A 17-tooth spur pinion has a diametral pitch of 8 teeth/in, runs at 1120 rev/min, and drives a gear at a speed of 544 rev/min. Find the number of teeth on the gear and the theoretical centerto- center distance.

Given the spur pinion teeth, [tex]N_p=17[/tex] and a diametral pitch, [tex]P=8[/tex]. Also given that the pinion runs at 1120r/min spinning a gear at 540r/min, we can Find the number of teeth on the gear as:

[tex]d_p=N_p/P\\\\=17/8=2.125\\\\d_G=\frac{n_2}{n_3}\times d_P\\\\=\frac{1120}{544}\times2.125\\\\=4.375\\\\N_G=Pd_G\\\\=8\times4.375\\\\=35 \ teeth[/tex]

Hence the number of teeth in the gear is 35 teeth

# The theoretical center to- center distance is calculated as:

[tex]C=\frac{d_p+d_G}{2}\\\\=\frac{2.125+4.375}{2}\\\\=3.25 \ in[/tex]

The theoretical center to- center distance is 3.25 in

xero099 xero099 · Answer 2 · 2022-01-07T20:45:13+01:00

The driven gear has 35 teeth and the theoretical center-to-center distance is 3.25 inches.

First, we calculate the number of teeth on the driven gear by definition of speed ratio:

[tex]\frac{N_{D}}{N_{S}} = \frac{n_{S}}{n_{D}}[/tex] (1)

Where:

[tex]N_{S}[/tex], [tex]N_{D}[/tex] - Number of teeth of the small gear and the driven gear, no unit.
[tex]n_{S}[/tex], [tex]n_{D}[/tex] - Speed of the small gear and the driven gear, in revolutions per second.

If we know that [tex]N_{S} = 17[/tex], [tex]n_{S} = 1120\,\frac{rev}{min}[/tex] and [tex]n_{D} = 544\,\frac{rev}{min}[/tex], then the number of teeth of the driven gear is:

[tex]N_{D} = 17\cdot \left(\frac{1120\,\frac{rev}{min} }{544\,\frac{rev}{min} } \right)[/tex]

[tex]N_{D} = 35[/tex]

Now we find the diameters of both gears:

Small gear ([tex]D_{S}[/tex]) - Diameter of the small gear)

[tex]D_{S} = \frac{17}{8\,\frac{1}{in} }[/tex]

[tex]D_{S} = 2.125\,in[/tex]

Driven gear ([tex]D_{D}[/tex] - Diameter of the driven gear)

[tex]\frac{N_{D}}{N_{S}} = \frac{D_{D}}{D_{S}}[/tex]

[tex]D_{D} = D_{S}\cdot \left(\frac{N_{D}}{N_{S}} \right)[/tex]

[tex]D_{D} = \left(\frac{35}{17} \right)\cdot (2.125\,in)[/tex]

[tex]D_{D} = 4.375\,in[/tex]

Lastly, the theoretical center-to-center distance ([tex]d[/tex]), is modelled after this formula:

[tex]d = \frac{1}{2}\cdot (D_{D}+D_{S})[/tex] (2)

If we know that [tex]D_{P} = 2.125\,in[/tex] and [tex]D_{D} = 4.375\,in[/tex], then the theoretical center-to-center distance is:

[tex]d = \frac{1}{2}\cdot (2.125\,in + 4.375\,in)[/tex]

[tex]d = 3.25\,in[/tex]

The driven gear has 35 teeth and the theoretical center-to-center distance is 3.25 inches.

To learn more on gears, we kindly invite to check this verified question: https://brainly.com/question/15541463