MECHANICAL ENGINEERING PAPER 1

Time Allowed: 3 Hours Maximum Marks: IIJO
CamlitlJItes s1wuJd aite..t questions 1 and 5 whkh are compdsory and01ry Ihree ojllte remaining queslions
sekclion aJ kast one question sekcting aJ kast one questionjromeach Seclion.
Thenumlersifmukscarriedby eachquestion isimlkaJedaJ!heendif!he question.
If01ry t1mIl is consitkred inslIjJkient, assume suitllhk value. Newton"Gl' be convertedto kg using /he equolliy 1
ki/onewton (1l1l/I 100 kg, ifjoumlnecesswy.

SECTION A
Answer any three of the folloWlng

In a vibrating system a cod spnng of stiffness 50 Nlmm supports a vibrating mass of250 kg at the free end. In adlltion; the motion of mass IS controlled by a dashpot whose reSiStance lS proportional to velocity. From measurement itlS found that the amplitude at the bellnmng of the fourth cycle lS 0.8 times the amplitude ofthe IIIrd cycle Delernune


For the follOWing states of stress, show the stresses on two given planes at nght angles of an element. Find the malGitude and directions of the pnnapal stresses and the maXimum shear stresses m each case


Simple Ull1 aXial tensiOn


Pure equal nonnal stresses on liven planes




dampmg co-effiaent of the dashpot
critical dampmg co-efficient
the dampmg factor
the ratio of the frequencies 0f damp ed and undamp ed Vibrations
"

Pure shear stresses on liven planes
"

DistinlNlSh between thin and IIIck cylinders A IIIn cylindrical shell haVing helll1Sphencal ends lS subjected to mtemal pressure The mtemal diameter lS and IIIcknesses of cylinder and henusphere are and respectively Assunung POisson's ratio v 0 prove the follOWing

For no IIstortion ofJuncture, It, 7/1 7


For eaual maximum stresses m cylindncal and helll1Sphencal portions, 0.5


"

What do you mean by 'plam carbon steels' and 'alloy steels'? Discuss the effect of addition of follOWing elements m making alloy steel s
"

Chromium Nickel Manganese Silicon Molybdenum Vanadium Tungsten
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A gear with 42 teeth and a plll1 on with I 9 teeth are cut with Involutes teeth 0f pressure angl e 20° and module pitch 6 mm. The addendum of each wheellS 6 nun. Find

the length of the arc of contact


the number ofpam of teeth m contact the angle turned through by the pln10n, while anyone palr of teeth lS m contact


the ratios of sliding veloCity to the rollmg veloCity at the mstant the engagement


commences, the engagementtenrunates and at the pitch pomt
A rotating shaft cames four masses B,CandD atradilof10 cm, 125cm, 20cmandrcm respectively. The planes m which the masses revolve are spaced 60 cm apart. The masses C and D are known to be 10 kg, 5 kg and 4 kg respectively
ltlS deSlfed that the rotating shaft should be m complete dyn3lll1c balance, For this to be achieved, detenmne

reqUired mass A


the relative angular settings of the four masses, giVen that the angular spaCing of the planes contammg C and D are 118 0 and 260 0 respectively relative to B measured m the same sense


find the radius at which mass D lS to be placed
Draw Shear Force and Bending Moment diagrams for the beam ACDB shown m figure where two couples are acting
Find the ratio of deflections m the beam at locations C and D where the couples are acting

Q

For a closed coil hellCal spnng under compreSSion illustrate the stress distribution across Wlre diameter


Differentiate between comp ound and comp osite heli cal spnngs The spnng load agalnst which a valve lS opened lS proVided by an mner helical spnng arranged within and concentnc with an outer hellCal spnng. The free length of lnner spnng lS 6 mm longer than the outer The outer spnng has 12 coils of mean diameter 25 mm, Wire diameter 3 mm, and 1ll1tial compreSSiOn 5 mm when the valve lS closed Find the stiffness of the outer spnng lfthe greatest force reqUired to open the valve by 10mmlS150N


If the radial clearance between the spnngs lS 1 6 mm, find the Wire diameter of the mner spnng lfit has 10 coils For both spnngs, G 82,000 Nlmm'

For engmeermg matenals; differentiate between the folloWing


A system and state


ExtrinSic and mtnnSlC properties
Degree 0f freedom and constralnt



Phase and component




Differentiate between the following


Homogeneous nucleation and heterogeneous nucleation


Nucleation and growth


Embryos and nucle!
Supercooling and sublimation


Explain the following


Cyruding


Nitriding
Flame harderung



Induction hardemng




Differentiate between


Directional and non-directional bond


Bondlength and bond energy




loruc bond and covalent bond
Metallic bond and hydrogen bond


SEcnON B
Answer any three of the folloWlng
ConSider the following time senes data
'Vokek I2345 6
Value IS 13 15 17 169

t

USing a 3-week moving average, what 1s the forecast for week


USing a 0 2 for exp onenti a1 smoothening, whatlS the forecast for week


USing the mean squared forecast error as a baSiS, which forecast for week 7 would you reconunend?
7
This program drills two holes uSing a CNC machimng center Indicate the meaning of the following commands
PROGRAM 4>000 I
N005 G" G90 S499M03
NOlO GCC X,.
NOl5 G" HOI ZO M08
N020 GC> Z-I.25 F3 5
N025 GCC
N030 XC
N035 GC> Z-I 25
N040 GCC Z.IM09

N045 G28 ZO
N050
Note ¢ mdicates letter 0 and 0 mdicates numeral zero
WhatlSTaylor's equation?

Explam the vanous critena 0f tool fatlure
WhatlS HSS?



How lS surface fimsh measured?


"
Bevel)' Company, a we!ghing machine manufacturer essentially manufactures a mechanlcal We! ghing machine and another deluxe verSlOn which 1s a digital welghing machine. The company glves comnusslOn on sales of the ordinary mechamcal type and comnusslOn on sales of the deluxe digital verSlOn. However, all such commlSSions are available, proVlded there lS a base level sale of at least Rs. 10,000 of ordinaryvanety and Rs. 15,000 of deluxe vanety. To motivate the sales engmeers, for a sales exceeding Rs. 20,000 and Rs. 25,000 for the ordinaty and deluxe vanety respectively, there lS a mcrease ln the commlSSion levels for both vaneties
Draw a flow chart to enable writing a computer programme forthe above
Write a computer progranune for the above situation 10 10
WhatlS a three high rolling mill? Show the direction of motion of rolls and the workplece on a neat sketch of three high rollmg mill Whatlubncants are used dunng hot rollmg? Whatls camb er? Explam m rel ation to rolling po cess the function of provlding camb er


How will you measure taper on a machined component? Describe the procedure With the help

of one example and neat sketches


DistingulSh between allowance and tolerance What are unilateral and btlateral systems of speclfying tolerances? What lS the condition for a force fit or mterference fit between mating parts? Why lS hole bas! s system preferred over a shaft baSiS system?



Aperson operates a machine that makes capacitors. He has been adVlsed to keep track of the percent defectives at his work centre. He knows that with this type they expect about defectives plus or mmus some chance vanation. He Wishes to mitially construct a control chart for defectives He has prep ared ten daily sampl es of hundred capaators each
8

i 12

Construct the relevant control chart. What are the upper and lower control limits?


Plot the datapomts on the proposed control chart Is the process under control? What follow up steps should be undertaken, lf any?


15 15
A matenals manager had recently attended a short tralll1ng programme on materlals management He thought of applymg some of the optimlzation concepts that he had leamt He plcked on one ltem haVln code BV 1960 which was essentially a brass valve. From the current records, he found that the average annual demand was for 10,000 valves. The accounting mfonnation system revealed that the canymg cost was Rs. OAO per valve per year, whereas the ordenng cost was Rs. 5.50 per order The current policy adopted m the
Sample Number 1 2 3 4 5 6 7
defediws 4 3 3 6 1 I 9 5

9 10
4 3

company was to order for 400 valves at a time. Is this an optimal policy? What would be the
annual savmgs lf the EOQ concept was applied?
I5 I5
A company produces two pnnapal product Imes a powerful portable arcular saw and preClSlon table saws. Both product lines share the same production capacity and are sold through the same sales channels. The average profitlS Rs. 900 for each arcular saw and Rs 600 for each table saw. The production capacity lS conslramed m fabncation and assembly capacity A maxlmum of 4000 hours offabncation capacity lS available per month, and each clrcular Sail{ reqUires two hours and each table sawreqU1res one hour. A maxlmum of 5000
hours of assembly capacity lS available per month, and each arcular saw reqUires one hour and each table saw reqU1res two hours. The marketing department estimates that there s a maXimum market demand next year of 3500 saws per month for both product lines combined

Is there a smgle managenal objective? Whatls it?


What are the altemative feasible product ffilX possibilities?

WhatlS the optimal product miX? [You can use either graphical or Simplex method]


How much could the company product optimally lfit was seen that the estimates of the next years market demand have been nnsed to 4000? What would be the maXimum total profit?


15+5
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