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In a gearing system, pump speed is one third of the motor. Shaft from motor is 6 cm in diameter and 30cm long, the impellar shaft is 10cm diameter and 60cm long. Mass moment of inertia is 1500 Kg-m2, C = 80Gn/m2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz.

In a gearing system, pump speed is one third of the motor. Shaft from motor is 6 cm in diameter and 30cm long, the impellar shaft is 10cm diameter and 60cm long. Mass moment of inertia is 1500 Kg-m2, C = 80Gn/m2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz. Correct Answer 4.7

Moment of inertia of rotor B : Ib = 166.7 Kg-m2 total length of equivalent shaft = 1000mm = 1m Position of node = 294mm from left end (from same frequency condition) J = 1.27×106 m4 substituting the values into the free torsional vibration relation we get f = 4.7 Hz.

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