FIGURE 9.1 below shows a gear drive system. Driver gear A on the shaft of an electric motor has 30 teeth and mesh with gear B with 40 teeth on a counter shaft. On the counter shaft is another driver, C, with 20 teeth that mesh with gear D with 60 teeth on a second counter shaft. The second counter shaft has driver gear E with 50 teeth, which drive gear F with 70 teeth on the output shaft. Calculate the: 9.1.1 Rotation frequency of the output shaft if the electric motor rotates at 2 300 r/min 9.1.2 Velocity ratio between the input and output shaft.

NSC Mechanical Technology Automotive Function and operation of drive shafts: FIGURE 9.1 below shows a gear dr

FIGURE 9.1 below shows a gear drive system - NSC Mechanical Technology Automotive - Question 9 - 2017 - Paper 1

Question 9

FIGURE 9.1 below shows a gear drive system. Driver gear A on the shaft of an electric motor has 30 teeth and mesh with gear B with 40 teeth on a counter shaft. On th... show full transcript

Worked Solution & Example Answer:FIGURE 9.1 below shows a gear drive system - NSC Mechanical Technology Automotive - Question 9 - 2017 - Paper 1

Step 1

9.1.1 Rotation frequency of the output shaft if the electric motor rotates at 2 300 r/min

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Answer

To find the rotation frequency of the output shaft, we'll use the gear ratio formula. The formula is given by:

$N_{F} = N_{A} \cdot \frac{T_{A}}{T_{B}} \cdot \frac{T_{C}}{T_{D}} \cdot \frac{T_{E}}{T_{F}}$

Where:

$N_{A}$ = input speed = 2300 r/min
$T_{A}$ = teeth of gear A = 30
$T_{B}$ = teeth of gear B = 40
$T_{C}$ = teeth of gear C = 20
$T_{D}$ = teeth of gear D = 60
$T_{E}$ = teeth of gear E = 50
$T_{F}$ = teeth of gear F = 70

Plugging in the values:

$N_{F} = 2300 \cdot \frac{30}{40} \cdot \frac{20}{60} \cdot \frac{50}{70}$

Calculating step-by-step:

First calculate the gear ratios:

$\frac{30}{40} = 0.75$
$\frac{20}{60} = \frac{1}{3} = 0.3333$
$\frac{50}{70} = 0.7143$

Now, substituting these back into our equation:

$N_{F} = 2300 \cdot 0.75 \cdot 0.3333 \cdot 0.7143 \approx 410.71 \text{ r/min}$

Therefore, the rotation frequency of the output shaft is approximately 410.71 r/min.

Step 2

9.1.2 Velocity ratio between the input and output shaft

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Answer

The velocity ratio (VR) can be calculated using the formula:

$VR = \frac{N_{OUTPUT}}{N_{INPUT}}$

Where:

$N_{OUTPUT}$ = output frequency = 410.71 r/min
$N_{INPUT}$ = input frequency = 2300 r/min

Substituting the values:

$VR = \frac{410.71}{2300} \approx 0.178$

Thus, the velocity ratio between the input and output shaft is approximately 0.178.

FIGURE 9.1 below shows a gear drive system - NSC Mechanical Technology Automotive - Question 9 - 2017 - Paper 1

Worked Solution & Example Answer:FIGURE 9.1 below shows a gear drive system - NSC Mechanical Technology Automotive - Question 9 - 2017 - Paper 1

9.1.1 Rotation frequency of the output shaft if the electric motor rotates at 2 300 r/min

9.1.2 Velocity ratio between the input and output shaft

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