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SHIRDI SAI ENGINEERING COLLEGE

SHIRDI SAI ENGG COLLEGE

Fifth Semester B.E. Degree Examination, May/June 2010Dynamics of Machines

Note: Answer any FIVE full questions, selectingat least TWO questions from each part.

a. What is "principle of virtual work"? Explain. (04 Marks)b. For the mechanism shown in Fig. Q1(b), determine the torque on the link AB for static

equilibrium of the mechanism. Given, AB = 20 mrn, BC = 60 mrn, CD = 35 mrn,AD = 50 mm, BE = 45 mrn, CE = 20 mrn and DG = 25 mrn. (16 Marks)

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a. State and explain D' Alembert's principle. (04 Marks)

b. Show that the coefficient of fluctuation of speed in a fly wheel is given by k -;.., where,Iw

e is the fluctuation of energy, I is the moment of inertia and w is the mean speed. (04 Marks)c. The turning moment diagram of a four-stroke engine is assumed to be represented by four

triangles, the areas of which from the line of zero pressure are :Suction stroke = 440 mrn2 (Negative)Compression stroke = 1600 mrn2 (Negative)Expansion stroke = 7200 mrn2 (Positive)Exhaust stroke = 660 mrn2(Negative)Each sq. mrn. of area represents 3N - m of energy. If the resisting torque is uniform,determine the mass of rim of the flywheel to keep the speed between 218 and 222 rpm.Mean radius of the rim is 1.25 m. (12 Marks)

a. Derive an expression for frictional torque in a flat pivot bearing. Assume uniform pressureacross the bearing surface. (06 Marks)

b. Show that the linear velocity of the belt in a belt drive, for maximum power transmission, is

given by v = ~ , where, T = maximum allowable tension in the belt, and m = mass per

unit length of the belt. (04 Marks)c. An open belt drive is required to transmit 10 kW from a motor running at 600 rpm. Diameter

of the driving pulley is 250 mrn and speed of driven pulley is 220 rpm. The belt is 12 mrnthick and has a mass density of 0.001 g/mrn3• Safe stress in the belt is not to exceed2.5 N/mrn2 The two shafts are 1.25 m apart. The coefficient of friction is 0.5. Determinethe width of belt. (10 Marks)

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4 a. Explain static and dynamic balance of a system of revolving masses. (06 Marks)b. Why two masses in different planes are necessary to rectify dynamic unbalance? (04 Marks)c. A system of four revolving masses A, B, C and D is completely balanced. Masses C and D

make angles 90° and 195° respectively, with B in the same sense. Planes B and C are250 mm apart. The radius of rotation of the four masses are 150 mm, 200 rom, 100 mm, and180 mm respectively. Masses B, C and Dare 25 kg, 40 kg and 35 kg respectively.Determine: i) Mass A and its angular position with mass B, ii) Axial positions of planesA and D. (10 Marks)

5 a. Explain the direct and reverse crank method of analysis of radial engines for primary andsecondary forces. (06 Marks)

b. Derive an expression for resultant unbalanced force in a partially balanced single cylinderengine. (04 Marks)

c. A v-twin engine has the cylinder axes at right angles and the connecting rods operate acommon crank. The reciprocating mass per cylinder is 11.5 kg and the crank radius is75 mm. Length of connecting rod is 0.3m. Show that the engine may be balanced forprimary force by means of a revolving mass. Also find the maximum secondary force if theengine speed is 500 rpm. (10 Marks)

6 a. Establish a relationship between speed and height of a porter governor, taking friction on thesleeve into account. (08 Marks)

b. In a porter governor, each of the four arms is 400 rom long. The upper arms are pivoted onthe axis of the sleeve, whereas the lower arms are attached to the sleeve at a distance of45 mm from the axis of rotation. Each ball has a mass of 8 kg and the load on the sleeve is60 kg. Determine the range of speed of the governor for extreme radii of rotation of250 mmand 300 rom. (12 Marks)

7 a. Derive an expression relating the angle of heel and linear velocity for dynamic stability of atwo wheel vehicle, negotiating a curve. (10 Marks)

b. The turbine rotor of a ship has a mass of 2200 kg and rotates at 1800 rpm clockwise whenviewed from the stem. The radius of gyration of rotor is 320 mm. Determine the gyroscopiccouple and state its effect when:i) The ship steers to the right at a speed of 25 krnph in a curve of radius 250 mii) The ship pitches, with the bow rising at an angular velocity of 0.8 rad/s. (10 Marks)

8 a. Find the velocity and acceleration of a roller follower operated by a tangent cam when theroller is making contact:i) On the flank, ii) With the nose. (12 Marks)

b. A tangent cam with straight working faces tangential to a base circle of 120 mm diameterhas a roller follower of 48 mm diameter. The nose circle radius of the cam is 12 mm and theangle between the tangential faces of the cam is 90°. If the speed of the carn is 180 rpm,determine the acceleration of the follower when:i) During lift, the roller just leaves the straight flankii) The roller is at the top of the nose. (08 Marks)


Fifth Semester B.E. Degree Examination, May/June 2010Dynamics of Machinery

Note:1. Answer any FIVE full questions.2. Use of drawing sheet is permitted.

For the static equilibrium of the mechanism, Fig. Q1, find the required input torque. Thedimensions are AB = 150 mm, BC =:: AD = 500 mm;DC = 300 mm; CE = 100 mm and EF =450 mm. (20 Marks)

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a. Obtain expression for ratio of driving tensions for flat belt drive. (06 Marks)b. Determine the width of a 9.75 mm thick belt required to transmit 15 kW from a motor

running at 900 rpm. The diameter of the driving pulley of the motor is 300 mm. The drivenpulley runs at 300 rpm and distance between centers of the two pulleys is 3 mts. The densityof leather is 1000 kg/m3. The maximum allowable stress in leather is 2.5 MPa. Thecoefficient of friction between leather and pulley is 0.3. Assume open belt drive and neglectslog and slip of the belt. (14 Marks)

a. Define the terms coefficient of fluctuation of speed and coefficient of fluctuation of energy.(06 Marks)

b. A punching press is driven by a constant torque electric motor. The press is provided with aflywheel that rotates at a maximum speed of 225 rpm. The radius of gyration of the flywheelis 0.5 m. The press punches 720 holes per hour, each punching operation takes 2 secondsand requires 15 kN-m of energy. Find the power of the motor and the minimum mass of theflywheel if speed of the same is not to fall below 200 rpm. (14 Marks)

a. Explain how a single rotating mass is balanced by balancing mass in same plane. (05 Marks)b. A shaft carries four masses A, B, C and D of magnitudes 200 kg, 300 kg, 400 kg and 200 kg

respectively and revolving at radii of 80 mm, 70 mm, 60 mm and 80 mm in planes measuredfrom A at 300 mID,400 mm and 700 mm. The angles measured in anticlockwise directionbetween cranks are A to B 45°, B to C 70° and C to D 120°. The balancing masses are to beplaced in planes X and Y. The distance between planes A and X is 100 mm, between X andY is 400 mm and between Y and D is 200 mm. If the balance masses revolve at a radii of100mm, find their magnitudes and angular positions. (15 Marks)


5 a. Explain the method of direct and reverse cranks for balancing of primary forces. (05 Marks)b. A five cylinder in line engine running at 750 rpmhas successive cranks 144° apart, the

distance between cylinder center lines being 375 rom. The piston stroke is 225 rom and ratioof connecting rod to crank is 4. Examine the engine for balance of primary and secondaryforces and couples. Find the maximum values of these and position of central crank at whichthese maximum values occur. The reciprocating mass for each cylinder is 15 kg. (15 Marks)

6 a. Explain the principle of operation of a centrifugal governor with a neat sketch. (05 Marks)b. The arms of a porter Governor are 300 rom long. The upper arms are pivoted on the axis of

rotation. The lower arms are attached to a sleeve at a distance of 40 rom from the axis ofrotation. The mass of the sleeve is 70 kg and mass of each ball is 10 kg. Determine theequilibrium speed when the radius of rotation of the balls is 200 mm. If the friction isequivalent to a load of 20 N at the sleeve, what will be the range of speed for this position?

(15 Marks)

7 a. Describe the effect of gyroscopic couple during pitching of ship. (05 Marks)b. A rear engine automobile is traveling along a track of 100 mts mean radius. Each of the four

road wheels has a moment of inertia of 2.5 kg_m2 and an effective diameter of 0.6 m. Therotating parts of the engine have a moment of inertia of 1.2 kg_m2 and rotate in the sarnesense as the road wheels. The ratio of engine speed to back axle speed is 3: 1. Theautomobile has a mass of 1600 kg and its centre of gravity 0.5 mts above road level. Thewidth of track of vehicle is 1.5 mts. Determine the limiting speed of the vehicle around thecurve for all four wheels to maintain contact with the road surface. Assume that the roadsurface is not cambered and center of gravity of the automobile lies centrally with respect tofour wheels. (15 Marks)

8 a. Derive an expression for velocity and acceleration for a tangent cam with roller follower,when the roller is in contact with straight flank. (08 Marks)

b. The following data refer to circular arc carn working with a flat faced reciprocating follower.Minimum radius of carn = 30 rom; Total angle of cam action 2ex= 120°; Radius of circulararc = 80 rom; Nose radius = 10 rom.i) Find the distance of the centre of Nose circle from the center of cam.ii) Find the velocity in m/s and acceleration in m/s2 of the follower when the carn has

turned through an angle of e = 20°. Angle e is measured from the point where thefollower just starts moving away from the cam. The angular velocity of the carn =

10 rad/s. (12 Marks)


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