800 = 35 990 psi[/latex]

From Fig. 14–6 the form factors are [latex]J_{P} = 0.32 and J_{G} = 0.41[/latex]. Equation (14–44) gives

[latex](S_{t})_{G} = (S_{t} )Pm^{β}_{G} \frac{J_{P}}{J_{G}}[/latex] (14–44)

[latex](S_{t})_{G}= 35 990 \left(\frac{64}{18}\right)^{−0.023} \frac{0.32}{0.41} = 27 280 psi[/latex]

Use the equation in Fig. 14–2 again.

[latex](H_{B})_{G} =\frac{27 280 − 12 800}{77.3} = 187[/latex] Brinell

Question 14.6: In a set of spur gears, a 300-Brinell 18-tooth 16-pitch 20° ...

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