GTU 3151911 Dynamics of Machinery Winter 2024 Question Paper & PDF

Why is the correction couple applied while considering the inertia of the connecting rod of a reciprocating engine?

In a vertical double-acting steam engine, the connecting rod is 4.5 times the crank. The weight of the reciprocating parts is 120 kg and the stroke of the piston is 440 mm. The engine runs at 250 rpm. If the net load on the piston due to steam pressure is 25 kN when the crank has turned through an angle of 120° from the top dead centre. Solve for thrust in the connecting rod, pressure on slide bars, and tangential force on the crank pin, thrust on the bearings, and turning moment on the crankshaft using the above information.

Compare the effect of Primary and Secondary Unbalanced Forces of Reciprocating Masses.

Explain the following terms using neat sketches and equations

A four-crank engine has two outer cranks set at 120° to each other, and their reciprocating masses are each 400 kg. The distance between the lanes of rotation of adjacent cranks are 450 mm, 750 mm, and 600 mm. If the engine is to be in complete primary balance, find the reciprocating mass and the relative angular position for each of the inner cranks. If the length of each crank is 300 mm, the length of each connecting rod is 1.2 m and the speed of rotation is 240 rpm., Calculate the maximum secondary unbalanced force.

Illustrate following terms in context to mechanical vibration

Derive the expression for natural frequency of free longitudinal vibration through “Energy method”.

The mass of a turbine rotor of a ship is 8000 kg and has a radius of gyration of 0.75 m. It rotates at 1800 rpm clockwise when viewed from the stern. Determine the gyroscopic effects in the following cases: (a) If the ship traveling at 100 km/h steers to the left along a curve of 80 m radius. (b) If the ship is pitching and the bow is descending with maximum velocity. The pitching is with simple harmonic motion with periodic time of 20 s and the total angular movement between extreme positions is 10°. (c) If the ship is rolling with an angular velocity of 0.03 rad/s clockwise when looking from stern. In each case, determine the direction in which the ship tends to move.

Discuss the effect of inertia of the shaft in longitudinal and transverse vibrations.

Evaluate the natural frequency of a vibratory system shown in figure. The mass of block is m and stiffness of springs are k1 and k2.

A spring-mass system consists of a spring of stiffness 350 N/m. The mass is 0.35 kg. The mass is displaced 20 mm beyond the equilibrium position and released. The damping coefficient is 14 Ns/m. Calculate (a) critical damping coefficient, (b) damped natural frequency, and (c) logarithmic decrement.

Compare the displacement-time curves for following damping conditions.

The rotor of a turbine of mass 15 kg is supported at the mid-span of a shaft of span 0.4 m. The rotor has an unbalance of 0.003 kg m. Determine the force exerted on the bearings at a speed of 6000 rpm. The diameter of steel shaft is 25 mm and E = 200 Gpa.