Question
A spur gear with 20° full depth teeth is 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
Options :
0.73 kN
2.78 kN
1.39 kN
0.36 kN
Answer :
0.73 kN
Solution :
φ= 20°
P = 20 kW
ω = 200 rad/s
D = 100 mm
We know that, power,
P = T × ω
20 × 103 = T • 200
T = 100 N-m
We know that, T = Ft × r
Ft = 2T/D = 2•100/(100•10-3 ) = 2kN
Radial force, Fr = Ft(tanφ) = 2•tan20° = 0.72794 kN = 0.728 kN = 0.73 kN
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