SHIRDI SAI ENGINEERING COLLEGESHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGINEERING COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE Fifth Semester B.E. DegreeExamination, May/June 2010 Dynamics of Machines Note: Answer any FIVE full questions, selecting at least TWO questions from eachpart. a. Whatis"principleof virtual work"? Explain. (04Marks) b. For themechanismshown inFig. Q1(b), determinethetorque onthelink AB for static equilibriumof the mechanism. Given, AB =20 mrn, BC = 60 mrn, CD = 35 mrn, AD=50mm, BE=45mrn, CE=20mrnandDG=25mrn. (16 Marks) £ F . = 2.5" N (fj~j 2..C'(\ i<I .! ) 3 c a. StateandexplainD' Alembert's principle. (04Marks) b. Showthat thecoefficient of fluctuationof speed inaflywheel isgivenby k-;.., where, I w eisthefluctuationof energy, I isthemomentof inertiaandwisthemeanspeed. (04Marks) c. Theturningmoment diagramof afour-strokeengineisassumed toberepresented byfour triangles, theareasof whichfromthelineof zeropressureare: Suctionstroke=440mrn 2 (Negative) Compressionstroke=1600mrn 2 (Negative) Expansionstroke=7200mrn 2 (Positive) Exhauststroke=660mrn 2 (Negative) Each sq. mrn. of arearepresents 3N - mof energy. I f the resisting torque is uniform, determinethemass of rimof theflywheel to keep the speed between 218 and 222rpm. Meanradiusof therimis1.25m. (12Marks) a. Deriveanexpressionfor frictional torqueinaflat pivot bearing. Assumeuniformpressure acrossthebearingsurface. (06 Marks) b. Showthatthelinear velocityof thebelt inabelt drive, for maximumpower transmission, is givenby v =~ , where, T =maximumallowabletensioninthebelt, and m=massper unitlengthof thebelt. (04Marks) c. Anopenbeltdriveisrequiredtotransmit 10kW fromamotor runningat600rpm. Diameter of thedrivingpulley is250mrnand speed of drivenpulley is220rpm. Thebelt is12mrn thick and has amass density of 0.001 g/mrn 3 • Safe stress in the belt is not to exceed 2.5N/mrn 2 Thetwoshaftsare1.25mapart. Thecoefficient of frictionis 0.5. Determine thewidthof belt. (10Marks) 10f2 SHIRDI SAI ENGG COLLEGE 4 a. Explainstatic and dynamic balance of asystemof revolving masses. (06 Marks) b. Whytwomasses indifferent planes arenecessary torectify dynamic unbalance? (04Marks) c. A systemof four revolving masses A, B, C and Dis completely balanced. Masses C and D make angles 90° and 195° respectively, with B in the same sense. Planes B and C are 250mmapart. Theradius of rotation of thefour masses are 150mm, 200rom, 100mm, and 180 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 planes A andD. (10Marks) 5 a. Explain the direct and reverse crank method of analysis of radial engines for primary and secondary forces. (06 Marks) b. Derive anexpression for resultant unbalanced force in apartially balanced single cylinder engine. (04Marks) c. A v-twin engine has the cylinder axes at right angles and the connecting rods operate a common crank. The reciprocating mass per cylinder is 11.5 kg and the crank radius is 75 mm. Length of connecting rod is 0.3m. Show that the engine may be balanced for primary force by means of arevolving mass. Also find themaximum secondary forceif the enginespeed is500rpm. (10Marks) 6 a. Establish arelationship between speed and height of aporter governor, taking friction onthe sleeveintoaccount. (08 Marks) b. I naporter governor, each of the four arms is400 romlong. Theupper arms arepivoted on theaxis of the sleeve, whereas the lower arms are attached to the sleeve at adistance of 45 mmfromthe axis of rotation. Each ball has amass of 8 kgand theload onthesleeveis 60kg. Determine therangeof speed of thegovernor for extreme radii of rotation of250 mm and 300rom. (12Marks) 7 a. Deriveanexpression relating theangle of heel and linear velocity for dynamic stability of a twowheel vehicle, negotiating acurve. (10Marks) b. Theturbine rotor of aship has amass of 2200 kgand rotates at 1800rpmclockwise when viewed fromthe stem. Theradius of gyration of rotor is 320 mm. Determine thegyroscopic coupleand stateitseffect when: i) Theship steers totheright at aspeed of 25 krnph inacurve of radius 250m ii) Theship pitches, withthebow rising atanangular velocity of 0.8 rad/s. (10Marks) 8 a. Find thevelocity and acceleration of aroller follower operated by atangent camwhenthe roller ismaking contact: i) Ontheflank, ii) Withthenose. (12Marks) b. A tangent camwith straight working faces tangential to abase circle of 120mmdiameter hasaroller follower of 48 mmdiameter. Thenosecircle radius of thecamis 12mmand the anglebetween the tangential faces of the camis 90°. I f the speed of the carn is 180rpm, determinetheacceleration of thefollower when: i) During lift, theroller just leaves thestraight flank ii) Theroller isat thetop of thenose. (08 Marks) SHIRDI SAI ENGG COLLEGE Fifth Semester B.E. DegreeExamination, May/June 2010 Dynamics of Machinery Note:1. Answer any FIVE full questions. 2. Use of drawing sheet ispermitted. For the static equilibriumof the mechanism, Fig. Q1, find the required input torque. The dimensionsareAB=150mm, BC =:: AD=500mm;DC =300mm; CE=100mmandEF = 450mm. (20Marks) f:.. a. Obtainexpressionforratioof drivingtensionsforflatbelt drive. (06Marks) b. Determinethewidth of a9.75 mmthick belt required to transmit 15 kW fromamotor runningat900rpm. Thediameter of thedrivingpulleyof themotor is300mm. Thedriven pulleyrunsat300rpmanddistancebetweencentersof thetwopulleysis3mts. Thedensity of leather is 1000 kg/m 3 . The maximumallowable stress in leather is 2.5 MPa. The coefficientof frictionbetweenleather andpulleyis0.3. Assumeopenbelt driveandneglect slogandslipof thebelt. (14 Marks) a. Definethetermscoefficient of fluctuationof speedand coefficient of fluctuationof energy. (06Marks) b. A punchingpressisdrivenbyaconstanttorqueelectric motor. Thepressisprovidedwitha flywheel thatrotatesatamaximumspeedof 225rpm. Theradiusof gyrationof theflywheel is0.5 m. Thepresspunches 720holesper hour, eachpunching operationtakes2seconds andrequires 15kN-mof energy. Findthepower of themotor andtheminimummassof the flywheel if speedof thesameisnottofall below200rpm. (14 Marks) a. Explainhowasinglerotatingmassisbalancedbybalancingmassinsameplane. (05 Marks) b. A shaftcarriesfourmassesA, B, C andDof magnitudes 200kg, 300kg, 400kgand200kg respectivelyandrevolvingatradii of 80mm, 70mm, 60mmand 80mminplanesmeasured fromA at 300mID,400mmand 700mm. Theanglesmeasured inanticlockwisedirection betweencranksareA toB45°, BtoC 70° andC toD120°.Thebalancingmassesaretobe placedinplanesX and Y. ThedistancebetweenplanesA andX is 100mm, betweenX and Y is400mmand betweenY and Dis200mm. If thebalancemasses revolveat aradii of 100mm, findtheir magnitudesandangularpositions. (15 Marks) SHIRDI SAI ENGG COLLEGE 5 a. Explain themethod of direct and reverse cranks for balancing of primary forces. (05Marks) b. A five cylinder in line engine running at 750 rpmhas successive cranks 144° apart, the distance between cylinder center lines being 375 rom. Thepiston stroke is225 romand ratio of connecting rod to crank is 4. Examine the engine for balance of primary and secondary forces and couples. Find themaximum values of these and position of central crank at which thesemaximum values occur. Thereciprocating mass for each cylinder is 15kg. (15 Marks) 6 a. Explain theprinciple of operation of acentrifugal governor with aneat sketch. (05Marks) b. Thearms of aporter Governor are300romlong. Theupper arms arepivoted ontheaxis of rotation. The lower arms are attached to asleeve at adistance of 40 romfromthe axis of rotation. The mass of the sleeve is 70 kg and mass of each ball is 10kg. Determine the equilibrium speed when the radius of rotation of the balls is 200 mm. If the friction is equivalent to aload of 20N at thesleeve, what will betherange of speed for this position? (15Marks) 7 a. Describe theeffect of gyroscopic couple during pitching of ship. (05Marks) b. A rear engine automobile istraveling along atrack of 100mts mean radius. Each of thefour road wheels has amoment of inertia of 2.5 kg_m 2 and an effective diameter of 0.6 m. The rotating parts of the engine have amoment of inertia of 1.2kg_m 2 and rotate inthe sarne sense as the road wheels. The ratio of engine speed to back axle speed is 3:1. The automobile has amass of 1600 kg and its centre of gravity 0.5 mts above road level. The width of track of vehicle is 1.5 mts. Determine the limiting speed of the vehicle around the curve for all four wheels to maintain contact with the road surface. Assume that the road surface isnot cambered and center of gravity of theautomobile lies centrally with respect to four wheels. (15Marks) 8 a. Derive an expression for velocity and acceleration for atangent camwith roller follower, whentheroller isincontact with straight flank. (08Marks) b. Thefollowing datarefer tocircular arc carnworking with aflat faced reciprocating follower. Minimum radius of carn =30rom; Total angle of camaction 2ex=120°; Radius of circular arc =80rom; Nose radius =10rom. i) Find thedistance of thecentre of Nose circle fromthecenter of cam. ii) Find the velocity in m/s and acceleration in m/s 2 of the follower when the carn has turned through an angle of e=20°. Angle eis measured from the point where the follower just starts moving away from the cam. The angular velocity of the carn = 10rad/s. (12Marks) SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE SHIRDI SAI ENGG COLLEGE