Question #241959

A truck and trailer must be able to accelerate at 0.3 m/s2 up an incline of 1 in 20. The truck’s engine generates a torque of 900Nm. It has a moment of inertia of 30kg.m2 . The efficiency of the truck’s transmission is 83%. The mass of the truck is 12 tons, and that of the trailer is 9tons. The tractive resistance for both the truck and the trailer combined is 60N/ton. The truck has 12 wheels and the trailer has 8 wheels. The wheels on both vehicles are identical. Each wheel has a diameter of 1.2m, a mass of 75kg and a radius of gyration of 500mm. Determine two suitable overall gear ratios.

Expert's answer

Find the incline:

Find the traction force required to provide this acceleration up the hill:

Find the torque that corresponds to this propulsive force:

The angular acceleration of truck's wheels is

The angular acceleration of truck's engine parts ( - gear ratio) is

Moment of inertial of wheels:

Find the transmission (output) torque that corresponds to *T*_{F} above:

Find the gear ratio that would make it possible for a 900 Nm engine to output 7590 Nm of mechanical torque:

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