# Anna University Mechanics of Machine II Model Test Paper

MECHANICS OF MACHINES – II.

MARINE ENGINEEERING

Time : 3 Hours Maximum Marks : 100

Answer All Questions

**PART – A (10 x 2 = 20 marks)**

1. Define the terms (i) Inertia force of piston, (ii) Inertia torque on crank shaft.

2. What is the procedure for accounting the inertia of the connecting rod in the force

analysis of engines.

3.What is meant by turning moment diagram? What is the application of turning moment diagram?

4. Distinguish unbalance due to revolving masses and unbalance due to reciprocating masses?

5. What is meant by ‘direct’ and ‘reverse’ cranks?

6. What is meant by ‘steady state’ and ‘transient Vibration’? Give one example for each?

7.What is the role of damping in vibrating system? What are the types of damping present in mechanical system?

8. What do you understand by self-excited vibration? Under What situation does it occur?

9.Briefly explain the Holzer’s procedure for the torsional vibration of multi-rotor system?

10.What is meant by ‘flexibility matrix’ of a multi-degree freedom vibrating system?

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**PART – B ( 5 x 16 = 80 marks)**

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11.The six cylinders of a single acting two stroke diesel engine are in line and are Symmetrically spaced on either side of the center line. The cranks are spaced at 60°intervals and the centerline of cylinders 1 and 6 are 4.8 m apart. Cylinders 2 and 5 are 3 m apart and cylinders 3 and 4 are 1.2 m apart. The reciprocating mass per cylinder is 800 kg, crank radius 0.3 m, speed is 180 rpm and the connecting rod is 1.35 m long. If the firing order 1-4-5-2-3-6, investigate the balancing condition of the engine for primary and secondary forces and couples.

12.a) In a vertical engine the connecting rod is 800 mm long. Its mass is 45 kg, the center of gravity is 525 mm from the axis of small end bearing and the radius of gyration is 275 mm. The crank is 200 mm long. When the crank has turned through 45º from the top dead center, its angular velocity and acceleration is 25 rad/s and 250 rad/s^{2}. Find the forces at the gudgeon pin and at the main bearings caused by gravity and inertia forces on the connecting rod.

**OR**

12.b) A small single cylinder 4-stroke cycle oil engine of 12.5cm stroke develops 5 kw at 1000 rpm. The excess energy delivered during the power stroke is 78% of the energy per cycle. The engine is filled with a combined flywheel and belt pulley of weight 800 N and radius of gyration 3 cm. The rotating parts of the engine are equivalent to 45 N concentrated at crank radius and are balanced by weights fixed to the crank webs, the center of gravity and radius of gyration of which are respectively 7.5 cm and 8.5 cm. Calculate the speed fluctuation of the engine and the calculate the percentage error that would be incurred in this estimate by considering only flywheel.

13.a) The bearing of a shaft at A and B are 5 m apart. The shaft carries three eccentric masses C, D and E which are 160 kg, 170 kg and 85 kg respectively. The respective eccentricity of each mass, measured from the axis of rotation, is 0.5 cm, 0.3 cm and 0.6 cm, and distance from A is 1.3 m, 3 m and 4 m. Determine the angular position of each mass with respect to C so that no dynamic force is exerted at bearing B and also find the dynamic force at bearing A for this arrangement when the shaft runs at 100 rpm.

OR

13.b) A centrifugal pump running at 1200 rpm has a rotor of mass 18 kg mounted overhanging on a shaft. The distance between the support bearings is very small compared to the overhanging end and thus the shaft can be considered as a cantilever whose effective length can be taken as 0.5 m. If the diameter of the shaft is 25 mm, find the natural frequency of transverse vibration of the system. What should be diameter of the shaft so that the natural frequency is 25 percent more than the running speed of the pump?

14 a) A periodic torque, having maximum value of 0.5 Nm at a frequency of 4 rad/s is applied on a flywheel suspended from a wire. The flywheel has a movement of inertia of 0.12 kgm^{2} and the wire has a stiffness of 1 Nm/rad. A viscous dashpot applies a damping couple of 0.4 Nm at an angular velocity of 1 rad/s. Calculate the (i) Maximum angular displacement from the rest position. (ii) Maximum couple applied to the dashpot.

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14.b) An electric motor of mass 120 kg is attached to the centre of a supported beam which deflects 0.75 mm under this mass. The armature of the motor has a mass of 40 kg. As the motor runs up gradually to a speed of 1500 rpm, it is observed that the maximum amplitude of vertical oscillation is 2.5 mm. diminishing to 0.5 mm at the running speed of 1500 rpm. Calculate the value of damping constant and the distance of center of gravity of the armature from the axis of rotation. The mass of the beam may be neglected.

15.a) An I.C. Engine operating at 1500 rpm is in resonance with the 3½ engine order excitation torque of 200 Nm. The mass moment of inertia of the engine is 0.8 kgm^{2 }inertia of the flywheel is relatively large, and hence can be treated as fixed. A torsional dynamic vibration absorber tuned to the natural frequency of the engine is to be used .The resulting two natural frequencies of the system are to be atleast 20% away from the 3½ engine order excitation frequency. Find the stiffness and mass moment of inertia of the absorber system.

**OR**

15.b)i) Determine the equation for the natural frequencies of a uniform rod in torsional oscillation with one end fixed and the other end free. (8 marks)

ii) A 100 m long transmission cable is held between supports with a tensile force of 400 KN. Its weight per unit length is 20 N/m. Determine the natural frequencies and mode shapes? (8 marks)

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