A 16-tooth pinion drives the double-reduction spur-gear train in the figure. All gears have 25° pressure angles. The pinion rotates ccw at 1200 rev/min and transmits power to the gear train. The shaft has not yet been designed, but the free bodies have been generated. The shaft speeds are 1200

Question

A 16-tooth pinion drives the double-reduction spur-gear train in the figure. All gears have 25° pressure angles. The pinion rotates ccw at 1200 rev/min and transmits power to the gear train. The shaft has not yet been designed, but the free bodies have been generated. The shaft speeds are 1200 rev/min, 240 rev/min, and 80 rev/min. A bearing study is commencing with a 10-kh life and a gearbox bearing ensemble reliability of 0.99. An application factor of 1.2 is appropriate. Specify the six bearings.

Accepted Answer

This problem is rich in useful variations. Here is one.

Decision: Make straight roller bearings identical on a given shaft. Use a reliability goal of [latex](0.99)^{1 / 6}=0.9983[/latex].

Shaft a

[latex]\begin{aligned}&F_{A}^{r}=\left(239^{2}+111^{2} ight)^{1 / 2}=264 lbf =1.175 kN \&F_{B}^{r}=\left(502^{2}+1075^{2} ight)^{1 / 2}=1186 lbf =5.28 kN\end{aligned}[/latex]

Thus the bearing at B controls.

[latex]\begin{aligned}&x_{D}=\frac{10000(1200)(60)}{10^{6}}=720 \&0.02+4.439[\ln (1 / 0.9983)]^{1 / .483}=0.08026 \&C_{10}=1.2(5.28)\left(\frac{720}{0.08026} ight)^{0.3}=97.2 kN\end{aligned}[/latex]

Select either an 02-80 mm with [latex]C_{10}=106 kN ext { or an } 03-55 mm ext { with } C_{10}=102 kN ext {. }[/latex]

Shaft b

[latex]\begin{aligned}&F_{C}^{r}=\left(874^{2}+2274^{2} ight)^{1 / 2}=2436 lbf \quad ext { or } \quad 10.84 kN \&F_{D}^{r}=\left(393^{2}+657^{2} ight)^{1 / 2}=766 lbf \quad ext { or } \quad 3.41 kN\end{aligned}[/latex]

The bearing at C controls.

[latex]\begin{aligned}&x_{D}=\frac{10000(240)(60)}{10^{6}}=144 \&C_{10}=1.2(10.84)\left(\frac{144}{0.08026} ight)^{0.3}=123 kN\end{aligned}[/latex]

Select either an 02-90 mm with [latex]C_{10}=142 kN ext { or an } 03-60 mm ext { with } C_{10}=123 kN[/latex] .

Shaft c

[latex]\begin{aligned}&F_{E}^{r}=\left(1113^{2}+2385^{2} ight)^{1 / 2}=2632 lbf \quad ext { or } \quad 11.71 kN \&F_{F}^{r}=\left(417^{2}+895^{2} ight)^{1 / 2}=987 lbf \quad ext { or } \quad 4.39 kN\end{aligned}[/latex]

The bearing at E controls.

[latex]\begin{aligned}&x_{D}=\frac{10000(80)(60)}{10^{6}}=48 \&C_{10}=1.2(11.71)\left(\frac{48}{0.08026} ight)^{0.3}=95.7 kN\end{aligned}[/latex]

Select an 02-80 mm with [latex]C_{10}=106 kN ext { or an } 03-60 mm ext { with } C_{10}=123 kN[/latex] .

Question 11.37: A 16-tooth pinion drives the double-reduction spur-gear trai...

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