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Zorluk: Çok zorGears and Gear Ratios

A mechanical winch uses a compound gear train to lift heavy loads. The input motor drives Gear A (30 teeth) clockwise at 300300 RPM. Gear A meshes directly with Gear B (45 teeth). Gear C (15 teeth) is fixed to the same shaft as Gear B, meaning they rotate together. Gear C meshes with an idler Gear D (30 teeth), which in turn meshes with the output Gear E (60 teeth).

Based on this configuration, what is the rotational speed and direction of the output Gear E?

  1. 50 RPM, counter-clockwiseCevap
  2. B
    50 RPM, clockwise
  3. C
    150 RPM, clockwise
  4. D
    1800 RPM, counter-clockwise

Cevap

The correct answer is 50 RPM, counter-clockwise.
The correct answer is calculated by tracking the speed reduction and direction reversal across each mesh. Shaft 2 rotates at 200 RPM CCW (300×3045300 \times \frac{30}{45}). Shaft 3 (idler) rotates at 100 RPM CW (200×1530200 \times \frac{15}{30}). The final output shaft rotates at 50 RPM CCW (100×3060100 \times \frac{30}{60}).

Adım Adım Çözüm

1
Calculate the speed and direction of the second shaft (Gears B and C).
Gear B speed = 300×3045=200300 \times \frac{30}{45} = 200 RPM. Direction = counter-clockwise.
When meshing, speed is inversely proportional to tooth count. Meshing gears rotate in opposite directions. Because Gears B and C share a shaft, Gear C also rotates at 200 RPM counter-clockwise.
2
Calculate the speed and direction of the idler Gear D.
Gear D speed = 200×1530=100200 \times \frac{15}{30} = 100 RPM. Direction = clockwise.
Gear C drives Gear D. The ratio is 1530\frac{15}{30}, and the direction reverses from counter-clockwise to clockwise.
3
Calculate the final speed and direction of output Gear E.
Gear E speed = 100×3060=50100 \times \frac{30}{60} = 50 RPM. Direction = counter-clockwise.
Gear D drives Gear E. The ratio is 3060\frac{30}{60}, and the direction reverses from clockwise to counter-clockwise.

Anahtar Kavram

Compound Gear Trains and Idler Mechanics
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Konular

Gears and Gear Ratios

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