Question 11.1: Geometric Properties of a Gearset A diametral pitch P set of...
Geometric Properties of a Gearset
A diametral pitch P set of gears consists of an N_{1} tooth pinion and N_{2} tooth gear (Figure 11.2b).
Find: The pitch diameters, module, circular pith, and center distance
Given: N_{1} = 19, N_{2} = 124, P = 16 in.^{−1}.
Through the use of Equation 11.2, diameters of pinion and gear, through the use of
Equation 11.2, are
P=\frac{N}{d} (11.2)
\begin{array}{l} d_1=\frac{N_1}{P}=\frac{19}{16}=1.1875 in .=30.16 mm \\ d_2=\frac{N_2}{P}=\frac{124}{16}=7.75 in .=196.85 mm \end{array}
Note that in SI units, from Equation 11.5b, the module is
P = \frac{1}{m} (11.5b)
m=\frac{1}{P}(25.4)=\frac{1}{16}(25.4)=1.5875 mm
and alternatively Equation 11.4 gives the preceding result for the diameters.
m = \frac{d}{N} (11.4)
Applying Equation 11.3, the circular pitch equals
p P=\pi (11.3)
p=\frac{\pi}{P}=\frac{\pi}{16}=0.1963 \text { in. }=4.99 mm
The center distance, by Equation 11.6, is therefore
c=r_1+r_2=\frac{N_1+N_2}{2 P} (11.6)
c=\frac{1}{2}\left(d_1+d_2\right)=\frac{1}{2}(1.1875+7.75)=4.4688 in .=113.51 mm