JNTU B.Tech III DYNAMICS OF MACHINERY Previous Question Paper (March - 2024 - R13)

The dimensions of a four-link mechanism are: AB = 400 mm, BC = 600 mm, CD = 500 mm, AD = 900 mm, and ∠DAB = 60°. AD is fixed link. E is a point on the link BC such that BE = 400 mm and CE = 300 mm (BEC clockwise). A force of 150 ∠45° N acts on DC at a distance of 250 mm from D. Another force of magnitude 100 ∠180° N acts at point E. Find the required input torque on the link AB for static equilibrium of the mechanism.

The rotor of a marine turbine has a moment of inertia of 750 kg.m² and rotates at 3000 rpm clockwise when viewed from stern. If the ship pitches with angular simple harmonic motion having a periodic time of 16 seconds and an amplitude of 0.1 radian, find the a) Maximum angular velocity of the rotor axis b) Maximum value of gyroscopic couple c) Gyroscopic effect as the bow dips.

A cone clutch of semi-cone angle 15° is used to transmit 30 kW at 800 rpm. The mean frictional surface radius is 150 mm and normal intensity of pressure of the mean radius is not to exceed 0.15 MPa. The coefficient of friction is 0.2. Assuming uniform wear, determine: (a) Width of contact surface, and (b) Axial force required to engage the clutch.

What is the advantage of an internal expanding shoe brake? Derive the relation for the friction torque for such brake.

The cranks of a three-cylinder single-acting engine are set equally at 120°. The engine speed is 540 rpm. The turning moment diagram for each cylinder is a triangle for the power stroke with a maximum torque of 100 N.m at 60° after the dead-centre of the corresponding crank. On the return stroke, the torque is sensibly zero. Determine the (a) power developed (b) coefficient of fluctuation of speed if the flywheel has a mass of 7.5 kg with a radius of gyration of 65 mm (c) coefficient of fluctuation of energy.

In a spring-loaded Hartnell type of governor, the mass of each ball is 4 kg, and the lift of the sleeve is 40 mm. The governor begins to float at 200 rpm when the radius of the ball path is 90 mm. The mean working speed of the governor is 16 times the range of speed when friction is neglected. The lengths of the ball and roller arms of the bell-crank lever are 100 mm and 80 mm respectively. The pivot centre and the axis of governor are 115 mm apart. Determine the initial compression of the spring, taking into account the obliquity of arms. Assuming the friction at the sleeve to be equivalent a force of 15 N, determine the total alteration in speed before the sleeve begins to move from the mid-position.

A rotor has the following properties: Mass Magnitude (kg), Radius (mm), Angle (°) and Axial distance from 1st mass (mm). Plane 1: 9, 100, 0, 0. Plane 2: 7, 120, 60, 160. Plane 3: 8, 140, 135, 320. Plane 4: 6, 120, 270, 560. If the shaft is balanced by two counter masses located at 100 mm radii and revolving in planes midway of planes 1 and 2, and midway of 3 and 4 determine the magnitude of the masses and their respective angular positions.

A shaft carries four rotating masses A, B, C and D in this order along its axis. The mass A may be assumed concentrated at a radius of 120 mm, B at 150 mm, C at 130 mm, and D at 180 mm. The masses at A, C and D are 10, 15 and 12 kg, respectively. The planes of rotation of A and B are 150 mm apart and of B and C are 200 mm apart. The angle between A and C is 90°. If the shaft is in complete dynamic balance, determine (a) the angles between the radii of A, B and D, (b) the distance between the planes of rotation of C and D, and (c) the mass B.

The following data relate to a machine supported on four springs: Mass of machine = 120 kg, stroke = 90 mm, mass of reciprocating parts = 2.5 kg and speed = 750 rpm. Springs are symmetrically placed with respect to the centre of mass of the machine. Neglecting damping, find the combined stiffness of the springs so that the force transmitted to the foundation is 1/22 of the impressed force. If under actual working conditions, the damping reduces the amplitude of the successive vibrations by 25%, determine the forces transmitted to the foundation at 750 rpm and at resonance. Also, find the amplitude of the vibrations at resonance.

A steel shaft 1.5 m long is 95 mm in diameter for the first 0.6 m of its length, 60 mm in diameter for the next 0.5 m of the length and 50 mm in diameter for the remaining 0.4 m of its length. The shaft carries two flywheels at two ends, the first having a mass of 900 kg and 0.85 m radius of gyration located at 95mm diameter end and second having a mass of 700 kg and 0.55 m radius of gyration located at the other end. Determine the location of the node and natural frequency of free torsional vibration of system. The modulus of rigidity of shaft is 80 GN/m².