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Zorluk: ZorGears and Gear Ratios

A portable hand-cranked emergency generator utilizes a compound gear train to step up the rotational speed of its internal rotor. The hand crank is directly attached to the driving gear (Gear A), which has 6060 teeth. Gear A meshes with Gear B, which has 1515 teeth. Gear B is fixed to the same solid shaft as Gear C, which has 4545 teeth. Finally, Gear C meshes with Gear D, which has 1010 teeth and is attached to the generator's rotor.

If a person turns the hand crank at a steady speed of 40 RPM40\text{ RPM}, what is the resulting speed of the generator's rotor in RPM\text{RPM}?

Cevap: 720 RPM

Cevap

720
In a compound gear train, the overall mechanical advantage (or speed ratio) is found by evaluating each meshing pair separately. The first pair (A to B) increases the speed by a factor of 44 (since 60/15=460/15 = 4). The input speed is 40 RPM40\text{ RPM}, so Gear B spins at 160 RPM160\text{ RPM}. Because Gear B and Gear C are fixed to the same shaft, Gear C also spins at 160 RPM160\text{ RPM}. The second meshing pair (C to D) increases the speed by a factor of 4.54.5 (since 45/10=4.545/10 = 4.5). Multiplying Gear C's speed by this ratio gives 160×4.5=720 RPM160 \times 4.5 = 720\text{ RPM}.

Adım Adım Çözüm

1
Determine the rotational speed of Gear B.
160 RPM160\text{ RPM}
Gear A (6060 teeth) drives Gear B (1515 teeth). The speed multiplier is 60/15=460 / 15 = 4. Therefore, Gear B spins at 40×4=160 RPM40 \times 4 = 160\text{ RPM}.
2
Determine the rotational speed of Gear C.
160 RPM160\text{ RPM}
Gears mounted on the exact same solid shaft rotate at the same speed, regardless of their size.
3
Determine the rotational speed of Gear D (the rotor).
720 RPM720\text{ RPM}
Gear C (4545 teeth) drives Gear D (1010 teeth). The speed multiplier is 45/10=4.545 / 10 = 4.5. Therefore, Gear D spins at 160×4.5=720 RPM160 \times 4.5 = 720\text{ RPM}.

Anahtar Kavram

Compound Gear Train Speed Ratios
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Konular

Gears and Gear Ratios

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