Engineering, 18.11.2020 17:10 swaggaming941

A spur gearset has a module of 6 mm and a velocity ratio of 4. The pinion has 16 teeth. Find the number of teeth on the driven gear, the pitch diameters, and the theoretical center-to-center distance

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Answer from: mv603177

The results are listed below:

The driven gear has 64 teeth.The pinion has a diameter of 96 millimeters and the driven gear has a diameter of 384 millimeters.The theoretical center-to-center distance is 240 millimeters.

First, we proceed to find the number of teeth of each gear ( $N_{D}, N_{P}$ ) based on the fact that gear only fit when they have the same module (). The velocity ratio ( $r_{v}$ ) is defined by the following relationship:

$r_{v} = \frac{N_{D}}{N_{P}}$ (1)

If we know that $r_{v} = 4$ and $N_{P} = 16$ , then the number of teeth of the driven gear is:

$N_{D} = r_{v}\cdot N_{P}$

$N_{D} = 4\cdot (16)$

$N_{D} = 64$

The driven gear has 64 teeth.

The pitch diameter () is obtained by multiplying the number of teeth () by module (), in milimeters.

Pinion

$D_{P} = m\cdot N_{P}$ (2)

( $m = 6\,mm$ , $N_{P} = 16$ )

$D_{P} = (6\,mm)\cdot (16)$

$D_{P} = 96\,mm$

Driven gear

$D_{D} = m\cdot N_{D}$ (3)

( $m = 6\,mm$ , $N_{D} = 64$ )

$D_{D} = (6\,mm)\cdot (64)$

$D_{D} = 384\,mm$

The pinion has a diameter of 96 millimeters and the driven gear has a diameter of 384 millimeters.

Lastly, the theoretical center-to-center distance is calculated by the following formula:

$d = \frac{1}{2}\cdot (D_{P}+D_{D})$ (4)

( $D_{P} = 96\,mm$ , $D_{D} = 384\,mm$ )

$d = \frac{1}{2}\cdot (96\,mm + 384\,mm)$

$d = 240\,mm$

The theoretical center-to-center distance is 240 millimeters.

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Answer from: john092103

NG=64 teeth

dG=384mm

dP=96mm

C=240mm

Explanation:

step one:

given data

module m=6mm

velocity ratio VR=4

number of teeth of pinion Np=16

Step two:

Required

1. Number of teeth on the driven gear

$N_G=N_P*V_R\\\\N_G=16*4\\\\N_G=64$

The driven gear has 64 teeth

2. The pitch diameters

The driven gear diameter

$d_G=N_G*m\\\\d_G=64*6\\\\d_G=384$

The driven gear diameter is 384mm

The pinion diameter

$d_P=N_P*m\\\\d_P=16*6\\\\d_P=96$

Pinion diameter is 96mm

3. Theoretical center-to-center distance

$C=\frac{d_G+d_P}{2} \\\\C=\frac{384+96}{2} \\\\C=\frac{480}{2}\\\\C=240$

The theoretical center-to-center distance is 240mm

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A spur gearset has a module of 6 mm and a velocity ratio of 4. The pinion has 16 teeth. Find the num...

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