Mechanical Engineering Paper - 1 1ZONE TECH

Q.1Sol. ABC analysis is done based on the concept "VITAL FEW TO TRIVIAL MANY". It is a consumption

analysis.Consumption is defined as the product of quantity and unit cost of the item.Accroding to ABC analysis:(i) 10% of total items having 70% of total consumption value are A class.(ii) 20% of total items having 20% of total consumption are B class.(iii) 70% of total items having 10% of total consumption are C class.

Q.2Sol. Porosity or permeability: It is the property of sand which permits the steam and other gases to pass

through the sand mould.Plasticity: It is that property of sand due to which it flows to all portions of the moulding box orflask.

Q.3Sol. Coefficient of friction is a value that shows the relationship between the force of friction between

two object and the normal reaction between the objects that are involved.The maximum value of the angle of inclination of a plane with the horizontal when the body startssliding of its own is known as the angle of repose or limiting angle of friction.

2 Marks

Mechanical Engineering Paper - 1 2ZONE TECHQ.4

Sol. Addendum: It is the radial height of a tooth above the pitch circle. Its standard value is one module.

Dedendum: It is the radial depth of a tooth below the pitch circle. Its standard value is 1.157 m.where m is modulue.

Clerance is the difference of actual depth and working depth.

Q.5

Sol. A flywheel is a device attached to the crankshaft, makes the moment of inertia of the rotating partsquite large and thus, acts as a reservoir of energy. During the periods when the supply of energy ismore than required, it stores energy and during the periods the requirements is more than thesupply, it releases energy. A flywheel is used to control the variations in speed during each cycle ofan engine.

Q.6

Sol. Arc blow: An AC arc once started is more stable, but it is not so with the DC arc. The predominantproblem faced with the DC arc is the 'arc blow', the deflection of the arc by means of the magneticfields set up due to the flow of the welding current. All electrical conductors are surrounded bymagnetic flux lines around them.

Q.7

Sol. Vibrations are produced in machines having unbalanced masses. These vibrations will be transmittedto the foundation upon which the machines are installed. These are usually undersirable. To diminishthe transmitted forces, machines are usually mounted on springs or dampers, or on some othervibrations isolating material.

Transmissibility is defined as the ratio of the force transmitted (to the foundation) to the forceapplied. It is a measure of the effectiveness of the vibration isolating material.

Q.8

Sol. Desirable properties of cutting tool are:

1. High hot hardness.

2. High wear resistance

3. High toughness so that impact forces on the tool and chatter during machining do not chip orfracture the tool.

4. Chemical stability or inertness with respect to the workpiece material, so that any adverse reactionscontributing to tool wear are avoided.

Q.9

Sol. The main factors those affect the fracture of a material are:

• Stress concentration

• Speed of loading

• Temperature

• Thermal shock

Q.10

Sol. Annealing carried out for the following:

(i) To soften the steel

(ii) To relieve the internal stresses, and

(iii) To refine the grains and reduce the hardness

Q.11

Sol. Surface finish can be measured by two methods: (a) surface inspection by comparative methods, (b)direct instrument measurements.

Mechanical Engineering Paper - 1 3ZONE TECHUnder comparative methods, various techniques are:

Touch inspection Visual inspection Microscopic inspection

Other techniques are:

Surface photographs Micro-interferometer Reflected light intensity

Under direct methods;

Profilometer Stylus probe instrument Skid

Q.12

Sol. I-section beam is more efficient than rectangular section for same cross-sectional area. Moment of

resistance, M Zwhere, Z = section modulus of beam.

For same cross sectional area, section modulus of I-section is more than that of rectangular section.Hence its moment of resistance is more and can bear more load.

Q.13

Sol. (i) BSW (British standard white worth):

• Used for fatigue loads (More fatigue strength thread)

• Applications in Automobile

(ii) ANS (American National Standard)

• Suitable for rough usage

• Also used for most general purpose

(iii) ACME:

• Modification of square• Used in lathe lead screw• Power transmitted in two directions

Q.14Sol. Anti-friction bearings not used at very high speed because.

(i) rolling bearing may eventually fail from fatigue.(ii) higher noise level(iii) higher friction

Q.15Sol. Extrusion is a process that uses a die in order to get a material with constant cross-section cut. The

material is pushed through die of the desired cross-section to complete the process. While drawingis a process which uses tensile forces to stretech the metal. As the metal is drawn (pulled), it stretchesthinner, into a desired shape and thickness.

Q.16Sol. • When the space is a constraint

• When velocity ratios should be constant• When the transmitting torques are relatively higher compared to the belts.

Q.17Sol. While designing a component, it is necessary to provide sufficient reserve strength in case of an

accident. This is achieved by taking a suitable factor of safety (fs).The factor of safety is defined as

(fs)failure stress

allowable stress

or (fs)failure load

working load

Mechanical Engineering Paper - 1 4ZONE TECHQ.18

Sol. Poisson's Ratio: It is defined as the ratio of lateral strain to longitudinal strain in the member. It isdimensionless quantity.

in

lat

l

lat lateral strain

inl linear strain

value for isotropic material is 0.25.

Creep: Creep is permanent elongation of a component under a static load maintain for a period of atime usually seen at elevated temperatures, results from grain boundary sliding.

Q.19

Sol. Tolerance is the limit of random (unintentional) deviation of a dimension from its nominal value.While allowance is the amount of designed (intentional) deviation between two mating dimensionsin a fit which, in combination with their respective tolerances, results into a maximum and minimumclearance or interference, Allowance is the planned deviation between actual dimension and desireddimension. Tolerance is the range of variation permitted in maintaining a specified dimension in amachined piece.

Q.20

Sol. When a spring is cut into two parts its stiffness doubles. (K 1/n)

Where n is number of coil.

If they are arranged in parallel.

Effective stiffness, Ke 2K 2K 4K

Q.21

Sol. PERT Vs CPM (Program Evaluation and Review Technique) are most commonly used networkmethods for project management. There are some similarities and differences between PERT andCPM. PERT can be applied to any field requiring planned, controlled and integrated work efforts toaccomplish defined objectives. On the other hand, CPM (Critical Path Method) is the method ofproject planning consisting of a number of well defined and clearly recognizable activities.

PERT vs. CPM

1. CPM -uses activity oriented network. PERT uses event oriented Network.

2. CPM-Durations of activity may be estimated with a fair degree of accuracy. PERT- Estimate oftime for activities are not so accurate and definite.

3. CPM-It is used extensively in construction project. PERT- It is used mostly in research anddevelopment projects, particularly projects of non-repetitive nature.

4. CPM-Deterministic concept is used. PERT-Probabilistic model concept is used.

5. CPM- can control both time and cost when planning. PERT is basically a tool for planning.

6. In CPM, cost optimization is given prime importance. The time for the completion of the projectdepends upon cost optimization. The cost is not directly proportioned to time. Thus, cost is thecontrolling factor. In PERT, it is assumed that cost varies directly with time. Attention is thereforegiven to minimize the time so that minimum cost results. Thus in PERT, time is the controllingfactor.

5 Marks

Mechanical Engineering Paper - 1 5ZONE TECHExamples of the application of PERT & CPM

• A new research project mission to mars

• Relocation of a major facility (e.g., a plant or a hospital)

• Performing a complex surgery

• Construction or renovation of a plant, an office complex, a residential housing plan, a sportsstadium, or a freeway.

Q.22

Sol. Various milling operations are:

* Plain or slab milling * Face milling

* End milling * Side milling

* Slot milling * Angular milling

* Form milling * Straddle milling

* Gang milling

* Gear cutting

Plain milling: It is the process of production of the plain, flat, horizontal surface parallel to the axisof rotation of a plain milling cutter. The operation is also called slab milling.

Face milling: The face milling operation is performed by a face milling cutter rotated about an axisperpendicular to the work surface.

Side milling: It is the operation of production of a flat vertical surface on the side of a work piece byusing the side milling cutter.

Q.23

Sol. Grashoffs Condition: Grashoff's condition checks the link proportions and classifies the chains/mechanisms.

If l + s < p + q for Groshoffs or Class - I

If l + s > p + q for Non grashoffs or Class - II

If l + s = p + q for special Grashoffs or Class - III

l = longest link,

s = shortest link

Shortest link fixed:- In this mechanism input link becomes crank, i.e. would complete full revolutionand output link also completes full revolution thus becomes double crank mechanism (C-C).

Ex. Whitworth quick return mechanism.

If shortest link is at input link position, it will lead to crank-rocker mechanism.

If shortest link is at coupler position, it will lead to double-rocker mechanism.

Q.24

Sol.

m

kk

k

Springs are connected in parallel

deflection, F force

Here total force sum of spring forces

Mechanical Engineering Paper - 1 6ZONE TECHTotal deflection,

individual spring deflections

1 2

F 1 2F F

eqk 1 2k k

eqk k k 2k (ii) Spring are connected in series.

m

k

k

Here forces same in two spings

But 1 2

eq

F

k eq

F F kk

k k 2

(iii)

m m

kk

k k

2k

eq

1

keq

1 1 2kk

k 2k 3

Q.25

Sol. Actual length of workpiece, L 150mm

Length of tapered portion, l 80 mm

Bigger diameter, D 80 mm

Diameter at tapered end, d 50mm

Angle, tanD d

2

l

1 80 50tan

2 80

10.62º

Mechanical Engineering Paper - 1 7ZONE TECHQ.26

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

4. Volume defects:

(a) Stacking faults

1. Point defects:

* Defect is aphysical discontinuity existing among the lattice of atoms.

* If the defect is confined to a single atom in the lattice called as point defect.

2. Line defects:

* If the defect is confined to more number of atoms in a lattice is known as line defect. Ex. Crackformation in a material, where along the line of crack, the atoms are missing. Hence it is a linedefect.

Q.27

Sol. Helix angle : It is angle at which the teeth are inclined to the axis of a gear. It is also known as

spiral angle.

Normal Circular Pitch (pn): Normal circular pitch or simply normal pitch is the shortest distance

measured along the normal to the helix between corresponding points on the adjacent teeth. Thenormal circular pitch of two mating gears must be same.

np p cos

Also, we have, p m as for spur gears

Axial Pitch : It is the distance between corresponding points on adjacent teeth measured along thedirection of the axis.

Lead (L) : The distance by which a helix advances along the axis of the gear for one turn around isknown as lead.

Q.28

Sol. Various types of chips produced are:

(i) Continuous chips (ii) Built-up edge

(iii) Serrated or segmented (iv) Discontinous Chips

Continuous chips: Continuous chips are usually formed under the following conditions:

1. Machining ductile materials 2. High cutting speeds

3. High rake angles 4. Low depth of cuts

5. Effective cutting fluid

Although these produce good surface finish, continuous chips are not always desirable as they tendto become tangled and interfere with the machining process.

Built-up edge chips: A built-up edge consists of layers of materials from the workpiece that aregradually deposited on the tool, may form at the tip of the tool during cutting. As its becomes larger,the BUE becomes unstable and eventually breaks up. Although BUE is generally undesirable, a thin,stable BUE is regarded as desirable because it reduces wear by protecting rake face. Condtions thatpromote BUE chips are machining ductile materials at low cutting speeds, high feed and depth of cutand ineffective cutting fluid.

Serrated chips: Serrated chips are semi-continuous chips with zones of low and high shear strain.Metals with low thermal conductivity and strength that decreases with temperature sharply, such astitanium exhibit this behaviour.

Mechanical Engineering Paper - 1 8ZONE TECHDiscontinuous chips: These chips are formed under the following conditions:1. Brittle workpiece materials.2. Workpiece materials that contain hard inclusions and impuritions:3. Very low or very high cutting speeds.4. Large depth of cut.5. Low rake angles.6. Lack of effective cutting fluid.

Q.29Sol. Relation between E and G is

E1

2G 1m

E2

3K 1m

Where K = Bulk modulus, G = Rigidity modulus, E = Young's modulus, 1/m = Poisson's ratioEquating the above two equations

12G 1

m

23K 1

m

m 12G

m

m 23K

m

K2(m 1)

G3(m 2)

Q.30

Sol.

FailurePoints

Goodman line

Soderberg line

OMean tensile stress

ytut

m

Yield line

Var

iab

le S

tres

s

e

yt

a

Intercepts on both the axis can be obtained by equating corresponding stress.

When a 0, it is pure static and criteria of failure is y or u on the abscissa.

When m 0, it becomes total reversal load and criteria of failure is e

am

yt e

1 for Soderberg line

am

ut e

1 for Goodman line

Mechanical Engineering Paper - 1 9ZONE TECHQ.31Sol. This theory states that the failure can be assumed to occur when the maximum shear stress developed

at a critical point in a component is greater than the value of maximum yield shear stress in uniaxialloading. It is also known as Guest-Tresca's theory.

2

3

1

For failure condition absolute max ys T.TS

Where Sys yield strength in shear

max maximum of 2 3 1 31 2 – ––, ,

2 2 2

At failure ysS y

2

hence for design

Maximum of y

1 2 2 3 1 3, – , –fos

• This theory is suitable for ductile material.• This theory is not suitable in hydrostatic loading.

Q.32

Sol.Brazing

1. Soldering joints are weakest joints out of welding

brazing and soldering methods. Not meant to

bear the load. Use to make electrical contacts

generally.

Brazing joints are weaker than welding

joints but stronger than soldering joints.

This can be used to bear the load up to

some extent.

2. Temperature requirement is up to 450ºC in

soldering joints

Temperature may go to 600ºC in brazing

joints

3. Heating of the work pieces is not required. Work pieces are heated but below their

melting point.

4. No change in mechanical properties after joining. May change in mechanical properties of

joint but it is almost negligible.

5. Cost involved and skill requirements are very

low.

Cost involved and skill required are in

between soldering and welding methods.

6. Preheating of workpiece before soldering is good

for making good quality of joint.

Preheating is desirable to make strong

joint as brazing is carried out at relatively

low temperature.

Soldering

Mechanical Engineering Paper - 1 10ZONE TECH

Q.33

Sol.

21

3

4

5

7

6

80

0

5

55

4

7

29 4

611

11

13

13

2

3

14

18

2

7

8

20

20

Activity Duration EST EFT LST LFT TF

1 2 5 0 5 0 5 0

2 3 2 5 7 7 9 2

2 4 6 5 11 5 11 0

3 5 4 7 11 9 13 2

4 5 2 11 13 11 13 0

3 6 4 5 9 8 12 3

4 7 3 11 14 15 18 4

6 8 8 11 19 12 20 1

5 8 7 13 20 13 20 0

7 8 2 14 16 18 20 4

Where EFT = Earliest Finish Time

EST = Earliest Start Time

LFT = Latest Finish Time

LST = Latest Start Time

TF = Total Float

EFT = EST + Duration

LST = LFT – duration

TF = LST – EST = LFT – EFT

Critical path is 1 –2 –4 –5 –8 20 days

Q.34

Sol. Static Balancing:- A system of rotating masses is said to be in static balance if the combined masscentre of the system lies on the axis of rotation. Figure shows a rigid rotor revolving with a constantangular velocity of rad/s. A number of masses, say three, are depicted by point masses at differentradii in the same transverse plane. They may represent different kinds of rotating masses such asturbine blades, eccentric discs, etc. If m

1, m

2 and m

3 are the masses revolving at radii r

1, r

2 and r

3

respectively in the same plane, then each mass produces a centrifugal force acting radially outwardsfrom the axis of rotation. Let F be the vector sum of these forces.

20 Marks

Mechanical Engineering Paper - 1 11ZONE TECH

F 2 2 2

1 1 1 2 2 2 3 3 3ˆ ˆ ˆm r n m r n m r n

where, 1n̂ unit directional vector

m2

m1

m3

mc

rc

3

r3

X

c

1

r1

r2

2

m r1 1

m rc c

m r3 3

m r2 2

Force polygon

The rotor is said to be statically balanced if the vector sum F is zero. If F s not zero, i.e., the rotor isunbalanced, then introduce a counterweight (balance weight) of mass m

c, at radius r

c to balance the

rotor so that2 2 2 2

1 1 1 2 2 2 3 3 3 c c cˆ ˆ ˆ ˆm r n m r n m r n m r n 0

or

1 1 2 2 3 3 c cm r m r m r m r 0The magnitude of either m

c or r

c may be selected and the other can be calculated. In general, if mr

is the vector sum of 1 1 2 2 3 3m r ,m r ,m r , etc. then

c cmr m r 0The equation can be solved either mathematically or graphically. To solve it mathematically, divideeach force into its x and y components.

i.e. c c cmr cos m r cos 0

and c c cmr sin m r sin 0

or c c cm r cos mr cos

c c cm r sin mr sin squaring and adding (i) and (ii)

c cm r 2 2mr cos mr sin

Dividing (ii) by (i)

ctanmr sin

mr cos

The signs of the numerator and denominator of this fuction identify the quadrant of the angle. Ingraphical solution, vectors, m

1r

1, m

2r

2, m

3r

3, etc., are added. If they close in a loop, the system is

balanced. Otherwise, the closing vector will be giving mcr

c. Its direction identifies the angular position

of the counter mass relative to the other masses.Dynamic balancing:- When several masses rotate in different planes, the centrifugal forces, in additionto being out of balance, also from couples. A system of rotating masses in dynamic balance whenthere does not exist any resultant centrifugal force as well as resultant couple. In the work thatfollows, the products of mr and mrl ( instead of mr2), usually, have been referred ;as froce andcouple respectively as it is more convenient to draw force and couple polygons with these quantities.

Mechanical Engineering Paper - 1 12ZONE TECH

m1

r1

m2

r2

l

m r = m r1 1 2 2l l 2 2

Extra mass would be places in the system to balance the couple and the resultant equations looks likeas below and solve for the unknowns as shown in the static analysis.

c c cmr m r l l 0

Q.35

Sol. Solid or single piece pattern: It is the simplest of all patterns is made in one piece and carries nojoints, partition or loose pieces. The pattern is cheap and it is best suited for limited production only.Since its molding involves a large number of manual operations like gate cutting, providing runnerand risers. So, such patterns are used for producing a few large castings for example, stuffing box ofsteam engine.

Split or Two piece patterns: These patterns are used for intricate casting of usual shapes. They aremade in two parts and these two parts of the pattern are joined together with the help of dowel pins.While molding one of the patterns is contained by the drag and other by the cope. For a morecomplex casting, the pattern may be split in more than two parts.

Gated pattern: These patterns are used in mass production and for such castings multi cavity mouldsare prepared i.e., a single sand mould carries a number of cavities patterns and these castings areconnected to each other by means of gate. Which provides suitable channels or gates in sand forfeeding all the cavities. Gated patterns reduce the moulding time fairly. Because of their higher cost,these patterns are used for producing small castings in mass production systems and on mouldingmachines.

Match plate pattern: These are used for mass production and these patterns find a great favour inmachine moulding. A match plate pattern is a split pattern having the cope and drags portions mountedon opposite sides of a plate (usually metallic), called the "match plate" that conforms to the contour ofthe parting surface. The gates and runners are also mounted on the match plate, so that very littlehand work is required. This results in higher productivity.

Skeleton pattern: For large castings having simple geometrical shapes, skeleton patterns are used.Just like sweep patterns, these are simple wooden frames that outline the shape of the part to be castand are also used as guides by the molder in the hand shaping of the mould. This type of pattern isalso used in pit or floor molding process.

Sweep pattern: Sweeps can be advantageously used for preparing moulds of large symmetricalcastings. This effects results in a large saving in time, labour and material. A sweep is a section orboard (wooden) of proper contour that is rotated about one edge to shape mould avities havingshapes of rotational symmetry. This type of pattern is used when a casting of large size is to beproduced in a short time.

Loose piece pattern: Some patterns usually single piece are made to have loose pieces in order toenable their easy withdrawal from the mould. These pieces from an integral part of the patternduring moulding. After the mould is complete, the pattern is withdrawn leaving the pieces in thesand, which are later withdrawal separately through the cavity formed by the pattern.

Mechanical Engineering Paper - 1 13ZONE TECHCope and drag pattern : When very large casting are to be made, the complete pattern becomes tooheavy to be handled by a single operator. Such pattern is made in two parts which are separatelymoulded in different moulding boxes. After completion of the moulds, the two boxes are assembledto form the complete cavity. It is similar to two-piece pattern.

Follow board pattern: A follow board is a wooden board used for support a pattern during moulding.It acts as a seat for the pattern. In the former case, the follow board is provided with a cavitycorresponding to the shape of the pattern in which the pattern is seated for moulding.

Q.36

Sol. (i) Carburising:

* Carburizing is a method of enriching the surface layer of low carbon steel with carbon in order toproduce a hard case.

* This can be carried out by incorporating C atoms on to the envelope of the L.C.S component itwill be turned as hard by forming Fe

3C phase in known as carburizing.

. .. ... .L.C.S.

CO gas

C C2+

O2

Fe C3

Heatingcoils

HeatingJacket

Case Depth = 0.5 mm/5 hour

CD

* By heating the component to 850ºC temperature CO gas is circulated, in the heating envelope.

* At that temp carbon monoxide decomposes into carbon and oxygen where carbon will penetrateinto the component and oxygen goes out.

* Due to continuous penetration of carbon atom, the outer envelope will be produced with moreiron carbide (Fe

3C) phase & turns as hard.

* The depth up to which form the surface of the component has been hardened is known as casedepth (C

D).

* Since the solubility of carbon is more in austenitic state than in ferritic state, fully austenitic stateis required for carburizing.

* This can be achieved by heating the steel above the critical temperature. And diffusion of carbonis made by holding the heated steel in contact with carbonaceous material which may be a solid,a liquid or a gas.

(ii) Nitriding:

* Nitriding is the process of enriching the surface of steel with nitrogen by holding for a prolongedperiod at temperature of ammonia (NH

3).

* In this process the machined and heat treated (hardening by heating to 930°C and quenching inoil, then tempering at 650ºC to obtain the required properties in core) components are heated toa temperature of 500ºC for between 40 to 100 hours (depending on case depth) in a gas tightchamber through which ammonia is allowed to circulate.

* By incorporating Nitrogen atom on the outer envelope of L.C.S. component it will be termed ashard by forming iron Nitride phase Case Depth = 0.5 mm/hrs.

Mechanical Engineering Paper - 1 14ZONE TECH* Ammonia dissociates according to the following reaction.

32 NH 23H 2N* The atomic nitrogen thus formed diffuses into iron forms hard nitrides by combining with iron

and certain alloying elements present in steel. The alloying elements having more affinity fornitrogen are aluminum, chromium and molybdenum.

(iii)Cyaniding:* During cyaniding the surface of steel is enriched with carbon and nitrogen by incorporating

carbon & Nitrogen atoms simultaneous on to the outer envelope of the low carbon steels it

will be turned as hard by form iron carbide & iron Nitride phases.* In this process the components are immersed in a liquid bath of 30% NaCN, 40% Na

2CO

3 and 30%

NaCl, maintained at a temperature of 800ºC to 850ºC.* Then a measured amount of air is passed through the molten bath.* Sodium cyanide reacts with oxygen of the air and is oxidized. The basic reactions in the bath are:

22 NaCN O 2 NaCNO

2 2 32 NaCNO O Na CO CO 2 N

22 CO CO C

L.C.S.

CD

. .. ... .

(Fe N+Fe C)3 3 Nothing

* Carbon and nitrogen thus formed in atomic form diffuse into steel surface.* Case Depth = 0.5 mm/10 hrs* This process usually requires 30 to 90 minutes for completion.* After cyaniding, the components are taken out and quenched in water or oil followed by low

temperature tempering.

Q.37Sol. Given: Full journal bearing:

Diameter of shaft, D 100mm

Length of journal Bearing, L 150mm

Speed, N 2000rpm

Redial load, W 43kN

N

P

630 10

D

C1000, K 0.002

fN D

0.326 KP C

Mechanical Engineering Paper - 1 15ZONE TECH(i) Coefficient of friction:-

Using McKee equation, The coefficient of friction is given by

fN D

0.326 KP C

substituting the value

f 60.326 30 10 1000 0.002

f 0.01178(ii) Bearing pressure (P)

Bearing pressure is the load per unit of projected area.

P 3

2W 43 10N /mm

L D 100 150

P 2.866MPa(iii) Heat generated:

Heat generated is nothing but the power loss due to friction. i.e. friction work is converted intoheat.

Hg Power loss due to friction.

Power loss sf W r 2 n

3 3 12000.01178 43 10 50 10 2

60

Hg

3.182 kW

Q.38Sol. Tool life: Tool wear is a time dependent process. As cutting proceeds the amount of tool wear

increases gradually. But tool wear must not be allowed to go beyond a certain limit in order to avoidtool failure. The most important wear type from the process point of view is the flank wear thereforethe parameter which has to be controlled is the width of flank wear land VB. This parameter mustnot exceed an initially set safe limit, which is about 0.4 mm for carbide cutting tools. The safe limit isreferred to as allowable wear-land (wear criterion) VB. The cutting time required for the cuttingtool to develop a flank wear land of width VB

k is called tool life. T, a fundamental parameter in

machining.The general relationship of VB versus cutting time is shown in the figure (so called wear curve).Although the wear curve shown is for flank wear a similar relationship occur to other wear types.The figure shows also how to define the tool life T for a given wear criterion VB.

Failure region

toolfailure

Steady-state wear regionbreak-inperiod

VB, mm

Vbk

T Cutting time, min

Mechanical Engineering Paper - 1 16ZONE TECHThe slope of the wear curve {that is the intensity of tool wear} depends on the same parameters,which affect the cutting temperature as the wear of cutting tool materials is a process extremelytemperature dependent.

Parameters, which affect the rate of tool wear are:

* cutting conditions (cutting speed V, feed f depth of cut d)

* cutting tool geometry (tool orthogonal rake angle)

* properties of work material

From these parameters, cutting speed is the most important one. As cutting speed is increased, wearrate increases, so the same wear criterion is reached in less time, i.e., tool life decreases with cuttingspeed:

If the tool life values for the three wear curves are plotted on a natural log-log graph of cutting speedversus tool life as shown in the right figure, the resulting relationship is a straight line expressed inequation form called the Taylor tool life equation.

nVT Cwhere n and C are constants, whose values depend on cutting conditions, work and tool materialproperties, and tool geometry. These constants are well tabulated and easily available.

An expanded version of Taylor equation can be formulated to include the effect of feed, depth of cutand even work material properties.

Q.39

Sol.

Bx

B2

L

xdx

B1

A

B

t

PP

Consider a strip of length 'dx' at distance x from end 'A'

Force acting on strip Px P

area of strip Ax (B

x)t

length of strip dx

if elongation of strip is d then

d

x

x x

P dx Pdx

A E B tE

Bx B

1 +

2 1B – Bx

L

B

1 + kx

Mechanical Engineering Paper - 1 17ZONE TECH

where K 2 1B – B

L

constant

d 1

P dx

B Kx tE

If total elongation of bar is '' then

d

L

10

Pdx

B Kx tE

P

tE

L

1

0

n B Kx

K

P

KE t 1 1n B KL – n B

P

KE t1

1

B KLn

B

2 11

2 1 1

B – BB L

P L Ln

B – B tE B

2

2 1 1

P L Bn

B – B tE B

total elongation of bar