The turbine rotor in the power plant of a ship as shown in Fig. 3 has a weight o

Question

The turbine rotor in the power plant of a ship as shown in Fig. 3 has a weight of
12.75 kN with centre of gravity at G and has a radius of gyration 200 mm. The rotor is
mounted in bearings A and B with its axis in the horizontal fore-and-aft direction. The
rotor turns at 5000 rpm anticlockwise when viewed from the stern.
Determine the vertical components of the bearing reactions at A and B if the ship is
making a turn to port (left) of 400 m radius at a speed of 35 km/hr.
[At A =7.179 kN, At B = 5.541 kN].

Explanation / Answer

W = 12750 Newton Radius = R = 400 meter radius of gyration k = 0.2 meter V = 35 km/hr w = 2 pi x 5000/60 = 523.598 rad/s I = W/g x k^2 = 12750/9.8 x 0.2^2 = 52.041 kgm^2 angular velocity of precession = wp = V/R = 25 x 1000/(3600 x 400) = 0.01736 rad/s Magnitude of Gyro Couple = Iw x wp = 473.035 N-m now, A + B = 12750 473.035 = A x ra + B x rb solving , we get, A = 7.179 kN B = 5.541 kN

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