Advanced Machining Processes of Metallic Materials || Orthogonal and Oblique Cutting Mechanics

'::~iiii~i!iii~i{!i~!iiii~}~ii~ .... C H A P T E R ...... ::~iiiiiiiiiiiiiiiiiiiiiiiiiiiiiii~:~ .....

SIX

ORTHOGONAL AND OBLIQUE CUTTING MECHANICS

Contents

6.1 Geometrical and Kinematical Characterization 6.2 Forces in the Cutting Zone 6.3 Cutting Energy 6.4 Stresses on the Shear Plane 6.5 Plastic Deformation in the Cutting Zone References

69 71 75

77

79 83

> ~> 6.1 GEOMETRICAL AND KINEMATICAL CHARACTERIZATION

In metal cutting theory all operations performed with the wedge-shaped tool when a layer of metal is removed in the form of continuous or discontinuous chip can be conventionally divided into two general cases termed orthogonal and oblique cutting. These two characteristic cutting arrangements are illustrated in Fig. 6.1 and comparison of their specific features is made in Table 6.1.

The wedge-shaped cutting tool basically consists of two surfaces intersecting to form the straight cutting edge. Functionally, the surface along which the chip flows is termed the rake face and the surface which contacts a new or machined workpiece surface is known as the flank face. Since orthogonal cutting represents a two-dimensional rather than a three-dimensional mechanical problem, it leads to a relatively simple cutting process which is therefore widely used in theoretical and experimental work. In particular, it enables the adoption of the process model assuming the plane state of both plastic deformation and stresses in the cutting zone. The vectors of the tool, the deformed material and the chip velocities for orthogonal and oblique cutting are shown in Fig. 6.2a and b, respectively. It should be noted that for oblique cutting (Fig. 6.2b) the chip formation process consists of two parallel subprocesses including the plane plastic flow of the work material in the plane perpendicular to the cutting edge, similarly to orthogonal cutting (plane Omn in the Olmn coordinate system), and lateral plastic flow along the cutting edge (axis I parallel to the cutting edge S). The lateral material flow causes the chip to flow at the angle r relative to the axis m 1, i.e. it is deviated from the direction perpendicular to the inclined cutting edge.

It is evident from the vector diagram of velocities shown in Fig. 6.2a that by using the rule of continuity, the velocity of sheafing v s along the shear plane inclined at the shear angle �9 is the vectorial sum of the chip

Advanced Machining Processes of Metallic Materials �9 2008 Elsevier B.V.

ISBN: 978-0-08-044534-2 All rights reserved.

69

70 Advanced Machining Processes of Metallic Materials

(a) (b)

Fig. 6.~ Geometries of orthogonal (a) and oblique cutting processes with straight cutting edge (b) [1, 2].

Table 6.~. Comparison of two basic cutting processes [2].

velocity Uch (the sliding velocity at the tool/chip interface) given by Eqn (6.1) and the cutting velocity v c.

It can be determined from Eqn (6.2).

sin Vch - - V c (6.1)

cos ( q ~ - 70)

COS ~/0 v, -- vc (6.2)

cos (cI, - 70)

where q) is the shear angle and To is the orthogonal rake angle.

Orthogonal and Oblique Cutting Mechanics 71

(a) (b)

Friction force---~ ,a direction . . ~ I x = m

Chip f low---~ ' ~ direction___] "~

Shear , hch m 1 plane , ~

L . . v. . . . . . ~ 1 7 6 /,oo, | ) ~ ~ T o o l | _ r

_ _ . . - . . t ~ ( \\\1 / , ' " > V ' - ~//\ n ~\ \~,\1 /..-" " - / vc "~ Workpiece

Ps

..~ 90~ %) Vch

% ",M / NN~/" )~s

z

Vc

Fig. 6.2 Velocity resolution for orthogonal (a) and oblique (b) cutting [2].

~~,~ 6.2 FORC ES IN THE CUTTING ZONE

In the general case, the force system exerted by a cutting tool is three dimensional, i.e. the resultant (total) cutting force F has three mutually perpendicular components shown in Fig. 6.1a. Typically, the resultant cutting force (RCF) is resolved into geometrical and physical components. In the first case the coordinate system is oriented based on the directions of primary and feed motions, i.e. the total force is resolved by perpendicular projection to these two directions. As a result, the cutting force and feed force denoted by symbols F( and Ff are distinguished. Moreover, the back (passive) force Fp tending to push the tool away from the work in a radial direction and perpendicularly to the working plane is defined. This force is usually ignored for orthogonal cutting and the total cutting force is reduced to the active force F,. As can be seen in Fig. 6.3 in orthogonal cutting the entire force system lies in a single plane and appropriate force components can be easily calculated by drawing the Merchant circle diagram. The force component in the direction of relative tool travel F c determines the amount of work required to move the cutting tool a given distance. The feed force Ff determines the power required to feed drives installed onto a machine tool.

Geometrical resolution of the total cutting force is done by assuming that the chip is a body in stable mechanical equilibrium under the action of the forces exerted on it at the rake face and at the shear plane as shown in the right upper detail.

The force components acting on the shear plane are F,h and F,h N. The shearing force Fsh represents the force required to shear the material on the shear plane. Force F,h N acts perpendicularly to the shear plane


Fig. 6.3 Geometrical (a) and physical (b) force resolution in the cutting zone for orthogonal cutting with a continuous-type chip [3].

and results in an additional compressive stress being applied on the shear plane. They can be calculated from the following equations:

cos ( 0 + �9 - 'Y0) F,h = F c (6.3)

cos ( 0 - "/o)

sin (| + � 9 To) Fsh N - - F c (6.4)

cos ( O - ' y o )

At the tool /chip interface, the force components F v and FvN act parallel and perpendicularly to the face. F v, k n o w n as friction force (the tangential force at the rake), represents the frictional resistance met by the chip as it slides over the tool rake face.

The friction force on the chip/ tool interface:

sin | G - Fc cos ( o - ~'o) (6.5)

where | is the friction angle. The normal force on the chip/ tool interface:

cos@ F~N = F~ cos (| -- To) (6.6)

T h e ratio o f F v to Fvz v is the apparent coefficient of friction between chip and tool, namely:

P ' v = tg6) - - F ~ _ _ F c sin To + Ff cos To (6.7)

F ~ N F c cos To -- F f sin To

It was experimentally proven that in cases such as cutting with a small undeformed chip thickness (UCT), cutt ing of materials with high elastic (Young's) modulus and when tool wear at the flank progresses, also the forces acting on the f lank/workpiece contact should be considered in the total cutting force. It can be


e- , } _ o / / ? o

v- t Workpiece - c t

{b)

LI..

0 t.. ,s E~

1.1-

'Y04 > '~03 > ~02 > ~01

(a)

~2

3'03

~oa

Undeformed chip thickness h

Fig. 6.4 Force distribution on the workpiece/flank contact (a) and projection of the cutting force on zero undeformed chip thickness (b) [2].

assumed that the force acting on the flank wear land VB B (Fig. 6.4) can be resolved into two components F~ and FaN which are independent of the rake angle value. These forces can be determined using the m e t h o d of extrapolation of F c and Ff components on zero undeformed chip thickness (Eqn (6.8)) proposed by Zorev [5]. As illustrated in Fig. 6.4b the Zorev method needs a few F c / U C T curves to be obtained for different rake angles.

From the definition

F~ = Fc(h~O) i G N = Fs (6.8)

In addition, forces acting on the flank face can be calculated by solving the problem of penetrat ion o f a rigid punch into a plastically deformed half-space using the slip-line method [2].

The normal force on the worn flank face

F~N ,~ co-eA,~ (6.9)

where coefficient c -- 2.6-4, O'p is the flow yield stress and A~ The tangential force on the flank face and

is the f lank/workpiece contact area.

F~ -- rcv A s -- (0.5 --0.6) UTS A,~ (6.10)

where rcv is the main shear stress on the rake face and UTS is ultimate tensile strength. As depicted in Figs 6.5 and 6.6, the cutting forces are influenced by the cutting parameters as well as

by tool geometry. Figure 6.5 a shows a linear increase of all components of R C F due to relevant increase of the cross-sectional area of the uncut chip. On the other hand, force/feed curves are non-l inear because increasing the feed results in decreasing the specific cutting pressure k c [4]. The kink in the force /cu t t ing speed curves in the medium speed range illustrates the effect of a built-up edge (BUE). Wi th steels, a B U E disappears when the speed is raised. The cutting forces are also influenced by tool geometry, the most important parameter being the rake angle. An increase in the rake angle lowers the force components but at the same time reduces the strength of the tool wedge and may lead to its fracture. The strongest tool edge is achieved with negative rake angle tools, and these are frequently used for the harder grades o f carbide and for ceramic and C B N tools which lack toughness. Tools with high positive inclination angles (Fig. 6.6b)


Fig. 6.5 Influence of cutting parameters on the components of resultant cutting force (RCF) [6].

Fig. 6.6 Influence of cutting tool angles on the components of I~CF [2].

generate high thrust forces causing the deflection of the workpiece. In contrast, this force is very small when using tools with a 90 ~ cutting edge angle (Fig. 6.6c) and machining of small diameter workpieces is possible. The tool material and deposited coatings can also influence the cutting forces mainly by changes in the area of seized contact between the chip and the tool [7]. Finally, the contact length and cutting forces may be greatly influenced by cutting lubricants or special soft low friction coatings. In the speed range used in most machine shop operations, it is not possible to prevent seizure near the cutting edge but liquid or gaseous lubricants, by penetrating from the periphery, can restrict the area of seizure to a small region. This phenomenon will be discussed in Chapter 11.


(a) (b)

~ , , d V # 7 l . ................ /

V "... / .<

.... / , ~ . ,

F~ J ......... !'i ....................... . . . . . . . . . . . . . . . . . . . . . .............

R ~ 7 ~ I TO01 insert i:i'~ii:~i:;ii::::::i:~i!ii:-':i:i;:>: ::::~ ;:: : ,..

Ff ;!~:~

Fe

~

Fp

~~j~:"::::~N ~ " ~i~::~ ......

Fig. 6.7 Measurement of cutting forces using biaxial strain-gauge (a) and piezoelectric (b) dynamometers [2, 9].

Measurements of cutting forces are carried out using strain-gauge and piezoelectric dynamometers. The principles of both types of tool dynamometers are shown in Fig. 6.7. In general, a tool dynamometer should have high sensitivity, high rigidity, high frequency response, high linearity and low drift [8]. A common type of dynamometer, a biaxial device shown in Fig. 6.7a, uses strain gauges to sense elastic strains caused by cutting forces. Typically, Wheatstone bridge circuits for each force component, consisting of two pairs of tension and compression gauges and amplifier system, are used to measure strain changes in the wire-type gauges. Before (prior to), the measurements force dynamometer is calibrated to find the relationship between voltage signal from the bridge and the actual value of a force. Figure 6.7b shows the piezoelectric type of dynamometer capable of measuring all three components of the RCF. Commercial machining dynamometers are available with natural frequencies from 2 kHz to 5 kHz, depending on size. The basic rule is that each force component is detected by a separate pure quartz crystal oriented relative to the force or torque in its piezoelectric sensitive direction. Quartz rings are used in pairs (low view in Fig. 6.7b) with a common electrode between them to yield double sensitivity. In Fig. 6.7b two pairs of shear quartzes for FZ and F1, and one pair of compression quartzes for Fc, assembled in a single housing, constitute a three-component force transducer. Two-, three- and four-component piezoelectric dynamometers and force plates for measuring cutting forces and torques in various machining operations (turning, milling, drilling, etc.) are produced by world leading manufacturer Kistler, Switzerland [9].

6.3 CUTTING ENERGY

The total work done by the cutting tool to remove metal, determined by the value of the force component F c, is dissipated in the following forms for a sharp tool: (1) as work done in shear deformation, (2) as work done to overcome chip/tool interracial friction and (3) as work done to generate a new surface


in cutting, but the third form is often neglected. Practically, all of the energy generated in metal cutting operations is dissipated in plastic deformation and friction.

In general, the energy required to perform primary and feed motions can be calculated using Eqns (6.11) and (6.12), respectively. As men t ioned above, Eqn (6.13) defined two basic components of the cutting energy required to perform plastic deformation (E,h) and overcome friction (Ef):

E c = / Fcvcdt (6.11)

o

-- j svsat (6.12) o

E = Ep + Ef = Es,, + Eh, + Ef~ (6.!3)

Often, equivalent specific (volumetric) cutting energy (SCE) and its components are used as defined by Eqns (6.14)-(6.17), where V denotes the volume of the layer removed and A c is cross-sectional area of the uncut chip:

Ec Fcvc Fc e c = - - = = - - = k c (6.14)

V bhv c A c

e c -- % + ef~ (6.15)

(a) (b)

e c

esh et 7 etol

far)

g g r

E O o

e c

eto~

r

Cutting speed V c SCE-specific cutting energy

E

or)

200

100 80 60 40

(.9 20

>' 10 a

e -

6

.c_ 4

o

o 2 . ~

o (D O.

1 - - 0 . 8 -

0 . 6 -

0 . 4 -

0 . 2

o. o

~"" Turning, shaPing, planning

F Milling, dri!l!ng. ~-i

�9 Grinding _1__1 . . . . . . Broaching ~l-I

o o o o o o o o oc5 o o d c5 q ~ ~ d d d d C~ 0 0 0

Mean undeformed chip thickness aca v, mm

F i g . 6.8 Influence of cutting speed on the components of specific cutting energy (a) and approximate values of the cutting energy for various materials and operations (b) [1, 2].


It is evident from Eqn (6.14) that the specific cutting energy is equal to the specific cutting pressure [4]. Using Eqns (6.3) and (6.4), components of specific cutting energy are equal:

cos ( ~ + 0 - 3'0) cos ~o e sh ~ F = 'Tsh ")/sh (6.16)

c & cos ( a , - Vo) cos ( o - Vo)

sin O ely -- F (6.17)

~A~ k h c o s ( | To)

where %h is shear stress of the material in the shear plane, Ysh is the shear strain and k h is the chip thickness compression ratio. All these quantities will be defined in section 6.5.

Figure 6.8a illustrates changes to the components of SCE with cutting speed, and Fig. 6.8b shows the influence of the undeformed chip thickness relative to typical machining operations and work materials. T h e shape of SCE/speed curve is the same as in Fig. 6.5c. It is important to note that all finishing operations, especially performed on hard materials like grinding, are more energy consuming due to removing a very small layer of material.

~~ ~!~:, ..... 6. 4 STR ESS ES O N TH E S H EAR PLAN E

Measurement of the forces and the chip thickness make it possible to estimate the stresses on the shear plane for orthogonal cutting conditions, where a continuous chip is formed without built-up edge. W i t h the assumption of uniform stress distribution and for known forces acting on the shear plane, the shear stress r, and normal stress o" s are found to be

F,h cos (| + ~ -- T0) sin (b r s - =Fc (6.18)

Ash bh cos (| -- Y0)

F,h N sin (| + �9 -- Y0) sin 0",-- = F c (6.19)

Ash bh cos (| -- T0)

where Ash is the shear plane a r e a (Ash -- bh/sin ~) , b is the width of cut and h is the uncut chip thickness. The ratio of the normal stress to the shear stress is

or, = tg (| + cI) -- To) (6.20) r,

The distribution of stresses along the shear plane is shown in Fig. 6.9a. The shear stresses are uniformly distributed but the normal stresses are constant only for zero or negative rake angle as indicated in case b. On the contrary, for positive rake angle (case a) normal stress decreases in the vicinity of the cutt ing edge and becomes tensile. Consequently, the stress ratio given by Eqn (6.20) is not constant.

The rake angle is also a predominant factor controlling the distribution of elastic stresses in the subsurface layer. As shown in Fig. 6.10, the compressive zone expands visibly when cutting wi th large negative rake angles (Fig. 6.10c) or with rounded cutting edges (Fig. 6.10d). As a consequence, in such cases the work-hardening effect will probably be more intensive than for cutting tools with positive rake angles.

In general, the shear strength of metals and alloys in cutting has been found to vary only slightly over a wide range of cutting speeds and feeds [7]. The problem is to correlate the shear stress magnitude in cut t ing with relevant values of shear yield strength determined in tensile, compression, torsion or hardness tests. In general, the shear yield strength in cutting exceeds the shear yield strength of a given material by a factor o f 2-4, depending on the intensity of plastic deformation in the primary deformation zone (PDZ). For example,

7 8 Advanced Machining Processes of Metallic Materials

(a)

4" .1,~%

&

(/)

0

(/) L

�9 900 ' - 700 or)

500

(b )

m, M P a ~-s, M P a

600 x ' f=o.156mm/rev 500 o f=0.51 mm/rev - 1,c, ; = " " " '

o " - -

4oo - : " f ' I T 300 -,o- J , i - " 1 " II

. . . . _~-~1 . - - - . - -2 ~ .~'r 7 700

! _ 1 ~ , ~ , l ' - i ' ~ --- / 500

i . . . . . ~,tl ~ ..-." " % " - l - 4 0 0

. . . . -- 3 __, - - ~ . ~ o ~ , , , - .

" i l ~ l ' w ' " ,

,

. . . . i - - ' - , , , , ,o: "-I J _ i t ens ion J. j . i i c o m p r e s s i o n

0 .05 0.1 0.2 0.3 0.5 1.0 1.4 2.0 3.0

S h e a r s t r a i n ,'y

700

500 400

Fig. 6.9 2D mode l o f stresses acting on the shear plane (a) and est imation of shear stress using simple tension and compress ion tests [2, 5].

(a)

- , ,~ aoo

) o Z - - ) . . . . . . . . . . . f 3 ~ i , / -,-...,/ t

(b )

"Yo = O~

t -

: :: ! \ I J Z

(c) ~ j O ~ ~ v V �9

?...L,~.-..~-.....-.:.• .--.,-::..,.........:~--. ~:...: ,.-~~---.,::;~-i:: :;.i#..-;:..

(d)

Fig, 6.1o Distr ibut ion o f stresses in the subsurface layer [2]. C Z - compressive zone, T Z - tensile zone.


Table 6.2 Mechan i ca l p roper t ies of d i f ferent work mater ia ls [2].

i ...... i~ii ii~ ~/i, ~:~ ~!i! ,i! �84184184184184 ~i ~i~i i ~�84 i! �84 �84184184 ~ ~ �84184 ~ . . . . . . . . . : , / : / i i ~i, : ,~i i,i,

.... .... rs (MPa) :strengm (UrS) crf (MPa) m = % t U T 5 : . . . . : , . . . . . : : . . . . . . : . . . . . . . . . .

Carbon steel 0.45%C 485 655 830 0.740 Alloy steel 0.4%C, 1%Cr 563 615 715 0.910 Die steel 1%C, 1.4%W, 603 630 830 0.960 1.1%Cr Austenitic stainless steel 775 628 925 1.230 0.12%C, 18%Cr, 9%Ni Heat-resistant alloy (Nimonic) 1175 1072 1460 1.100 20.5%Cr, 2.5%Ti, 4%Fe, 0.75%A1 Duralumin A1Cu4Mgl 430 474 575 0.910 Muminium alloy 200 264 295 0.760 MCu2SilMg Copper 280 243 310 1.150 Leaded brass CuZn40Pbl 490 465 640 1.050 Muminium bronze CuA19Fe3 735 577 870 1.270 Titanium alloy (/3) TiA16Mo3 718 990 1050 0.725

Fig. 6.9b compares the shear stresses obtained for cutting of different steels with stresses de te rmined in bo th tensile and compression tests. Based on this comparison, Zorev [5] concluded that the agreement exists only for very high shear strains, approximately in the range of %h = 2.5. Some other trials correlate the shear stress measured in cutting with the UTS or fracture stress. Table 6.2 lists all the above-ment ioned mechanical properties of both ferrous and non-ferrous materials.

~ 6.5 PLASTIC DEFORMATION IN THE CUTTING ZONE

In metal cutting, a chip formation area consisting of three characteristic zones I-III can be schematically presented as in Fig. 6.11a. The extensive primary deformation (shear) zone I (PDZ) is distinguished wi th in the OAB area by a number o f slip lines including the OFA line (the entry boundary) on w h i c h plastic deformation begins and the O C Q B line (the exit boundary) on which chip material is entirely w o r k hardened. A material particle during deformation moves along the F Q path but the deformation process does no t take place uniformly but it is more intensive between the shear band o f Ax thick and the upper bounda ry OB. Then, the material adjacent to the tool/chip interface of O D length is subsequently deformed in depth A 1 due to intensive interracial friction. The relevant OCD region is called the secondary deformat ion (shear) zone II (SDZ). Additionally, the tertiary deformation zone III (TDZ) localized below the cut t ing edge in depth A 2 is separated. This zone is characterized in Chapter 20.

The engineering approach to the characterization of plastic deformation in the cutting zone is based on three basic simplifications (b l - b 3 in Fig. 6.11) including replacing curvilinear boundaries by straight lines OP and O K ( 'fan'-type or pie-shaped shear zone model proposed by Zorev [5]), parallel-sided shear band inclined at angle ~ to the tool motion (model with parallel boundaries proposed by Oxley [10]) and one shear surface being a plane Psh (the shear plane model proposed by Merchant [11]. It should be no ted that in the last case the work material is assumed to be perfectly plastic (incompressible), i.e. work -ha rden ing effect


(a)

B A Fa

1 i I I / /

&

(bl) (b2)

I i Vc o ! i Vc - -

J r - - - - - - - - - ! 4

(b3)

,, I _

Fig. 6.aa Schematic (a) and simplified models (b) of the chip formation zone [2].

does not occur. Moreover , it ignores BUE, which may be present, as well as chip curl, and depicts tool face fr ict ion as elastic rather than plastic.

Accord ing to International Standard ISO 3002/4, the chip compress ion ratio (A h or kh) is the ratio of the idealized chip thickness to the nominal thickness of the cut. It can also be de termined using the weight m e t h o d , as follows:

hch inch (6.21) kh -- --h -- pblh

w h e r e inch is mass o f the chip spec imen, /9 is density of the workp iece material, b, t and h are dimensions (width, length and thickness) o f the uncut chip. In experimental work , the chip thickness can be easily measu red with a bal l -ended micrometer .

F rom the geomet ry o f cut (Fig. 6.12) it can be shown that the shear plane (AB) length is

h hch IA/3 = = (6.22)

sin q) cos (q3 -- T0)

T h e shear angle is derived as a funct ion of the chip compression ratio and the rake angle:

t g ~ - - cosT0 _ _ cosTo (6.23)

h ch/h -- sin T0 k h - - sin To

T o derive an expression for the shear strain, the deformation can be idealized as a process o f block slip, as s h o w n in Fig. 6.12b. F rom definition, the shear strain for pure shearing is the ratio o f absolute deformat ion As to the nominal distance Ax b e t w e e n the deformed and unde fo rmed planes, namely

As A B ' FB' + A F FB' A F C F ctg~ C F tg (dO - T0) %h -- --- ----= = ~ + = + (6.24)

A x C F CF CF CF C F C F


(a) (b)

i ; . . . . . 1 1 - " > I I -q/ '--~,o \

B " i B ~ as , m . .y 4.V----.. Z l[ .<: <i,

- " " . . . . o

Wor,<p eoe " 7 i,,,

Fig. 6.12 Geometry of cut (a) and the shear-strain model [2, 7, 11].

After simple trigonometrical rearrangements three formulae for the shear strain can be obtained. Thus,

%h = ago + tg ( 0 - %) (6.25a)

cos 3'o 3"sh - - sin �9 cos ( 0 -- 3'0) (6.25b)

k~ - 2 k h sin To + 1 %h = (6.25c)

k h cos To

The strain may also be expressed in terms of the shearing velocity (see Fig. 6.2):

v, 3"sh = (6.26)

v c sin

It is interesting to note that the shear strain defined by Eqn (6.25c) will be equal to zero only for k h -- 1 and To = 90~ For example, for the rake angle 3'o = 0~ the strain %h = 2, and covertly %h = 1 w h e n for rake angle 3'0 = 36~

The shear strain rate in cutting is defined as

,i/sh __ 'Ysh = A s = v s = cos 3'o Vc (6.27) At Ax At Ax cos ( ~ - - %) Ax

where At is the time elapsed for the material element to travel a distance As along the shear plane, and Ax is the thickness of the shear zone.

The final formula is derived using Eqns (6.25b) and (6.2). Since the shear plane is usually very thin, as shown by photomicrographs (exemplarily in Fig. 6.13), it is expected that very few slip lines will be active at any one time. A reasonable mean value for the spacing of successive slip planes (Ax) would appear to be about 25 Ixm [11]. By assuming 3'0 = 0~ A x - 0.02 mm, ( I )= 30 ~ the shear strain rate is equal to 2.3 x 105 s -1 [2]. In many practical operations, peak shear stain rates are of the order of 104 s -1, but for high speed machining and grinding processes it can reach a value of 105-107 s -1.

One piece of the experimental evidence of chip formation by shearing and existence of both P D Z and SDZ zones is characteristic deformation texture of the chip observed on the etched chip roots (Fig. 6.13b)


(a) (b)

Fig. 6.13 Deformation texture of the chip [2]: preferred orientation of grains (a) and micrograph of the chip root (b).

obtained by means of a special quick-stopping device. The angle r / b e t w e e n the chain of preferably oriented grains and the shear plane, shown in Fig. 6.13a, is given by

sh ctgrl----Eh+ 1 + 4 (6.28)

In the parallel-sided shear zone model (Fig. 6.14a) proposed by Oxley and Welsh [10], elaborated for higher cut t ing speeds, the shear plane is assumed to open up so the entry boundary CD between the shear zone and work and the exit boundary EF between the shear zone and chip are parallel to and equidistant from

(a) (b)

r 0

Chip I [ ~ ~

~ 16

12

B\D ~ ...... - ~ , =E 4 v ~ I / . / / W orkpiece E 0

~8 -6 -4 ~2

" - _ I 1 I I I t I I I

3 2 - h=O.127mm -

'- ill

~28 II E Ji

" ~ 2 4 I 1

- - .

2 4 6 8 AB

distance travelled through zone, As/0.023 mm

Fig. 6.~t4 Parallel-sided shear zone model (a) and distribution of maximum shear strain in chip formation zone for T0 = 10 ~ and v c = 120 m/min (b). After Oxley [10].

Orthogonai and Oblique Cutting Mechanics 83

A B and like A B are slip lines. The overall geometry of the shear model is practically the same as for the shear plane model with A B and @ but the resultant force F a will not in general pass through the mid-poin t of A B as in Fig. 6.1 l a. Oxley proposed [10] the solution for the shear angle to be a function of variations of the ratio of hydrostatic pressure in point A at the free surface to the shear flow stress on the shear plane AB, i.e. pA/rAB which is close to the upper boundary predicted by the slip-line field theory [8].

) PA __ 1 -+- 2 -- cI) (6.29) r ~ 7

Then

tan ( ~ + | - Y0) - - 1 + 2 ( r e / 4 - ~ ) AT l

2tAB AS 2 = 1 + 2 ( r r / 4 - cI)) - Cn (6.30)

Where the term Cn (c is the strain-hardening index) may be considered as a correction to the value pA/'rAB that tan(~ + | To) would have in the absence of any strain-hardening effects.

The expression for the shear strain along the exit boundary EF is the same as for the shear strain as material crosses the shear plane:

COS ")/0

Tm~ = sin cI) cos ( ~ - To) (6.31)

The flow shear stress at A B is calculated by assuming that half of the total strain Tel: will have occurred at AB. r o is the shear flow at zero plastic strain (for the machining model used r 0 -- rCD ) and m is the slope of linear plastic stress/strain relation:

1 r -- rm3 = r 0 + 7 rnyEv (6.32)

z

The thickness of the shear zone is given by

h As2 = (6.33)

10sin

In the tests performed by Oxley the strain rate increased with increase in cutting speed and had a m a x i m u m value which occurs in the region defined by the plane AB, as shown in Fig. 6.14b. From the results in Fig. 6.14b and others discussed in [10] the line of best fit passing through the origin is

m a x ('J/max) - - 2-59 h (6.34)

where the unit of v~/h is s -1. It can be seen in Fig. 6.14b that plastic deformation starts well in advance of A B and continues well

beyond it. The chip formation zone is therefore of substantial thickness, which changes only slightly with cutting speed but significantly with undeformed chip thickness.

~i~..~:~. REFERENCES [1] G. Boothroyd, W.A. Knight, Fundamentals of Machining and Machine Tools, CIKC Press, Boca 1Katon, 2006. [2] W. Grzesik, Fundamentals of Machining of Metallic Materials (in Polish), WNT, Warsaw, 1998. [3] Ed. by T.J. Drozda, C. Wick, Tool Manufacturing Engineers Handbook, Vol. 1, Machining, SME, 1983.


[4] J. Kaczmarek, Principles of Machining by Cutting, Abrasion and Erosion, Peter Peregrinus Ltd, Stevenage, 1976. [5] N.N. Zorev, Metal Cutting Mechanics, Pergamon Press, Oxford, 1966. [6] W. K6nig, F. Klocke, Fertigungsve~farhen. Drehen, Friisen, Bohren. Springer, Berlin, 1997. [7] E.M. Trent, P.K. Wright, Metal Cutting, Butterworth-Heinemann, Boston, 2000. [8] T.H.C. Childs, K. Maekawa, T. Obikawa, Y. Yamane, Metal Cutting. Theory and Applications, Arnold, London,

2000. [9] Optimize metal cutting by measuring cutting forces, www.kistler.com.

[10] P.L.B. Oxley, Mechanics of Machining. An Analytical Approach to Assessing Machinability, Ellis Horwood, Chicester, 1989.

[11] M.C. Shaw, Metal Cutting Principles, Clarendon Press, Oxford, 1989.

Documents

Advanced Machining Processes of Metallic Materials || Orthogonal and Oblique Cutting Mechanics