SSC SOLVED PAPER 2007 (CONVENTIONAL)Dual cycle = area 2¢3¢365 on the T-s diagram. Q1 Otto cycle = area 2365 on the T-s diagram. Now, area 2¢¢365 > area 2¢3¢365 > area 2365 Q1

1. A. Describe about Francis turbine with respectto its component parts, construction andoperation.

B. Establish the ratio of forces exerted by awater jet when it is made to strike:(i) a stationary flat plate held normal to

it;(ii) a flat plate moving in the direction of

jet at one-third the velocity of jet;(iii) a series of flat plates mounted on a

wheel and moving at one-third thevelocity of jet.

2. A. Make a comparison of Otto, Diesel andDual combustion cycle for:(i) maximum compression ratio and same

heat input;(ii) constant maximum pressure and same

heat input;(iii) same maximum temperature and

pressure.B. Explain the function and working of a

simple carburetor with a neat sketch.

3. A. What are the advantages of using taperturning attachment in lathe?

B. Explain cutting speed, feed and depth ofcut in case of lathe.

C. With a neat sketch, show the details of atail-stock.

4. A. What are the various operations performedon milling machine? Explain plainmilling, face milling and side milling.

B. Explain tool head of a shaper with thehelp of a neat sketch.

5. A. Explain the function of Hartnell governor.B. With the help of a neat sketch, describe

crank and slotted lever mechanism.C. The external and internal radii of a

friction plate of a single clutch are 120mm and 60 mm, respectively. The totalaxial thrust with which the frictionsurfaces are held together is 1500 N. Foruniform wear, find the maximum,minimum and average pressure on thecontact surfaces.

EXPLANATORY ANSWERS

1.A. Francis Turbine: The main parts of a Francisturbine are :(a) Spiral/volute casing: It constitutes a

closed passage whose cross-sectional areagradually decreases along the directionof the flow. Area is maximum at inlet andnearly zero at exit.

(b) Guide vanes: These vanes direct the wateronto the runner vanes at an angleappropriate to the design. It is possible

to adjust the guide vanes either manuallyor by a governor.

(c) Governing mechanism: It changes theposition of the guide vanes to affect avariation in water flow rate, when there isa change of load on the turbine.

(d) Runner vanes: The torque is generateddue to the flow of water on runner vaneswhich reduce the angular momentum ofthe flowing water.

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(e) Penstock: It consists of a pipe whichconveys water from the dam or reservoirto the turbine inlet.

(f ) Draft tube: It is a gradually expandingtube which discharges water which hasrun through the runner to the tail race.

Figure illustrates the construction of a Francisturbine. The inlet is spiral shaped. The casingis scrolled to distribute water around the entireperimeter of the runner. The guide vanes

direct the water tangentially to the runner.The runner blades are profiled in a complexmanner. In operation, water enters around theperiphery of the runner through guide vanes,passes through the runner blades beforeexiting axially from the centre of the runner.This radial flow acts on the runner vanes(blades), causing the runner to spin. The guidevanes (or wicket gate) may be adjustable toallow efficient turbine operation for a rangeof water-flow conditions.

Fig. : Francis turbine

As the water moves through the runner, itsspinning radius decreases, further acting onthe runner. The water imparts most of its‘pressure’ energy to the runner and leaves theturbine via a draught tube.

The guide vanes regulate the water flow as itenters the runner, and usually are linked to agovernor system which matches the flow toturbine loading.

1.B. (i) Force exerted by the jet on a stationaryvertical plate

Consider a jet of water coming out from thenozzle strikes the vertical plate

V = velocity of jet,d = diameter of the jet,a = area of x-section of the jet

The force exerted by the jet on the plate inthe direction of jet.

Fx = Rate of change of momentum in thedirection of force

= initial momentum – final momentum/ time

= (mass × initial velocity – mass × finalvelocity) / time

= mass/time (initial velocity – finalvelocity)

= mass / sec × (velocity of jet beforestriking – final velocity of jet afterstriking)

= raV(V-O)

= raV2

\ Ratio of forces = 1.



(ii) Force on flat moving plate in the directionof jet

Consider, a jet of water strikes the flat movingplate moving with a uniform velocity awayfrom the jet.

V = Velocity of jeta = area of x-section of jetU = velocity of flat plate

Relative velocity of jet w.r.t plate = V – u

Mass of water striking/ sec on the plate= ra(V – u)

Force exerted by jet on the moving plate inthe direction of jet

Fx = Mass of water striking/sec ×[Initial velocity – Final velocity]

= ra(V – u) [(V – u) – 0]= Fx = ra(V – u)2

Here u =V3

\ Fx =2

VV

3a

æ ör -ç ÷è ø

= 24V

9ar

\ Ratio of forces =49

.

(iii) Force exerted by the jet of water on seriesof vanesForce exerted by jet of water on singlemoving plate (Flat or curved) is not feasibleone, it is only theoretical one.Let,

V = Velocity of jeta = area of x-section of jetu = velocity of vane

In this, mass of water coming out from thenozzle/s is always in constant with plate.When all plate are considered.Mass of water striking/s w.r.t plate = raVJet strikes the plate with a velocity = V – u

Force exerted by the jet on the plate in thedirection of motion of plate

= Mass/sec × (Initial velocity –Final velocity)

Fx = raV (V – u)

Here u =V3

\ Fx =V

V V3

aæ ör -ç ÷è ø

= 22V

3ar

Thus, the ratio of forces =23

2.A. Comparison of Otto, Diesel and DualCombustion CyclesThe significant parameters in cycle analysisare compression ratio, peak pressure, peaktemperature, heat addition, heat rejection andthe net work. In order to compare theperformance of these cycles, some of theparameters are kept fixed.

(i) For the same compression ratio and heatadditionFor the comparison of Otto, Diesel and Dualcombustion cycles, these cycles are drawn ona single p-V and T-s diagram, as shown inFigures 1(a) and 2(b) respectively. In drawingthese diagrams, the compression ratio and theheat input are kept the same for the threecycles. Here,1–2–3–4–1 represents the Otto cycle.l–2–2¢–3¢–4¢–l represents the Dual combustioncycle.



l–2–3¢¢–4¢¢–l represents the Diesel cycle.

1

2

VV

is the compression ratio for all the three

cycles.

(a)

(b)Figure 1 : p-V and T-s diagrams having thesame compression ratio and heat addition for

the three cycles

The T-s diagram is drawn in such a way, sothat the area 5236 = area 522¢3¢6¢ = area523¢¢6¢¢. These areas represent heat inputwhich is the same for the three cycles. Area5146, area 514¢6¢ and area 514¢¢6¢¢ representheat rejection in Otto cycle, Dual combustioncycle and Diesel cycle respectively. As thearea 5146 < area 514¢6¢ < area 514¢¢6¢¢ and

h =heat rejected

1 ,heat supplied

-

therefore, h of the Otto cycle > h of the Dualcombustion cycle > h of the Diesel cycle.

(ii) Same Maximum Pressure and Heat InputFor same maximum pressure and same heatinput the Otto cycle (12341) and Diesel cycle(12¢3¢4¢1) are shown on p-V and T-s diagramsin Figs. 2(a) and 2(b) respectively.

(a) (b)Fig.2: Same maximum pressure and heat input

It is evident from the figure that the heatrejection for Otto cycle (area 1564 on T-sdiagram) is more than the heat rejected inDiesel cycle (156¢4¢).

(iii) For the same peak pressure, peaktemperature and heat rejectionFigure 3(a) and 3(b) represents the p-V andT-s diagrams for the three cycles having thesame peak pressure, peak temperature, andheal rejection.



Figure 3: p-V and T-s diagrams having thesame peak pressure, peak temperature and

heat rejection for the three cycles

Here:1–2–3–4–1 represents the Otto cycle.1–2¢–3¢–3–4–1 represents the Dualcombustion cycle.l–2¢¢–3–4–l represents the Diesel cycle.In all the three cycles, the maximum pressurepmax is the same. The peak temperature is thetemperature at point 3, i.e. T3 is also the samefor the three cycles. Heat rejection is duringthe process 4–1—this is also the same for thethree cycles.

The compression ratio will now be differentfor the three cycles, such as:

r = 1

2

VV

for Otto cycle

r = 1

2

VV ¢

for Dual combustion cycle

r = 1

2

VV ¢¢

for Diesel cycle

\ rDiesel cycle > rDual cycle > rOtto cycle

Heat supplied is as follows:

Q1Diesel cycle = area 2¢¢365 on the T-s diagram.

Q1Dual cycle = area 2¢3¢365 on the T-s diagram.

Q1Otto cycle = area 2365 on the T-s diagram.

Now, area 2¢¢365 > area 2¢3¢365 > area 2365Q1Diesel cycle

> Q1Dual cycle > Q1Otto cycle

h = 2

1

Q1

Q-

For a given value of Q2,hDiesel cycle > hDual cycle > hOtto cycle

This comparison is more realistic. In an actualcompression-ignition engine, i.e. dieselengine, a higher compression ratio is used incomparison with the compression ratio usedin the spark-ignition, i.e. petrol engine.Keeping the same peak temperature and peakpressure, both the engines can withstand thesame thermal and mechanical stresses.

2.B The Simple CarburetorCarburetors are highly complex. Let us firstunderstand the working principle of a simpleor elementary carburetor which provides anair-fuel mixture for cruising or normal rangeat a single speed. Later, other mechanisms toprovide for the various special requirementslike starting, idling, variable load and speedoperation and acceleration will be included.Figure shows the details of a simplecarburetor. The simple carburetor mainlyconsists of a float chamber, fuel discharge

Fig. : Simple Carburetor



nozzle and a metering orifice, a venturi, athrottle valve and a choke. The float and aneedle valve system maintains a constantlevel of gasoline in the float chamber. If theamount of fuel in the float chamber falls belowthe designed level, the float goes down,thereby opening the fuel supply valve andadmitting fuel. When the designed level hasbeen reached, the float closes the fuel supplyvalve thus stopping additional fuel flow fromthe supply system. Float chamber is ventedeither to the atmosphere or to the upstreamside of the veuturi.

During suction stroke air is drawn throughthe venturi. As already described, venturi isa tube of decreasing cross-section with aminimum area at the throat. Venturi tube isalso known as the choke tube and is so shapedthat it offers minimum resistance to the airflow. As the air passes through the venturithe velocity increases reaching a maximumat the venturi throat. Correspondingly, thepressure decreases reaching a minimum. Fromthe float chamber, the fuel is fed to a dischargejet, the tip of which is located in the throatof the venturi. Because of the differentialpressure between the float chamber and thethroat of the venturi, known as carburetordepression, fuel is discharged into the airstream. The fuel discharge is affected by thesize of the discharge jet and it is chosen togive the required air-fuel ratio. The pressureat the throat at the fully open throttlecondition lies between 4 to 5 cm of Hg, belowatmospheric and seldom exceeds 8 cm Hgbelow atmospheric. To avoid overflow of fuelthrough the jet, the level of the liquid in thefloat chamber is maintained at a level slightlybelow the tip of the discharge jet. This iscalled the tip of the nozzle. The difference inthe height between the top of the nozzle andthe float chamber level is marked h in Fig.

The gasoline engine is quantity governed,which means that when power output is to bevaried at a particular speed, the amount of

charge delivered to the cylinder is varied.This is achieved by means of a throttle valveusually of the butterfly type which is situatedafter the venturi tube. As the throttle is closedless air flows through the venturi tube andless is the quantity of air-fuel mixturedelivered to the cylinder and hence poweroutput is reduced. As the throttle is opened,more air flows through the choke tuberesulting in increased quantity of mixturebeing delivered to the engine. This increasesthe engine power output.

A simple carburetor of the type describedabove suffers from a fundamental drawbackin that it provides the required A/F ratio onlyat one throttle position. At the other throttlepositions the mixture is either leaner or richerdepending on whether the throttle is openedless or more. As the throttle opening is varied,the air flow varies and creates a certainpressure differential between the floatchamber and the venturi throat. The samepressure differential regulates the flow of fuelthrough the nozzle. Therefore, the velocity offlow of air and fuel vary in a similar manner.At the same time, the density of air decreasesas the pressure at the venturi throat decreaseswith increasing air flow whereas that of thefuel remains unchanged. This results in asimple carburetor producing a progressivelyrich mixture with increasing throttle opening.

3.A. Lathe with taper turning attachment: Theseattachments are available for turning taperson lathe. Longer tapers are easily turned withthese. The attachment is also useful for cuttingthreads on tapered sections.

The attachment is shown in Fig. The nut (C)is loosened to disconnect the motion of crossslide (having tool post on it) from the controlof cross feed screw, and thus the cross slideis made floating by disconnecting it from thesaddle so that it can move along its ways.The link (D) connects cross slide and theblock (E) (which can slide in slot (H) through



Fig. : Schematic of a taper turningattachment used on lathe

an adjustable clamp (A)). During normalturning operations, nut (C) is kept tightenedto connect cross slides with cross feed screwand the motion cross to the bed length maybe given by simply loosening the clamp nut(A), so that nut (A) becomes free over the slot(B) provided in the link (D). The link (F) ishinged at one end and has a guide (H) throughwhich block (E) can travel. On the other endof the link (F), an indicator is provided whichis graduated in degrees.

To turn a taper, hold the job properly betweenthe lathe centres and set the link (F) at desiredangle to give the required taper on the job.Loose nut (C) and tight the clamp (A). Thetool will now be restricted to follow thedirection parallel to the centre line of link (F)and will be guided by the movement of block(E) through the guide (H). This will vary thedepth of the cut of the tool while movingalong the job length and will render a taperon the job. The feed to the tool is given byworking the handle of compound rest. Thecompound rest is positioned at 90° to theaxis of job. The feeding of the tool is givenby compound rest because the cross slidescrew is disconnected.

Advantages of using a taper turningattachment are as follows:1. The attachment can be quickly and easily

set.

2. With the use of this attachment, tapersare turned without disturbing the normalset-up of the lathe.

3. External and internal tapers can be turned.

4. Tapers are turned with the longitudinalpower feed and thus the work can bemachined quickly and with better finish.

5. Long tapers are easily given.

6. Taper turning attachment is also used forcutting threads on a tapered surface.

3.B. Operating Conditions in a Lathe

Here, the term operating conditions or cuttingconditions refers to speed, feed and depth ofcut motions required for the metal cutting. Aswe discussed earlier, the definition ofoperating conditions is different for differentmachine tools. For example, in a lathe, theterm speed refers to the speed of job and incase of drilling machine it refers to the speedof the tool. Hence, here we first explain howthe speed, feed and depth of cut motions areprovided in a lathe.

Cutting Speed

In a lathe, for the turning operation, cuttingspeed is the peripheral speed of the workpiecepast the cutting tool. For a workpiece, say acircular bar of diameter D rotating at Nrevolutions per minute (rpm), the peripheralspeed is given by

S = Peripheral speed =DN

m/min1000p

where the diameter of the job D is in mm andto get speed in m/min conversion factor of1000 mm/m is used. The material passes thestationary cutting tool with this peripheralspeed, as shown in Fig.

Hence, v = Cutting speed

= Peripheral speed = S

or v =DN

1000p



Figure : Cutting speed and peripheral speedof workpiece in turning operation

FeedIn lathe operations, the term feed f impliesthe distance that the tool advances for eachrevolution of the work. Feed is expressed inmm/revolution. For example, if the feed isspecified as 2 mm/revolution, it implies thatthe tool moves a distance of 2 mm for everyrevolution of the job.

Depth of Cut

The depth of cut d is the perpendiculardistance measured from the machined surfaceto the uncut (or previous cut) surface of theworkpiece. For the turning operations, thedepth of cut is expressed as:

Depth of cut d = 1 2D D mm

2-

where

DI = original diameter of the workpiece in mm

D2 = final diameter of the workpiece in mm.

In a turning operation if the depth of cut is1 mm, then the diameter will be reduced by2 mm.

The values of speed, feed and depth of cutdepend upon the type of workpiece material,tool material, and type of surface finishrequired. In order to produce the desireddimension, the metal to be cut may beremoved in two possible ways. Initially largeamount of metal is removed to come closer tothe desired final dimension without botheringabout the accuracy of dimension and surface

finish. The only care to be taken is that thedimension should not be reduced below thevalue. This type of metal cutting is calledrough cutting or roughing operation. Afinishing cut or finishing operation obtainsthe final dimension to the desired accuracyand surface finish. In the finishing cut, verysmall amount of material is removed.Normally, only one finishing cut is madewhile there can be more than one roughingcut depending upon the amount of materialto be removed and permissible depth of cut.Roughing operation requires stronger toolsfor faster material removal, while for finishingcut new or freshly sharpened tool is used. Inroughing, large feed and large depth of cutare used and in finishing, small depth of cutand small feed are used.

3.C. TailstockFig. shows the various parts of a tailstock. Thebase of body (1) is planed and is providedwith four feet which fit into the parallelmachined ways of the lathe bed. Thus, the tailstock is constrained to move in a straight lineon lathe bed. The upper cylindrical part of thebody is cast hollow and is machined to receivethe barrel (2). The barrel is provided withthreads at one end in which the spindle(3) works and on the other end, a conical holeis made to carry the centre (4). On the righthand end of the body, the spindle bearing(5) is fitted by means of screws (6), againstwhich rests the collar of the spindle. The handwheel (7) is mounted on the end of the spindleby means of a key (8) and is retained in positionby a nut (10) and a washer (not shown). Thefeather (9) when put in its place under side ofthe barrel prevents its rotation.

When the hand wheel is turned, it causes thebarrel to move in or out of tail stock body.The spindle is confined by the collar on oneend and hand wheel on the other end, thus itrotates the spindle only about the axis andnot to move along the axis.



Tailstock has two main uses, namely:1. It supports the other end of the work

when the work/job is being machinedbetween the centres.

2. It holds the tool for performing operationssuch as drilling, reaming, tapping, and soon. It is used for supporting and feedingdrills, reamers, and so on when it isnecessary to use for drilling work held inthe chuck.

4.A. Milling processes performed by differentmilling cutters can be grouped into thefollowing broad categories:(a) Peripheral milling; (b) Face milling;(c) End milling.

Fundamentals of cutting action of millingcutters used to perform the above processesare discussed in the following:(a) Peripheral milling or plain milling or

slab milling results in the production ofa machined surface parallel to the axis ofrotation of the cutter [Fig. 1]. In thisprocess, cutting force is not uniformthroughout the length of the cut by eachtooth. Also, the quality of the surfacegenerated and the shape of the chipformed depend on the rotation of cutterrelative to the direction of feed movementof the work. Due to these factors,peripheral milling results into thedevelopment of vibrations during cutting.



In view of the relative movement betweenthe cutter and the workpiece, peripheralmilling is of the following two types:(i) Up milling or conventional milling(ii) Down milling or climb milling

Up milling or conventional milling isshown in Fig.1. This is the process ofremoving metal by a milling cutter whichis rotated against the direction of feedingof work to the cutter. Note the chipthickness which is minimum (zero) at thebeginning of the cut and reaches to themaximum when the cut terminates.Because of this, the cutting force in upmilling increases from zero to themaximum per tooth movement of thecutter. Since the cutting force is directedupwards, it tends to lift the workpiecefrom the table (or the work holdingfixture). Further, as the cutting progressesand there is difficulty in pouring coolanton the cutting edge of cutter to flush outchips, there is accumulation of chips atthe cutting zone and when chips arecarried over with cutter, they spoil thework surface. Since the cutter teeth donot begin cutting as soon as they touchthe work surface, in the first instance,sliding of cutter teeth takes place for asmall distance on the work surface whichresults in waviness of the resultingmachined surface of the work.

Fig. 1: Up milling or conventional milling

Down milling or climb milling is shownin Fig. 2. It is the process of removingmetal by a milling cutter which is rotated

in the same direction as the travel of theworkpiece. Note the thickness of the chipwhich is maximum when the cutter toothbegins its cut and it reduces to theminimum (zero) when the cut terminates.In down milling, the cutter tooth startsremoving metal as soon as it touches thework surface and without sliding (as inup milling). It will be observed that thecutting force in down milling is alsovariable throughout the cut, maximumwhen tooth begins to cut and minimumwhen tooth leaves the work. Since thecutting force is directed downwards, ittends to seat the work firmly in the fixturewhich suites more for machining thinnerjobs being easily and firmly clamped infixtures. Coolant is more effectivelyprovided in the process, thereby avoidingoverheating and accumulation of chipsin cutting area. Better surface finish onthe work is attained in climb milling asthe cutter takes a chip of zero thicknessat the end of the cut. There is, however,a tendency of the cutter to pull the workforwards.

Fig. 2: Down milling or climb milling

Although the down milling process seemsto have several advantages, it cannot,however, be conducted on old machineshaving backlash error between the tablefeed screw and the nut. The backlashcauses the work to be pulled below thecutter when the cut begins and leaves thework free when the cut is terminated. Asthis action is repeated during machining,vibrations in the machine are set updamaging the work surface considerably.



It is because of this that down milling isperformed only on those machines whichare rigid and have backlash eliminationarrangement.

(b) Face milling is the operation performedby a face milling cutter to produce a flatmachined surface perpendicular to theaxis of rotation of the cutter [Fig. 3(b)].In the process, the peripheral cuttingedges of the cutter perform the actualcutting (or facing) and the face cuttingedges only finish up the work.

(c) End milling [Fig. 3(e)] is the combinationof peripheral and face milling operations.The cutter has teeth both on the end faceand on the periphery. When peripheralcutting edges are used for cutting, thedirection of rotation and direction ofhelix of the cutter should be opposite toeach other and when only the end cuttingedges are used for cutting, the directionof rotation and the direction of helix ofthe cutter should be the same.

Fig. 3: Different milling operations

Milling Machine Operations

Although various jobs are performed on amilling machine, the basic milling operationsdone on them fall under the followingcategories:

1. Plain milling or slab milling orperipheral milling in which a flat surfaceis produced by a rotating cutter with itsaxis parallel to the surface being machined[Fig. 3(a)]. Up milling and down millingare two types of plain milling.

2. Face milling in which a flat surface isproduced at right angle to the axis of thecutter [Fig. 3(b)].

3. Side milling in which a flat verticalsurface is produced on the side of aworkpiece using a side milling cutter.

4. Straddle milling in which flat verticalsurfaces on both sides of a workpiece areproduced using two side milling cuttersmounted on the same arbor [Fig. 3(c)].Distance between the two cutters isadjusted by using suitable spacing collars.Straddle milling is commonly used formaking square or hexagonal surfaces.

5. Gang milling in which several plainmilling cutters of same or differentdiameters and width may be used at thesame time for production of severaldifferent parallel horizontal surfaces onthe workpieces [Fig. 3(d)].

6. End milling in which narrow slots,grooves or keyways are produced usingan end mill cutter on a vertical millingmachine [Fig. 3(e)].

7. Angular milling in which angularsurfaces such as angular grooves onV-blocks are produced using an anglemilling cutter [Fig. 3(f )].

8. Form milling in which irregular contoursare made using form cutters [Fig. 3(g)].



9. T-slot milling in which first a plain slotis cut on the work surface using a sideand face milling cutter. Then the T-slotis cut feeding the T-slot cutter from oneend of the plain slot [Fig. 3(h)].

10. Dovetail milling in which dovetailsurfaces are made using a dovetail cutter[Fig. 3(i)].

11. Saw milling is the operation ofproduction of narrow slot and groovesusing a saw milling cutter. The processcan be used for complete parting off also[Fig. 3(j)].

Besides the above, milling keyways, slotsand grooves, cutting of all types of gears andworm wheels and milling of cam profiles,thread milling, helical milling of flutes indrills, etc. are also performed on millingmachines.

4.B. The shaper also called shaping machine, is areciprocating type of machine tool in whichthe ram moves the cutting tool backward andforward in a straight line to generate the flatsurface. The flat surface may be horizontal,inclined or vertical as shown in the Fig. 1.

Fig. 1: Surface Produced by a Shaper

Tool head or shaper head (Fig. 2) is mountedat the front end of ram and has the provisionof being swivelled in any direction forshaping angular surfaces. The tool is held intool post. The vertical feed of tool may begiven with tool-feed handle (F) because itsrotation makes the slide (E) to go up anddown. Feed screw (I) has a graduated collar(J) for accurate adjustment of the depth ofcut. The clapper block (D) carrying the toolpost (G) is hinged with the clapper boxthrough a pin (B). When tool cuts in forward

stroke only, the clapper block gets a rigidsupport at its back because of the clapperwall, but in the return stroke the clapper blockswings forward and moves the tool on the jobsurface without giving any cut or scratch. Forswivelling the shaper head to any desiredangle for machining taper surfaces likedovetail, etc., loosen the bolt (C) and tilt theshaper head to the required angle and latertighten the bolt (C). Tilling angle may beread from the graduations made on the shaperhead. Apron may also be swivelled todifferent angles and clamped there with thehelp of the bolt (A).

Fig. 2: Shaper head (or tool head)

Operations Performed on Shaper

Shaper is used for machining of (i) horizontalflat surfaces, (ii) vertical flat surfaces,(iii) angular flat surfaces, (iv) irregular surface,(v) curved surfaces, (vi) slots, keyways,grooves, gear teeth, etc. (using indexingattachment).

Quick Return Mechanisms of ShaperShaper is a reciprocating type machine toolwherein the rotary motion of motor isconverted into reciprocating movement of ramby the mechanism housed within the columnof the machine. In a standard shaper, toolcuts metal in its forward stroke only and thereturn stroke goes idle as no metal is cutduring the return stroke. To reduce the total



machining time, the return stroke should beperformed by the machine quickly. Hence,shaper mechanism should be designed suchthat it may allow the ram (or tool) to moveat a comparatively slower speed during theforward cutting stroke, whereas during thereturn or idle stroke, it may allow the ram tomove at a faster rate. This feature is achievedin a shaper with the help of ‘quick returnmechanism’ based on either of the followingtwo methods:

(a) Crank and slotted link mechanism

(b) Hydraulic shaper mechanism

5.A. A governor may be defined as a device forregulating automatically output of a machineby regulating the supply of working fluid.When the speed decreases due to increase inload the supply valve is opened by mechanismoperated by the governor and the enginetherefore speeds up again to its original speed.If the speed increases due to a decreases ofload the governor mechanism closes thesupply valve sufficiently to slow the engineto its original speed. Thus the function of agovernor is to control the fluctuations ofengine speed due to changes of load.

Hartnell governor: The Hartnell governor isa spring loaded governor in which thecontrolling force, to a great extent, is providedby the spring thrust.

Figure shows one of the types of Hartnellgovernors. It consists of casing fixed to thespindle. A compressed spring is placed insidethe casing which presses against the top ofthe casing and on adjustable collars. Thesleeve can move up and down on the verticalspindle depending upon the speed of thegovernor. Governor balls are carried on bellcrank lever which are pivoted on the lowerend of the casing. The balls will fly outwardsor inwards as the speed of the governor shaftincreases or decreases respectively.

Fig.: Hartnell governor

Crank and Slotted Lever MechanismA crank and slotted lever mechanism, whichis one type of quick return motion mechanism,is widely used in shaper machines. It executesthe return stroke in the shortest possible time(Figure). In this mechanism, the crank OBrotates with uniform angular velocity w rad/sabout the fixed point O. At the end B of thecrank, a slider is pivoted such that C be apoint on the link AD immediately below theslider B. As the crank OB rotates about thepoint O, the slider reciprocates along the leverAD and there is a relative motion betweenthe points B and C. The lever AD oscillatesabout the fulcrum point A. The other end ofthe lever is connected to ram R through alink DR. A cutting tool is attached to the ramwhich performs cutting and idle stroke.

The velocities of various links of a crankslotted lever mechanism can be determinedby drawing a velocity polygon as discussedbelow:

1. Compute tangential velocity of crank OB,vbo = w × OB



2. Choose a convenient point o and draw avector ob

uur perpendicular to crank OB in

counterclockwise direction to somesuitable scale as shown in Figure (b).

(a) Crank and slotted lever mechanism

(b) Velocity polygon

Fig.: Velocity analysis of crank andslotted lever mechanism

The vector obuur

has two components, oneparallel to the lever AD and anotherperpendicular to it, such that thefollowing vector equation is satisfied:

vbo = vca + vbc

or obuur

= ac cb+uur uur

where velocity of point C relative to pointA, vca is perpendicular to lever AD andVbc. is parallel to the lever AD.

3. Therefore, draw a line ac perpendicularto the lever AD. Also draw another linebc from point b which is parallel to thelever AD. These lines intersect at point c.

4. The velocity of point C on the lever AD

is represented by vector acuur

. Extend thisline up to point d in proportion such thatit satisfies the following relation:

ac

ad

uuruur =

ACAD

5. Draw a vector druur

of unknown magnitudeperpendicular to the link DR.

6. The velocity of the ram R relative to thefixed guide G, vrg is along the line ofstroke. Thus from point g, draw a lineparallel to the line of stroke to intersect

vector druur

at point r. The vector gruur

represents the velocity of the ram relativeto the fixed point G.

In a crank and slotted lever mechanism, whenthe crank takes the position OB1 and OB2,the component of velocity of crank pinperpendicular to the lever is zero. Thus duringforward stroke, the crank moves through(360°–2a) and during return stroke, it executeswhen the crank moves through 2a [See Figure(a)]. Therefore,

Time of cuttingTime of return

=360° 2

2- aa

Further, when the crank pin reaches either atposition B3 or B4, the component of velocityalong the lever AD is zero. Thus the velocityof lever AD at the crank pin is equal tow . OB. The maximum velocity of cutting isequal to the maximum velocity of point D.When the crank pin is at position B3 (assumingthat the effect of obliquity of link DR isneglected.), then the maximum velocity offorward stroke (cutting):

vc,max =3

AD.OB

ABw ´

=1

lr

l rw ´

+

whereOB = crank radius (= r)



AD = length of the lever (= l)and l1 = length of the fixed link OA.Similarly, the maximum velocity of returnstroke:

vr, max =4

AD.OB

ABw ´

=1

lr

l rw ´

-Therefore, the ratio of velocities is:

,max

,max

r

c

v

v =

Maximum velocity of returnMaximum velocity of cutting

= 1

1

l rl r

+-

5.C. Given data:External radius r1 = 120 mm = 0.12 mInternal radius r2 = 60 mm = 0.060 mAxial thrust w = 1500 NFor uniform wear,

Pressure P =Cr

For maximum pressure r = r2

and for minimum pressure r = r1

Here C =1 22 ( )wr rp -

=1500

2 3.14 (0.12 0.06)´ ´ -

=1500

2 3.14 0.06´ ´= 3980.89 N/m

Pmax =2

Cr

=3980.89

0.06

= 66348.2 = 0.066 Mpa

Pmin =1

Cr

=3980.89

0.12

= 33174.08 = 0.033 Mpa

Paverage = ( )2 21 2

w

r rp -

= 2 2

15003.14 (0.12 0.06 )´ -

=1500

3.14 (0.0144 0.0036)´ -

= 44274.78= 0.044 Mpa

\ Pmax = 0.066 Mpa

Pmin = 0.033 Mpa

Paverage = 0.044 MPa



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SSC SOLVED PAPER 2007 (CONVENTIONAL)Dual cycle = area 2¢3¢365 on the T-s diagram. Q1 Otto cycle = area 2365 on the T-s diagram. Now, area 2¢¢365 > area 2¢3¢365 > area 2365 Q1