UNIVERSITI TEKNIKAL MALAYSIA MELAKA FAKULTI KEJURUTERAAN MEKANIKAL

BMCM 2723 MEKANIK MESIN

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Tutorial 9 Gyroscope

1. A system with an axle is pivoted on the centre as shown in the diagram below. It is connected with a weight, 5 kg at one end and a wheel with weight 8 kg at the other end. The wheel radius is 40 cm and rotates with a speed 800 rpm counter-clock wise looking from right-side. Determine the precession velocity and direction of the system at vertical axis through the axis centre.

[Ans : 0.33 rad/s, counter-clockwise from top]

5 kg

0.6 m 0.6 m

8 kg

2. The moment inertia of the engine and fan of an airplane is 50 kgm2 and rotates at 3000 rpm clockwise looking from back of the airplane. The airplane makes a half circle movement to the left in 5 s. Calculate the gyroscopic couple act on the airplane and describe the effect on the airplane.

[Ans : 9866 Nm, the front side upward]

3. A rotor of a steam turbine have moment of inertia 2500 kgm2 and rotates with

speed of 1200 rpm clock wise looking from back of the turbine. The rotor moves a ship to the right with a speed of 50 km/h in a curvature with radius 500 m. Determine the magnitude and direction of gyroscopic couple on the ship body.

[Ans : 8729 Nm, the front side downward]

4. A car with mass 2500kg drives into the left side curve with radius 120 m.

Moment of inertia of each wheel is 3 kgm2 and its effective radius is 25 cm. Rotating engine parts and gear transmission have a moment of inertia 2 kgm2. Engine axis is parallel with back axle and the crankshaft rotates with the same direction of the wheel. The gear ratio between engine and wheel is 4 : 1. The car width is 1.6 m and the centre of gravity is 0.6 m from road pavement. Determine the maximum speed for the car if it is driven in to a curve with all of the wheels touching the road.

[Ans: 38.6 m/s]

UNIVERSITI TEKNIKAL MALAYSIA MELAKA FAKULTI KEJURUTERAAN MEKANIKAL

BMCM 2723 MEKANIK MESIN

5. A pair of locomotive driving wheels with the axle have a moment of inertia of

380 kgm2 . The diameter of the wheel treads is 2 m and the distance between the wheel is 1.5 m. When the locomotive is travelling on a level track at 110 km/hr, defective ballasting causes one wheel to fall 10 mm and to rise again in a total time of 0.1 s. If the displacement of the wheel takes place with simple harmonic motion, find the gyroscopic reaction on the locomotive.

[Ans: 2.435 kN]

6. A motor vehicle having a rigid rear axle is travelling along a straight level road at 160 km/hr. The rear wheel on the left-hand side of the vehicle drops into a pot-hole which lowers the end of the axle by 80 mm. The track of the vehicle is 1.5 m, the rolling radius of the wheels is 0.3 m and the movement of the wheel into and out of the pot-hole may be regarded as approximating in form to a complete sine wave, 0.45 m long, having its mean 40 mm below the road level. The polar moment of inertia of the axle with its two wheels is 2.5 kg m2. Determine the maximum gyroscopic couple that acts on the vehicle and the effects of this on the course of the vehicle. Explain clearly, with the aid of diagrams, how you determine the direction of the gyroscopic couple. [Ans: 6.12 kNm , turning car to left]

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Tutorial 9 Gyroscope