A rotor is centered on a massless, flexible solid steel shaft. The shaft is simp

Question

A rotor is centered on a massless, flexible solid steel shaft. The shaft is simply supported at both ends. The mass of the rotor is 10 kg and the whole rotor has an eccentricity of 0.25 mm. The length of the shaft is 50 cm and the diameter is 5 cm. Find the critical speed of the rotor. If the rotor operates at the critical speed, how much time will it take for the maximum bending stress in the shaft to be about 70% of its yield stress? Assume the rotor starts from rest. The bending stress is row=My/I where y is the distance from the centroid of the beam and/is the area moment of inertia. The desired speed of the rotor is twice the critical speed. Assuming that the rotor starts from rest, suggest a constant angular acceleration of the rotor that will allow it to reach its operating speed without exceeding 50 percent of the shaft's yield stress. Verify your results using numerical integration of the differential equation and provide a plot showing that the bending stress in the shaft remains below 50% of its yield stress.

Explanation / Answer

rpm = (4.76)(102) df/(kl2) here substitute f.s = 2.3

15090 rpm

converting into rpd/s = 1525 rad/s

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