Embed Size (px)
Citation preview
Wew, 139 (1990) 235-260 235
COMPUTER-AIDED SIMULATION AND EXPERIMENTAL STUDIES OF CHIP FLOW AND TOOL WEAR IN THE TURNING OF LOW ALLOY STEELS BY CEMENTED CARBIDE TOOLS*
T. H. C. CHILD.9 and K. MAEKAWA’ Department qf Mechanical Engineering University c$L.eeds, Leeds LS2 9JT (U.K.)
A finite element modelling @‘EM) analysis of chip flow has been developed on a CAD (computer-aided design) computer and used to aid studies of the wear of cemented carbide tools turning an aluminium-deoxidized and an ahuninium-deoxidized, calcium-treated resulphurized low alloy steel. The latter steel formed a Ca-Mn-S deposit on the tool rake face and, at a given feed and speed, machined with 20% lower tool forces and 60-fold less crater wear than the former. Subsidiary tests showed both steels to have the same mechanical properties but that the Ca-Mn-S deposit reduced chip-tool friction; input of these data to the FEM analysis resulted in lower predicted cutting forces and temperatures for the deposit-forming steel. The temperature calculations, with a thermal activation wear model, indicate provisionally that the crater-wear-reducing properties of the deposit were multiplicatively 20-fold due to its effect as a diffusion barrier and three-fold due to lower temperatures.
1. Introduction
This paper has two purposes: to report on the development of an elastic-plastic and thermal finite element analysis of chip flow and stresses, tool temperatures and wear in metal turning; and to report experiments on the machinability of low alloy steels that have been used both to test the analysis and to gain a more quantitative insight into the steelmaking factors that affect machinability. The analysis needs further refinement, particularly in its tool force prediction capacity, but has been helpful in tool temperature and wear prediction.
*Paper presented at The Institute of Metals 1st International Conference on the Behaviour of Materials in Machining, Stratford-upon-Avon, U.K., November S-10, 1988.
‘Present address: Department of Mechanical Engineering, lbaraki University, Japan.
Elsevier Sequoiw’Printed in The Netherlands
236
Slip-line field plasticity analyses of metal machining, in which the variation of a metal’s yield stress with flow is neglected, conclude that in any machining circumstances there are ranges of allowable values of chip thickness and tool force and hence temperature [l-4]; such analyses cannot give unique predictions of chip formation or therefore of tool wear.
In practice, unique predictions of machining parameters have been achieved by including yield stress dependence on flow in the analysis and by coupling the chip-tool friction to the flow, for example requiring it to depend locally on the chip shear flow stress or on contact pressure. The first studies in this area were by Oxley and coworkers [5, 61, but their analytical method required a number of averaging approximations to be made. Subsequent advances have been made by numerical, finite element, analysis.
Large strains, strain rates and temperatures make machining a diflicult subject for numerical analysis, and any analysis is only as good as its mechanical property and friction assumptions. There have been demonstrations of finite element modelling (FEN) solutions of machining problems which have used simplified material or friction models [ 7, 81, but the major detailed study has been by Usui and his group [9 I; the present paper is based on their work. A programme previously written for a supercomputer IlO] has been simplified and pre- and postprocessors added for interactive use on a CAD (computer-~ded design) computer. The principles are summarized in Section 2.
Differences in non-metallic inclusion content and form are well known to be the source of major differences in machinability between differently produced steels. Inclusions can have at least four separate effects on tool wear: (1) lubrication of the tool rake face by deposits formed from the inclusions can cause lower tool forces and temperatures; (2) these deposits can also act directly as a protective barrier between the tool and the sliding chip or work material; (3) other inclusions can be abrasive to the tool; (4) others again can embrittle the work material to weaken its resistance to chip formation. Calcium treatment of ~~~-deo~~ed steels, to convert abrasive ahunina to softer inclusions which also form beneficial deposits on mixed cemented carbide and TiN-coated tools, has been one steelmaking development for reduced tool wear [ 11-131. Another has been inclusion control by resulphurization [ 14, 151. Both approaches have come together in the commercial development of ahuninium-deoxidized, calcium-treated and slightly resulphurized semi-free-cutting low alloy steels [ 16, 171. However, although it is qualitatively clear that reduced abrasion, lower cutting forces and temperatures and a barrier effect all play a part in reducing tool wear by these steels, there is no quantitative model for assessing the relative importance of these factors nor for predicting tool wear dependence on cutting speed and feed.
237
Earlier studies on the wear of cemented carbide tools used to turn steels which did not form rake face deposits have established that at high cutting speeds crater wear is, and flank wear may be, thermally activated. Depth wear per unit time (dwldt) or per unit sliding distance (dwldl) has been proposed to depend on temperature T and also on contact stress a, [ 18-211:
or
(lb)
It is diflicult to distinguish experimentally between these forms because of the dominance of the temperature term and also because of the diiliculty of determining temperature.
In this paper, flank and crater wear rates are reported for a steel-cutting grade of carbide turning two low alloy steels, and temperatures are calculated by the finite element analysis. The data are reduced to the form of eqn. (lb); the activation energies Q are found to be the same for each steel but the coefficients A are found to differ, and this is discussed in terms of the steels’ inclusion contents,
2. The finite element machining simulation
The analysis applies to steady state orthogonal machining. An initial guess is required of the shape of a chip: most simply the guess may be a straight chip defined entirely by its shear plane angle, the feed and the tool rake angle; or it could be the result of a previous analysis. The chip is supposed to be preformed on the surface of the work material and to be stress free. Calculation proceeds by incrementally displacing the workpiece towards the tool so that a load develops between the chip and tool. A plastic state develops in the chip formation zone and it is checked whether the consequent plastic flow is consistent with the assumed chip shape. If it is not, the assumed shape is systematically and automatically altered and the calculation repeated. The cycle continues until the assumed and calculated flows converge.
The CAD implementation includes a preprocessor which generates from a primitive mesh (F’ig. l(a)) the ilnite element mesh of an initial guess (F’ig. l(b)). After a successful calculation a postprocessor constructs graphical output, e.g. chip and tool temperature contours (F’ig. l(c)). Further details have been published previously [ 221.
238
Fig. 1. (a) Finite element preprocessor primitive me& (b) hMal guess mesh and (cl exmph of postprocessar temperature contour output.
The work material is assumed to obey the Prandti--Reuse flow rules and the van M&es yield eriteriort f23, 241. The element stifhess equations are formal&ted for large strain increments in an updated hgra@an approach, ~clu~ element shape change and rot&on terms [2Sf but exchIing relax&ion of over-constraint of ~~ornp~~ib~~ [26f. The steady state
239
temperature distribution in the chip and tool is obtained by solving the thermal diffusion equation in its variational form [ 271, which has been used previously in metal-cutting analyses [28, 291.
2.2. Flow stress and j+iction characteristics Good physical property data are essential inputs to the analysis. In the analysis, following ref. 9, the unisxial yield stress u of the work
material is assumed to vary with strain, strain rate and temperature according to
a=B (lo+)? (2)
where the coefficients B, M and N vary with temperature and are obtained from experiments. The strain path dependence [9] of the yield stress is ignored.
Friction conditions between chip and tool vary from heavily loaded near the cutting edge to lightly loaded where the chip leaves the tool. The friction stress 7 is empirically related to the shear flow stress k of the chip material by PI
7= k [ 1 - exp { - (pq$c)} (3)
As the normal stress a, tends to zero, AT,, tends to p and p is seen to be a friction coefficient, but as a,, becomes greater than k, 7 saturates at k.
3. Experimental procedure
Hot forged bars, nominally 100 mm in diameter, from two casts of a low alloy steel, grades BS970 708M40 and 708M40 MAXIM*, were provided by British Steel plc, heat treated by oil quenching to 960 “C, followed by air cooling from 600 “C. Their compositions and hardnesses are recorded in Table 1. The calcium-treated and resulphurized steel is seen to be the MAXIM grade.
These were turned on a lathe without coolant by cemented carbide tools (8% Co, 75% WC, 17% (Ti-Ta-W)C, Sandvik Grade S2). In alI cases the tool end and side clearance angles were 6”, the approach angle was 14” and the nose radius was 0.25 mm. Three side rake angles (O’, 6” and 12”) and two feed and depth of cut combinations (0.125 mm rev-‘, 1.25 mm and 0.254 mm rev”, 2 mm) were tested. In the iirst instance the cutting speed was varied from 150 to 300 m min-‘, but it was later raised to 450 m min-’ for the MAXIM steel.
Tool cutting and thrust forces were measured in an initial set of short tests, before tool wear developed, using a Kistler piezoelectric force platform. Swarf was also collected, chip thickness measured and shear plane angle
*MAXIM is a registered trade name of United Engineering Steels.
TG
BL
E
1
Ch
emic
al
anal
ysis
an
d ha
rdne
ss
of
the
stee
ls
Mat
eria
l E
lem
ent
(wt.
%)*
N
V30
@
Pa)
N
%
c S
i M
O
P
S
Gr
MO
N
i A
L
cu
Sn
C
a
708M
40
0.36
0.
21
0.77
0.
02
0.04
0.
94
0.15
0.
22
0.03
0.
24
0.02
<
0.0
005
2.65
kO.l
708M
40
0.41
0.
32
0.85
0.
01
0.09
1.
11
0.21
0.
08
0.02
5 0.
09
0.01
0.
0046
2.
7OkO
.l M
AX
IM
*Bal
ance
: ir
on.
241
calculated. Shear stresses on the primary shear plane were calculated from the forces and shear plane angles.
Flank wear land length and crater shape were measured in tests of total cut distance up to 1.8 km, at cut distance increments initially of 75 m and later of 150 or 300 m. Flank wear land lengths were converted to flank wear depths, from a knowledge of the side clearance angle, prior to expressing flank wear rate as wear depth per unit sliding (or cut) distance. Crater shape was measured by a surface profilometer at the midpoint of the depth of cut. Crater wear rate was expressed as maximum depth wear rate per unit sliding distance; in this case sliding distance was the distance that the chip slid over the tool, which is less than the cut distance since the chip speed was less than the cutting speed.
Tool rake face deposits were studied by scanning electron microscopy (SEM) using backscattered electron images and energy dispersive X-ray analysis.
Subsidiary measurements were performed to establish the steels’ me- chanical and friction characteristics. High strain rate compression testing, using a Hopkinson bar apparatus, was carried out on cylindrical samples machined from the steels, initially 10 mm Iong and 6 mm in diameter. Strains up to 1.0 were achieved by repeated impacts each of strain increment 0.05, at strain rates from 200 to 2000 s’ and at temperatures up to 700 “C. Rapid heating was achieved by an ~duc~on coil round the sample and rapid cooling by quenching in water. Earlier work [30] has demonstrated that with this equipment, strains up to a level of 1.0 can be achieved at the higher temperatures before thermally controlled microstructural alterations start to affect the flow stress signi6cantly. The equipment is thus relevant to metal machining in which room temperature microstructures pass through the straining and heating cycle in fractions of a millisecond.
Friction between the chip and tool was studied in a special machining test, using a split tool dynamometer [9), at a cutting speed of 100 m min-‘, a feed of 0.2 mm rev-’ and with a 0” rake angle tool. Measurement of the variation of force over the rake face of the tool enabled the normal and friction stress distributions to be calculated.
4. Results
Table 2 summarizes the measured initial cutting and thrust forces, F, and FT, the chip shear plane angles $ and calculated primary shear plane shear stresses k, and the steady state crater and flank wear rates.
In any cutting condition the cutting force of the MAXIM steel was about 20% less than, the thrust force about 40% less than, the chip thickness about 10% less than but the primary shear plane shear stress about the same as that of the 708M40 steel. The lower forces and thinner chips of the MAXIM steel are not due to lower flow stress.
TM
LE
2
iz
Exp
erim
enta
l re
sult
s of
for
ces,
ch
ip t
hic
kn
ess
and
too
l w
ear
rate
Rak
e F
eed
S
pee
d
7osM
40
708M
40 L
%fA
XlM
D
epth
wea
r/sl
idin
g
dis
tan
ce (
pm
km-‘)
an
gle
(mm
rev
-‘)
(m m
id)
@f-
s)
PC
F
T
(P
k F
c F
T
rb
708L
u40
~~~~
40 M
Axi
M
CN
) (N
) (d
a)
(MW
(N
> (N
> (d
e&
&‘a
) cr
ater
F
lank
c-
r-
Fla
nk
0 0.
125
150
435
305
25
718
357
155
29
737
13
10.5
22
5 42
5 27
4 27
74
0 37
0 17
4 32
75
1 52
10
.5
300
417
260
30
740
357
164
32
732
130
8.4
2.8
3.5
6 0.
125
100
0 5.
8 12
0 15
12
.1
150
416
259
26
727
339
152
31
701
226
412
258
30
729
339
162
32
702
54
9.5
0 3.
0 30
0 39
7 23
7 30
72
0 33
3 14
2 34
70
4 12
0.
125
150
415
259
26
727
311
118
35
701
13
6.3
0 3.
8 22
5 41
5 27
0 30
71
6 31
1 11
7 36
68
7 36
9.
1 30
0 37
6 19
4 31
72
8 32
0 12
4 37
68
8 96
13
.2
0 0.
254
450
45
15.8
6
0.25
4 15
0 11
07
506
30
705
962
277
32
702
42
3.7
225
1098
53
8 31
68
4 90
0 29
2 35
65
4 19
5 9.
5 3.
4 2.
9 30
0 11
35
567
33
701
924
270
34
689
468
8.3
7.2
375
916
263
34
679
22
5.9
450
988
294
34
720
51
15.7
12
0.
254
150
1034
40
3 31
70
0 87
8 24
6 39
66
5 22
5 10
06
356
33
707
888
212
36
699
300
1006
37
8 34
69
6 86
9 23
0 38
66
9
243
0 0.4 0.8 1.2 1.6
CUT OISTANCE.km
.
/ I . / . A0 a-0 ,
100 200 300 400
CUTTING SPEED, m imln
Fig. 2. Crater (A) and flank (m) depth wear increase with cut distance for 708M40; a=6”, f=0.125 mm, U-225 m mix?.
Fig. 3. Crater depth wear rate increase with cutting speed for 708M40 MAXIM (0) and 708M40 (0); a= 6”, f= 0.254 mm.
0 &- 100
CUTTING SPEED m/mfn
Fig. 4. Flank depth wear rate increase with cutting speed for 708M40 MAXIM (0) and 708M40 (0); for all rake angles and feeds.
Figure 2 shows the typical linear increase of maximum crater depth with cut distance and the initial nmning-in of flank wear depth.
The crater wear rate when turning the MAXIM steel was only large at a feed of 0.254 mm rev-’ and cutting speeds greater than 300 m mini. In these conditions the 708M40 steel caused rapid tool failure. There are therefore few direct comparisons of crater wear rate in Table 2 but, as shown in Fig. 3, at a feed of 0.254 mm rev-’ the 708M40 steel showed a 60-fold greater wear rate than the MAXIM grade at speeds of 225 and 300 m min-‘.
The flank wear rate of the 708M40 steel was also greater than that of the MAXIM grade, but a dependence on speed and feed was scarcely noticeable. Figure 4 shows flank wear rates plotted against cutting speed without identification of rake angle or feed. The MAXIM flank wear rate is about
244
half that of the other steel except at the highest cutting speed of 450 m &-? when a jump occurred in its wear rate.
Figure 5 shows backscattered SEM images of rake face deposits formed on the tools, typical af all feeds and speeds. The lower magniiication images show the cutting edge horizontal at the top and the full contact length between chip and tool: a shorter contact length is seen for the MAXIM than for the 708M40 steei. The deposit from the MAXIM grade is also seen to be thin: cemented carbide can be seen through it as the light material; the deposit co&&ted calcium, manganese and suiphur but no ahuninium. The deposit from the 7OSM40 steel was mainly iron.
Figure 6 shows representative results from the Hopkinsun bar tests. The flow stresses of the two steels were almost ~~t~~~le from one another. Mean estimates of B, M and N in equation (2) are (with temperatures 8 in “C and cr in GPa1
Fig. 5 SEM images of tool rake faces used to turn (a), (c) 7OSM40 MAXIM and (b), fd) 708M4~ steels; a= 6”, f- 0.254 mm, U= 225 m mi&.
245
with strain and temperature at a strain rate of 1000 s-'; solid symbols, 708M40; open symbols, 708M40 MAXIM.
\ * on \
La)
0 0.L 0.8 1.2
(a) DISTANCE FROM CUTTING EDGE, mm @I
0.8 DISTANCE FROM CUTTING EDGE, mm
Fig. 7. Contact stresses on the rake face for (a) 708M40 and (b) 708M40 MAXIM; a=OO, j=O.2 mm, U=lOO m mirP.
B=l.W exp(-0.00188)+0.38 exp(-O.OOOOl(&-445)2}
+0.16 exp{-0.0002(0-570)2}
M= 0.017 +0.0000686
N=0.135 e~(-0.0012e)+O.O7 e~(-0.00002(~-465~}
(4)
The complexity of I3 copes with the blue-brittle peak in flow stress at around 550 “C in Fig. 6.
Figure 7 shows the variations of normal and friction contact stresses over the tool rake face obtained from the split tool tests. For the 708M40 steel the friction stress in the lightly loaded region at the end of the contact was greater than the normal stress, but for the 708M40 MAXIM steel it was less. Figure 8 plots friction stress against normal stress: the low load gradients give p= 1.3 for the 708M40 and 0.75 for the MAXIM steel. The saturated value of friction stress of the MAXIM steel is 0.86 times that of the 708M40,
I I I t
0 100 200 300
CUTTING SPEED , m/h
Fig. 8. Variation of friction stress with normal stress on the rake face for 708M40 (0) and 708M40 MAXIM (0).
Fig. 9. Tool forces and maximum rake face temperatures for 708M40 (a) and 708M40 MAXIM (0) with n=6”,f=O.f25 mm, d=1.25 mm: ---, FEM calculations; -, experiment.
suggesting a modified form of equation for the MAXIM steel:
r=0.86 k {l-exp(-l.l6pa,/k)) (3a)
4.3. Finite element calculutim Equation (Z), with coefficients from eqn. (4), and eqn. (3) or (3a) were
input to the Gnite element programme. Calculated tool forces and maximum rake face temperatures for 6” rake angle tools, a feed of 0.125 mm rev-’ and a depth of cut of 1.25 mm are presented in Fig. 9; the forces obtained experimentahy are included for comparison. The programme correctly predicts lower forces and temperatures for the 708M40 MAXIM than for the 708M40 steel. However, the predicted cutting forces are twice as large as measured. Although the predicted thrust forces are at the same level as the measured forces, the predicted differences between the 708M40 and 708M40 MAXIM steels are less than those measured. The predicted temperature differences of about 80 “C have not been tested experimentally.
Measured maximum crater depth wear rates have been paired with calculated maximum rake face temperatures, and flank wear rates have been paired with calculated cutting edge temperatures to test the validity of eqn. l(b). The data are presented in F’ig. 10. At high temperatures (Z’> 1070 K for 708M40 and T> 1170 K for 708M40 MAXIM) the wear is thermally activated: a value of & of 40 + 2 kcal mol-’ may be deduced for both steels. At lower temperatures the wear depends only slightly on temperature. The data for the two steels are displaced signScantly from one another: at high temperatures A (eqn. l(b)) is 140 X 10’ @rn km-’ for 708M40 and
247
TEMPERATURE, Y 1200 1000 800 600
’ 0’ I 1
\
‘. 100
0 - \ b
t\ 0
E
t 0%
_--/
E ‘O , =>.-r-._ - ?a
0 0 m
G
G 00 m-p -a
1 6 8 10 12
1 IT, IO-“'K-l
F'ig. 10. Crater ($0) and flank (H, Cl) depth wear rate variations with temperature for 708M40 (0, II) and 708M40 UAXIM (0, Cl).
6.3 X lo-? pm km-’ for 708M40 MAXIM. At lower tempers the wear rate of the 708M40 steel is three times that of the 708M40 MAXIM steel: this ratio differs from the two times quoted in the context of F’ig. 4. It is seen in Fig. 10 that the higher flank wear rates of the MAXIM steel that led to the two times factor of Fig. 4 belong to the high temperature part of the wear characteristic.
5;. Discussion
The turning tests con&m earlier work [ 16 ] that the calcium-treated and resulphurized MAXIM grade of i’OSM40 steel machines with lower forces than the untreated 708M40 steel; the Hopkinson bar tests confirm that the two steels have the same yield properties. The lower forces come not from lower yield stresses but from a thin lubricating layer of Ca-Mn-S that is deposited on the rake face when turning the MAXIM steel.
The friction properties of the layer have been measured directly. Near the cutting edge the layer’s presence limits the friction stress to 0.86 of the shear yield stress of the chip mate&& 0.86 agrees well with other indirect assessments of the friction factor of free-machining steels (41. In the region where the chip leaves the tool the layer is associated with a friction coefficient of 0.75, compared with 1.3 for the untreated steel.
248
The turning tests also confirm the lower tool wear rates caused by the ~I~ steel, Figure 10 shows that at tempera~es above 1120 K the wear is theory activated with an activation energy of 40 kcal mole-“: this value is in agreement with other studies IS]. Figure 10 also shows that at any temperature above 1120 K the wear of the 70811140 steel is 20 times that of the MAXIM grade: this is a measure of the effectiveness of the Ca-Mn-S layer as a barrier to diffusion wear. However, Fig. 3 shows that at a given feed and speed the wear of the ~0~~~~ steel is 60 times that of the ~~ grade. The 6U-fold factor is the product of the 20”fold factor due to the barrier effect of the Ca-MnS layer and a three-fold factor due to the Xower temperature when turning the MAXIM grade. ~ub~titut~~ values of A and Q in eqn. l(b) shows that the three-fold factor is eq~valent to a 100 “C lower rn~~ rake face tempe~~e between tug the ~~ aJlzd untreated 7~SM4~ steels; 100 “C is typical of temperature differences cal- culated by the fYinite element analysis (Fig. 9f and also measured in other work [15].
The relative influence on high temperature wear of the lubricating and barrier properties of non-metallic inclusions in steels can thus be considered qu~ti~~vely by means of eqn. (1). The p~i~~~ values, threefold and ZQ- fold, deduced above depend, however, on the finite element turnpike ~~c~atio~. Some ~~e~~es with the finite element analysis, considered in the next subsection, must make these quantitative conchtsions provisional.
At ~rnpe~~es less than 1120 K the wear is not achy activated. It is suggested that the lesser wear produced by the ~~ steel is due to the absence of abrasive alumina inclusions f 161.
It has been demonstrated that, starting from flow stress information and friction characteristics, finite element predictions may be made of machining parameters using a CAD computer fan Apollo II ma&tine). Figure 9 shows guod agreement between predicted and measured thrust forces but poor agreement between cutting forces. This is rapport since better sternest has been experienced previously in the analysis of an 18% Iv& steel [22]. Other output from the programme shows the force errors tu be due at least in part to excessively large calculated hy~os~~c stresses. This is a recognized problem of el~tic-pl~tic finite element analyses: attempts are to be made to overcome this after the manner of ref. 26. A further question to be faced concerns the vahdity of applying mechanical property data obtained from testing up to 700 “C and at strain rates up to 2000 s-’ to conditions in which maximum temperatures and strain rates of 1100 “C and lo4 s-l are calculated. Nevertheless, the present resuI&? are sufficiently promising to warrant further development, and these are planned.
It has been conGrmed that ~~g~~~ ~~ low alloy steeI when turned by ~~l-cu~g grade cemented carbide tools causes lower tool forces and
249
much less crater and flank tool wear than does standard 708M40 sted, and that the two steels have the same yield proper&s.
Differences between the machinabihty of the steela come from a thin Ca-Mn-S layer that deposits on the rake face when turning the MAXIM grade. This layer both lubricates the rake face contact to cause lower temperatures to be generated and acts as a barrier to diffusion wear. Friction properties of the layer have been measured directly. On the flank face the lower abrasiveness of the MAXIM steel brings benefits.
A finite element analysis of chip formation has been developed on a CAD computer. It has given good predictions of tool thrust forces but has been in error with respect to cutting forces. It needs more development before it can be a reliable tool to aid mac~ab~~ studies.
Acknowledgments
This work was supported by the ACME Directorate of the SERC and by British Steel plc. The Hopkinson bar and split tool friction tests were ad~tion~y carried out at Kitami Institute of Technology, Japan, under the direction of Professor T. Kitagawa; we wish partiparticucucucucucucuc to acknowledge his help.
References
1 R. Hill, J. Mech. Phys. Solids, 3 (1954) 47-53. 2 H. Kudo, Int. J. Mech. Sci., 7 (1966) 43-65. 3 P. Dewhurst, Proc. R. Sot. Immdon, Ser. A, 360, (1978) 587-610, 4 T. H. C. ChiIds, In-t. J. Me&. SC&, 22 (1980) 467-466. 5 W. F. Hastlugs et al, Proc. Is& Me&. Eng., 288 (1974) 245-252. 6 P. L. B. Oxley and W. F. Hastin@, Ph&s. Trans. R. Sm. Lvmbz, Serv. A, 282 (1976j
565-584. 7 K. Iwata et uL, FRZS. A.!SlE, J. Eng. Ma&r. Techml, 106 (1984) 132-138. 8 J. S. S~~o~~ and J. T. Carroll, [prans. ASME, J. Eng. Iti, 207 (1985) 349-354. 9 E. Usui and T. Shirakashi, ASME Pi.&& PBD-7 (1962) 13-36.
10 E. Usui e$ CA, BAl. &a SAG Pmt. En@., 15 (1981) 237-242. 11 H. Opitz et aL, AT-G& ~~~~~ 33 (1962) 841-851. 12 2. Palmi, Met&l. B&&w.., 8 (1974) 326-330. 13 Z. Palmai, Met. Techml, 11 (1984) 34-37. 14 D. J. Naylor et a& Met. Xechnol, 3 (1976) 254-271. 15 R. Milovic et CA, Muter. Sti Z’e&ml*, 2 (1986) 59-68. 16 M. L. Picket% et a& Pmt. Cm on X&h Productivity Machining, NW Orkans, LA,
Muv 2985, ASM, Metals Park, OH, 1986, pp. 253-264. I7 II. Pontinen, Pmt. C&q& on i9tmM@mfw Automation ~M~h~~~~, CWmdo, I%, Masf
198?, AS&f, Metals Park, OH, 1987, pp. 65-71. 18 K. J. Trigger and 3. T. Chao, !%ms. AS&B, 78 (1956) iilQ-1126. 19 H. Takeyama and R. Murata, Tmns. ASME* J. Eng. I&, 83 (1963) 33-33. 20 N. H. Cook, !&x-ms. ~, J. Eng. I&., 95 (1973) 931-938. 21 E. Usui et a& Trans. ASME, J. Eng. Ind, IO0 (1978) 236-243.
250
22 T. H. C. Childs and K. Maekawa, Proc. Conf: on Strategies for Automation of Machining, Orlando, FL, May 1987, ASM, Metals Park, OH, 1987, pp. 157-166.
23 R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, 1950, Chap. 2.
24 Y. Yamada et al., Znt. J. Mech. Sci., 10 (1968) 343-354. 25 R. M. McMeeking and J. R. Rice, Znt. J. Solids Strut., I1 (1975) 601-616. 26 J. C. Nagtegaal et al., Comput. Methods AppL Mech. Eng., 4 (1974) 153-177. 27 M. Hiraoka and K. Tanaka, Ma. Fat. Eng. Kyoto Univ., 30 (1968) 235-263. 28 A. 0. Tay et al., Z+oc. Inst. Mech. Eng., 188 (1974) 627-638. 29 T. H. C. Chids, K. Maekawa and P. Maulik, Mater. Sci. TechnoL, 4 (1984) 1006-1019. 30 T. Shirakashi et aL, B&L Jpn. Sot. Prec. Eng., 17 (1983) 161-166.
