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?

Question

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?

Accepted Answer

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

[latex]\left(S_{t} ight)_{P}=77.3(300)+12800=35990 psi[/latex]

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

[latex]\left(S_{t} ight)_{G}=\left(S_{t} ight)_{P} m_{G}^{\beta} \frac{J_{P}}{J_{G}}[/latex] (14–44)

[latex]\left(S_{t} ight)_{G}=35990\left(\frac{64}{18} ight)^{-0.023} \frac{0.32}{0.41}=27280 psi[/latex]

Use the equation in Fig. 14–2 again.

[latex]\left(H_{B} ight)_{G}=\frac{27280-12800}{77.3}=187 ext { Brinell }[/latex]

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