The engine would produce 110hp and 200 f t ? lbf of torque maximum. The manual t

Question

The engine would produce 110hp and 200 f t ? lbf of torque maximum. The manual transmission had gear ratios as in table 1. Assume maximum torque to start a heavy load in reverse. Assume the outer diameter of the drive shaft, which lies beyond the transmission toward the rear differential, is 3inches. Placement of the driveshaft beyond the transmission is the important thing here. If the driveline is made of A307 grade A mild steel with a shear strength of 250MPa determine an inner diameter for a driveshaft having a safety factor of 3.0 and which weighs as little as possible. Assume 100% efficiency for the transmission.

Table 1. Gear ratios for the F5 Four speed manual transmission. First gear for example produces one ro- tation of the driveline for each 6.4 engine rotations.

Explanation / Answer

3 inches = 3/12 ft = 0.25 ft

250 MPa = 250*10^6 Pa = 5.2213*10^6 lb/ft^2

For a hollow shaft,

Max torque = pi/16*(D^4 - d^4) / D *Shear stress

We have max.torque in reverse gear = 7.82*200 = 1564 ft-lbf

Because safety factor is 3, max. allowed torque = 1564 / 3 = 521.33 ft-lbf

521.33 = (3.14/16)*(0.25^4 - d^4) / 0.25 *5.2213*10^6

d = 0.2479 ft = 2.975 inches

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