Question 8.1: For the pair of gears shown in Figure 8–1, compute all of th...

Given P_d = 12; N_p = 11; N_G = 18; \phi = 20°.
Analysis Unless otherwise noted, we use equations from Table 8–1 to compute the features. Refer to the text in this section for explanation of terms.

Note that results are reported to four decimal places as is typical for precise mechanical devices like gears.
A similar level of accuracy is expected for problems in this book.

Results Pitch Diameters
For the pinion,

D_{p}=N_{p} / P_{d}=11 / 12=0.9167 \text { in }
For the gear,
D_{G}=N_{G} /P_{d}=18 / 12=1.5000 \mathrm{in}
Circular Pitch
Three different approaches could be used.
p=\pi / P_{d}=\pi / 12=0.2618 \text { in }
Note that data for either the pinion or the gear data may also be used. For the pinion,
p=\pi D_{p} / N_{p}=\pi(0.9167 \mathrm{in}) / 11=0.2618 \mathrm{in}
For the gear,
p=\pi D_{G} / N_{G}=\pi(1.500 \mathrm{in}) / 18=0.2618 \mathrm{in}
Addendum
a=1 / P_{d}=1 / 12=0.8333 \text { in }
Dedendum
Note that the 12-pitch gear is considered to be coarse. Thus,
b=1.25 / P_{d}=1.25 / 12=0.1042 \text { in }

Clearance
c=0.25 / P_{d}=0.25 / 12=0.0208 \text { in }
Outside Diameters
For the pinion,
D_{o P}=\left(N_{P}+2\right) / P_{d}=(11+2) / 12=1.0833 \text { in }
For the gear,
D_{o G}=\left(N_{G}+2\right) / P_{d}=(18+2) / 12=1.6667 \text { in }
Root Diameters
First, for the pinion,
D_{R P}=D_{P}-2 b=0.9167 \text { in }-2(0.1042 \text { in })=0.7083 \text { in }

For the gear,
D_{R G}=D_{G}-2 b=1.500 \text { in }-2(0.1042 \text { in })=1.2917 \text { in }
Whole Depth
h_{t}=a+b=0.0833 \text { in }+0.1042 \text { in }=0.1875 \text { in }
Working Depth
h_{k}=2 a=2(0.0833 \mathrm{in})=0.1667 \mathrm{in}
Tooth Thickness
t=\pi /\left[2\left(P_{d}\right)\right]=\pi /[2(12)]=0.1309 \text { in }
Center Distance
C=\left(N_{G}+N_{P}\right) /\left(2 P_{d}\right)=(18+11) /[2(12)]=1.2083 \text { in }

Base Circle Diameter
\begin{aligned}&D_{b P}=D_{P} \cos \phi=(0.9167 \mathrm{in}) \cos \left(20^{\circ}\right)=0.8614 \mathrm{in} \\&D_{b G}=D_{G} \cos \phi=(1.5000 \mathrm{in}) \cos \left(20^{\circ}\right)=1.4095 \mathrm{in}\end{aligned}