In a transmission gear reduction set, an input driving gear with 12 teeth meshes directly … — Armed Services Vocational Aptitude Battery (ASVAB)

In a transmission gear reduction set, an input driving gear with $12$ teeth meshes directly with an output driven gear with $36$ teeth. If the engine supplies $100\text{ lb-ft}$ of torque to the input gear, what is the resulting gear ratio and torque delivered by the driven gear?

A
Gear ratio of $1:3$ with an output torque of $33.3\text{ lb-ft}$ to allow drive wheels to turn at different speeds during cornering
Gear ratio of $3:1$ with an output torque of $300\text{ lb-ft}$ Cevap
C
Gear ratio of $3:1$ with an output torque of $33.3\text{ lb-ft}$ due to friction dissipation across the gears
D
Gear ratio of $1:3$ with an output torque of $300\text{ lb-ft}$ to dampen driveline spring oscillations

Cevap

A gear ratio of

3:1

with an output torque of

300\text{ lb-ft}

The gear ratio is determined by dividing the number of teeth on the driven gear (

36

) by the number of teeth on the driving gear (

12

), yielding a ratio of

3:1

. In gear reduction, rotational output speed is reduced to one-third, while output torque is multiplied by

3

, producing

300\text{ lb-ft}

of torque.

Adım Adım Çözüm

Calculate the mechanical gear ratio by dividing the number of teeth on the driven gear by the number of teeth on the driving gear

\text{Gear Ratio} = \frac{\text{Driven Teeth}}{\text{Driving Teeth}} = \frac{36}{12} = 3:1

The gear ratio defines the mechanical advantage provided by the meshed gearset.

Calculate the output torque by multiplying the input torque by the gear ratio

\text{Output Torque} = 100\text{ lb-ft} \times 3 = 300\text{ lb-ft}

In a reduction gearset (ratio greater than

1:1

), rotational speed decreases while output torque multiplies proportionally.

Anahtar Kavram

Transmission gear ratios dictate the trade-off between rotational speed and mechanical torque. A smaller gear driving a larger gear produces gear reduction (

>1:1

), which decreases output shaft speed and increases output torque.

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