M A N U F A C TU R IN G P R O C E S S E S , Second Edition J .P . Kaushish
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28. In centrifugal castings, impurities are: (a) uniform ly distributed in casting (b) forced tow ards outer surface
(c) collected close to centre o f casting 29. C entrifugally cast products have
(a) large grain structure with high porosity (b) fine grain structures with high density (c) fine grain structure with low density
(d) segregation o f slag towards the outer skin o f casting 30. In green-sand m olding process, uniform ram m ing leads to
(a) less chance o f gas porosity
(b) uniform flow o f m olten metal into the old (c) greater dim ensional stability o f casting (d) less sand expansion type o f casting defect
A n s w e r s o f o b je c tiv e ty p e q u e s tio n s
1. (a) 2. (b) and (c) 3. (c) 4. (d) 5. (d)
6. (a) 7. (c) 8. (a) 9. (b) 10. (a) 11. (c)
12. (c) 13. (d) 14. (a) 15. (b) 16. (b) 17. (c)
18. (b) 19. (c) 20. (b) 21. (c) 22. (b) 23. (c)
24. (d) 25. (c) 26. (b) 27. (e) 28. (c) 29. (b)
■*u •
Metal Machining
Processes and Machine Too
6.1
IN T R O D U C T IO N
Various m anufacturing processes used for transform ing m etals into som e usable products are based on basic properties o f metals, for exam ple, the process o f castin g is based on the property o f ‘feasibility’ (or m elting), forging on the property o f ‘m a lle ab ility ’, and rolling or form in g on the property o f ‘ductility’ . Likew ise, the process o f m ach ining is based on the property o f ‘divisibility’, w hich is the capability o f metal for getting divided into small bits and separated from the w orkpiece in the form o f chips. B lank is the piece o f metal out o f w hich a product o r a com ponent o f som e use is m achined out. M ach in in g consists o f forcing a cutting tool o f harder material through the excess (or surplus) material on the w orkpiece blank; the ex cess m aterial being progressively separated from the blank in the form o f chip s because o f the relative m otion m aintained betw een the tool and the w orkpiece. T h e operation finally results into a transform ed product m achined to the desired shape and size.
M etal m achining o r metal cutting com prises those processes wherein removal o f material from a w orkpiece is effected by relative m otion betw een the cutting tool and the w orkpiece. T h e cutting tool m ay be (a) sin g le-p o in t cu ttin g to o l as used for turning on lathe o r shaping o r (b) m u lti-p o in t cu ttin g to o l as used for drilling o r m illing operations. Basic elem ents o f a m achining operation include (a) w orkpiece, (b) tool and (c) chip. W ork p iece provides the parent m etal from w hich unw anted m etal in the form o f chip is rem oved by the cutting action o f tool for getting the desired shape and size o f the m anufactured product. T h e m achining operation is greatly affected by the chem ical com position and physical properties o f w orkpiece metal. Tool material and tool geom etry play an im portant role in m achining effectively and econom ically. Similarly, type and geom etry o f chip are affected by m etals o f w orkpieces and tool, geom etry o f tool and cutting fluid. T h e process o f m achining has gained im portance as it successfully and econom ically m eets the basic objectives o f m anufacturing a product, such as h ig h e r m etal rem oval rates, high class finish on the w o rk p iece , p ro d u c tio n o f com ponents o f intricate shapes, less pow er consum ption in com parison to many other production
m ethods, etc. H ow ever, one m ajor draw back o f m achining process is loss o f m aterial in the form o f chips. M etal cutting processes are perform ed on m etal cutting m ach ines o r m ach ine tools using different types o f cutting tools.
6.1.1
C la s s ific a tio n o f M a c h in in g P ro c e s s e s
M achining processes can be broadly classified as follows:(a) M etal cu ttin g processes using (i) sin g le-p o in t cu ttin g to o l include turning, boring, threading, shaping, planing and slotting and (ii) m u lti-p o in t cu ttin g to o l include drilling, milling, tapping, broaching and hobbing.
(b) G rind in g processes include surface grinding, cylindrical grinding and centreless grinding.
(c) F inishing processes include lapping, honing and super-finishing.
(d) U n c o n v e n t io n a l m a c h in i n g p r o c e s s e s in c lu d e e l e c t r o - d is c h a r g e m a c h in in g , ultrasonic m achining, electrochem ical m achining, electron beam m achining, laser beam m achining, etc.
Selection o f a suitable m achining process depends on w orkpiece material, shape, size and quantity o f product to be m ade, expected degree o f accuracy in the dim en sio n s o f product, requirem ent o f surface finish and finally the cost o f production.
6 .2 C U T T IN G T O O L S A N D T H E IR N O M E N C L A T U R E
As already m entioned that during m achining a w orkpiece, a cutting tool o f harder material is forced through the surplus m aterial o f the w orkpiece blank, the surplus m aterial being progressively separated from the blank in the form o f ‘chip* because o f the relative m otion m aintained betw een tool and w orkpiece. T he cutting tools are m ade from high strength and harder m aterials such as high carbon steel, high speed steel, cem en ted carbide, etc. Various cu ttin g tool m aterials have been described u n d er Section 3.18.
It m ay be noted that a cutting tool never peels the material aw ay from the w orkpiece like a knife does. T h e tool has a ‘cutting e d g e ’ w hich is blunt and needs sufficient force to pry the chip from the jo b (Fig. 6.1). In fact, the cutting edge causes the internal shearing action in the metal such that the metal below the cutting edge o f the tool yields and flow s plastically. First o f all, the compression o f the metal under the tool edge takes place [Fig. 6.2(a)] w hich is follow ed by the separation o f the metal in the form o f chip [Fig. 6.2(b)] w hen the com pression limit o f the metal ju st under the tool edge has been exceeded. T he cutting tools as used on lathes have o nly a ‘sin g le cu ttin g ed g e ’ o r 'point ’ at one end o f its body, it is then called ‘sin g le-p o in t to o l’. T he ‘p o in t’, w hich is w edge-shaped portion, form s the cutting part o f the tool. There are m u lti-p o in t cu ttin g to o ls ’ also as will be discussed in the following.
Fig. 6.1 T urning w ith a sin g le -p o in t tool.
Fig. 6 .2 S how ing the princip le of m etal cu ttin g w ith a sin g le -p o in t to o l: (a) C om pression o f m etal under to o l edge and (b) The cu ttin g edge causes internal shearing action in the metal. The m etal below the to o l edge yields and flo w s plastically, w h ich is follow e d by the separation o f sheared m etal in the fo rm of a chip.
6.2.1
C la s s ific a tio n o f C u ttin g T o o ls
All cutting tools can be broadly classified as:(i) S ingle-point cu tting tools having only one cutting edge. T hese tools find wide applications for lathe, shaper, planer, slotter, boring m achine, etc.
(ii) M ulti-point cu ttin g tools have more than one cutting edge such as twist drills, ream ers, taps, m illing cutters, broaches, etc. A m ulti-point cutting tool m ay differ in overall appearance and purpose but each cutting edge o f the tool acts as and has its basic features o f a single-point cutting tool. A lso, the cutting process perform ed by multi-point cutting tools closely resembles m achining as perform ed by single-point cutting tools.
C utting tools are som etim es classified based on their m otion during cutting, for exam ple,
lin ea r m otion tools as that o f lathe, shaper, planer and slotter; rotary m otion tools as milling
cutters and grinding w heels; ro ta ry a n d lin ea r m otion tools as twist drills, ream ers, honing tools, etc.
Besides above, a tool m ay be a solid o r forged tool (Fig. 6.3) m ade from high carbon steel o r high speed steel. C utting bits o r inserts m ade o f high speed steel, stellite o r cem ented carbide are available, w hich can be brazed on a high carbon steel shank and tools thus made arc called brazed tools. T he cutting bits can be held w ith the tool shank with som e clam ping system. T h e tool bit is inserted in a slot (in the tool holder) m ade at 15° to the base, thus reducing the effective clearance angle and increasing the to p rake angle by 15°. Tool bit is less expensive than solid tool. Also, the tool can be adjusted to the correct height easily by adjusting the position o f the tool bit in the slot. R egrinding o f tool is easier as only the end cutting edges are required to be ground. It is very easy to w ithdraw o r replace the tool bit
w ithout disturbing the setting.
T e rm s relating to the geom etry o f sin gle-p oint tool: Im portant term s relating to the geom etry o f a single-point cutting tool are explained in the follow ing with reference to Fig. 6.4.
C lam ping screw
Shank ' ' ' ' - V (To o l holder)
(iv)
Fig. 6.3 D iffe re nt types o f lathe to o ls: (i) Solid or forged to o l, (ii) Brazed tipped to o l, (iii) M echanically held to o l tip o r insert and (iv) Tool bit held in a to o l shank.
Shank
End-cutting edge angle (C*)
Side rake angle +
Auxiliary cutting edge or end cutting edge
Front or auxiliary flank
Main cutting ed g e or side cutting edge Back rake angle ( a j Main flank
Side relief angle (9S)
or side clearance angle Side cutting
edge angle (0 $ )
Front clearance or end relief angle ( 0 J
F ig. 6 .4 G eom etry of a sin g le -p o in t cu ttin g to o l.
Shank is the body o f the tool and is usually rectangular in cross-section. Face is the surface against w hich the chip slides upw ards. Flank (main) is that surface which faces the w orkpiece. It is the surface adjacent to and below the m ain cutting edge w hen the tool lies in horizontal position. Heel is the lowest portion o f the side-cutting and end-cutting edges. N ose or point is the w edge-shaped portion and is the conjunction o f side- and end-cutting edge. Base is the underside o f shank. Rake refers to the slope o f the tool top aw ay from the cutting edge. Tool has side rake and back rake.
Besides the body parts o f the tool as m entioned above, the tool geom etry also includes various tool angles w hich have been explained in the following.
6 .2 .2 A n g le s o f a S in g le -p o in t C u ttin g T o o l
A ngles o f the tool play a significant role in efficient and econom ical m achining o f different m etals. T hese tool angles vary according to the m etal to be m achined and the tool material. A change in the c h ie f angles o f cutting tool will correspondingly change the forces due to the cutting action as also the conditions fo r heat transm ission through the cutting elem ents o f the tool. T hus, the tool angles o f a cutting tool influence its perform ance and life. Im portant angles o f a single-point tool are discussed in the follow ing w ith reference to Fig. 6.5.
• Side cutting ed ge angle (CJ
Approach angle
as = U ° T
V an 9*e \ 0, = 6° 8 14 6 ab Back rake a , S id e rake 0„ E n d relief 0S Side relief Cb E n d cutting edge Cs S id e cutting edge R N o s e radius To o l designation 20 15Fig. 6.5 Im p o rta n t angles and cu ttin g to o l signature o f a sin g le -p o in t cu ttin g to o l.
1. R ake angle is the rake o r slope o f the tool face and is form ed betw een tool face and a plane parallel to its base. W hen this slope is tow ards the shank, it is called b a ck rake o r top ra ke and w hen m easured tow ards the side o f the tool, it is called sid e rake. R ake angle has the follow ing functions:
(i) A llow s chips to flow in a convenient direction aw ay from the cutting edge.
(ii) R educes chip pressure on tool face and provides keenness to the cutting e d g e and consequently im proves finish on the w orkpiece.
(iii) R educes cutting forces required to shear the m etal and thus helps increasing tool life and reduces po w er consum ption.
Provision o f rake angle d epends upon follow ing m ain factors:
(i) W orkpiece m a teria ls as harder m aterials (cast iron) need sm a lle r rake angle than softer m aterials such as alum inium o r steel.
(ii) Tool m a teria l, for exam ple, cem en ted carbide perm its m achining at very high cutting speeds w ith little effect o f rake angle on cutting pressure and hence rake angle in such cases m ay be reduced to zero o r even negative rake m ay be provided to increase tool strength.
(iii) D ep th o f cut, for exam ple, higher depth o f cut (as in rough cutting) gives severe cutting pressures on tool and hence rake is decreased to increase tip angle that results in strong cutting edge.
Front rake is important when tool removes metal from its front cutting edge (a parting-off tool).
Side rak e influences m achining w hen tool rem oves metal on its side cutting edge only. S ide rake allow s chips to flow by the side o f the tool and aw ay from tool post. Since the single-point tools generally rem o v e metal both on its end and side cutting edges, a slope on the face o f the tool is given suitably com bining the front and side rake together, and this resultant slope is called true rake.
T h e rake o r slope o f the face o f the tool m ay be positive, zero o r negative as show n in Fig. 6.6.
(a ) Positive rake (c) Negative rake
Fig. 6 .6 Positive, zero and negative rake. Note the po sitio n and direction o f th ru s t on the to o l in each case. R— Rake and T— Thrust.
Positive rake: A tool has positive rake w hen face o f the tool slopes aw ay from the cutting edges and also slants tow ards the back (shank) o r side o f the tool [Fig. 6.6(a)]. A rake angle specifies the ease with w hich a metal is m achined. T he higher the rake angle, the better is the cutting and less are cutting forces. Since an increase in rake angle reduces the strength o f tool tip, heat dissipation and tool life, it is, therefore, usually kept not m ore than 15° (for high speed steel tool).
Zero rake: A tool has zero rake w hen no rake is provided on tool, i.e. the tool face has no slope and is parallel to the upper surface o f the tool shank [Fig. 6.6(b)!. A zero rake increases tool strength and avoids digging o f the tool into the w orkpiece. Brass is turned well with tools having zero rake angle.
N egative rake: A tool has negative rake w hen the tool face slopes aw ay from the cutting edge and slants upw ards tow ards the side o r back o f the tool [Fig. 6.6(c)]. Negative rake is used on cem ented carbide o r ceram ic tools. N egative rake results into a tool with reduced keenness but stronger cutting edge (and hence stronger tool) o r tool tip. C arbide tools with negative rake are used for m achining extra hard surfaces and stronger m aterials in mass production.
Cutting action o f a tool with positive and negative rake is show n in Fig. 6.7.
Built-up edge Cutting edge
(a) (b)
Fig. 6 .7 S how ing the cu ttin g actio n o f a tool w ith positive rake (a) and negative rake (b ). Note that in positive rake cu ttin g , there exists a tendency fo r the m etal to build up and also m ore pronounced crater fo rm a tio n . In negative rake cu ttin g , the tendency o f cra te r fo rm a tio n is less and the cu ttin g edge in the process gives a bu rn ishin g (p o lish in g ) e ffect on the machined surface o f w orkpieces. The th ru s t of cut sh ow n by a rro w passes throu gh the cu ttin g edge of the tool at (a) and th u s intro du ce s a bending load at the cu ttin g edge, w hereas at (b) the th ru s t passes throu gh the to o l shank and th is gives a com pression load on the stronger portion of the tool.
A dvan tage o f using negative rake on tool
(i) N egative rake gives larger tip angle and hence a stronger tool.
(ii) In case o f tipped tools, an advantage with negative rake is that there is a tendency o f the chip pressure to press lip against the body o f tool, a favourable factor since carbide tips are very good for com pressive loads. Negative rake on these tools varies from 5° to 10°.
(iii) T h e point o f application o f cutting force is altered from cutting edge (a w eak er tip) to a stronger section.
(iv) Very high cutting speeds can be used for faster metal removal. (v) Tool w ear is decreased and hence tool life is increased.
(vi) H eavier depth o f cut can be taken as negative rake increases tip angle o f the tool. T here are certain lim itations o f using negative rake, for exam ple, h ig h e r cu ttin g s p e e d should be kept to take full advantage o f negative rake; rig id ity o f the m a ch in e to o l m ust be ensured against higher cutting speeds and vibrations; high h ea t generated by negative rake turning m ust be taken c a re o f for better tool life and h ig h er p o w e r requirem ent, above 10 to
15% more than what required for positive rake m achining.
2. C learance angles: C learance angle is the angle between the m achined surface and the Hank faces (Fig. 6.4) o f the tool. It helps preventing the flank o f the tool from rubbing against the surface o f the w orkpiece, thus allow ing the cutting edge o f the tool only to com e in contact with the w orkpiece, for exam ple, front clearan ce angle (also called end relief angle) prevents the front o r auxiliary flank o f the tool from rubbing against the finished surface o f the w orkpiece. In case the angle is too small, the tool will rub on the surface o f the jo b and spoil surface finish. Too large end relie f angle m ay give tool digging tendency and m ay chatter. T he side clearance angle (or side relief angle)
prevents the side o r m ain flank o f the tool from rubbing against the w orkpiece under longitudinal feeds. Values o f these angles for turning tools vary between 5° and 15°. 3. S ide cu ttin g ed ge angle: Side cutting edge angle is the angle betw een the side cutting
edge and the longitudinal axis o f tool. Its com plim entary angle is approach angle, (Fig. 6.5) w hich is betw een feed direction and side cutting edge. Side cutting edge angle helps providing a w ider cutting edge and thus an increased tool life as cutting force, distributed on w ider surface, provides greater cutting speeds and quick heat dissipation and gives a better finish on work surface. It controls direction o f chip flow. Too large side cutting edge angle produces chatter. It is usually kept around 15° although in turning tools, it varies from 0 to 90°, for exam ple, a knife edge turning tool has 0° side cutting edge angle and its cutting edge is perpendicular to the work surface and such a tool is used for turning slender w orkpiece as no bending stress is produced w hen tool is fed. A square nose tool with side cutting edge angle 90° is used for finish turning. 4. End cu ttin g ed ge angle: It prevents the trailing end o f the cutting edge o f tool from rubbing against the w orkpiece. A larger end cutting edge angle w eakens the tool. It is usually kept betw een 8° and 15°.
5. Lip angle: L ip angle o r cu ttin g angle depends on the rake and clearance angle provided
on tool and determ ines the strength o f cutting edge. T he lip angle is m axim um when rake (positive) and clearance angle are m inim um . But in negative rake, lip angle increases as rake increases. A larger lip angle perm its m achining o f harder m etals, allow s heavier depth o f cut and increases tool life and better heat dissipation. This sim ultaneously calls for reduced cutting speeds, w hich is a disadvantage.
6. N ose radius: W hile greater nose radius increases abrasion, it also helps in im proving surface finish, tool strength and tool life. Large nose radius m ay cause chatter. For rough turning, it is kept about 0.4 mm and for finish turning, 0.8 to 1.6 mm.
Average recom m ended tool angles for m achining different m etals are given in Table 6.1. TABLE 6.1 Recom m ended angles fo r high carbon and high speed steel tu rn in g too ls
Material Front rake, deg Front clearance, deg Side rake, deg Side clearance, deg
Mild steel 10-12 6-8 10-12 6-8 Stainless steel 5-7 6-8 8-10 7-9 Aluminium 30-35 8-10 14-16 12-14 Brass 0-6 8-10 1-5 10-12 Cast iron 3-5 6-8 10-12 6-9 Copper 14-16 12-14 18-20 12-14
6 .2 .3 N o m e n c la tu re o f a L a th e T o o l
N o m en cla tu re o f a cu ttin g to o l m eans system atic n am ing o f various parts and angles o f the
tool. C om plete nom enclature o f various parts o f a single-point tool is shown in Fig. 6 .4 and Fig. 6.5 w hich includes shank, face, flank, heel, nose, base, back rake, side rake, side clearance,
end clearance, end cutting edge, side cutting edge and lip angle. T hese elem ents define the shape o f a cutting tool.
C utting tool signature: T he cu ttin g to o l sig n a tu re (o r tool design ation) is a sequence o f num bers listing various angles, in degrees and the size o f nose radius. T he A m erican Standards A ssociation (A S A ) has standardized the num erical m ethod o f tool identification. T he seven elem ents com prising the signature o f a single-point tool are alw ays w ritten in the following order: back rake angle, side rake angle, end relie f angle, side relie f angle, end cutting edge angle, side cutting edge angle and nose radius.
Exam ple: A tool shape specified as p er A SA system is given below (Fig. 6.5): 8-14-6-6-20-15-4
has back rake angle 8°, side rake angle 14°, end relie f angle 6°, side re lie f angle 6°, end cutting edge angle 20°, side cutting edge angle 15° and nose radius 4 mm.
B esides the A m erican S tan d ard s Association (A S A ) System , also called coordinate system (or X-Y-Z Plane System ) w hich has been described in the above, the other system s o f tool designation include British S ystem , C ontinen tal System and International System (or O rthogonal R ake System ).
In O rth ogonal R ake System (O R S ) o r International System , main param eters o f a single-point tool are designated in the follow ing order: inclination angle (X), orthogonal rake angle (O'), side relie f angle ()), end relie f angle (y x), auxiliary cutting angle (0 ,), approach angle (0 O) and nose radius (/?). F o r exam ple, a cutting tool designated as 0-10-5-5-7-90-1 will have the follow ing values o f its param eters.
X = 0° (inclination angle)
a = 10° (orthogonal rake angle)
Y = 5° (side relief angle) Y\ = 5° (end relie f angle)
0> = 7° (auxiliary cutting angle) 0Q = 90° (approach angle)
R = 1 mm (nose radius)
6 .3 M E C H A N IC S O F M E T A L C U T T IN G
The topics generally co v ered under the treatm ent on m ech a n ics o f m eta l cu ttin g include basic m echanism o f m etal cu ttin g and shear zone, form ation o f chip, orthogonal and oblique cutting, forces on chip (M erch a n t’s A nalysis), etc. T hese are discussed in the following.
6.3.1
F o rm a tio n o f C h ip
To understand clearly the fundam entals o f the m echanism o f m etal cutting o n m achine tools, let us first try to understand a sim ple case o f cutting w ith an ordinary h an d tool, say a flat chisel, under the blow s o f h am m er because the cutting principle as applied to any hand tool used in bench w orking o r a cutting tool used on a m achine tool is the same.
R efer Fig. 6.8 w herein shearing action o f a cold chisel is show n during the process o f cutting surplus m etal from a w orkpiece under the blow o f a hammer. T he chisel is show n flat o n the w orkpiece surface w ithout any clearance angle, prim arily to ensure that depth o f cut can be m aintained and secondly, the clearance angle takes no actual part in the cutting o r shearing action o f the chisel. Note that the force (F ) o f the h am m er blow is transm itted at approxim ately 90° to the cutting face AC, and this sets u p shear stress across a narrow region in the w orkpiece say the shear plane AB. U n d er the effect o f heavy blow s o f ham m er, the m etal ahead o f the cutting edge o f chisel will shear across the shear plane and m oves up the chisel face A C in the form o f a ‘segm ent o f c h ip ’. Since the energy required to shear o r rupture the m etal will be the shearing force along the shear plane A B , this shearing force will, therefore, be proportional to the length AB. Hence, the sm aller the rake angle o f chisel, the g reater will be the length (AB) o f shear plane and the larger will be the energy required to sh e ar the metal.
Fig. 6 .8 Illu stra tin g the shearing action o f a cold chisel.
C hip form ation m ay be com pared to the m o vem ent o f card stack w hen pushed along the tool face. T he consecutive displacem ents o f lam ellae o f form ing chip are depicted in Fig. 6.9 w herein the segm ents o f the chip num bered from 1 to 6 earlier occupied the positions shown by the dotted lines. W hen the tool advances, the segm ent 7 slips a finite distance relative to the uncut metal. As the tool advances further, the next segm ent 8 slips sim ilarly and previous segm ent 7 m oves o ver the tool as a part o f the chip. A lthough the card model is a little over sim plification o f w hat happens during metal cutting, it does illustrate som e o f the m ajor considerations in the m etal cutting process.
T h e basic m ech an ism o f chip form ation , therefore, consists o f a deform ation o f metal lying ju st ahead o f the cutting edge o f tool, by process o f shear, in a narrow zone (called sh ear zo n e o r p rim ary d eform ation zone) extending from the cutting edge o f the tool obliquely up to the uncut surface o f w orkpiece in front o f the tool (Fig. 6.10). D uring metal cutting, the m etal in the area in front o f the cutting edge o f the tool is severely com pressed causing high tem perature shear stress in the m etal, the shear stress being m axim um along a narrow zone o r plane called the sh ear plane (Fig. 6.11). W hen the shear stress in the workpiece metal ju st ahead o f the cutting e d g e o f tool reaches a value exceeding the ultim ate strength o f the m etal, particles o f the metal start shearing aw ay (or rupture) and flow plastically along the shear plane, form ing ‘segm ents o f c h ip ’ w hich flow upw ards along the face o f the tool. In this way, m ore and m ore new chip segm ents are form ed and the cycle o f com pression, plastic flow and rupture is repeated resulting into the birth o f a continuously flow ing chip. Since the w idth o f shear zone is sm all, chip form ation is often described as a process o f successive shears o f thin layers o f w orkpiece metal along particular surfaces. C hips are highly com pressed body and have burnished and deform ed underside (due to deformation at secondary sh ear zon e on account o f friction betw een chip and tool face). The prim ary shear zone deform ations are required for the form ation o f chip, w hereas deform ations in secondary shear zone are secondary deform ations w hich, in fact, are disturbances and are not required.
T h e shearing o f the metal in the process o f chip form ation does not, how ever, take place sharply along the shear plane show n by a straight line LM (Fig. 6.11). In actual case, the com plete plastic deform ation occurs o ver a definite area, represented by A B D C . Form ation o f chip starts w hen the metal structure begins elongating along the line BA w hich is below the shear plane and continues to do so until it is com pletely deform ed along the line D C above the shear plane and is bo m as ‘c h ip ’. S hear zon e (or prim ary> d eform ation zone) lies between the lines BA and DC. T hese tw o lines m ay not be parallel (giving uniform w idth o f shear zone) but m ay produce a w edge-shaped zone thicker near the tool face at the right and thinner o n opposite to it, a feature w hich is considered responsible for ‘curling o f c h ip s’ during m achining. A nother cause o f chips to curl aw ay from the cutting face o f tool m ay be non- uniform distribution o f forces at the tool-chip interface and on the shear plane resulting into a shear plane slightly curved concave dow nw ards. At high speed cutting, shear zone can be assum ed to be restricted to a straight line plane called sh ear plane inclined at an angle
<p (shear angle). T he shear plane (sharp line LM ) thus separates the deform ed and un-deform ed
w orkpiece metal. T he value o f shear angle ( <p) depends on w orkpiece m etal, tool material, tool geom etry and cutting conditions (feed, speed and depth o f cut). Note that with a small shear angle (0), plane o f shear is larger (in length) and consequently chip will be thicker, thus requiring larger cutting force to rem ove the chip. But a larger shear angle gives shorter shear plane, thinner chip and reduced cutting forces. T h e shear angle (0) is determ ined from
‘chip thickness ra tio ’ discussed later.
6 .3 .2 T y p e s o f C h ip s
T he chip because o f its form and dim ensions is the indication o f the nature and quality o f a particular m achining process. C hips can be broadly classified into the follow ing types. The type o f chip form ed is affected by the properties o f w orkpiece m aterial and cutting conditions.
(a) D iscontinuous chip o r segm ental chip consists o f elem ents separated into short seg m en ts (Fig. 6.12). This type o f chip is obtained in m achining hard and brittle m etals such
as cast iron and bronze. W hen w orkpiece metal is brittle, it has little capacity for deform ation before fracture and the chip separates along the shear plane. C hips m ay be in the form o f com pletely individual segm ents o r loose chips form ed by adhering o f segments. T hese loose chips fracture easily. It may be noted that in m achining hard and brittle metals, as the tool advances ahead, the shear plane angle gradually reduces until the value o f com pressive stress w orking on the shear plane becom es too low to prevent rupture. It is at this stage that any further advancem ent o f the tool results in the fracture o f the metal ahead o f it, thus producing
a segm ent o f chip, repetition o f w hich results in discontinuous chips. M achining o f ductile m etals at very slow speed m ay also give discontinuous chips. In case o f brittle metal, the presence o f these chips affords Fine Finish, increased tool life and low po w er consum ption. D iscontinuous chips in m achining ductile m etal result in poor Finish and excessive tool wear.
(b) C o n tin u o u s chip has its elem ents bonded together and is form ed by continuous deform ation o f metal w ithout fracture ahead o f the cutting edge o f tool and followed by sm ooth flow o f chip up the tool face (Fig. 6.13). U p p er side o f a continuous chip has small notches and the low er side is sm ooth and shiny as the chip slides o ver the tool. This type o f chip is form ed in m achining at high speed soft ductile m etals such as m ild steel and copper and is considered the m ost desirable type o f chip.
(c) C ontin u ou s chip w ith built-up ed ge is very much sim ilar to the continuous type chip except that a built-up edge is found adhering on the nose o f the tool (Fig. 6.14). Such
Fig. 6.14 Form ation o f a co n tin u o u s chip w ith a b u ilt-u p edge.
a chip is form ed w hile m achining ductile m etal and existence o f high friction at the chip-tool interface. T h e upw ard flow ing chip exerts pressure on the tool face w hich is very high being m axim um at the cutting edge o r nose o f the tool. As a result o f this, excessively high tem perature is g enerated because o f w hich the co m p re ssed metal adjacent to tool nose gets w elded to it. This extra metal w elded to the nose o r point o f the tool is called built-up edge. T he built-up edge is highly strain-hardened and brittle because o f w hich w hen the chip flows up the tool, a part o f the built-up edge is broken and carried aw ay with the chip while the rest o f it keeps adhering with the w orkpiece surface, m aking it rough. T he presence o f built-up edge at the nose o f the tool alters the rake angle o f the tool and consequently the cutting forces are changed. Factors responsible for form ation o f built-up edge are low cutting
speed, excessive feed, sm aller rake angle and poor lubrication o r cooling o f tool during cutting. B esides giving rough m achined surface and fluctuating cutting force and tool vibration, built-up edge also carries aw ay som e m aterial from the tool leading to the form ation o f a
cra ter w hich results in tool wear. Form ation o f a built-up edge can be avoided by (i) reducing
friction at chip tool interface by m eans o f polishing the tool face and use o f adequate supply o f lubricant, (ii) keeping larger rake angle and (iii) m aintaining low feeds and higher cutting speed as the latter generates high tem perature w hich reduces weld strength and reduces possibility o f form ation o f built-up edge through welding.
Besides the above types o f chips, h om ogeneous strain chips are also there w hich are produced in m achining metals like titanium alloys and others suffering a m arked decrease in yield strength w ith tem perature and poor therm al conductivity. Such chips are banded with regions o f large and small strains.
6 .3 .3 C h ip C o n tro l a n d C h ip B re a k e rs
M achining o f specially high tensile strength m etals at higher speeds generates chips that need to be handled w ith care, particularly if the carbide tools are used. H igher speeds generate high tem peratures and continuous type o f chips with blue colour w hich get collected in the shape o f a coil. Large continuous coils (if allow ed to be form ed) m ay prove quite dangerous as they m ay engage the entire m achine and w orkpiece and give a lot o f difficulties in their removal. B esides this, cutting edge o f the tool is spoiled due to crater form ation. T he finish on the w orkpiece is poor. I f the chip gets curled around the revolving w orkpiece o r the tool, it may be a hazardous situation for the operator. W hen brass and cast iron are m achined, they d o not generate co ntinuous chips o f the type as g enerated in case o f high speed m achining o f high tensile strength m etals. C hip b reakers are, therefore, used with the tool w hich help in breaking the c h ip s into small pieces (as it is easy to break the chips w hich are w ork-hardened during the ch ip form ation). A few sim ple chip breaking m ethods are show n in Fig. 6.15.
(a ) G ro o ve type (b ) Step type (c ) C la m p type
Fig. 6 .1 5 D iffe re nt types o f chip breakers (o r chip breaking m ethod).
breaker
insert (tip)
6 .3 .4 O rth o g o n a l a n d O b liq u e C u ttin g
T h ere are tw o basic m ethods o f metal cutting with a single-point tool: (i) o rth o g o n a l cutting (or tw o -d im e n sio n a l cu ttin g ) and (ii) oblique cu ttin g (or th ree-d im en sio n a l cutting).
O rthogonal cu ttin g takes place when the cutting face (or cutting edge) o f the tool
rem ains at right angles to the direction o f cutting velocity o r w ork feed [Fig. 6.16(a)].
O blique cu ttin g takes place w hen the cutting face o r cutting edge o f the tool is inclined
at an angle less than 90° with the direction o f tool feed o r work feed, the chip being disposed o ff at a certain angle [Fig. 6.16(b)).
Fig. 6 .1 6 O rthogonal and oblique cu ttin g .
In m achining with sam e depth o f cut and feed by the above tw o m ethods, the cutting force that shears the m etal acts on a larger area in the case o f oblique cutting. It results in sm aller heat developed per unit area due to friction along the tool-w orkpiecc interface and consequently longer tool life.
C h ip flow in orthogonal and oblique cutting is show n in Fig. 6.17. In orthogonal cutting at (a) w here cutting edge o f the tool (O C ) is at right angle to relative velocity V o f the work, the ch ip coils in a tight, flat spiral. In oblique cutting at (b) w here cutting edge o f the tool is inclined at an angle (/), the chip flow s sidew ays in a long curl. T h e in clination angle (/') is the angle betw een the cutting edge and the norm al to the direction o f the w o rk velocity ( V). T he ch ip f l o w angle (tjc) is the angle m easured in the plane o f the cutting face between the
chip flow direction and the norm al to the cutting edge. In orthogonal cutting, / = 0 and rjc = 0. M ain features o f orthogonal cutting and oblique cutting are sum m arized in Table 6.2 with reference to Fig. 6.17.
TABLE 6 .2 Features o f orthogonal and obliq ue cu ttin g
Orthogonal cutting Oblique cutting
Cutting edge remains normal to the direction of Cutting edge remains inclined at an acute angle to work feed (or velocity V). the direction of work feed.
Direction of chip flow velocity is normal to the Direction o f chip flow velocity is at angle (rjc). cutting edge.
Angle of inclination (/') is zero.
Chip flow angle (rjc) is zero.
Cutting edge is larger than the width of cut.
Cutting edge inclined at an angle (/) with normal to work feed (or velocity
10-Three mutually perpendicular components of cutting forces act at the cutting edge of the tool.
Cutting edge may or may not be longer than the width of cut.
Fig. 6 .1 7 D irection o f ch ip flo w in orthogonal cu ttin g (a) and oblique cu ttin g (b). In clin a tio n angle (/) and chip flo w angle (rjc) are show n at (c).
Bulk m etal m achining carried out in shops is through oblique cutting m ethod only; the orthogonal cutting is confined mainly to such operations as parting off, facing, knife turning, broaching, slotting, etc. O rthogonal cutting being the sim plest type is considered in the m ajor part o f this chapter. H owever, the principle developed for orthogonal cutting applies generally to oblique cutting also.
6 .3 .5 C h ip T h ic k n e s s R a tio (o r C u ttin g R a tio )
It is observed during practice that the thickness o f the chip produced is more than the actual depth o f cut. T he reason is that a chip flows upw ards at a slo w e r speed than the velocity o f cut. T he velocity o f chip flow is directly affected by the shear plane angle (0); the sm aller this angle, the slow er will be the chip flow velocity and thicker will be the chip.
R efer Fig. 6.18. Let
t - chip thickness prior to deform ation
= depth o f cut, w hich in a turning operation, is ‘fe e d ’ per revolution /. = chip thickness after deform ation
Then, chip thickness ratio (r) = — (6.1)
*c
Further, the reverse o f V is called chip reduction ratio o r coefficient (K).
Then, chip reduction ratio (K ) = — = — (6.2)
r t
Since is alw ays m ore than 7 \ chip thickness ratio (r) is alw ays less than unity. The higher the value o f V \ the better will be the m achining operation.
Since orthogonal cutting is being considered, width o f chip equals to w idth o f cut. Taking volum e o f chip produced equal to volum e o f m etal cut, and width and specific gravity o f metal being same for both cases,
C h ip
t = Original depth of cut
tc = Th ick n e s s of chip
Fig. 6 .1 8 Illu stra tin g shear angle (
0
). shear plane and rake angle (a ) o f the to o l. Note th a t the thickness o f chip (/c) is m ore than the depth o f the cu t (/).w here / = length o f chip before cutting = nD Irev
lc = length o f chip
C hip thickness ratio (or cu ttin g ratio) r m a y a ls o b e d e fin e d a s th e r a tio o f c h ip v e lo c ity ( Vc) to th e c u ttin g s p e e d ( V) (Fig. 6.19).
V = Cutting velocity; Vc = Velocity of chip; Vs = Velocity of shear; a = T o o l rake angle; ^ = S h e a r angle
Fig. 6 .1 9 V e lo city relationship in orthogonal cu ttin g.
or (6.3)
Length o f chip cut
Length o f chip before cutting (or uncut chip length/rev)
Then, (6.4)
r lc t
In Fig. 6.18, 0 = shear angle and a - tool rake angle depth o f cut = / = M L sin 0
and ch ip thickness = tc = M L cos ( 0 - a) T hen, ch ip thickness ratio (r):
/ M L sin 0 s i n 0 s in 0
r = — = = = :--- = ---:--- (6.5A)
tc M L cos(0 - a ) c o s ^ c o s o r + s in ^ s in fl' c o s ( 0 - a )
(D ividing num erator and d enom inator by sin 0)
_ 1____________ c o t^ c o s o r + sin a o r r(c o t 0 cos a + sin a ) = 1 1 - / • sin a o r cot 0 cot a - ---r r C 0 S a c ’ r * \ o r tan 0 - --- (6.5B) 1 - r sin or Hence.
sh e ar angle (0) = tan-1 r cos a 1 - r sin a
(
6
.6
)6 .3 .6 V e lo c ity R e la tio n s h ip in O rth o g o n a l C u ttin g
T he follow ing three velocities are involved in orthogonal cutting [Fig. 6.19(a)].
V = cutting velocity o r velocity o f tool relative to work
Vc = velocity o f chip How o r velocity o f chip flow relative to tool
Vg = velocity o f sh e ar or velocity o f displacem ent o f the chip along the shear plane
relative to work
T h e cutting velocity (F ) and rake angle ( a ) are know n. T he follow ing approach is undertaken to find V; and F and the relationship betw een the three velocities.
R efer Fig. 6.19(b) w hich show's the velocity diagram wherein:
v = vc + vs
By applying sine rule.
F F T c _______________ S sin 0 s i n [ ( 9 O ° - 0 ) + (0-<2')] s i n ( ( 1 8 O - ( 9 O - 0 + 0 - a r + 0)) F F F T c r s ' o r ^ 7 --- — —— : sin 0 cos a c o s(0 - a ) Hence. F • sin 0 velocity o f ch ip flow ( F J = --- (6.7) c c o s(0 - a )
A nd V • COS OL velocity o f sh ea r
( V )
= ---1--- (6.8) c o s ( 0 - a ) Since, r - — — , then cos ( 0 - a )velocity o f chip flow (V c) = cutting velocity (V) x chip thickness ratio (r),
or Vc = V ■ r (6.9)
6 .3 .7 F o rc e s A c tin g o n C h ip in O rth o g o n a l C u ttin g (M e rc h a n t’s A n a ly s is )
M erchant established relationship betw een various forces acting on the chip during orthogonal
metal cutting but with the follow ing assum ptions: (i) Cutting velocity alw ays rem ains constant.
(ii) Cutting edge o f tool rem ains sharp alw ays during cutting with no contact betw een w orkpiece and tool flank.
(iii) C hip does not flow sidew ays. (iv) O nly continuous chip is produced.
(v) T here is no built-up edge.
(vi) No consideration is m ade o f the inertia force o f the chip. (vii) W idth o f tool is greater than width o f cut.
(viii) B ehaviour o f the chip is like that o f a free body w hich is in the state o f a stable equilibrium due to the action o f tw o resultant forces w hich are equal, opposite and collinear.
Because o f a num ber o f flaws and practical difficulties, the above assum ptions were m odified later.
T he forces acting on the chip in orthogonal cutting are as a result o f the cutting force (/?) (Fig. 6.23) applied through the tool. T hese forces are given in the follow ing with reference to Fig. 6.20(a).
Fs = Shear force o r metal resistance to shear during chip formation. It acts along shear
plane.
F c = B acking up or com pressive norm al force exerted by w orkpiece on the chip. It acts
normal to shear plane.
N = Force exerted by tool on the chip. It acts norm al to the tool face.
F = Frictional force (or p N ) o r resistance o f the tool against the chip flow.^It acts along
tool face. Here ju is kinetic coefficient o f friction betw een tool face and chip and ^i - F I N = tan /?, w here /? is angle o f friction.
Figure 6.20(b) show s the free-body diagram o f chip. Forces F and Fc have their resultant force R w hereas forces F and N have their resultant force R '. The resultant fo r c e s R a n d R '
a re e q u a l in m agnitude, o p p o site in direction a n d collinear. T h e chip can, therefore, be
regarded as an independent body held in mechanical equilibrium by the action o f tw o equal and opposite forces R which the w orkpiece exerts on chip and R ' w hich the tool exerts on the chip.
(a ) (b )
Fig. 6.20 S how ing the forces acting on the chip in orthogonal cu ttin g at (a) and free-body diagram of chip at (b). p— angle o f fric tio n ; o ^ r a k e angle of to o l; $>— shear angle.
It w as m entioned above that the resultant force R has tw o-com ponent forces F c and F v. Now, let the resultant force R be further resolved in tw o m ore com ponent forces (Ff{)
Ff/ = H orizontal com ponent o f resultant force (R ). It is know n as cu ttin g force (F t) or
tangential force o f tool on w orkpiece.
F v = Vertical com ponent o f resultant force (R). It is know n as axial feed force (F ^o r F J or th ru st fo r c e acting in direction opposite to feed (also see Fig. 6.25).
Henceforth in further discussion, F,(= Ff/) will be considered cutting force and / y ( = F y = Fa) and (F y) as show n in Fig. 6.21 with the follow ing explanation. Also sim ultaneously refer “ ,,u v* v*
Fig. 6.22.
Sh ear plane
/
W orkpiece
Fig. 6.21 Free-body diagram o f chip. Fig. 6.22 Force system on the chip.
Fig. 6 .2 3 M erchant’s circle diagram .
F o r the convenience o f further relationships betw een various forces, the tw o triangles o f forces o f the free-body diagram o f chip [Fig. 6.20(b)] have been considered together in Fig. 6.23, called the M erchan t circle diagram . F o r the sake o f sim plicity, the cutting forces are plotted at the tool point instead o f their actual point o f application and a com p o site cutting force circle (Fig. 6.23) is obtained w herein d iam eter o f the circle is R (note that R = /?'). From this diagram , various force relationships can be obtained.
T he cutting force ( F f) and feed force ( F , o r Fg) can be found with the help o f force dynam om eter. W hen laid as in Fig. 6.23, resultant R can be found easily. K now ing the rake angle (or) o f the tool, forces F and N can be determ ined. S hear angle (0) can be found as:
cos a
t a n 0 = F ^ k T a <6 1 0 >
w here a = rake angle
K = chip reduction coefficient
Chip thickness (tc )
Uncut thickness (or feed in tumingXO
K now ing above, all other com ponent forces on the chip m ay be d eterm ined from the geom etry o f Fig. 6.23 wherein
Ft - Cutting force
F c = F , = F = N = Now, or Then, or Further, or Then, or and Also, and o r and or or
(forces exerted by w orkpiece on the chip) the chips) C o m p ressiv e o r norm al force
on shear plane
S hear force on the shear plane
Frictional force along rake face o f the tool I (forces exerted by tool on N orm al force at the rake face o f tool
F = A Q + QB = AQ + D C (as Q B = DC) F =
Ft
sina +
Ff cosa
N = PQ - PD = F t cos a - Ff sin aN
=Ft
cosa - F f
sina
Fs = A O - O K = A O - P E = Ft cos 0 - F f sin 0 Fs = F t cos 0 - F f sin 0 Fc = C K = C E + EK = C E + PO (as EK = PO)F c
=F f
cos 0 +F(
sin 0Ft
=R
cos(fi - a)
F f - R
sin- a)
F = R
cos( 3 - a
+ 0) F, R cos(/? - a ) cos(/? - a ) F s R cos( p - a + 0 ) cos( P - a + 0) F = F l t s cospg - a ) cos (P - a + 0 ) F Ft s \ n a + F fC o s a N Ft c o s a - F j sin a F F f + F. tan a — = - L --- = i z n p Ar F, - F f tan a— = tan P - n (kinetic coefficient o f friction)
N
w here P angle o f friction = tan-1 /7
Also, tan PAC = tan( p - a ) = —- = —C P P f
A P F, (6.11) (6.12) (6.13) (6.14) (6.15) (6.16) (6.17) (6.18) (6.19) or - f = t a n ( / ? - t f ) (6.20)
M erchant developed a relationship betw een shear angle (0), angle o f friction (ft) and tool rake angle ( a ) as follows:
2<f> + f t - a = C (6.21) w here C is a m a ch in e co n sta n t w hich depends on the rate o f ch a n g e o f sh e ar strength o f the w orkpiece metal with applied com pressive stress as also the internal coefficient o f friction.
6 .3 .8 S tre s s a n d S tra in o n th e C h ip
C hips are produced due to the plastic deform ation o f the metal; they experience stress and strain. As show n in Fig. 6.20(a), tw o forces F : and Fs (perpendicular to each other) act at the shear plane. Now refer Fig. 6.24 wherein:
A = cross-sectional area o f uncut chip = h x t
w here b = width o f cut and t = depth o f cut o r uncut chip thickness
A y = shear plane area
o r A = A sin <p C h ip A Shear \ plane t - H b H - W orkpiece
Fig. 6 .2 4 G eom etry of chip fo rm a tio n in orthogonal cu ttin g. Mean n orm al stress (
o)
a = ^ = F- = F' s m ‘t‘ (6.22)
A A!s\n<p A
Putting the values o f F . = Ff cos <p + Ft sin <p
( F s c o s fl + F, sin 0) sin 0
M ean norm al stress (o ) = — --- (6.23)
A
M ean sh ear stress (t)
F F. sin <p T = — = —
-As A
o r Fs = ^ ~ - ~ (6.24)
It ca n be show n that
^ cos sin (p ( F , c o s 0 - / y s i n 0 ) s i n 0
(6.25) S h e a r strain (£)
S h ear strain is given by the follow ing expressions:
e - cot <p + ta n (0 - a ) and also € = cos a (6.26) (6.27) sin <f> cos(<p- a )
6 .3 .9
F o rc e s o f a S in g le -p o in t T o o l
D uring m etal cutting, the w orkpiece metal offers resistance to the cutting tool. T his resistance is o v e rc o m e by the cu ttin g force a p p lied through the tool. T h e w ork d o n e by this force in cu ttin g is spent in sh e arin g the ch ip from the w o rk p iece , d efo rm in g the chip and o v e rc o m in g the friction o f the ch ip on the tool face. T he m a g n itu d e o f cu ttin g force d e p e n d s on w o rk p ie c e m aterial, feed, d ep th o f cut, cu ttin g speed, tool an g les and lubricant o r coolant used.
Forces acting on a single-point turning tool in ob liq ue or conventional cu ttin g are show n in Fig. 6.25 and these are:
F a = A xial feed force o r th ru st fo rc e acting in horizontal plane parallel to the axis o f
w ork but in the direction opposite to the feed.
Fr = R adial force acting in horizontal plane along a radius o f w ork, i.e. along the axis
o f tool.
Ft = C u ttin g force o r ta n g en tia l fo r c e acting in vertical plane and tangential to the
w ork surface.
Fig. 6 .2 5 S h o w in g c u ttin g fo rc e s in c o n v e n tio n a l (o b liq u e ) tu rn in g process, /?— re s u lta n t fo rc e ; F — axial feed force ; F— radial force; F,— cu ttin g force.
In the above three forces, F t is the largest in m agnitude and F r the smallest. F o r turning operation, F a varies between 0.3 Ft and 0.6 F( and Fr betw een 0.2 F t and 0 .4 Fr T he com ponents
F t and Fa arc d eterm ined easily with the help o f suitable force dynam om eter. T he resultant
force (R ) ca n be com puted as below:
R = ^ F 2 + F 2 + F 2 (6.28)
In orth ogonal cutting, o nly tw o forces (Fa and F f) com e into play and Fr is zero (Fig. 6.26). T he resultant force (R ) is as follow s w herein Fa an d F t are axial (feed) force and cutting force (or tangential force), respectively.
R = sjFa2 + F ,: (6.29)
Fig. 6 .2 6 Forces actin g on a cu ttin g to o l in o rtho go nal cu ttin g.
(a) T o r q u e (T) d evelop ed on w orkpiece N eglecting Fq and Fr being very small,
Torque (T ) = ^ D (Nm )
2 x 1 0 0 0 w here D = dia. o f work, m m , F t = cutting force, N (b) H eat p rod uced (H )
Heat produced = w ork done in m etal cutting
/ / = 5 - - - T kN m /s o r k W o r kJ/s 6 0 x 1 0 0 0
w here V = cutting speed, m /m in, F t = cutting force, N
H eat produced is also equal to the follow ing w here F t is in k g f and V is m /m in
F V (6.30) (6.31) 427 , kcal/min (6.32) (c) P o w er required (F) P = F .- V 60 x 1000 x i], kW (6.33)
w here F t - cutting force, N
V - cu ttin g speed, m /m in
11 = efficiency (say 80 to 90% )
(d) M etal rem oval rate (M R R )
= V • b • /, c m 3/m in (6.34)
w here V = cutting velocity, cm /m in
h = w idth o f cut (cm ) o r feed rate, cm/rev.
/ = d ep th o f cut o r uncut chip thickness, cm M a x im u m m etal rem oval rate (M R R ) max.
Max. pow er available at m achine spindle (kW) , v
= --- — --- - , (cm /m in) (6.35) Power required (kW /cm ' /min)
6 .3 .1 0 P o p u la r T h e o rie s o n M e c h a n ic s o f M e ta l C u ttin g
Various relationships have been derived earlier for shear angle ( <p), friction angle (/?) and rake angle (a ). Several investigators have carried out a lot o f work to establish realistic relationship am ong a , <p and /? and developed several theories with slight variations in their assum ptions and results. M ore im portant theories include:
(i) E a m s t-M e rc h a n t Theory (ii) M erchant Theory
(iii) Stabler T heory
(iv) Lee and S haffe r’s T heory
T he follow ing tw o theories are more popular am ong metal cutting engineers.
Ea rn st-M e rch a n t theory
T his theory is based on the principle o f m inim um energy consum ption and im plies that during cutting, the m etal sh e ar should o ccu r in that direction in w hich energy requirem ent for shearing is m inim um . Further, the behaviour o f m etal being m achined is like that o f an ideal plastic. Also, the shear stress is m axim um and constant at shear plane and independent o f shear angle <p. T h ey cam e up w ith the follow ing relationship:
6 = --- — + — i f i - a ) (6.36)
y 4 2 2 4 ’
Lee an d Shaffer’s theory
In this theory, the process o f orthogonal cutting has been analyzed by applying theory o f plasticity for an ideal rigid plastic material. F ollow ing assum ptions are made:
(i) W orkpiece m etal ahead o f the cutting tool behaves like an ideal plastic material. (ii) D eform ation o f metal takes place on a single shear plane.
(iii) C h ip does not get hardened.
T hey derived the follow ing relationship:
(p = ^ + a - = 45° + a - {)
o r 0 + P - a = 45° (6.37)
This w as further m odified as:
0 = — + a + 6 - p (6.38)
4
w here 0 covers the changes in different param eters because o f the form ation o f built-up edge.
6 .4 H E A T IN M E T A L C U T T IN G
W hen a metal is deform ed plastically as in metal cutting, m ost o f the energy used is converted into heat. The energy available at the cutting edge in a metal cutting process is converted into heat, mostly in frictional heat as also the heat caused by destruction o f molecular o r atomic bonds in metal in the shear plane. The main sources o f heat are: (i) the shear zone w here the main plastic deform ation takes place, (ii) the chip-tool interface zone where secondary plastic deform ation takes place due to friction and (iii) the work-tool interface where frictional rubbing takes place (Fig. 6.27). As a result o f this heat, high tem peratures are generated in the region o f tool cutting edge which have a controlling influence on the ra te o f w ear o f to o l and on the
fric tio n betw een ch ip and to o l; for example, the temperature plays a m ajor role in the formation
o f crater on the tool face and leads to failure o f tool by softening and thermal stresses.
Fig. 6 .2 7 R egions o f heat generation in m etal cu ttin g include: (1) P rim a ry shear zone, (2) Secondary shear zone and (3) W o rk-to o l interface zone.
T he three m ain regions o f heat generation in metal cutting show n in Fig. 6.27 are discussed in the following:
I. T h e sh ea r zone or p rim ary d eform ation zon e No. 1 is the region in w hich plastic deform ation o f metal o ccu rs during m achining. D ue to this deform ation, about 80% o f total heat is generated in shear zone. A portion o f this heat (about 7 5 % ) is carried
aw ay by chip and hence the tem perature o f chip is increased. T he heat produced per minute is equal to the product o f cutting speed and cutting force divided by mechanical equivalent o f heat. T he am ount o f heat conducted from chip to the tool and w orkpiece d epends on tem perature differential betw een these elem ents, their m asses and time o f co n tact with ea ch other. Therefore, higher cutting speeds show greater am ount and percentage o f heat in the chips because the heat has less tim e to be conducted from chip to tool and w orkpiece (Fig. 6.28).
1 0 0 % total heat
2. T h e secondary d eform ation or chip -tool interface zon e No. 2 is the region w here secondary plastic deform ation takes place due to friction between heated chip and tool causing a further rise in chip tem perature. A bout 15 to 20% o f total heat generated is produced in this secondary plastic deform ation zone. T he frictional heat increases with increasing cutting speed.
3. T he w ork-tool interface zone No. 3 is that portion o f tool flank w hich rubs against the w ork surface and generates heat due to friction. In this region, only 1 to 3% o f heat is generated. Heat generation is higher if the tool is not sufficiently sharp. 6.4.1 H e a t G e n e ra te d in M etal C u ttin g
A m ount o f heat generated p er unit time is given by the thermal equivalent o f the mechanical w ork done in metal cutting.
Work done (W.D.) = cutting force (F t) x cutting speed (V) = F t x V, k g f m/min
w here F f is in k g f and V in m/min
Then, total heat generated (Q ) = ^ l!? 1 , kcal/m in 427
F x V
o r Q = ' kcal/m in (6.39)
6 .4 .2 F a c to rs A ffe c tin g T e m p e ra tu re in M e ta l C u ttin g
All the above discussed three zones o f heat generation in m etal cutting lead to tem perature rise at tool-chip interface. T he tem perature plays a m ajor role in the form ation o f crater on the tool face and leads to the failure o f tool by softening and therm al stresses. Factors affecting tem perature in metal cutting are given in the following:
(a)
Materials o f workpiece and tool:
T hese affect tem perature in metal cutting since m aterials w ith higher therm al conductivity are responsible for production o f low er tem peratures at cutting edge.(b)
Tool geometry:
I f the rake angle is increased in positive direction, both cutting force and am ount o f heat generated are reduced but too large rake angle w eakens the cutting edge and reduces the heat conducting capacity o f tool.(c)
Cutting conditions:
Cutting speed has great influence on the production o f temperature. Since frictional heat increases with cutting speed, the tool-chip interface tem perature increases with cutting speed. T he tool-chip interface tem perature rises but less rapidly than for a rise in cutting speed.C hanges in depth o f cut have little effect on tem perature. L ess heat is generated when higher feed rates are used but surface quality is adversely affected.
6 .4 .3 M e a s u re m e n t o f C h ip -to o l In te rfa c e T e m p e ra tu re
A nu m b e r o f m ethods are available for the m easurem ent o f chip-tool interface tem perature and these include tool w ork therm ocouples, em bedded therm ocouples, infrared photographic technique, tem perature sensitive techniques, etc. Tool w ork therm ocouple technique is most w idely used.
6 .5 C U T T IN G F L U ID S
C u ttin g fluids (or
