# A straight tooth gear having involute profile with 20° pressure angle transmits 20Nm torque. Pitch diameter of the gear is 24 cm. If only one pair of tooth is engaged at any instant of time, the force experienced by the tooth will be ______

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A straight tooth gear having involute profile with 20° pressure angle transmits 20Nm torque. Pitch diameter of the gear is 24 cm. If only one pair of tooth is engaged at any instant of time, the force experienced by the tooth will be ______

(a) 78.30 N

(b) 88.70 N

(c) 156.60 N

(d) 177.36 N

The question was asked in homework.

Enquiry is from Numericals on Estimation of Tractor Power in portion Tillage, Disc Plough & Numericals of Farm Machinery

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The correct answer is (d) 177.36 N

To elaborate: Torque = Ft * r

20 = Ft * 0.12

Ft = 20/0.12 = 166.67 N

Ft = F cos φ

F = $\frac{Ft}{cosφ} = \frac{166.67}{cos20°}$ = 177.36 N.

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