A spur gear has module of 5mm, number of teeth 24, a face width of 30mm and pressure angle of 20°. It is transmitting power of 4kW at 20rad/s. Velocity and form factor for gear are 1.5 and 0.3, respectively. The beam strength of gear, if allowable bending stress is 150MPa, is

6750N

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10125N

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3333.33N

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14130N

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Solution

The correct option is A 6750N
Given data:
$σ_{b} = 150 M P a, m = 5 m m, T = 24, b = 30 m m$
P = 4kW, $ω = 20 r a d / s, C_{v} = 1.5, Y = 0.3$
We know that beam strength of gear is given by:
$W_{T} = σ_{b} . b . m Y$
$W_{T} = 150 \times 30 \times 5 \times 0.3$
$W_{T} = 6750 N$

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