Dynamics of Machines - May 2016
Mechanical Engg. (Semester 5)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1(a) Discuss the equilibrium of the following systems:
i) Two force members i) Three force members iii) Member with two forces and a torque.(9 marks) 1(b) With usual notations, explain the principle of virtual work, considering a slider crank mechanism.(11 marks) 2(a) Discuss the following terms: i) Turning moment diagram ii) Co-efficient of fluctuation of energy iii) Co-efficient of fluctuation of speed.(6 marks) 2(b) The turning moment diagram for an engine consists of 2 Isosceles triangles. Maximum height of each triangle represent turning moment 1000Nm. The base of each triangle = π radians. If the engine runs 200 rpm and total fluctuation of speed is not to exceed 3% find :
i) Power of the engine
ii) Mass of rim type fly wheel concentrated at 0.25m, radius neglecting the effect of arms and boss.(14 marks) 3(a) Derive an expression of total frictional torque for a Flat collar bearing subjected to uniform pressure.(8 marks) 3(b) A belt which is embracing 165° of a pulley of effective diameter 1000mm is transmitting 10KW. The pulley is running at 250 rpm. The coefficient of friction is 0.3 Mass of belt material is 0.0012gm/mm3. Thickness of belt = 10mm. Considering centrifugal tension, find width of belt. Safe working stress is 1.5MPa. Also detrmine the Initial tension in the belt drive.(12 marks) 4(a) What do you mean by static balancing and dynamic balancing?(4 marks) 4(b) A rotating shaft carries four radial masses A = 8kg, B, C = 6kg, D = 5kg.The mass centres are 30, 40, 40 and 50mm respectively from the axis of shaft. The axial distance between the planes of rotation of A and B is 400mm and between B and C is 500mm. The masses A and C are at right angles to each other. Find for a complete balance i) the angle of the masses B and D from mass A ii) the axial distance between the planes of rotation of C and D and iii) the magnitude of mass B.(16 marks) 5(a) The cranks and connecting rod of a 4 cylinders in line engine running at 1800 rpm are 50mm, 250mm each respectively and the cylinders are spaced 150mm apart. If the cylinders are numbered 1 to 4 in sequence from one end and the cranks appear at intervals of 90° in an end view in the order 1-4-2-3. The reciprocating mass corresponding to each cylinders is 1.5kg. Determine i) Unbalanced primary and secondary forces if any ii) Unbalanced primary and secondary couples with reference to central plane of engine.(20 marks) 6(a) Explain the terms Sensitiveness, Stability, Efforts and Power of governor.(8 marks) 6(b) The length of upper arm and lower arms of a porter governor are 200mm and 250mm repectively. Both the arm are pivoted to the axis of rotation. The central load is 150N, the weight of each ball is 20N and the friction of the sleeve togther with the resistance of the operating gear is equuivalent to a force of 30N at the sleeve. If the limiting inclinations of the upper arm to the vertical are 30° and 40°, determine the range of speed of the governor.(12 marks) 7(a) Derive an expression for the gyrosocopic couple.(5 marks) 7(b) The motor of a marine having a mass of 1000 kg and radius of gyration 300mm rotates at 1550 rpm clockwise when looking from the bow. Determine the gyroscopic couple and its effect on the ship in the following cases:
i) When the ship pitches with an angular velocity of 1 rad/sec when the bow
ii) When the ship is speeding at 40km/hr and takes a right turn in a circular path of 200m radius.
iii) When the ship rolls at certain instant, it has an angular velocity 0.5 rad/sec when viewed from the stern.(15 marks) 8 The following data relate to a symmetrical circularcam operating on a flat faced follower. Least radius = 25mm, Nose radius = 8mm, Lift of the valve = 10mm, Angle of action ofcam = 120°, Cam shift speed = 1000rpm. Determine i) Flank radius ii) Maximum velocity iii) Maximum acceleration iv) maximum retardation. If the mass of the follower and valve with which it is in contact is 4 kg, find the minimum force exerted by the spring to overcome the inertia of the moving parts.(20 marks)