ESE – Offline Test-2018 - ACE Engineering Academy

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: 2 : ESE – Offline Test-2018


01(a).

Sol: Preventive Methods for Prevention of

Corrosion:

1. Cathodic Protection:

Cathodic protection is one of the most

important method to control corrosion of

machine parts immersed in soil or liquid. In

this method, the anodic metal is converted

into cathodic metal which is not corroded.

This method is of two types:

(a) Sacrificial anodic protection.

(b) Impressed current protection.

Sacrificial Anodic Protection:

The metallic structure which is to be protected

is connected with a more anodic metal.

By this, all the corrosion get concentrated at a

more anodic metal and protected metal act as

cathode and can be saved from corrosion.

The more active metal (anodic metal) used for

this purpose is known as sacrificial anode.

Commonly used metals for this purpose are

Mg, Zn, Al and their alloys.

These sacrificial metals should be replaced by

fresh one at appropriate time.

This method of corrosion control is used in

following areas:

(a) For protecting buried pipe lines of oil and

water.

(b) Protecting marine structure, ship parts etc.

(c) Protecting domestic water boilers or tanks.

Impressed Current Protection:

The protecting metal in connected to

external DC source with its negative

terminal. The positive terminal is

connected to a insoluble anode like

graphite, platinum or scrap iron, D.C.

source supply impressed current in the

opposite direction of the corrosion current

produced by protecting metal.

Impressed current nullify the corrosion

current as the protecting metal gets

electrons and become cathode.

The anode material should also be

replaced periodically.

2. Protective Coatings:

Metal having wide range application in field

of engineering suffers with the problem of

corrosion.

The metal or alloys having good resistance

to corrosion have less availability, high cost

and fabrication problem.

The coating forms the continuous physical

barriers between the coated surface and the

environment.

The coated surfaces not only have resistance

to corrosion but also provides decoration,

improved wear-resistance, resistance to

oxidation, thermal insulation, hardness and

improved electrical properties.

(i) Metallic Coating:

The deposition of a metal on the surface of

substrate (base metal) is called metallic

coating.

Depending on the position of base metal and

coating metal in electrochemical series, the

metallic coating is classified as anodic coating

and cathodic coating. The anodic or cathodic

behaviour of metal deposited on the surface of

other metal depends on its electrode potential.

: 3 : ME–Conventional Test–6 (Solutions)


(a) Anodic Coating: When the coating on the

surface of base metal is done with the metal

having lower reduction potential value then

the coating is called anodic coating because

the coating metal gets oxidized in contact of

atmospheric.

The electron released at anode moves

freely in base metal. Thus coating metal

acts as sacrificial anode.

(b) Cathodic Coating: When the coating on the

base metal is done with metal having higher

electrode potential (reduction potential)

value, the coating is called cathodic coating

because the coating metal have higher

resistance to corrosive environment then the

base metal and when electrochemical cell is

set up between two metals the coating metal

would behave as cathode and the base metal

as anode.

The coating metal provides better

protection to base metal unless there is no

discontinuity or any cracks in the coating.

The common example is coating of tin on

iron.

(ii) Drip Coating or Hot Dipping:

Hot dipping process the substrate (base

metal) is literally dipped (or immersed) into

a liquid bath of coating metal.

After immersion the substrate (base metal) is

withdrawn and the excess coating material is

removed by suitable methods like

centrifugation, rolling, etc.

Here we discuss the coating on iron or steel

sheets by zinc and tin by the process of hot

dipping respectively known as Galvanization

and Tinning.

(a) Galvanization: Hot dipping coating of zinc

known as galvanizing has been used to

protect iron and steel parts against corrosion

of base metal. The process is carried out is

shown schematically.

Major applications: The major application

the galvanizing is also done for smaller iron

article like nuts, bolts, pipes, roofing sheets,

screw, bucket tubes etc.

(b) Tinning: The coating of tin over iron article

is known as tinning.

Applications:

Protective coating for food handling

(container for food stuffs, ghee, oils kerosene

and packing material), to facilitate the

soldering of a variety of components used in

electronic equipment.

Tinning is widely used for coating of steel,

copper and brass sheets.

(iii) Electroplating:

The electroplating or electrodeposition or

electrochemical deposition is the production

of metallic coating on the solid surface by

passing electric current (direct current)

through an electrolytic solution containing

the soluble salt of coating metal.

3. Organic Coatings (Paints)

Organic coatings are inert organic barriers

like paints, varnishes, lacquers and enamels

applied on metallic/non-metallic surfaces for

corrosion protection as well as decoration.

The protective value of organic coatings

depends on:

(a) Chemical inertness to corrosive

environment



(b) surface adhesion

(c) impermeability to salt and water, gases

and

(d) its proper application method

Paint:

Paint is a mechanical dispersion mixture

formed by the dispersion of pigments,

which are solids, into the drying oils.

These two substances are essential

constituents in the formation of paints.

The pigment constitute the body of the

paints while drying oils bind together the

grains of the body.

The other ingredients known as driers

and thinners are added only to develop

certain qualities in the paints.

01(b)(i).

Sol: Jig or fixture construction

The jig or fixture can be constructed by

using the following methods

1. Casting

2. Fabrication

3. Welding

The advantages of cast construction:

jigs and fixtures with complicated shapes can

be easily cast

Cast iron has the property of absorbing and

damping out the vibrations.

Any number of castings with the same

characteristics can be made from one pattern.

If a cast jig or fixture drops down, it will

probably break. It is not likely to bend and get

out of alignment so as to result in the

production of defective pieces.

The advantages of fabricated construction:

Standard parts can be used to build up the

body.

The jig or fixture can be built up quickly by

using standard parts.

After use the jig or fixture can disassembled.

The advantages of welded construction:

The jig or fixture can be constructed speedily.

The welded construction is cheaper.

Less machining is needed than for fabricated

parts.

The casted jigs and fixtures are costly and time

consuming, but can have a property of

absorbing and damping out the vibrations,

which is very useful characteristic in milling

fixtures.

Castings are heavy and where lightness is

needed welded or fabricated structures are

used.

If a fabricated or welded jig or fixture dropped,

it will get distorted.

The defect will remain unnoticed until the

device is used again when it produces defective

parts, but cast construction will simply breaks.

The ease and quickness in manufacture of jig

and fixtures is in the order of welded,

fabricated and castled.

The welded construction must be stress

relieved by heat treatment, to relieve all

internal stresses induced during welding.

Otherwise the stresses will gradually distort the

jig or fixture as they relieve themselves.

Since the machining must be done after

assembly, it is some times difficult machine

internal surfaces of a welded construction.



In a fabricated construction, all the component

parts can be completely machined before

assembly.

01(b)(ii).

Sol: Advantages:

(i) No vacuum is required hence process will be

easier.

(ii) The size f hole and slots produced is same as

that of EBM.

(iii) Because the Ruby rod is flexible, to same

extent the zigzag holes can be produced by

using LBM.

(iv) No need to have electrical conductivity of

work piece material.

Disadvantages:

Energy or power required for LBM is very high

Limitations:

(i) Max. MRR is 5mm3/min

(ii) Specific power consumption is 1000

W/mm3/min.

(iii) Cannot cut materials with high ‘K’ (Thermal

conductivity) and high reflectivity material.

01(c).

Sol:

(i) Cold shut: The discontinuity present in the

casting due to hindered contraction is called

cold shut. It is mainly produced in step gating

system.

(ii) Misrun: It is due to non filling of projected

portion of casting cavity using molten metal is

called Misrun.

This is due to

Solidification of molten metal has been

started before complete filling of casting

cavity.

It is eliminated by reducing pouring time

or increasing pouring temperature or

degree of superheat.

(iii)Blow or blow holes: Presence of air or gas

bubbles in the casting is called blow holes.

The reasons are

Low porosity of the molding sand

Aspiration effect present in gating system

Allowing partial flow of molten metal in

gating system

(iv) Shrinkage cavity or void:

A open space or void produced due to non-

availability of molten metal for

compensating liquid shrinkages taking

place during solidification

This is eliminated by directional

solidification, i.e., by providing chills in

the casting process.

(v) Scab: The rough, thin layer of a metal

protruding above the casting surface is called

scab.

(vi) Dross: The presence of impurities or foreign

particles inside the castings is called as dross.

This is due to

Improper separation of impurities present

in molten metal.

It is eliminated by using

i) Providing projections in pouring basin

ii) using strainer or skim bob.

iii) offsetting the axis of the runner & ingate.

01(d).

Sol: Preventive Maintenance: All actions

carried out on a planned, periodic, and

specific schedule to keep an item/equipment

in stated working condition through the

process of checking and reconditioning.



These actions are precautionary steps

undertaken to forestall or lower the

probability of failures or an unacceptable

level of degradation in later service, rather

than correcting them after they occur.

Predictive Maintenances: The use of

modern measurement and signal processing

methods to accurately diagnose

item/equipment condition during operation.

This action will help to understand the

condition of the system before major failure.

Differences between Preventive Maintenance

and Predictive Maintenances:

Preventive

Maintenance

Predictive

Maintenances

Reduces break down

and thereby down

time

Less odd-time repair

and reduces over time

of crews

Lower maintenance

and repair costs

Less stand-by

equipments and spare

parts

Better product quality

and fewer reworks

and scraps

Greater safety of

workers

Increases plant life

Increases chances to

get production

incentive bonus

Increased

component

operational

life/availability

Allows for pre-

emptive corrective

actions

Decrease in

equipment or

process downtime

Decrease in costs

for parts and labor

Better product

quality

Improved worker

and environmental

safety

Improved worker

morale

Energy savings

Catastrophic failures

still likely to occur

and sometimes

unneeded

maintenance may be

required

Potential for

incidental damage to

components in

conducting unneeded

maintenance.

Estimated 8% to

12% cost savings

over preventive

maintenance

program

Increased

investment in

diagnostic

equipment and in

staff training

Savings potential

not readily seen by

management

01(e).

Sol: Consolidated requirements are determined

by summing the forecast and order data.

Week 1 = 40 + 15 = 55

Week 2 = 5 + 40 + 10 = 55

Required production is determined by

Production = beginning inventory –

consolidated requirements

Week 1 = 60 – 55

= 5 (No new production is needed.)

Week 2 = 5 – 55

= (50) (Schedule a production run.)

Ending inventory is determined by

Ending inventory = beginning inventory +

production – requirements

Week 2 = 5 + 90 – 55 = 40

The Production required row shows the

tentative master schedule amounts.

Initial inventory = 60 Week

Production run = 90 1 2 3 4 5 6 7 8 9 10

Requirements 55 55 65 55 60 50 50 50 55 50

Beginning inventory 60 5 40 65 10 40 80 30 70 15

Production required 90 90 90 90 90 90

Ending inventory 5 40 65 10 40 80 30 70 15 55



Laser beam

Substrate

Vacuum chamber

Target

material

02(a).

Sol:

BOTTOM-UP APPROACHE METHOD :

Bottom up approach refers to the build up of a

material from the bottom; atom by atom,

molecule by molecule or cluster by cluster.

The colloidal dispersion is a good example of

bottom up approach in the synthesis of nano

particles.

This method is not a new concept. All the living

beings in nature observe growth by this

approach only and also it has been in industrial

use for over a century.

Ex: The production of salt and nitrate in

chemical industry.

Bottom up approach gives a better chance to

obtain nano structures with less defects, more

homogeneous chemical composition.

Bottom up methods can be divided into gas-

phase and liquid-phase methods.

Gas-phase methods:

Plasma arcing and chemical vapour deposition

Liquid phase methods:

Sol-gel synthesis, molecular self-assembly

Laser ablation process:

Laser ablation technique consists of two important

elements: the high-power laser beam with the

optical focusing system and the feeding device of

the metal-target Figure .

The laser beam is focused at the surface of the

target and a supersonic jet of evaporated

material (known as plume) is ejected

perpendicular to the target surface, expanding

into the gas space above the target. The

particles formed are transported with the

carrier gas to the product collector. The use of

metals and metal oxides as precursors is the

main advantage of this method as well as the

production of high crystalline materials. The

concentration of particles and their size

distribution depends on the experimental

medium in the ablation chamber (ambient air,

argon and water), the target material and the

laser operating parameters (wavelength, pulse

duration, energy, repetition time and beam

scanning speed). Experimental estimations

showed that the mass of generated

nanoparticles in ambient air was up to 100

times higher than in water and that in argon

gas was up to 100 times higher than in

ambient air. For example, using nanosecond-

laser the generation of Nickel particle

concentration was estimated up to 1.2 105

cm–3

in ambient air and 1.4 106·cm

-3 in argon

gas flow. However, the high concentration of

evaporated material in the plume can lead to

the formation of agglomerates. This process is

not often applied, especially in large-scale,

due to its low yield and high operation cost.

02(b)(i).

Sol: Data given :

ρ = 7.87g/cc, Cp = 0.44J/g,

Fc = 1600 N, Ft = 500 N,

t1 = d = 0.3mm,

b = w = 5mm, r = 0.42,



α = 10, Vc = 35m/min

The shear plane angle

= tan–1

[r cos / (1 – r sin )] = 24.04

Resultant force R = [16002 + 500

2]1/2

1676 N

Now, tan( – ) = 500/1600 = 0.3125

– = 17.35

= 27.35

Now Fs = R cos ( + – )

= 1676 cos (41.39) = 1258.15 N

Vs = V cos / cos( – )

= 35.52 m/min.

Rate of energy dissipated per unit volume at

the shear plane

= Fs Vs / (b. t. Vc)

= 1258.15 35.52 / (5 0.3 35 1000)

= 0.851 N-m/mm3 or J/mm

3.

Temperature rise at the shear plane is given

by = 0.851 1000/(0.44 7.87) = 245.82C

02(b)(ii).

Sol: Boring: The operation of enlarging the

existing hole by some extent by using

internal turning operation is called boring

operation. It is done on the lathe machine

and it is done by using single point cutting

tool.

Counter boring: The operation of enlarging

the end of an existing hole by internal

turning operation is called counter boring

operation.

Counter sinking: The operation of making

conical enlargement at the end of an existing

hole is called counter sinking. This is done

by using large size drill bit.

Spot facing: The operation of making the

surface of hole flat and square is called spot

facing. This is done by using end mill cutter

with drilling machine.

Data given:

Feed = 0.1mm/rev,

Width of work = 100 mm,

L = stroke length = 140 mm

Approach = over travel = 5mm width wise

B = 100 + 5 + 5 = 110 mm,

V = 25m/min, M = 0.67

M+L

V=(N)strokesofno

1.

67.01140

25000

= 106.9 rpm

Time per cut N

1

f

B

= min10.3106.90.1

110=

02(c)(i).

Sol: This is n jobs and 3 machines condition,

To convert into n jobs and two machines its

should satisfy one of the below two

conditions.

Condition 1 : The minimum of the times for

different jobs on machine A is at least equal

to the maximum of the times of different

jobs on machine B.

Boring

Counter sinking

Counter boring

Counter boring

spots

Spot facing



Condition 2: The minimum of the times of

various jobs on machine C is at least equal

to the maximum of the times of the different

jobs on machine B.

According to the given information,

Min Ii = 3

Max, IIi =5; and

Min IIIi = 5

Clearly, since Min IIIi = Max IIi, the second

of the conditions specified is met.

Consolidation Table is prepared as:

Job Gi(=Ii + IIi) Hi(= IIi + IIIi)

A 7 10

B 11 10

C 9 7

D 9 16

E 10 6

F 12 10

G 10 15

According to this, there are two optimal

sequences. They are:

S1: A D G B F C E

S2: A D G F B C E

We can now evaluate S1 for the value of T. It is

done in the following table.

Determination of Total Elapsed Time :

Job Machine I Machine II Machine III

A 0 3 3 7 7 13

D 3 7 7 12 13 24

G 7 14 14 17 24 36

B 14 22 22 25 36 43

F 22 30 30 34 43 49

C 30 37 37 39 49 54

E 37 46 46 47 54 59

From the table, T = 59 hours.

The idle time for machines II and III are

given as follows:

Machine II: 3 + 2 + 5 + 5 + 3 + 7 + 12 = 37

hours

(0–3)+(12–14)+ (17–22) +(25–30)+ (34–37)

+(39–46)+ (47–59)

Machine III: 7 hours (0-7)

02(c)(ii).

Sol:

Total transportation cost by least cost method is

= 60700+51000+20200+101000+50100

= 66000 /-

03(a).

Sol: Figure shows a typical open die forging of a

flat strip.

P Q R

700 700 20 15 A

B

C

1000 40 200 1200

1100

20

1000 100

3000 1000 1000 1000

30

5

3000

60

50 10

Supply

Demand

dx

Workpiece

x

x

o

y F

h

Moving

platen

Fixed

platen

Fig.(a) Details of forging operation



To simplify our analysis, we shall make the

following assumptions:

The forging force F attains its maximum value

at the end of the operation.

The coefficient of friction between the

workpiece and the dies (platens) is constant.

The thickness of the workpiece is small as

compared with its other dimensions, and the

variation of the stress field along the y-

direction is negligible.

The length of the strip is much more than the

width and the problem is one of plane strain

type.

The entire workpiece is in the plastic state

during the process.

At the instant shown in figure(a), the thickness

of the workpiece is h and the width is 2l. Let

us consider an element of width dx at a

distance x from the origin. [In our analysis, we

take the length of the workpiece as unity (in

the z-direction)]. Figure (b) shows the same

element with all the stresses acting on it.

Considering the equilibrium of the element in

the x-direction, we get

h dx + 2 dx = 0 -----(1)

Where is the frictional stress. To make the

analysis simpler, –p and x are considered as

the principal stresses. The problem being of a

plane strain type, equation may be used as the

yield criterion. Thus,

x + p = 2K or dx = –dp

Substituting dx from the foregoing relation in

equation(1), we get

dxh

2dp

--------- (2)

Near the free ends, i.e., when x is small (and

also at x 2l; the problem being symmetric

about the midplane, we are considering only

one-half in our analysis, i.e., 0 x l), a

sliding between the workpiece and the dies

must take place to allow for the required

expansion of the workpiece. However, beyond

a certain value of x (in the region 0 x l),

say xs there is no sliding between the

workpiece and the dies. This is due to the

increasing frictional stress which reaches the

maximum value, equal to the shear yield

stress, at x = xs and remains so in the rest of

the zone, xs x l. Hence, for 0 x xs .

= p ----- (3)

and, for xs x l ,

= K ---------(4)

For the sliding (nonsticking) zone, using eq.(3)

in eq.(2) and integrating, we have

1Cdxh

2

p

dp (0 x xs )

or 1Ch

x2pn

Now, at x = 0, x = 0, i.e., p = 2K (from the

yield criterion). So, C1 = ln 2K

or p = 2K e2x/h

(0 x xs) -------(5)

For the sticking zone, using eq.(4) in eq.(2)

and integrating, we have

2Cdxh

K2dp (xs x l)

x x + dx

dx

h

p

p

Fig.(b) Stresses on element



G(3,2)

E(6, 0) A(5, 0) C(4, 0) 1 2 3 4 5

D(0, 8)

B(0, 7)

F(0, 4)

O(0, 0) 6 7 8 x

y

1

2

3

5

6

7

8

or 2Ch

Kx2p

If p = ps at x = xs ,then C2 = ps – 2 Kxs/h. Thus,

ss xxh

K2pp ------- (6)

Again, from eq. (5)

ps = 2 K exp(2xs/h)

or

ss xx

h

1h/x2expK2p ---- (7)

At x = xs , = ps = K.

Using this along with the expression for ps,

we get, 2K exp(2xs/h) = K

or

2

1ln

h

x2 s

or

2

1ln

2

hx s ---- (8)

Substituting this value of xs in eq.(7), we

obtain

h

x

2

1ln1

2

1K2p ,

Xs x l --------(9)

The total forging force per unit length of the

workpiece is given as

s

s

x2

x

01 dxpdxp2F -----(10)

where p1 and p2 are the pressures given by

eq.(5) and (9) respectively.

03(b).

Sol:

(i)

A B capacity

Casting 7 5 35

Machining 8 4 32

Inspection 4 6 24

Profit/Unit 30 40

x y

Zmax = 30x + 40y

Subject to

7x + 5y 35

8x + 4y 32

4x + 6y 24

x 0, y 0

Zmax = 30x + 40y

(ii)

17

y

5

x ………. (1)

18

y

4

x ………..(2)

14

y

6

x ………..(3)

x 0, y 0

“G” is the intersection of equations (2) and (3)

2y

16y8

48y12x8

32y4x8

24y6x4

32y4x8

4x + 6y = 24

4x + 6 × 2 = 24

4x = 12

x = 3



Zmax = 30x + 40y

Corner points of solution space are

O(0,0); C(4,0); G(3,2); F(0,4)

ZO = 0

ZC = 30 × 4 + 40 × 0 = 120

ZG = 30 × 3 + 40 × 2 = 170

ZF = 30 × 0 + 40 × 4 = 160

Zmax = 170; x = 3; y = 2

03(c)(i).

Sol: Dynamic microphone works on the

principle of electro-mechanical induction.

This type of microphone is called moving

coil microphone also. Here a very small coil

is used which is attached to a diaphragm and

suspended in a magnetic field of a magnet as

shown in the diagram below. When sound

waves impinge on the diaphragm it vibrates

and attached coil moves. This movement of

the coil inside the magnetic field produces a

emf across the terminals of the coil. The

current so produced in the coil is in

proportion to the sound.

Condenser Microphone called as Capacitor

Microphone or Electrostatic Microphone

also, is made up of two parallel very thin

plates, positively and negatively charged

respectively. The diagram 6.1 below shows

a condenser microphone. It has a very thin

diaphragm of thickness 1 to 10 micrometers.

One micrometer (or micron) is one millionth

of a meter or one thousandth of a millimeter.

Close to this plate (metallic or metalised

plastic) stands another metallic plate with

holes. These 2 plates act as electrodes and

are kept at opposite polarities by supplying

D C to behave as a condenser, they should

be insulated from each other. When sound

wave pushes the diaphragm, it vibrates and

the capacitance of the condenser (or

capacitor) changes. This is because the

capacitance is proportional to the potential

difference and inversely proportional to the

separation between the plates. Any change

in the separation changes the capacitance.

The capacitance is also dependent upon the

medium but as the medium here remains the

same, so we ignore this parameter. The

values of the resistance and the capacitance

are chosen such that the change in voltage is

immediately reflected in the voltage across

the resistance in series. Any change in sound

leads to change of the capacitance and leads

to voltage change. The voltage is fed to an

amplifier to amplify the level of the signal.

Condenser microphones were invented in

Bell Labs in 1916.



03(c)(ii)

Sol: Static Balancing (Two plane balancing)

used for rigid rotors only when cr , this

method can be used. Represent eccentricities

and centrifugal forces as vectors, for which

both magnitude and direction are necessary.

Balancing is attained if the centrifugal force

F = me2 is cancelled by the other

centrifugal forces, due to balancing weights

m1 and m2. In practical machines, the

positions of the correction planes are

determined from the shape of the rotor.

Balancing is done by removing parts of the

rotor or by attaching correction masses in

plane I and II. In practice, removing some

part is done by drilling, milling or grinding.

Addition of weight would require the use of

wire solders, bolted or riveted washers and

welded weights. Let the masses m1 and m2

are attached to the surface at radii a1 and a2 ,

respectively.

To cancel the unbalance force F = me2 by

centrifugal force FI = ma2 and FII = ma

2,

the following relationship must hold

FFF III and 2II1I FF

21

21

FF

and

21

1II

FF

04(a).

Sol:

(i) The constants a and b for the trend line

Yt = a + bX can be obtained by solving the

following pair of equations simultaneously.

Y = na + b X ---------(i)

XY = a X + b X2 ---------(ii)

Year X Demand

(Y)

XY X2

Y

2002 0 77 0 0 83

2003 1 88 88 1 85

2004 2 94 188 4 87

2005 3 85 255 9 89

2006 4 91 364 16 91

2007 5 98 490 25 93

2008 6 90 540 36 95

Total 21 623 1925 91

Substituting the calculated values in the two

equations, we get

623 = 7a + 21b

1925 = 21a + 91 b

Solving these equations simultaneously, we

get a = 83 and b = 2.

Accordingly, the trend equation is

Yt = 83 + 2 X

Origin: 2002

X unit : 1 year

Y unit: Annual demand (‘000 mt)

II

m2

m22a2

M12a1

I

m1

a1 a2

me2

(a) Actual system

F

F1 l1 l2 F2

(b) Equivalent force model



(ii) The trend values for various years may be

obtained by substituting the relevant X

values in the trend equation. These are given

in the last column of the table. Further, the

actual and trend values are shown

graphically here.

(iii) Forecast for year 2010

With 2002 = 0,

The X-value for 2010 is 8.

Yt(2010) = 83 + 2 8 = 99 (‘000 mt)

04(b)(i).

Ans: Pitting is a surface fatigue failure which

occurs due to repeated loading of tooth

surface and the contact stress exceeding the

surface fatigue strength of the material. The

pit itself will cause stress concentration and

soon the pitting spreads to adjacent region

till the whole surface is covered with pits.

Subsequently, higher impact load resulting

from pitting may cause fracture of already

weakened tooth. Sometimes impurities in

materials provide nucleus for crack

generation as shown in Fig. (c). Fig. (d)

shows merger of generated cracks, which

finally detaches from the surface as shown

in Fig.(e). Such formation of pits (removal

of material) comes under measurable wear.

Fretting wear refers to small amplitude (1

to 300 μm), with high frequency oscillatory

movement mainly originated by vibration.

This generally occurs in mechanical

assemblies (press fit parts, rivet / bolt joints,

strands of wire ropes, rolling element

bearings), in which relative sliding on

micron level is allowed. It is very difficult to

eliminate such movements and the result is

fretting. Fretting wear and fretting fatigue

are present in almost all machinery and are

the cause of total failure of some otherwise

robust components.

The accumulating wear debris gradually

separates both surfaces and, in some cases,

may contribute to the acceleration of the

wear process by abrasion. The process of

fretting wear can be further accelerated by

temperature and reciprocating movements as

short as 0.1 micron in amplitude can cause

failure of the component when the sliding is

maintained for one million cycles or more.

The below graphs explains the fretting wear

phenomenon over different conditions.

Fitting the straight line trend

2003

Demand (‘000 mt)

74

78

82

90

2002 2004 2005 2006 2007 2008 2009 2010

86

94

98

102

Trend line

(c) (d) (e)



L

x 2a

Causing for Material removal

Wi

tan

ax

/2

a

x x

atan

04(b)(ii).

Sol: All theories which predict wear rates start

from the concept of true area of contact

between two real metal surfaces determined

by the plastic deformation of their highest

asperities. Based on area of contact the

severity of adhesive wear is defined.

Archard has defined the wear volume law

and is most popular to calculate the wear

volume,

Laws of Adhesive Wear:

Wear Volume proportional to sliding

distance of travel (L)

Wear Volume proportional to the

load(W)

Wear volume inversely proportional to

hardness (H) of softer material

Archard’s Wear Equation

Wear volume (V) =

H3

WLk1

The value of k1 depends on elastic plastic

contacts, shearing of those contacts, effect of

environment, mode of lubrication, etc.

Two-body Abrasion: This wear mechanism

happens between two interacting asperities

in physical contact, and one of it is harder

than other. Normal load causes penetration

of harder asperities into softer surface thus

producing plastic deformation.

The material is displaced/removed from the

softer surface by combined action of micro

ploughing and micro cutting.

The two-body abrasion mechanism

between softer and hard materials

Assuming conical asperities indenting soft

surface during traverse motion and all

material displaced by the cone is lost as

wear debris. Rabinowiz‟s Quantitative, law

for 2- Body abusive wear

All asperities can be represented by

equal dimensions cones

All the material displaced by conical

asperity in a single pass in removed as

wear particular

Wi = Hs area of load acting an asperity,

Hs = Hardness of soft material

Mixed stick

and slip

Stick Gross slip

Reciprocating

sliding

1000 300 100 30 10 3 1 t2 t1

10–15

10–14

10–16

Displacement , ( m)

Wea

r (m

3 N

m–

1)

W

F

a

x



Wear volume of by single asperity

L.x.a22

1v

ax a2/ tan ------ (1)

Load acting on single asperity i.e., ith

Wi = 2

s a2

1H

s

i2

H

W2a ------- (2)

Substitute (2) in (1),

tanH

LW2v

s

i

Wear volume by all asperities,

Ve v

tanH

LW2

s

i

tanH

WL2

s

tanH

WL2KV

s

1e

s

eH

WLKV

tan

2KK 1

04(c).

Sol:

Material

type

Major

alloying

elements

Properties Applications

(i) Ferritic

stainless

steel

12%- 25% Cr

,

0.1 - 0.35% C

Stronger than

L.C.S

Magnetic in

nature

Annealed

condition

strength is

high

strengthened

by work

hardening

Decorative

trim, high

pressure and

high temp

applications

(ii)

Austenitic

stainless

steel

16- 26% Cr,

6 - 23% Ni, <

0.15% C

Shock resistant,

difficult to

machine

without

addition of

sulphur, Highly

anti corrosive,

Non-magnetic

Domestic

utensils,

chemical

processing

equipment

(iii)

Martensitic

stainless

steel

6- 18% Cr,

up to 2% Ni,

0.1-1.5% C

High hard

Cold workable,

easily

hardenable

High creep and

anti corrosive

Machine parts,

knives

(iv) High

speed steel

0.65-0.8C,

3.75-4 Cr,

17.25-

18.75W,

0.9-1.3V, 0.1-

0.4Mn,

0.2-0.4 Si

High hard with

little ductility,

wear resistant

Drills, milling

cutters, tool bits,

gear cutters, saw

blades, punches,

dies

05(a).

Sol: Reliability Centered Maintenance

(RCM): RCM methodology deals with

some key issues not dealt with by other

maintenance programs. RCM is a systematic

approach to evaluate a facility’s equipment

and resources to best mate the two and result

in a high degree of facility reliability and

cost-effectiveness. “It is a process used to

determine the maintenance requirements of

any physical asset in its operating context to

maximize the level of reliability and safety.”

RCM leads to a maintenance program that

focuses preventive maintenance (PM) on

specific failure modes likely to occur.

Advantages

Can be the most efficient maintenance

program

Lower costs by eliminating

unnecessary maintenance or overhauls



Minimize frequency of overhauls

Reduced probability of sudden

equipment failures

Able to focus maintenance activities on

critical components

Increased component reliability

Incorporates root cause analysis

Disadvantages

Can have significant start-up cost,

training, equipment, etc.

Savings potential not readily seen by

management.

05(b).

Sol:

(i) We convert the problem into a maximization

problem and add an artificial variable to the

first constraint. The simplex iterations are

shown in table.

–8

X1

6

X2

0

S1

0

S2

RHS

0 S1 1 –1 1 0 4

0 S2 4 –2 0 1 8

Cj – Zj –8 6 0 0 0

Variable X2 enters the basis but there is no

leaving variable. The problem has an

unbounded solution. This can be seen from

the problem itself because variable X2 has

both the constraint coefficients negative.

(ii) When the first constraint is X1 – X2 4, we

introduce an artificial variable in the first

constraint which becomes an initial basic

variable. The simplex iterations are shown in

table.

–8

X1

6

X2

0

S1

0

S2

–M

a1

RHS

–M

0

a1

S2

1

4 ()

-1

-2

-1

0

0

1

1

0

4

8

Cj – Zj –8+M 6–M –M 0 0 0

–M

–8

a1

X1

0

1

-1/2

-1/2

-1

0

-1/4

1/4

1

0

2

2

Cj – Zj 0 2 – M/2 –M 2 – M/4 0

All Cj – Zj values are 0 .

The optimum is reached. However, the

artificial variables is still in the basis

indicating infeasible solution.

(iii). When the objective function is to Minimize

Z = 8 X1 + 6 X2 , the initial tableau is

optimal because Cj – Zj is also 0 . The

optimal solution is X1 = X2 = 0 with Z = 0.

05(c)(i).

Sol: DNC: If many number of CNC machines in

shop floor can be connected to a Host

computer having bulk memory through

telecommunication lines or also called as

LAN is called DNC. Hence all the machine

in the shop floor can be controlled by using

one person sitting in front of the host

computer.

The basic components in the DNC system are

CNC machines

Host computer having bulk memory

LAN or telecommunication lines

Part programs required for producing

components

Material handling systems like belt

conveyors etc.





05(c)(ii).

Sol: The DNC with flexible and random

movement of the material is called flexible

manufacturing system (FMS). To get the

flexible and random movement of the

material the automated guided vehicle

(AGV) will be used in the manufacturing

system. Hence FMS = DNC + AGV. If the

FMS is implemented in each every shop

floor of the group technology layout

independently is called flexible

manufacturing cell (FMC) or cellular

manufacturing. In FMS because the total

industry is integrated the material is required

to move from any machine to any machine

but in FMC there is no movement of

material is required among the shop floors

because if the raw material enters into one

shop floor, it comes out as final finished

goods.

05(d).

Sol: Fit: Fit is defined as the relationship

between hole and shaft during assembly.

These are of 3 types:

(i) Clearance fit

(ii) Interference fit

(iii) Transition fit.

(i) Clearance Fit:

In this type of fit, the largest permitted shaft

diameter is smaller than the diameter of the

smallest hole, so that any shaft can freely

rotate or slide through any hole i.e. when

L.limit of hole is greater than H.limit of

shaft.

There will always be a clearance fit between

mating parts.

Ex: piston cylinder

Maximum clearance = H.hole – L.shaft

= diff b/w minimum material limits

Minimum clearance = L.hole – H.shaft

= diff b/w maximum material limits

(ii) Interference fit:

In this type of fit, the minimum permitted

diameter of the shaft is larger than the

maximum allowable diameter of the hole,

i.e. when H.limit of hole is smaller than

L.limit of shaft.

There always the non mating parts will

assembled only with application force,

called interference fit.

Here allowance is greater than sum of

tolerances on hole and shaft.

Ex: Bearing bushes fitted into housings

Maximum interference (H. shaft L. hole)

= Difference between maximum material

limits of hole and shaft.

Minimum interference (L. shaft H hole)

= Diff b/w minimum material limit of hole

and shaft.

(iii) Transition fit:

In this type, the diameter of the largest

allowable hole is greater than that of the

Hole

shaft

Hole

Shaft



smallest shaft, but the smallest hole is

smaller than the largest shaft or smallest

shaft.

When the L.limit of the hole is smaller than

the H.limit of shaft and the allowance is less

than the sum of the tolerances on the hole

and shaft, we will have a clearance fit.

Interference fit depending upon the actual

size of the hole and shaft such as fit is called

transition fit.

Ex: Spigot in mating holes, coupling rings

etc

Case 1:

Case2:

Note: If H.limit of one of component is lying in

between the L.limit and H limit of other

components is called as transition fits.

05(e).

Sol: Types of Nano Materials:

1. Zero dimensional(0-D): These nanomaterials

have Nano-dimensions in all the three

directions. Metallic nanoparticles including

gold and silver nanoparticles and

semiconductor such as quantam dots are the

perfect example of this kind of nanoparticles.

Most of these nanoparticles are spherical in

size and the diameter of these particles will be

in the1-50 nm range. Cubes and polygons

shapes are also found for this kind of

nanomaterials.

2. One dimensional (1-D): In these

nanostructures, one dimension of the

nanostructure will be outside the nanometer

range. These include nanowires, nanorods, and

nanotubes. These materials are long (several

micrometer in length), but with diameter of

only a few nanometer. Nanowire and

nanotubes of metals, oxides and other

materials are few examples of this kind of

materials

3. Two dimensional (2-D): In this type of

nanomaterials, two dimensions are outside the

nanometer range. These include different kind

of Nano films such as coatings and thin-film-

multilayers, nano sheets or nano-walls. The

area of the nano films can be large (several

square micrometer), but the thickness is

always in nano scale range

4. Three Dimensional (3-D): All dimensions of

these are outside the nano meter range. These

include bulk materials composed of the

individual blocks which are in the nanometer

scale (1-100 nm)

06(a)(i).

Sol: Hexagonal close packed structure

(H.C.P.):

Figure shows the unit cell of H.C.P. structure.

The H.C.P. structure contains i) One atom at

each corner of the hexagon ii) One atom at the

centre of the two hexagonal faces and iii)

Three atoms in the form of a triangle midway

between the two basal planes. Metals that

crystallize into H.C.P. structure are zinc,

Hole Shaft

Hole Shaft



cadmium, beryllium, magnesium, titanium,

zirconium etc.

Number of atoms in the unit cell of H.C.P.

structure:

Since each corner atom of the hexagon is

shared by six surrounding hexagons, the centre

atom of the hexagon face is shared by two

surrounding hexagons and the three middle

layer atoms can not be shared by any other

hexagons, the unit cell of the H.C.P. structure

contains.

12 atoms at the concerns 6

1 = 2 atoms

2 face centered atoms 2

1 = 1 atom

3 middle layer atoms = 3 atoms

Total = 6 atoms

Atomic packing factor of H.C.P. structure:

The volume of the unit cell can be found out by

finding out the area of the basal plane and then

multiplying this by its height.

The area of the basal plane is the area ABCDEFG.

This area is six times the area of equilateral

triangle ABC.

Area of triangle ABC = 2

1(base) (height)

= 2

1 a a sin 60 =

o2 60sina2

1

Total area of the basal plane

= o2 60sina2

16 = 3 a

2 sin 60

Volume of unit cell

= Area of basal planeheight

= 3 a2 sin 60 h

For HCP structures, a = 2r r = 2

a

Also we know that the number of atoms in the

unit cell of HCP structure are six.

Volume of atoms in the unit cell = 3

46

3r

Atomic packing factor

= cellunitofVolume

cellunittheinatomsofVolume

= ha

r

o

60sin3

3

46

2

3

= ha

a

o

60sin3

23

46

2

3

= oh

a

60sin3

The h/a ratio for an ideal HCP crystal structure

consisting of uniform spheres packed tightly

together is 1.633.

Therefore, substituting h/a = 1.633

We get

Atomic packing factor = 0.74

A B

C D

E F

G

a a

a

60 60

A B

C

a b

c

120

Hexagonal

a=bc

==90, =120



06(a)(ii).

Sol: Types of imperfections or defects:

The various types of crystal imperfections are:

1. Point defects

a) Vacancies

b) Displacement of atoms

c) Impurities/ Inclusions

d) Frankel defect

e) Schottky defect

2. Line defects:

a) Edge Dislocation

b) Screw Dislocation

3. Surface or Grain boundaries defects

a) Grain boundaries

b) Tilt boundaries

c) Twin boundaries

d) Stacking faults

4. Volume defects:

Example Voids

06(b)(i).

Sol: Investment Casting Process:

Here wax is used as the pattern material

In investment casting, cement concrete will be

used as a mould material.

Because of cement concrete mould, the same

mold can be used for producing a few number

of castings

It is also called as semi-permanent mold

casting process.

Surface hardening heat treatment effect will

take place. i.e., if casting is produced by

investment casting it will always have hard

surface and soft interior

The term investment derives for the fact that

the pattern is invested with the refractory

material. The pattern is made by injecting

molten wax or plastic into a metal die in the

shape of the pattern. The pattern is then dipped

into a slurry of refractory material such as

very fine silica and binders, including water,

ethyle silicate, and acids. After this initial

coating has dried, the pattern is coated

repeatedly to increase the thickness.

FIGURE: Steps in investment casting: (1) wax

patterns are produced; (2) several patterns are

attached to a sprue to form a pattern tree; (3) the

pattern tree is coated with a thin layer of

refractory material; (4) the full mold is formed by

covering the coated tree with sufficient refractory

material to make it rigid; (5) the mold is held in

an inverted position and heated to melt the wax

and permit it to drip out of the cavity; (6) the mold

is preheated to a high temperature, which ensures

that all contaminants are eliminated from the

mold; it also permits the liquid metal to flow more

easily into the detailed cavity; the molten metal is

poured; it solidifies; and (7) the mold is broken

away from the finished casting. Parts are

separated from the sprue.



Process:

A die is made out of a soft metal (Al), using

this die a pattern is made with wax or plastic,

after removing pattern from die, it is rinsed in

alcohol to remove grease and dirt, then precoat

is given and now the pattern is placed in the

box which is filled with self hardening

refractory concrete, then it is kept in a oven

for 24 hours so that most of the wax or plastic

melts and flows out of mold leaving a cavity

with the shape of the intended casting. Now it

is ready for pouring molten metal

06(b)(ii).

Sol:

Oxy acetylene cutting is used for ferrous

alloys. As melting point of iron oxide is lesser

than that of iron, a lot of fuel is saved by

meting by oxidation. Moreover it is an

exothermic reaction supplying additional heat

which saves the fuel costs further. So oxy fuel

mixture is sent through the peripheral holes

and the metal is pre-heated beyond the melting

point of iron oxide and oxygen is supplied

from the central hole so that instantaneous

melting by oxidation cuts the metal.

Inter gas passed from the inner nozzle is used

to generate plasma and the inter gas passed

from the outer nozzle protects the weld pool

from oxidation.

Electron beam can be generated in vacuum

only. If passed through air arc is formed there

by intensity will be less. So vacuum is

essential for the generating a high intensity

fine beam of electrons.

Flux is used to prevent oxidation of weld pool.

Metal deposition rates and productivity are

less in SMAW as the electrodes need to be

changed frequently. To improve productivity a

continuous electrode may be used. In such a

case it should be made of coil for handling.

Flux coated electrode can be made as coil as

the coating breaks and peels off due to its

brittleness, when the electrode is bent. So flux

in granular form is supplied from a hooper

separately.

06(c).

Sol: We have, h

AD2EOQ

in which h = 10% of the unit price. Using

the lowest unit price of Rs. 18.50, we get

50.1810.0

80001802EOQ

= 1248 units

But it is not feasible because the unit price

of Rs. 18.50 is not available for an order size

of 1248 units. Now, with the price equal to

Rs. 19, we get

1910.0

80001802EOQ

= 1231 units

This again is not feasible.

With the unit price of Rs. 20, we have

2010.0

80001802EOQ

= 1200 units

This is a feasible order quantity.

Now, the total cost corresponding to 1200

units,

202

1200

100

10180

1200

80002080001200TC

= 160000 + 1200 + 1200 = Rs. 1,62,400

We shall determine the total cost at cut-off

points 1500 and 2000.



Workpiece

Table

Cutter

Arbor

Workpiece

Table

Cutter

Arbor 192

1500

100

10180

1500

80001980001500TC

= 152000 + 960 + 1425 = Rs. 1,54,385

50.182

2000

100

10180

2000

800050.1880002000TC

= 148000 + 720 + 1850

= Rs. 1,50,570

Since the total cost is minimum at Q = 2000,

it represents the optimal order quantity.

07(a)(i).

Sol: The milling operation performed using

peripheral milling cutter can be divided

into two methods :

1. Up milling operation

2. Down milling operation

1. Up milling operation (Conventional):

In this method of milling the cutter rotates in

a direction opposite to that in which the

work is fed

2. Down or climb milling operation:

In this method the direction of rotation of

the cutter coincides with the direction of

work feed.

An important difference is that in

conventional milling as the cut proceeds the

chip thickness increases gradually against

this the chip thickness decreases in place of

climb milling.

In other words we can say that the chip

thickness in conventional milling, is

minimum (zero) at the start of the cut and

maximum at the end of the cut, whereas in

climb or down milling, it is a reverse case,

i.e., maximum in the beginning and zero at

the end.

Down milling is used for finishing

operations such as slot cutting groove

cutting etc. and also it is the most commonly

used milling operation.

07(a)(ii).

Sol: Minor Operations:

(i) Perforating:

The method of producing many no. of

smaller size of holes in the sheet is

called perforating.

(ii) Notching:

The method of removing a piece of

material from the edge of the sheet is

called notching



(iii) Slitting:

The method of producing an incomplete

hole or blank at the centre of sheet is called

slitting.

(iv) Lancing:

The method of producing an incomplete blank

or hole at the edge of sheet is called lancing

(v) Trimming:

The method of removing a small amount of

material from complete circumference of

sheet is called trimming operation or edge

trimming operation.

07(b)(i).

Sol: tE = 6

tt4t pmo

Variance, 2 =

2

op

6

tt

Activity Expected time (tE) Variance (2)

A 5.17 0.69

B 7.17 0.25

C 5.5 0.69

D 5.17 0.09

E 6.17 0.69

F 8 1

G 6 1

H 3 1.78

7.17

7.17

1

3

2

4 6 7 H(3) F(8)

G(6)

C(5.5)

D(5.17)

B(7.17)

A(5.17) LS

12.34

12.34

20.34

20.34

23.34

23.34

11.34

17.34

0 0

ES

5.17 6.84

E(6.17) Dummy

5



(ii) Expected duration on the variance have been

computed in the above table.

(iii) Critical path, 1 3 4 6 7 (B, D, F

and H are the critical activities).

Expected project completion time = 23.34

(iv) tcp = 23.34

Variance of critical activities

= 0.252 + 0.69

2 + 1

2 + 1.78

2 = 3.72

Standard deviation of critical path,

cp = 72.3 = 1.93

Z = 93.1

34.2330tD

cp

cp

= 3.45

P(3.45) = 0.997

07(b)(ii).

Sol: Break even analysis a marginal costing

principle here we basically deal with sales,

variable cost, Fixed cost, Profit and quantity

Total cost (TC) = F + qV

At break even:

Sales revenue = Total cost

S –V = F+P marginal costing equation.

Where, TC = F + qV

S = sales , V = variable cost

F = Fixed cost, P = Profit , q = quantity

It is the quantity of sales which gives no loss

no profit situation.

Linearity of relationships are assumed in

break even chart.

07(c)(i).

Sol: Failure analysis is the process of collecting

and analyzing data to determine the cause of

a failure, often with the goal of determining

corrective actions or liability. According to

Machinery Failure Analysis and

Troubleshooting, machinery failures reveal a

reaction chain of cause and effect. It’s

beneficial to understand why your product

failed. Perhaps there was a design flaw that

prevented it from performing its intended

function. Perhaps it had a manufacturing or

material defect. Perhaps the product was

misused or abused or maybe it exceeded its

useful life and wore out. By closely

inspecting the product, its fracture surfaces,

and its environment, an experienced failure

analyst is able to collect the evidence and

observations needed to make conclusions

regarding root cause(s) of failure.

07(c)(ii).

Sol:

Fault Tree Analysis Event Tree Analysis

FTA is a deductive analysis approach for

resolving an undesired event into its causes

FTA is a backward looking analysis,

looking backward at the causes of a given

event

Specific stepwise logic is used in the

process

An event tree analysis (ETA) is an inductive

procedure that shows all possible outcomes

resulting from an initiating event

Used to Identify (and define) a relevant initial

event that may give rise to unwanted

consequences and its barriers

It describe the potential resulting accident

https://en.wikipedia.org/wiki/Failure



Specific logic symbols are used to illustrate

the event relationships

A logic diagram is constructed showing the

event relationships

Used identify the causes of a failure and

weaknesses in a system

To assess a proposed design for its

reliability or safety

To identify effects of human errors

To prioritize contributors to failure

To identify effective upgrades to a system

To quantify the failure probability and

contributors

To optimize tests and maintenances

sequences and determine the frequency of the

accidental event and the (conditional)

probabilities of the branches in the event tree

Calculate the probabilities/frequencies for the

identified consequences (outcomes) and

Compile and present the results from the

analysis

No standard for the graphical representation

of the event tree

Only one initiating event can be studied in

each analysis

Easy to overlook subtle system dependencies

Not well suited for handling common cause

failures in the quantitative analyses

The event tree does not show acts of omission

07(c)(iii).

Sol: DR Ferrography is the most acceptable

instrument for wear analysis. It analyses the

particles present in lubricant that indicates

the mechanical wear of the system.

Ferrography can be used to detect the both

metallic and non metallic wear particles.

Working Principle: It allows the test

sample through a calibrated glass tube which

is mounted on a specially designed magnetic

field. The separation causes that the particles

to be sorted by the size at the bottom of the

tube.

The apparatus uses photocells to convert the

measured light intensifies attained by

passing light to the tube to electric signals.

The measured region of the apparatus is 0 –

190 DR units, where maximum value is 190

DR corresponding to the cases where the

bottom of tube is completely covered with

metal particles.

Fig: DR Ferrography analyser

The system detects the mechanical system

condition by measuring particle size

distribution. It has capability to measure

large particles (DL) and small particle

densities (Ds). Based on these two values the

following can be derived,

DL+Ds = Wear Particle Concentration

DL-Ds = Size distribution

DL2+Ds

2 = Wear Severity index

Based on wear severity index, a warning of

an incipient failure earlier than the standard

spectrometric method.



08(a)(i).

Sol: Martempering is a modified quenching

procedure used to minimize distortion and

cracking that may develop during uneven

cooling of the heat-treated material. It

involves cooling the austenized steel to

temperature just above Ms temperature,

holding it there until temperature is uniform

followed by cooling at a moderate rate to

room temperature before austenite-to-bainite

transformation begins. The final structure of

martempered steel is tempered Martensite.

Austempering is different from

martempering in the sense that it involves

austenite-to bainite transformation. Thus, the

structure of austempered steel is bainite.

Advantages of austempering are improved

ductility, decreased distortion and

disadvantages are need for special molten

bath; process can be applied to limited

number of steels.

08(a)(ii).

Sol: The smaller the grain size, the more frequent

is the pile up of dislocations. With decrease

in grain size, the mean distance of a

dislocation can travel decreases and soon

starts pile up of dislocations at grain

boundaries. This leads to increase in yield

strength of the material.

08(b).

Sol:

(a).

Each group producing noise level is = 80 dBA

Total sound pressure level (SPLT)

=

n

1i

10

SPL

10log10

=

10

SPL

10.Nlog10 ;

when N is the no. of noise sources

= SPL + 10log10 3

= 84.77 dB

(b)(i) Three groups A, B and C producing the

noise levels as follows,

SPLA = 80 dBA

SPLB = 90 dBA

SPLC = 85 dBA

Total sound pressure level (SPLT)

=

1010010 101010log10

CBA SPLSPLSPL

=

10

85

10

90

10

80

101010log10

= 5.898 101010log10

= 91.51 dBA

A B

C

Hall



I

II

III

40

H

F

35

E

D G

C

B A

20 55

05

40 14

25

(ii) Noise percentage dosing

= 100C

T.........

C

T

C

T

C

T

n

n

3

3

2

2

1

1

T1, T2, T3…….Tn are actual time exposed to

noise level.

C1, C2, C3,……. Cn are theoretical time

exposed to noise level.

T1 = 2 hrs, T2 = 4 hrs, T3 = 4 hrs

SPL1 = 80 dBA, SPL2 = 90 dBA,

SPL3 = 85 dBA

C1 = 32 hrs, C2 = 8 hrs,

C3 = 16 hrs as per HCA 1983

% dosing = 10016

4

8

4

32

2

= 81.25%

08(c)(i).

Sol: Given data:

= 0.5 customer/minute,

= 4, customer/minute

=

4

5.0 = 0.125

(i) Expected number of customers in the

system, LS = 125.01

125.0

1

= 0.1429

(ii) Expected length of queues,

Lq = 125.01

125.0

1

22

= 0.0179

(iii) Expected time a customer spends in the

system, 5.04

11WS

= 0.2857 minute.

(iv) Expected time a customer spends in the

queue,

Wq

= 05.4

125.0= 0.0357 minute.

(v) Probability that the system is completely

idle, 1429.0110P = 0.875

08(c)(ii).

Sol:

(i) Time available for production

T = 60 × 60 seconds

No. of ovens to be manufactured = N = 40

Cycle time, C = 9040

360

N

T seconds

Time to assemble one unit

ti = 234 seconds

Theoretical number of work stations

= 390

234

C

t i

Technological precedence diagram :



Work station Elements Time

I A, B, E 80

II C, D, G 79

III F, H 75

Actual number of work stations = y = 3

(ii) Idle time = (90 – 80) + (90 – 79) + (90 – 75) = 10 + 11 + 15 = 36 seconds

100yc

t iline

= %67.86100

903

234

Balance delay = 100 – line = 100 – 86.67 = 13.33%

(iii) The highest allotment is 80 seconds to work station (1)

Technically 1 unit rolls out of the line every 80 seconds.



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