CHHATTISGARH SWAMI VTVEKANAND TECHNICALUNIVERSITYO BHILAI (C G)Semester:V -' Branch:MechanicalEngg.

Subfect: Dynamics of Machines

UNIT.I

Governorc:

Characteristics of centrifugal govemors, gravi$ controlled govemors such as Porter, and Proell. Spring controlledcentrifugalgovernors such as Hartung, and Hartnellgovernor, performance parameters: sensitivity, stability,isochronism and hunting, governor effort and power

uNlT - ll

Balancing:

Balancing of rotating ma$ses, static and dynamic balancing, determination of balancing masses in two planebalancing, balancing of internal combustion engines, balancing of in-line engines, firing order, balancing of V-twinand radial engines, forward and reverse crank method, balancing of rotors.

uNlT-ilt

Gyroscope:Gyroscopic forces and couple, gyroscopic stabilization of airplanes, ship motion and vehicles moving on curued

Path.

UNIT.IV

Mechanicql Vibratlons:

One dimensional longitudinal, transverse, and torsional vibrations, natural frequency, effect of damping onvibrations, types of damping, different types of damping. Forced vibration, forces and displacement, transmissibility,vibration isolation, vibration sensors: seismometer and accelerometers\Alhirling of shafts with single rotor.

UNIT.V

lnertia force analysis

Effective force and inertia force of a link, lnertia forces in the reciprocating engine, lnertia forces in four bar chain.

Turning moment diagram and flywheel

Turning moment diagram for single and multi cylinder intemal combustion engine, coefficient fluctuation of speed,coefficient of fluctuation of energy, flywheel

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e'recf'' 1rifth semester) Examination (Aprir-May) 201 0Subyecf; Dynamics of Machines

Branch : Mechanical EngineeringTime: Three Hours

r'\tonnes and rotates at

of the rotor is 32b mm"

l{6a95t3Code:

{r.;

1800 rpm

Deterrnine

NoTE: Attempt any five questior?s. Assume suitabte data if required.

Max. illarks: g0

Min. Pass lVlarks : 2g

.a'

,fl . jn t Porter governor, each of the four arms is 400 mm long. The upper arms arepivoted on the axis of the sleeve, whereas the lower arms are attalneo to the sreeve at adistance of 45 mm from the axis of rotation. Each ball has a mass of g kg and load on thesleeve is 60 kg' what will be the equilibrium speeds for the two extreme radii of 250 mmand 300 mm of rotation of the governor balls? (16)

,4 A circular disc mounted on a shaft carries three attached masses 4 kg, 3 kg and2'5 kg at radial distances 75 mm, 85 mm and 50 mm and at the angular positions of 4so,1350 and 2400 respectively' The angular positions are measured counter-crockwise fromthe reference line along x-axis. Determine the amount of the countermass at a radialdistance of 75 mm required for the static batance. (16)

Q3 A radial aero-engine has seven cylinders equally spaced with all the connectingrods coupled to a common crank' The crank and each of the connecting rods are 200mm and 800 mm respectively. The reciprocating mass per cylinder is 3 kg. Determinethe magnitude and angutar position of the balance masses reguired at the crank radiusfor comprete primary and secondary barancing of the engine. (16)/

' -6+ The turbine rotor of a ship has a mass of 2.2Vclockwise when vigyieqjgn ?XI. The radius of gyrationthe gyroscopic couple and its effect when(i) the ship turns right at a radius of 25om with a speed of 25 kms/hr(ii) the ship pitches with the bow rising at an angular verocity of 0.g rad/sec(iii) the ship rolls at an angular velocity of 0.1 radlsec

(16)

N,lGoq9t)CSVTU Code:lIl

\,/d5 Each wheel of a motorcycle is of OO6\ mm diameter and nr$,, moment of inertia of

:1.2 kg-m'. The total mass of the motorcycle and the rider is 1Ab kg and the combined

center of mass ir bg6 mm above the ground level when the motor cycle is upright. The

moment of inertia of the rotating parts of the engine is O./ftg-mz. The engine speed is S Q

times the speed of the wheels and is in the same sense. Determine the angle of heel

necessary when the motorcycle takes a turn of 35 m radius at a speed of S/kms/hr.

QO ln a single-degree damped vibrating

oscillations in 18 seconds. The amplitude

oscillations. Determine:

(i) the stitfness of the spring

(ii) the logarithmic decrement

(iii) the damping factor, and

(iv) the damping coefficient.

(16)

system, a suspended mass of I kg makes 30

decreases to 0.25 of the initial value after 5

3'q

Q7 A rotor has a mass of 12 kg and is mounted midway on a 24 mm diameter

horizontal shaft supported at the ends by two bearings. The bearings are 1 m apart. The

shaft rotates at 2400 rpm. lf the centre of mass of the rotor is 0.11 mm away from the

geometric center of the rotor due to certain manufacturing defect, find the amplitude of

the steady state vibration and the dynamic force transmitted to the bearing. Take E = 200

GN/mz.

(16)

(16)

The turning moment diagram for a petrol engine is drawn to a vertical scale of 1 mm =

500 N-m and a horizontal scale of 1 mm = 30. The turning moment diagram repeats itself after

every half revolution of the crankshaft. The areas above and below the mean torgue line are 260,

-580, 80, -380, 870, and -250 mm2. Tpe rotating parts have a mass of 55 kg and radius of

gyration of 2.1 m. lf the engine speed is 1600 rpm, determine the coefficient of fluctuation ofcrK' i*'

(16)

a

speed"

ffiSVTU #ode: Mffi09513El"Tee h" 200s

Time; Three $-fiours Max, Marks: 80

Min. Pass Marks: 2&

NOTE: Attempt any five questions. Assume suitable data if required.

\Ol All the arms of a Porter governor are 178 mm long and are hinged at a distance of 38 mm from the\axis of rotation. The mass of each ball is 1.15 kg and mass of the sleeve is 20 kg. The governorsleeve

begins to rise at 280 rpm when the links are at an angle of 300 to the vertical. Assuming the friction force tobe constant, determine the minimum and maximum speed of rotation when the inclination of the arms tothe vertical is 450.

, (16)

Q2 A shaft has three eccentrics, each 75 mm diameter and 25 mm thick, machined in one piece with

the shaft. The central planes of the eccentric are 60 mm apart. The distances of centers from the axis ofrotation are 12 mm, 18 mm, and 12 mm and their angular positions are 1200 apart. The density of metal is7000 kg/mt. Find the amount of out-of-balance force and couple at 600 rpm. !f the shaft is balanced by

adding two masses at a radius of 75 mm and atdistance of 100 mm from the central plane of the middle

eccentric, find the amount of the masses and their angular positions.

imation {Nov-Dee}

of folachines

Enginebring

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tm

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bje

tnct

(Fifth I

Sur

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single

radius

(16)

A radial aero-engine has nine cylinders equispaced. All connecting rods are coupled direct to acrank. The reciprocating mass per cylinder is R kg; the connecting rod length is L m and the crank

is r meters.

(b) Discuss with equations the gyroscopic effect on ships during pitching.'

t;

' )

:,.

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Determine the magnitude and angular position of the balance mass at a radius of r meters

necessary to completeiy balance the engine for primary and secondary forces at N r.p.m.

(16)

Q4 (a) Derive equation for angle of heel which a motorcycle makes while turning with verticql. Take M

and m as mass of motorcycle and rider, V in kms/hr as velocity during turning, R and r as radius of turn

,and wheel, h as distance of C.G. from ground level when motorcycle is in upright position, l" and I, as')/ moment of inertia of engine and wheel, Gr. and trlw as angular sp6ed of engine and wheel. The engineI( rotates in direction opposite to the wheels.

(08)

(08)

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€+: A four wheeled car have axis of rotation of engine parts along the longitudinal axis. The engit;e\.-parts rotate in clockwise direction when viewed from front. Determine the reaction on each wheelwhen the

car takes turn towards left with a velocity of V kms/hr'

Take w as weight of car, l* and I* as moment of

reaction on Rear inner, front inner, rear outer and front

engrne and wheel, R and r as radius of turn and wheel, h

track and wheel base, G as gear ratio.

Find also the limiting speed of the car.

.r.lc**Fil

inertia of engine and wheel, R;, Fi, Ro and Fo as

outef wheels, Lrls and Ld1ry aS angular Speed Of

as distance of C.G" from ground level, a and I as

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j t':rr,:: t

t rtt*ls'-'-'1tr' 1-i'r"c! !k

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.e6 Find the naturalfrequencies of a vibratory system having a flywheel suspended at the free end of a

/massless shaft forIt til longitudinalvibration

\ (ii) transverse vibration

\ Find also the natural frequencies for both vibrations when inertia of shaft is taken into account'

(16)

\oz The mass of an electric motor is 120 kg and it runs at 1500 ipm. The armature mass is 35 kg and

its c.G. lies 0.5 mm from the axis of rotation. The motor is mounted on five springs of negligible damping

so that the force tr.ansmitted is one-eleventh of the impressed force. Assume that the mass of the motor is

equally distributed among the five springs' Determine t '

(i) stitfness of each sPring

(ii)dynamicforcetransmittedtothebaseattheoperatingspeedand

(iii) natural frequency of the system

(16)

\o, The crank-pin circle radius of a horizontal engine is 300 mm" The mass of the reciprocating parts is

2s0 kg. when the crank has traveled 600 from lDC, the differ:ence between the driving and the back

pressure is 0.35 N/mmz. The connecting rod length between centers is 1.2 m and the cylinder bore is 0'5

m. lf the engine runs at 250 rpm and if the effect of piston rod diameter is neglected, calculate

(i) pressure on slide bars

(ii) thrust in the connecting rod

(iii) tangentialforce on the crank pin, and

(iv) turning moment on the crank shaft'

't'l-6)

({ 6}

B.Tech,

TinTe: Three Hours

NOTE : Attempt any fiveques/ions. Assum e suitable data if required.

Je1 The lengths of the ball and sleeve arms of the bell

and 120 mrn respectivety, The mass of each governor ball

a distance of 160 mm. At the mean speed of the governor

the sleeve arms are horizontal. The sleeve moves up

Neglecting friction, determine

(i) the spring stiffneps

lli,*,- *u**?t?t?i: M Eo* s' 3

Max. Marks: 80

Min. Pas$ Marks: 28

crank lever ofi a Hartnell governor are 140 mm:;

is 5 kg, The fullcrum sf the bell-crank lever is at

which is 250 rpm, the ball arrns are vertiCal and

by 12 mm fcii an increase of speed of 4o/o,

speed. (16)

makes angles of 900 and

rotating masses have the

( F rt h $ e m e s t e,l .1J L X fi j*$ubyecf; DYnamics 0f Machines

Branch; Mechanical Engineering

c)

(ii)the minimum equilibrium speed when the sleeve moves by 24 l1m'

I(iii) the sensitiveness of the governor.

il

(iv) the spring stiffness for the governor to be isochronou-s at the nhean

Iii

Q2 Four masses A, B, C and D

1950" respectively with that of mass

following proPerlies:

are completely balanced. Masses C' and D

B in the counterclockwise direction. The:

'iI,l

mm, fc = 100 rfirm, [d = 180 mm.i

that of ma$s B i

plane of mass A.'l

a

equispaced. Atl connecting rods are coupled Cirect to a

is R kg; the connecting rod length is L m and the crank

l

osition of the balanc€| mas$ at a radius of r.rleters,;

mary and secondary fclrces at N r.p.rn.

(i) the mass A and its angular position with

(ii) the positions of all the planes relative to

\_/Q3 A radial aero-engine has eleven cylinders

single crank, The reciprocating rnass per cylinder

radius is r meters.

Determine the magnitude and angular p

necessary to completely balance the engine for pri

tTlb = 25 kg, lTtc ='40 kg, rfld = 35 kg, Fa = 150 mm, [b = 200

Planes B and C are 250 mm apart, Determine

Itor of the turbine of a ship has a mass of 2500 kgJQ4 The rc a snlp nas a mass or

counter-Clockwise when viewed from stern. The rotor has radius of

gyroscopic couple and its effect when

(i) the ship steers to the left in a curve 0f B0 m

( 1 knot = 1860 miles/hr, 1 rnile * 1.6 kilometers eppro

d rotates

yration of

adius at

imately).

(16)

at a Speed of 3200 rPm

"0.4 m. Determine the

a speed of 15 knots

l-TO

(ii) The ship Pitches 50 above an'J

with its maxirnlttn velocitY. TheI

40 seconds. 11

ii

S0 below the normal po$ition and the bow is clrss':ei-l,,".,,,,,

pitching rrrotion is simple harmonic with a perioclic tinre i:i

(iii)

,/-+6a A rnachine\,/\--/ .'\''

cPrings is 12 I'J,In:m

The ship rollr{l and at the instant, its angular velocity is C,4 rad/s clockwise when ','iewed

frcm stern.

angular acceleration during pitching.

As A 2,2 tohne racing car has a vyheel base of 2.4 mand a track of 1.4 m. The center of nrass of ther./\\-/ car lies at 0.6 m above the groLnd and 1.4 m from the rear axle. Equivalent mass of engine parts iq 140 kg

with radius of gyration of 1S0 nrm. Tlre back axle ratio is 5. The engine shaft and flywheel rotate clctckwise

when viewed from front. Each yvheel has a diameter of 0.8 m and a moment of inertia of 0.7 kgm2.

Determine the load OisiriOution on the wheels when the car is iounding a curve of 100 m radius at

;l

a speed cf T2kmlhr to the (a)fleft (b) right.

Find also the maximunhiil,

ii

iii

weighs 18,ikg and is $upported on springs

and dgq'lgSl 3lry9 rhe sv$tem is

(1s)

and dashpots. The total stiffness of the

irritialiy at rest and a velocity of 12fr mm/s

(16)

is irnparted to the mass. Deternline:

{i) the displacement ancl velocity of rna$s as a function of time.

(ii) the displacemei'rrt and velocity after 0.4 secund.

,/, ,/QA The turning moment cliagram for a multicylinder engine has beenV/v I

1 mm = 650 N,m and a norizoqltal scale of 1 mm = 4.50. The areas above and

ef A machine ,supported symmetrically o1 four. sprlgs . has a rnass of 80 kg. The rnass of

reciprocatipg parts is 2.2 kg wtriclr move thr:ough a vertical stroke of 100 mm rvith simple harmonic motion.

Neglecting rJamping, cJetermine the combined stiffness of the springs so that the force transmitted to the

fgundation is 1/20th of the impqessed force, The ntachine crankshaft rotates at 800 rpm.

lf, under actual workin$ conditions, the damping reduces the amplitudes of successive rrihrrations

by 30%, find, I

(i) the force transnlitteo to the foundation at 800 rpm,

(ii) the force trrn.n{itt"a to the foundatipn at resonance, and

(iii) the amplitude of the vibrations at resonance'

(1 6)

{1s}

(1$)

drawn to venical scale of

beiow the ntean torque line

are -28, +380, -260, +3'10, +09, +242, -380, +265 and -229 mrnz.

Thefluctuationof spegFislimitedtotl.s\/oof themeanspeed whichis400rpm. Densityof the

rim material is 7000 kg/rr3 arlcl width qf the rim is 4.5 times its thickness: The centrifugal stress (hoop

stres$) in the 6m material is tiniriteO to 6 N/mm2. Neglecting the effect of the boss and arms, determine the

iJiam*ter and crCIs$-$e0tion 0f {l're flyrruheel rim,

C*dc; {}65t}2'4 S

II.IJ:.(Fil'th Semcstc'r) flxttmlnation Apr-May 2{}0?

Su bi ect: I)7'numir:s r .f llrl uch in es

Ilrtnclr : Mec:lt an irnl lingineering

'I'intc:'l'hrcc l'l ou rli Max Mnt'l<s: I {}t}

Min ltitss Marks:35

_-"**_'--.-*-_*:-

N0tc: Attempt any fivc qucstions. All questions cflrry cqual marks.

Assumc suitablc data", if necc$sary.

,"e,l t Write.in brief about classitication oJ'lbllowers. l)raw neat ske{chcs' 10

D(;* Lpl Derive expression lor acceleration an<J veJocity l'or any olle type of cam with

It)sPecificd contours'

O.i (a) "['hree rnasses ol'8 kg, l2 kg and 15 kg atlached at radial distaticcs of]80 mnt,

l)cterminc 1hc angular positions of ths rrr$sses 1,.2 kg and l5 kg relative to ll l6

lcg mass"

(h) .l)cl-tne :

G*F" (i) Static llnlilncirrg

(ii) DYtlltt'llic l,lalancing.

Q"3 , M 'l'rvo spur gears have a veloci{y ratio ol' 1/3. 'l'he driven gc;rr has 72 tceth o| 8

I mm nrgclule ancl r"otates at 300 rpnt. Calctrlate the rtumbcr ol'tectlr and theI

\ ,p.*d ot'tlre driver..WSat wil! be the pitch lirrc vel'cities?:vl

I

$!-Definc lirnction of a gear train. Hxplain with neat skctches the lbllowing gear

tr:ilni;.:(i) SirnPlc gear train

(ii) ComPouncl gear trerin'

l2

i) li

e.4 (a) Discuss in br:icf with,neat sketclres the dilibrent types of vibrations.

(b) What clo ;-,e11 mean by whirling of shalts'? What is whirling or critical spccd?

I')xplairr. == p..t..O.

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)

05

(c)

:

what arc thc basic clcmcnts ol'a vibrating system? what is the degrcc ol'liceclorn. '\

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Q,5

Q,6

W l"ixpl*in will'r ncnt sl<otihcs thc l?rllou'ing:

{b)

{Xr

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(i) Steering

(ii) Itolling

(iii) Pitching. ,

)

i

(b) f)erivc cxpression tbr arrgle of hecl lbr a two whecl vehicle whilc taking aturn.

(a) lixplain nrctlxrd oficlircct *fd rcuur** cranks usicltlbr balancing ol radialcngines. ,, .

!

'l'he length of each "unnf.ting

rocl of a 60" V-engine is 220 mm ancJ the stroke

is 100 rnm .'flrc,nas fl'thc rcciprocating parts is 1.2 kg-per.cylincler and rhc

c"'.ill spcccl is 2400'Srn. Find the values of the primary and the seconclerry

t?

0ft

I2

frlrccs. **. fA'*f-F

/

t

|!F-li***{-**.

." -:

r€h"Q,7- -df :

r:;1-g

DiamctrHl llitch

(ii) Mocllrlc

{iiil ficar ltatin i

iiv) Vclocity llatic:

( vi Aclclcnriuur

(b) Sho,iv with line sketches thc el-lbct of gyrcrscopic eouple for dille.rent dircctionof rotation ol'propcllcr and stecrirrg.

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B.E. ( Fifth Semester) Examination, NoY.'Dec.2006AICTE COURSE

Subiectl fYnuttdcs of MachbesBrrnch: Mechanical Engineering

Time: Three Hours

Notei Attempt all questions. Assume suitable daia if required.

Ql, A cam rotating clockwise at

fotlower the motion defined below:a uniform speed is required to give a knife-edge

Code: 065024 l*{

Max, Marlrs: 100Min. Pass Marlcs: 35

during 12S of carna ----] .i

,... i. I

- 315 kg;:260 kg: 1.6 m}:7.0 m]: 1.9 trtry '

=- 130 kg' J00 nrm

-eF-: CI@.':2

1'' (l) follower to move outwards through a distance of 2.5 cms

,) rotation h

: (ii) follower to dwell for 60 ofcam rgtltiorl 'i r F , ..i iiill followertoreturntoitsinitialpositionduringg0o ofcamrotation ,'l',t

'{ ) iinf foflower to dwell for tlre remaining 900 of cam rotation\ '-'' 1.n" *ini-,r* radius of the cam is l qrng, the line of stroke of the follower is oftl

2 cms from the a:ris of the cam and the di$ffimgo! of th,e follower is to lake place- Yt$unitbrm r*i *qr"f acceleration and retardatiorr on both the'9ut*.:r:d..Tq q1i:tttrn 1*$::tfuw the profile oft$ie carn ''s'r.. cv 1i 2 -{- s "

20

e2. The following data refer to a four-coupled wheel locomotive with two inside

Pitch of the cylindersRwiprccating lrmss P€r cYlinder

Revolving nutss Per cYlinder

Distance between driving wheels

Distance betwesn coupling rods' Diameter of driving wheelsRevolving parts for each coupling rod crarlk

Engine crank radiusCorryling rod crank radiusDistance of center of balance firass in planes ofdriv'xrg wheels from axle center = 750 mm )Angle-between engine cranks :900 )

e"Et between coupling rod cranks with ad$acent engine crank : 18_00

The balanc" *ss required for the reciprocating parts is equally divided between

each pair of coupled wheels. Detennine(r) ttte *agnit"ae and position of the balance mass required to balance two-

tnird oitle reciprociting and whole of the revolving parts

(ii) the hammer-blow and the maximum variation of tractive force wlren the

locomotive sPeed is 80 kms/hr .20

PTO

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Q3. Attempt any two parts from the following:

- (a) Write cor4parison of cycloidal and involute tooth profile in tabular form10

(b) What is a differential gear of anautomobile ? How does it firnction !

10(c) An epicyclic gear train consists of gears A, B, C, D and a arm a. The arm a calies

gears C and D onpins attached at the ends ofthe arrn Gears A and B along with arm ahave common axis of rotation at O. The gears C and D engage with externat teeth ofgear A and intemal teeth of gear B. The number of teeth on A and B are 80 and 200.Determine the speed ofthe ann a

(t) if A rotates at 100 rpm clockwise and B at 50 rpm counter cloclnvise(il) if A rotates at 100 rpm clockwise and B is stationary

1044. Answer any two questions fromthe following:

-:- (a) * -hrry rypqgrted freely a,'. the ends has a mass of 120 kg placed 250 mm from one end. y-.a i

The shaft diarneter is 40 mrn Determine the frequency of the natural transverse_, Ivibrations ifthe length of the shaft is 700 mm" E :200 GN / m2 't

10(b) What will be the natural frequency of the torsional vib,ration if inertia effect of mass of

shaft is taken into account.

10

..(e) UFat$rill be the naturat frequency of the longitudinal vibration f inertia efect of rqar* .' of spring is taken into account. Assurne a rnasi m attached at the liee end"--<--- ts

Q5. (a) The twbine rotor of a ship has a nrass of 2.2 tonnes and rotates at 1800 rpm clockwise-?'i when viewed from aft. The radius of gyration of the rotor is 320 mrn Determine thegyroscopic couple and its effect when(r) the ship turns right at a radius of250 m with a speed of 25 kmslhr(ii) the ship pitches with the bow rising at an angular velocity of 0.8 radlsec(iii) the ship rolls at an angular velocity of 0.1 radlseq

t2

(b) Each-wheel of a motorcycle is of 600 mm diameter and has a moment of inertia ofl.2kg-n:i. The total mass of the motorcycle and the rider is 180 kg and the combinedcenter of mass is 580 mm above the grormd level when the motor cycle is upright. Themoment of inertia of the rotating parts of the engine is 0.2 kg-m'. The engine speed is 5times the speed of'the wheels and is in the sarrc sense. Determine the angle of heelnecessary when the motorcycle takes a turn of 35 m radius at a speed of 54 kmslhr.

08

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Tini* : Three F{ours.

Code:0S5024 M$punester) Exanrirr*fion, November ?005 ii Mechanical Engineering i

Sub : Dynamic of lllachines _ ,

Fic't* : Ati*ffitpt ;lll questi*ns. Assurn* su;t$bl* dnia

fufax.Marks : 100 \

__S:rPassh,tarks:35 ',

r,vlr r:r*v*r ro{ju *'*# ,

Q' J Dmrv t|1,nrofiie, of a casn" eiperaring a knife-edge follower w-hen the axi,1of the foilower is oftet by Z0nrnito the right cf axis of the ,;-;# z0tiom rhe following data :

(i) iroilower io l*ove outwards through 4c mm during 600 of cam ..-{.rot4iion. /(ii) Follo.,ver ro dweli for the next 450,(iii) Fr:rlower to return to its original positron duri*g next 900,(iv) Follower ro dweil fbr the .*rt of tiu cam roiatisln.

The dispiacement of the fcllower is to take olace l,rith simnl*harrnonic motion ciuring both the outward anci rbe rci,:rn silok-r,ir,-'i-;riradius of, catn is 50 m.ru. if the cam aitates at 300 r'pm, determine t5ernaxirnum. veiocity and acceleration cf thc follorver i"ri"g il;-or,t..*ardstroke and return sfioke.

Q::

i-

!";*' -' _.1

The parricul:rrs forl" 4-couu[.d locomoti,,.e hi,c j,:suju r:ylincer:r a;e rlir, t

rr,tbiicrving: , , rc-Pital;r+1.'-+'iin;"-r* : . ;,_?iis:+j)F.*v'*ivtrrg n:as:;/cyiincer =i ;150 kg iIlcciprucal massicyiincler :Ou;,i i" _

liisiaace't;etr,veen driving rteeis -- 15* c":rsDiameter of the Criving rvheels = 200 +i.*sDislance benveen coupling lcds = 2ilC cprsRevuiviilg pans of each coupiing rcci crank = 120 h;Engirie ci'ank radi.us : j2 cisConptling rod cra:rk raci.ius = 27 cms'rire engi're cranks

1re 9!0 out of prane with eacir .rrrer while ooupiing

roC E;ranlis ait': 1800 to th+ adjacerit.r:ngine crunk.'i'.ir'- whoJe of the revoiving paits inct 2i3 rd of the:.eciprocal parts are

to. be balanced by inasses in thi ptanes of tle rvheeh aJa riaiur of g'cms.'i'he brlanced mass requirecr for the reciprocar.ing pirrs ,r*;;;.iry irrre"abrirveen the parts of coupled wheels. Detennini(i) the magnitude and poiitior of the halance m.iss req*.iied.(ii) the hammer blorv and the maxifirurn ,,,ariation of lractive eftbrt whenthe speed is 100 kn:&r.

9) Explain interface ancl methods of eliminating interfereiloe.(b) Derive expression for minimum number of tieth on a pinion. .sff 10

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/il

u-_rurrturL-\ "-r 38 e 6a t ( l -[ L'

kr a revenecl epicycile .lrain,,ihc amr [: caries t+"' r''!]eeis tf;tir?fii-1ffi;;il-*ii-i'g,c. The hheel A nieshes rviih whee! B i

D meshes vrith rvheei c. irr", n.rm'i:sr of teeth on $4reel /n ii an<i c is.E0'

48 i::d ?1 respecti-,";iv, F:nd the speed and Cirection of ll'heel l) when

wireel A is fixed and arnr F makes 200 rpm clockw'ise

Aflywheelofrnass'T5Okgismountgdg114verticnls|iafte.'fdiameter50i:lrn at a distance of,i:SO"*,n fronr toP cnd alid !lu0 rri*r,il'orn ti'ie bottorn

' end- The both ,nO, of the shqt are tixed If E: ?;)0 Glllin:' ti:en fr'd ti:e

iratural fi-equencies ;i A- iorlgrt';.t in al artd trans'-'erse vibrations' i'tr eglect

il; *ishi;r,h; 'nu't OR

Asbaftoflengthi..?5:nis?5rrminciameterfbrtlrefirst275mmitsiil;,"rx*,,, i" drarnerer r.or the next 3?5 m': lerrgth and i?Snrnr ir,

ciaraeter for the rer-r:raining 100mm of its lengtli. The shalt cirriics r'r'\'o

rotor:i at tlvo ends. 'l'he mass moment uf inertia of tha fi$t rotor is 75 kg-

mz whereas of tir* =*"trri roior is 50 kg-mt. Find th* freqr:*nc,v of nat";rai

tcrsi.oial vibrationr; -;i

;h" systerrr. 'i:ire mort.rlus of rigiiiir,v of shiiji

rrraterial maY be kku;; as 80CN/rn''

(a) .|he mornent of inerlia r;ithe air screrv i'i,ith more iiiaii lr''o i.]:"cjes :rnd tlre

r{}titing *u,,",, uii rissumed t,: be spinliitrg abcirt.tlir):iaiii.j a;it:. is 15 kg. ii

, d\':, o.ra ti"r" ir*ou, urf rolrtiol is ciockwire. t''he'' lockillg at ihe fioni

-- -{iitt;;;;il"-. T;r'; +quivaie;it speei of iohti'a <;irl''e i:ii sci'*w anrl ihe

..2 rlt_tting ,r.,*n*o ;, iscd rpni, wh+1 the speerl r:itiie.fl.ight is 240 kmslirr. If

ii,+ar.i.rillirl* rrni,+, * rig.iri''hancleci tr.rrn c:n ir p:tt'li ni ili-lm iarlir:s' tinii

fnC 5;viOSUcl''lt'*tt"''"t"''i:tl " ar::tiui" r'ir "r:-'i ' ''l'l'''l:;"' i 'il"'ii'

"'(b) Period of cscilLtiiln Gf^the pitching ':f a sea-':*:;sei is i('r :i';i;r-'ncis i":;:

angie trarre;J;;-i;co. tlu *otion ma1" be ;rssut:'ii:d t'r 1;' iir'nplc !2

harnronic.Particui.trlof"theiuriiineroiorsaretheicliowing'\'ei'Mass = 500kg, Raiii'"rs of gyrat.ion = 40c'ms' P-Pj'-i : 2000'

"</O*t**rin" tire rnagni*iie cf maxilnuln gyroscoliic c"Lti'tlc

";ausr:rt 1'''i' ''''

t lie l'c\tor: *fl th e t*lb i rt*'

Fii:fi air,* ',ir{: :jii*:Ctiti: in "','hiCii

f i:e: bl;r''-' 1""'i ii ie'lili iO

., ihiiirrg ii tlie rfitllir ;:i.;t iq-itritir-Lg iii clcr.iii,vis'J tJiisslii';:] iis viLr"'o'*

3ri\Yirat viiii

iri'Lching.

th* ittaH:ilnuJn Anttililr irgoeierafirir, of

OR

A trollev ciir w*ighing 3 ton*s run on rails llu apai-i at speed oi:tll)

krns/lr. Tir* irack i, ",.,-"J*ith a rirclius of Boni tc;wards right -s:ide of tire

rlrives. The oar flno t*i wheels each cf cliameter '7O+ms anil mass tiio;ilcnt 2i)

;i#;; oi;i":"i'he car is driven bi, ii motor of'mass noilrent of i"*crtia

;;;;:;t:ii* **r"," is placccl ceni.:eriiy in the car and r-otaies nine tii'es

tfr* ,i**a of the ai:i* in tire :.a;:re sFinse. The height of *entr* af graviry *f*.he qar is im alii:,,,e

"he rail level. Determine the height'b'1,' ivirich lh* 6ri*"ei

rail should be lirteri up uu compared to the ittnei rail to ou*tttse the

-rf-"i "rgvroscairic

coupie anci::*:.l* ji-:.:"t''o-gal rorcc . ooe.,

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