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 11.2(b)).
Find: The pitch diameters, module, circular pith, and center distance.
Given: N_1=19, N_2=124, P=16 \text { in. }^{-1} .
Through the use of Equation (11.4), diameters of pinion and gear are
m=\frac{d}{N} (11.4)
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 \text { in. }=196.85 mm
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.
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