Engineering, 13.03.2020 05:00 krutikov686

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.

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Answer from: antcobra

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:

$\frac{N_{D}}{N_{S}} = \frac{n_{S}}{n_{D}}$ (1)

Where:

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

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

$N_{D} = 17\cdot \left(\frac{1120\,\frac{rev}{min} }{544\,\frac{rev}{min} } \right)$

$N_{D} = 35$

Now we find the diameters of both gears:

Small gear ( $D_{S}$ ) - Diameter of the small gear)

$D_{S} = \frac{17}{8\,\frac{1}{in} }$

$D_{S} = 2.125\,in$

Driven gear ( $D_{D}$ - Diameter of the driven gear)

$\frac{N_{D}}{N_{S}} = \frac{D_{D}}{D_{S}}$

$D_{D} = D_{S}\cdot \left(\frac{N_{D}}{N_{S}} \right)$

$D_{D} = \left(\frac{35}{17} \right)\cdot (2.125\,in)$

$D_{D} = 4.375\,in$

Lastly, the theoretical center-to-center distance (), is modelled after this formula:

$d = \frac{1}{2}\cdot (D_{D}+D_{S})$ (2)

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

$d = \frac{1}{2}\cdot (2.125\,in + 4.375\,in)$

$d = 3.25\,in$

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: link

Answer from: AmyGonzalez1385

-35 teeth

-3.25in

Explanation:

Given the spur pinion teeth, N_p=17 and a diametral pitch, P=8 . 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:

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

Hence the number of teeth in the gear is 35 teeth

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

$C=\frac{d_p+d_G}{2}\\\\=\frac{2.125+4.375}{2}\\\\=3.25 \ in$

The theoretical center to- center distance is 3.25 in

Answer from: Quest

answer:

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Answer from: Quest

Ireally wish i could but i will do some research and when i find the answer i will come back to assist you ; )

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A 17-tooth spur pinion has a diametral pitch of 8 teeth/in, runs at 1120 rev/min, and drives a gear...

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