Question

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-m^2, C = 80Gn/m^2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz.

(a) 4.7

(b) 5.7

(c) 4.5

(d) 5.5

This question was addressed to me in exam.

I need to ask this question from Free Torsional Vibrations of a Geared System in section Torsional Vibrations of Machine Dynamics

Answer 1

Correct option is (a) 4.7

For explanation I would say: Moment of inertia of rotor B : Ib = 166.7 Kg-m^2

total length of equivalent shaft = 1000mm = 1m

Position of node = 294mm from left end (from same frequency condition)

J = 1.27×10^6 m^4

substituting the values into the free torsional vibration relation we get

f = 4.7 Hz.