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A spur gear wi t h 20° full dept h teeth i s transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is
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- 0.36 kN
- 2.78 kN
- 0.73 kN
- 1.39 kN
- 0.36 kN
Correct Option: C
Given: φ = 20°
P = 20 kW, ω = 200 rad/s Pitch Circle Diameter = 100 mm
Now, force on radial direction (Fr),
| Now , | = | = tanφ | ||
| Ft | F cosφ |
⇒ Fr = Ft tanφ
| Also , T = | = | = 100 N-m | ||
| ω | 200 |
T = Ft × r
| Ft = | = | = 2000 N | ||
| r | (100/2) × 10-3 |
Fr = Ft tan φ = 2000 tan 20 = 727.9 N
= 727.9 × 10-3 kN = 0.73 kN
