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Dynamics of Machinery - Jun 18
Mechanical Engineering (Semester 5)
Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
Module - 1
1.a. State the condition for static Equilibrim of a body subjected to a system.
1.Two forces
2.Three forces
3.Member with two forces and a torque.
1.b. For the mechanisim shown in fig. find the required input torque for the static equilibrium.The length of OA are 250mm and 650mm respectively.F=500N.
OR
2.a. Explain in brief D'Alembert's principle and state why it is used.
2.b. In vertical double acting engine.the connecting rod is 4.5 times the crank .Stroke of the piston is 400mm and the mass of the reciprocating parts is 100kg.The engine runs at 250 rmp .If the net load on the piston due to the steam pressure is 25kN when the crank has turned through an angle of 120° from the top dead centre determine.
1.Piston effort
2.Thrust in the connecting rod
3.Pressure on slide bars.
4.Crank pin effort.
5.Thrust on crank shaft bearing
6.Turning moment on the crank shaft.
Module-2
3.a. Briefly explain the statie and dyanamic balancing.
3.b. Four masses A<B<C and D are carried by a roating shaft at radii 100mm , 125mm , 200mm and 150mm respectively .The planes in which the masses revolve are spaced 600mm apart and the mass of B.C and D are 10kg 5kg and 4kg respectively .Find the required mass 'A' and the relative angular position of the four masses.So that the shaft shall be in complete balance. </div> (12 marks) 00
OR
4.a. What do you mean by primary and secondary unbalance in recripocating engines?
4.b. The cranks and connecting rod of a 4 cylinder in line engine running at 1800 rpmare 50mm , 250 mm each respectively and the cylinders are spaced 150mm apart.If the cylinders are numbered 1 to 4 in sequence from one end and cranks appear at intervals of 90° in an end view in order 1 - 4 - 2 - 3.The reciprocating masses corresponding to each cylinder is 1.5kg Determine Unbalanced primary and secondary forces if any,Unbalanced primary and secondary couples with reference to central plane of engine.
Module - 3
5.a. Derive the expression for speed of a porter governor with usual notations taking friction in to account.
5.b. In a porter governor,the upper and lower arms are 200 mm and 250 mm respectively and pivoted on the axis of rotation.The mass of central load is 15kg .The mass of each ball is 2kg and friction of the sleeve together with the resistance of the operating gear is equal to a load of 24 N at the sleeve.If the limiting inclinations of upper arms to vertical are 30° and 40° Find the range of speed taking friction in to account.
OR
6.a. Explain the effect of Gyroscopic couple of a ship under:
1.Steering
2.Pitching
3.Rolling.
6.b. Analyze the stability of a two wheel vechile turning right.Derive the necessary equation.
Module -4
7.a. Define following
1.Simple harmonic motion
2.Resonance
3.Degree of freedom
4.Phase difference.
7.b. With a neat sketch explain the beats phenomenon and obtain its resultant motion.
7.c.
Add following motion analytically and check the solution graphically.
OR
8.a. Explain energy method of finding natural frequency of a spring mass system.
8.b. Find the natural frequency of the system shown below by using newton's method and energy method.
Module -5
9.a. Set up the differential equation for a spring mass damper system and obtain complete solution for the under damped system.
9.b. For a spring mass damper system of mass 3.5 kg spring of stiffness 2.5 N/mm and damping co-efficient of 0.018 N-S/mm find Logarithmic decrement,Ratio of any two successive amplitude,Number of cycles after which original amplitude reduces to 20%
OR
10.a. Derive expression for steady state amplitude of vibration of mass in a spring mass damper system when the mass is subjected to harmonic excitation .Also find phase angle
10.b. A pump of 200 kg is driven through a belt by an electric motor at 3000rmp.The pump is mounted on isolators with total stiffness 5MN/m and damping 3.125 kN-S/m. Determine the vibratory amplitude when pump is switched on and motor speed passes through resonant condition..
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