instructions for use - huscap3)_241-272.pdf242 koichi hoshi and tetsutaro hosm 1. introduction. in...
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Instructions for use
Title On the Metal Cutting Mechanism with the Built-up Edge
Author(s) Hoshi, Koichi; Hoshi, Tetsutaro
Citation Memoirs of the Faculty of Engineering, Hokkaido University, 12(3), 241-271
Issue Date 1969-01
Doc URL http://hdl.handle.net/2115/37863
Type bulletin (article)
File Information 12(3)_241-272.pdf
Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP
'
On the Metal Cutting Mechanism with
the Bullt-up Edge
Koichi HosHl*
Tetsutaro HosHl**
(Received August 31, 1968)
Abstracts
An experimental study was undertaken in order to study the formation
and the cutting mechanism of the built-up edge.
Investigations of the quick-stopped partly formed chip produced at various
cutting parameters clearly demonstrated that the secondary plastic flow in chip
formation was the direct source of the work-hardened metal which forms the
built-up layer or the built-up edge. Adhesion of the bui!t-up edge nucleus
onto the tool face was discussed from the mechanical inlaying principle.
Growth and fracture of the typical built-up edge and the metal cutting
model were described. Variation of the built-up edge and the metal cutting
model geometries were explored by a series of quick-stop tests, and the test
results were processed by a computer simulation of the cutting force equilibrium,
which results indicated that the variation of the cutting force was mainly
controlled by the contact length between the built-up edge and the chip.
Contents
1. Introduction ............................ 242 2. Material and equipment for the study ..........,..... 242 3. Experimental results and interpretation ............... 245 3.1. Formation of the built-up edge ................ 245 3,2. Metal cutting modei with the built-up eclge ........,. 252 3.3. Metal cutting model geometries under various cutting parameters 253
4. Analytical simulation of the metal cutting model with the built-up edge 357
4.1. Purpose of simulation..,..,,,....,,.....,. 257 4.2. Method of simulation ......,....,....,.,.. 258 4,3. Result of Simu]ation ..,.......,,.,,,.,,.. 268 Reference ......,........................ 270 Nomenclature ............................. 270 * Precision Engineering Laboratory, Faculty of Engineering, Hokkaido University, Sapporo,
Japan.
** Precision Engineering Laboratory, Facuity of Engineering, Kyoto University, Kyoto,
Japan.
242 Koichi HosHI and Tetsutaro Hosm
1. Introduction.
In the history of metal cutting research, the built-up edge has been one
of the most interesting subjectsi)-6), and is still producing diversified discussions.
One of the authors has continued to work on')'S) this problematic point;
recently, he finished a series of metal cutting tests from which many formerly
uncovered facts came to light.
In this study, orthogonal cutting of carbon steels were investigated for
the purpose of obtaining advanced knowledges on the formation of the built-up
edge and the metal cutting mechanism when it was present.
In particular, the following points were explored:-
1) the type of the physical process by which a portion of the work metal
was deformed to form the built-up edge;
2) the type of adhesion of the built-up edge material onto the tool face;
3) the metai removal model by which the worked meta} plastically trans-
formed into chips when the built-up edge was present;
4) the manner in which the size and shape of the built-up edge varied according to the change in cutting speed and tool rake angle; also peri-
odical fluctuations of the built-up edge in a cutting at a given condition
were observed' and the cause of such variations were studied. , Experimental data were presented in the form of micro-photographs of the
middle sections of the partly formed chips obtained by quick-stopping the
orthogonal turning tests of the steel tube ends, at cutting speeds ranging from
8 mpm (meters per minute) to 165 mpm. By those micro-photographs, the size
and shape of the built-up edge were analyzed, its formation and cutting me-
chanism were estimated, and a simplified metal flow model was proposed, which
was further followed by a simulation of mechanical force equilibrium in cutting
with the built-up edge.
Z. Material and equipment for the study.
For the quick-stop tests to obtain the partly formed orthogonai chip having
a built-up edge, a tubular worl< piece was machined beforehand out of a solid
block of O.25% carbon steel with mechanical properties and compositions as
listed below.
Mechanica! properties Qf material.
Yielding pointkg!mm2
Tensilestrength1<glmm2
Totalelongation
%
Reduction of area %
Hardness
HB
Impact value1<g-mlcm2
30.7 52.6 34.7 58,O 145 5.1
Chemical
On the
composMon
Metal Cutting Mechanism with
of material (wt. pt/)
the Built-up Edge 243
C si Mn P s Ni Cr Mo Cu
O.24 O,30 O.68 O.O15 O.O12, O.14 O.13 O.04 O.28
The quick-stop orthogonal turning tests employed P20 carbide tools and
also 5% Co and 10% Co type high speed steel tools. The tool was mounted
on a quick-stop device fixed in such a way that the tool could be suddenly
removed along the direction of cutting, from the cutting position.
The speed of the tool escape was preliminarily calibrated using high speed
flash light photography as shown in Fig. 1. From the 170 mpm initial average
X>tx(
b
170mpm
470mpm
Fig. 1. High speed flash light photograph to show the speed of the
escaping tool when the cutting process is quick-stopped. The
average speed of the escaping tool is found to be 170 mpm during the initial l/700 sec, fotlowed by a constant speed of
470 mpm.
speed calculated from the photograph, the test rig was found to be capable
of stopping the cutting without interfering with the chip formation from
a cutting speed of 65 mpm or below.
The quick-stop tests were performed on an engine lathe Shoun-Cazeneuve,
having a 500mm swing over bed, a 1,OOO min distance between centers anda variable speed spindle drive motor rated at 11 kw.
l
244 Koichi HosHI and Tetsutaro HosHI
（a）
…醸運
『畿’
蕪i繋’；
縣欝il饗燕§
≒灘撫
難論1
鱈 べ， ぐ。拍．・砲醜煙き湿欝欝、
Fig．2． Typical photographs showing the e鉦ect o重
cutting speed on the built－up edge．
S25CST－2
α；10deg’1；0．3m皿
∂；3．Omm
Tρ＝188mpm
t，二41mpm
uコ35mpm
On the Metal Cutting Mechanism with the Built-up Edge 245
3. Experimental resu!ts and interpretations.
3.l. Formation of built-up edge.
3.1.1. Secondary flow, built-up layer and built-up edge.
Partly formed chip quick-stopped frorR various cutting speeds contain
built-up edges of different size. In a series of micro-photographs shown in
Fig. 2, the specimen of a relatively high cutting speed, top picture (a) at
188 mpm, involves no built-up edge, but only a flow of metal along the tool
face which is conventionally termed as "the secondary fiow". A 20 to 30 pt
(pt:=:10-3rbm) thick secondary flow zone is observed at the cutting speed of
130 mpm and above.
At slower cutting, a layer of stationary metal is observed between the
secondary flow and the tool face as shown in the figure taken at 41 mpm,
Fig. 2 (b). Micro-hardness tests indicated that this kind of layer (297 to 322 Hv)
was as hard as the typically formed built-up edge (297 to 439 Hv) and was
more work-hardened than the original work piece (153 to 159 Hv) or the formed
chip (236 to 256 Hv). The stationary layer is the bulk of metal formed by the
secondary fiow, thus it becomes work-hardened and stationary. The removed
chip is separated from this layer by the secondary flow inside the chip. The
S25CST-2a == /O dley
ti=O,3mmb=±3.0mm
li;i2
-u Xst/ if x l' ti
--i---m-------l- N<N5x
e ::-K".,C<.;- T- x
Vmpm
3i4I56102
13Pl88
ummO,44O,08O.06a.o4O.03
O.02
qMmO,08O.040.020.02o,oo
aoo
Fig. 3. Effect of eutting speed on the thiclmess u and the
over-cut depth ¢ of the built-up edge, depicted from the quick-stopped photographs.
246 Koichi HosHI and Tetsutaro HoSIII
thickness of the layer increases when the cutting speed is reduced, as shown
in Fig. 3, until the !ayer attains the size of a typical built-up edge such as
that seen at 35mpm as shown in Fig. 2(c). Therefore, it is proposed that
this layer be tentatively referred to as the "built-up Iayer" and may by treated
as a premature body of the built-up edge according to the definition as listed
below.
Proposed definition of built-up layer and built-up edge
Thickness tt asindicated in Fig. 3
[mm]
Typical cutting speedrange in steel cutting [mpm]
built-up layer
built-up edge
O to O,1
O.1 and above
40 to 130
under 40
Above the speed range of the built-up layer, only the secondary flow zone
exists.
In a magnified view of the typically formed built-up edge (Fig. 4), there
appears no clear boundary between the built-up edge and the removed chip.
The flow of structure indicates that a secondary flow is occurring between
the stationary metal and the removed chip. Since the metal is work-hardened
by the secondary flow, a portion of metal joins up with the built-up edge as
a new addition to it. Thus, the built-up edge constantly tends to grow in
size as long as the metal in the secondary fiow zone is work-hardenable. At
a higher cutting speed, however, the metal is less work-hardeBable due to the
higher cutting temperature; therefore, the secondary flow zone loses its harden-
ability as soon as a thinner built-up layer is formed. Hence, the layer does
not grow further.
3.1.2. Growth and fracture of built-up edge.
When a cutting is started, a layer of initially cut metal is work-hardened
due to the secondary flow and adhered to the tool face to form a nucleus of
the built-up edge. As seen in the example of Fig. 5, a continuous secondary
flow occurs outside the nuclear layer, so much so that the metal is continuously
work-hardened and added to the nuclear layer; as a result, a built-up edge is
brought up to its typical size as shown by the dotted curve DEG in Fig. 6,
in an extremely short time after the starting of cutting.
In its formation process, the built-up edge grows not only in the cutting
direction but also toward the generated surface. The growth in the latter
direction results in metal removal in excess of the given depth of cut. The
over-cut depth is empir!cally proportional to the thickness u of the built-up
edge, so that the following approximation holds
E
× 75 × 600
-be N ""fi"asS. xxsx"- $SliiSL tN
.twebeec,ny, !ra!h--tCN x
ge tlll!"ilii("gmki.e." "
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Fig.
h'
1 Stii
381
ik
322 f'gisw
W`rk8
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R4
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4. Magnified view of the
carbide P20 tool at a
Numbers in the left Vickers hardness test
eeI
s.i ,
"
ps ,bl sSve"
k 'N ,ktk
Sk
"･･ ,Rk`
viili$121112il` /l,,
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"w126
built-up edge found on a
cutting of 10 rnpm speed
photograph indicate the
at room temperature.
"¥.
-4 x
1tP5
" st
'Si
S"g
trS, ,,
"
5s l
`'.XffS, <
,<`:
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si!l' sa- ikN･
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ve k10 deg rake angle
and O.3 mm depth.
reading of Micro-
o:rt;g"
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di
Kggl-
:.･
e
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trroavE,rt-,
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9xo
t"ptN
248 Koichi HosHI and Tetsutaro Hosyll
S25C
ST-2
cr = 10 deg
tl=O.3rnm
b = 3.0 mm
v := 48 mpm
u =O,08 mm
297
322
Fig. S. Observation of metal removal with the built-up Layer.
On the Metal Cutting Mechanism with the Built-up Edge
,
249
4
a
c
u
p, ,,E, iZ.? r/}ci{21tts:,.r"･,･,t･ -･-･ID
f)E;,iii,ze,g,,t,fz,,,.,,,,,,,. :C"'
Lo
.B
t'
J.-.gb = xtu
:th---
Dt
,tl
G'
L
. Z-"ss- -...
-HZiii)ii
T
of metaledge,
gll :2.---G
.l"
Fig.6.Proposedmodel cuttingwith the built-up
¢ =- k･u
where k is a constant with a value lying around O.283,
At a low cutting speed, the metal in the secondary flow zone is always
work-hardenable even after the built-up edge attains its typical size. Thus the
built-up edge continually grows in width and depth,
When it grows, however, to such a size that the shearing stress along
an inner boundary such as D'E'G' (Fig. 6) exceeds a certain limit, fracture
occurs along the inner boundary and the upper part of the fractured layer
DEE'D' s!ides up with the chip while the lower part EGG'E' slides down to
remain over the generated surface. The built-up edge continues another growth
after the fracture so that the growth and fracture alternates periodically, main-
taining an average size of the bui}t-up edge representative of the given set
of catting conditions.
3.1.3. Adhesion of built-up edge nucleus.
Past knowledge explains that the built-up edge adheres to the tool face
250 Koichi HosHI and Tetsutaro Hosm
p
1ss2
B(f<(
700L
.aNS :
Y
Fig. 7. Inlaying the tool
of the built-up edge onto
surface.
-.pmt:al n
-
t'
"･･:' ･}"-vY'.ir 'tvr"ptliP.-
Fig･ 8. Example of the buil-up edge formed at an low cutting speed. O.15C steel was being cut at 28 mm
per min. speed and O.1 mm depth by a 8 deg rake angle
high speed steel tool (10% Co type).
w･ ebu- .eth'
extremely
ts
On the Metal Cutting Mechanism with the Built-up Edge 251
by a kind of welding process resulting from the high stress and temperatureof cutting. In addition to the theory above described, the present study sug-
gests that the mechanical inlaying of the deformed metal into the asperities
of the too! surface as depicted in Fig. 7, is one of the primary causes of the
adhesion based on the following observations.
First, the built-up edge occurs at an extremely slow cut of small depth.
Fig. 8 shows a built-up edge formed in a O.1 mm deep cut at 28 mm per minute
speed. Cutting temperature measured even at a higher cutting speed (1081mm
per min., work metal; brass) indicated that the maximum temperature was oniy
105 deg C registered near the tool-chip interface as seen in Fig. 9. According
it .../CCmsMN]AN uaRE
ttss
700L
BEtaSSnuaft
Dc AMR gRECORDER (61JB
th
xgasrl ua sc
x Kas
xsa
XS We&,,･5S 6a 65 re rs 8e e5p
loa / AfRM C2F maMMUM as 7EMRERATtffilE
.x. .g
¢
s
s
s
gS 70s
ss
1
ssst
s c (100)
L:0:::::--l5mm
.
to the conventional
a low cutting
Second,
built-up edge,
cuttlng ls
indicates that
' .' s e. s '. '. '. '. `"3' ,,..1/ '
e 70
Fig. 9. Cutting temperature measured by the embedded constantan wire at a low speed cutting. Numbers indicate temperatttres
in deg C. Worlc material: 60% Cu brass, Pb under O,3%, T.S. above 36kg!mm2, Tool material: 10% Co type HSS, room temperature: 18,3 deg C, tool ralce angle cr=::25 deg,
cutting speed w=1081 mm per min, depth of cut t=1,07 mm. O.17 mm dia, constantan wire put in O.2 mm dia. hole.
welding theory, adhesion is not likely to occur at such
temperature. all of the qu!ck-stopped partly formed chips are left with the
while the built-up edge is always left on the tool face when the
finished in the conventional manner instead of quick-stopping. This
the built-up edge is anchored to the tool face strongly against
252 Koichi HosHI and Tetsutaro HOSm
the force acting parallel to the tool face as force P in Fig. 7, but weakly
against the horizontal force Q which exerts itse!f at the instant of quick-
stoppmg.
3.2. Metal cutting model with built-up edge.
Although the hardness of the built-up edge is measured at room tempera-
ture at about three times higher than that of the original work metal, this
must not Iead to an interpretation that the built-up edge is acting as a sub-
stitute of the cutting tool on which the chip slides. Instead, the chip and
the built-up edge are actually a continuous body and are separated by the
shear of the secondary plastic flow.
A model as depicted in the Fig. 6 is proposed to explain the chip formation
with the buiit-up edge. Tool-chip contact length is L, at the start of a cut-
ting; though, as the built-up edge grows, the contact length is reduced to L
and the over-cut of a depth ¢ occurs. The boundary where the original workmetal firstly undergoes plastic flow is indicated by the curve BHIG. The
plastic flow in the region of BHIG produces a deformed layer of a depth h
left over from the generated surface. The largest portion of the primary plastic
flow occurs right after the metal passes the boundary curve BHIG, and the
rest of the plastic fiow continues slowly until the metal reaches an end boundary
curve somewhat like the curve PD. Although no clear-cut boundary of built-up
edge exlsts, it may be well surrr}ized that the stationary piie of work-hardened
metal lies between the dotted curve passing through point E and the tool face,
where point E is the intersection of the line of cutting direction passing through
the tool tip point A and a line parallel to the tool face passing through point
D where the chip escapes from contact with the built-up edge.
It is commonly known that the presence of a built-up edge at the tool
tip reduces the cutting force. The reason for this was formerly sought based
on the assumption that the face slope of the built-up edge served as a tool
face with an increased rake angle so that the chip was formed in a shear
plane with an increased shear angle. However, the chip formations observed
in the present study did not agree with the above theory. First of all, the
chip departs from the built-up edge at point D (Fig. 6) and does not slide over
the face slope DC. Real contact length L between the chip and the built-up
edge is at only a small portion of the surface of the built-up edge, Second,
the built-up edge does not have a sharp edge but has a round tip so that it
is impossible to define a simple shear plane in which most of the chip for-
mation takes place.
When the metal cutting involves the built-up edge, the chip formation
should be discussed on a more complex model than the conventional shear
OntheMetalCuttingMechanismwiththeBuilt-upEdge 253
plane concept. The following chapter will present results of an experimental
study on the geometries of the metal cutting model as proposed in the Fig. 6
under variations in cutting parameters.
3.3. Metal cutting model geometries under various cutting parameters.
3.3.1. Test procedure.
A total of 44 quick-stop cutting tests were carefully planned to investigate
the effect of the size fiuctuation of the built-up edge, the cutting speed, and
the tool rake angle on the geometries of the metal cutting model. On every
TABLE 1. Test records of cutting geometries by
change in cutting speed z).
S25C, SKH3, cr=19.2 deg, ti =O,3 mm
Test
No.
1
4
2
3
16
10
7
5
6
11
13
8
9
12
14
15
17
18
20
19
21
22
23
mpm v
810
10
10
17
17
17
17
!7
17
17
17
17
17
17
17
31
31
41
41
56
70
165
mm Zl.
O,64
O,52
O,36
O,27
O.45
O.42
O,40
O,40
O,39
O.35
O,30
O,30
O.30
O.28
O.20
020
O.42
O,28
O.24
O,16
O,05
OD6
o
mmL
(O.80)
O.35
O.36
O.44
O,56
O,37
O,43
O.50
O.43
O.30
O.30
(O.60)
O.33
O.37
O.26
O.37
O.80
O,75
(O.80)
(O,65)
(1,10)
(O.73)
mmip
O,20
O,18
O,12
O,10
O,10
O.08
O,14
O.11
O.11
O.09
O.09
O.08
O.08
O.09
O.09
O.08
O.08
O.05
O.03
O.03
O.Ol
O.Ol
o
mm t2
O.82
O.76
O.70
O.70
O.75
O,62
O,78
O,90
O,60
O.70
O.68
O,70
O.63
O.62
O,69
O.60
O,77
O,66
O,80
O,80
O,90
O.80
O,65
mmh
O.20
O.11
O.10
O.08
O,09
O,08
O,09
O,10
O,10
O,08
O.08
O,08
O,08
O,07
O.06
O.06
O,08
O.06
O.05
O.05
O.04
O.04
O.04
degdi
25
25
27
26
25
26
27
25
29
27
26
25
25
26
27
25
27
27
26
27
25
27
25
mmT
O,90
O.55
O.60
O.53
O.68
O,60
O,70
O,72
O,53
O,57
Q.48
O.55
O.49
O.37
O.44
O.38
O.80
O,40
O.73
O.48
O,52
O,40
O.15
mmL
1.46
0,84
O.81
O,85
1,22
1,10
1.60
1.00
O.90
O.53
1.10
1.60
O.55
O,70
O,64
O,60
1,86
1,70
O.94
gbltt.
fe
O.30
O.34
O,33
O,37
O.20
O.19
O.33
028
O,30
O,26
O,30
O,27
O,27
O,32
O,45
O.40
O.20
O,13
O,12
O.20
O,20
O,13
Llzt.
m
(1.2)
O,69
1.0
1.6
1.2
O.9
1.1
1,2
1,1
O,85
1,O
*
1,1
1,3
1,3
1.8
1.9
1.9
3.3
4.0
(22)
12
254 Koichi HosHI and Tetsutaro Hosm
micro-photograph of the partly formed chip, characteristic geometries such as
the thickness of the built-up edge u, contact length L etc. were readily obtained
as listed in Table 1 and Table 2 from the pattern of the metal flow. Statical
tests were applied on those data to identify the response of those geometries
to the investigated effects, and the conclusions were drawn as summarized in
Table 3.
TABLE 2. Test records of cutting geometries by change in tool rake angle cr.
S25C, SKH3, v=17 mpm
Test
No.
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
deg
ev
-11.0
- 5,8
- 5,8
o
o
4.2
4.2
9.0
9,O
9,O
14,2
14,2
24,2
24,2
29.2
29.2
34.2
34,2
34,2
39.2
44,4
mm tl
O.30
O.30
0.23
O,33
O,10
O,20
O.30
O.30
O.30
O.27
O.28
O.30
O,31
O,25
O.30
O,28
O.30
O.38
O.30
O.30
O.30
mm t2
O,87
O.87
O.88
O,66
*
O,95
1,04
1.04
O,66
O,75
O,63
O,75
O.69
O.50
O.50
O,50
O,46
O,59
O,43
O,49
O,45
mm zt
O.95
O,73
O.77
O,55
O,73
O,44
O,42
O,44
O,38
O.27
O.20
O.33
O.18
O.18
O,21
O.26
O.15
021
O.27
O.11
O,12
mmL
O.76
O.62
O.98
O.66
O.23
O.51
O.53
O.66
O,55
O,51
O,37
O,53
O.71
O,50
O.47
O,42
O,35
O,58
O.46
O.45
O,37
mmip
O,30
O.27
O.23
O.16
O.27
O,13
O,16
O,16
O,13
O.13
O.08
O,15
O.05
O.07
O,05
O,05
O,04
O.05
O.03
O,Ol
O,Ol
mmh
O.24
O,23
020
O,16
O.23
O.16
O.16
O,16
O,13
O,15
O,08
O,15
O.07
O.08
O,07
O,07
O.04
O,06
O.07
O.05
O,05
mmT
1.51
O.98
1,41
O,71
1.02
1,22
O,84
1,OO
O.70
O.43
O.58
0.65
O,48
O.45
O,33
O,47
O.26
O.39
O,33
O,47
O,40
degdi
25
24
25
27
38
22
23
22
27
26
29
31
34
34
37
37
39
39
40
43
44
iplu
k
O,31
O.37
O.30
O.29
O.37
O.30
O.38
O.36
O.34
O.48
O.40
O,45
O,28
O,38
O,24
O.20
O,27
O,24
O,11
O.10
O.09
Llte
m
O,80
O.85
1.20
1,20
O.32
120
1.20
1,50
1.50
1 90
1.90
1.60
3,90
2,80
2,40
2.40
2.30
1,80
1.70
4.10
3.10
3.3.2. Fluctuation of built-up edge in a continuous gutting.
In cutting under identical condition, growth and fracture of the built-up
edge alternates so that its size fluctuates continually. The test data show that
a thicker built-up edge (greater zt) is accompanied by a longer contact with
the chip (greater L), as illustrated by three selected test results in Fig. 10.
On the
TABLE 3.
Metal Cutting Mechanism with the Built-up Edge
Response of the metal cutting model geometries
to the change in eutting conditions.
255
ItemWhen built-up edgegrows m a contmu-ous out so that thethickness u is in-creased
When cutting speed v is increased
When teol rake angle cr is increased
Thickness oftt is
built-up edgedecreased decreased
Contact length L is increasea increased decreased
Chip thickness t2 is unaffected unaffected decreased
Inclinationof primary
of startflow di
planeis
unaffected unaffected increased
Distanceand H is
T between G increased decreased decreased
Over-cut depth ip is unaffected decreased decreased
Thicknesslayer overh is
of distortedfinished surface increased decreased decreased
u=.45 odi .t 25
L==.561 --- .68
c
{
U--.30 if n aso
li'Il;l}}))s.'te. ("
)"
D
L ".33T--,6s
..2s
-44z
cc
B
Fig. 10.
D
EA -;u2
E G
HFIuctuation of built-up edge in a continuous cutting.
Depth of cut ti==O.3mm, Cutting speed v:=:17 mpm,
5% Co type high speed steel tool.
256 Koichi HosHI and Tetsutaro HoSHI
v == 56
u=.05 L=Li
BB
Fig. IL
v==4l u=.t6 L=.65 D
Y=17 l u=,30 L=,ea D
d-
(fr.5}?t!"(fO.,.es /
DD
EE
G
Variation of built-up edge and cutting geometries by change
in cutting speed w mpm. Depth of cut ti==O.3 mm. u indicates
thickness of built-up edge, L contact Iength both in mm. 5%
Co type high speed steel tool.
o -r -ll
9o
d =-11 o
c
d=kpotr":.fige
44e
c
BB
D
E
B
D
E
s
XD
va
Fig. IZ.
H
Variation of
by change in
Depth of cut
5% Co type
cTOOL
G
built-up edge and cutting
tool rake angle cr.
ti =O.3 mm, cutting speed
high speed steel tool.
.geometrles
v=17mpm,
OntheMetalCuttingMechanismwiththeBuilt-upEdge 257
3. 3. 3. Effect of cutting speed on the buiit-up edge and cutting geometries.
Increased cutting speed brings about a thinner built-up edge (less u) as is
commonly known, but a Ionger contact with the chip is present (greater L) as
illustrated by four test results in Fig. 11. ,It is not clear whether the chip
thickness ip is effected by those variations.
3. 3. 4. Effect of tool rake angle on the built-up edge and cutting geometries.
Cutting by a tool with a greater rake angle results in a smaller built-up
edge (less ze), a shorter contact (less L), and a thinner chip (less t2) as illustrated
in Fig, 12.
c
U
4. 1.
P ax. x, Nh,
B >s >. N $l . tsLtsS`4 l ×-.N tsts. m.N NC{di)eiEl. >'L)`LH.. iRf"3iii7eiLli sx..
N
Fig. 13. Simplified stress
plane of primary boundary DEG.
4. Analytical simulation model with
Purpose of simulation.
In order to simulate the principle which
D-N,-･.z x L ×/ l Xxl ",}.l '"s--.1
.-.:x,ilc-ouaO? veEsStON)
"k N-----.- )4
E" di hK bs - --t..i.Ixiifi':l G
-q +eg (TzlALsvatv)
distribution Assumed on the start
flow BHIG and the built-up edge
of the metal cutting
built-up edge.
ruled the variations of the built-up
/flta-
258 Koichi }{osm and Tetsutaro HosHI
edge and the metal cutting model geometries as observed in the preceding
chapter, the equilibrium of cutting force was computed for the 44 test con-
ditions, in such a may that the normal to shear stress ratios were obtained
on the start boundary of primary flow and on the built-up edge boundary,based on the observed metal cutting geometries.
4.2. Method of simulatioh.
a. (Assumptions on the start boundary of primary flow) As proposed in the
metal cutting model, the work metal started a primary plastic flow when it
crossed the boundary surface BHIG (Fig. 13). A simplified assumption was
made in which the shear strain and therefore the maximum shear stress on
the start boundary was acting in the direction along the boundary itself. As
illustrated in Fig. 13, the magnitude of the maximum shear stress was denoted
by -T, and it was uniformly distributed. The normal stress to the start
boundary was assumed constant and was denoted by -a, (compression) along
the straight part of the start boundary BH, while it varied linearly along the
curved part HIG in such a way that a tensile stress of +a, was attained at the
end point G.
××{
-a
c
u
B .
t'J.nv.
di
the
t/
v]t=
-.nv.-.Ee
,- H '-ss fSimplified model cutting
built-up edge.
D.
/
A-.-. -'x< 's-. .
Llt.. (-
Fig. 14.
-- G---,m-'.li--O.c:1-.---..-.-.m.-
geometries with
On the Metal Cutting Mechanism with the Built－up Edge 259、
．癩
ぜ，夢。
8
為
⊥φ
＼
／
＼
／
∠／
’臥序＼＼、な
妨’｛｝
～1、煙
＼／’
毒
．駆
、塑
，調“
戸
暢〃
⑦、差、．厨
7
刈
②
o
伽一’ ¥一φ
〃．0〃ε〈1アσ〃
轟厨〔2．、為・加（鋸射・7・・確伽1薯）一φη
③
Fig。15。 Equili1〕rium equations on the plane B－H・
（1）magnitude of force
（2） direction of force
f3）momentum
260 Koichi HosHI and Tetsutaro HosHI
b. (Assumptions on the built-up edge bondary) Along the built-up edge
boundary, a uniform shear stress, which magnitude was denoted by Tf, was
assumed since the stationary built-up edge adjoined the deforming secondary
flow region over this boundary. Opposite to the shear on the upper part of
the built-up edge boundary･DE, the Iower part EG slides over the underlying
metal, so that the sign of the shear stress was negative on the latter part.
Normal stress to the built-up edge boundary was simply assumed to be uniform
and was designated by -af. Among the stress ratios: si=af!zf, s2=a,lzf, and
s3=T,!Tf, defined from the above stress assumptions, an equation (si +s2)2+s3=1
should hold according to the Mohr's stress circle at the point G.
! 1 / 1 t l t N N
H -Tk ---
1
+%A
-clb
T
G
oq･r
MOMEzvrt"vf
z@=al12x 2Tx qdu
T2,x-s-q
Fig. 16. Equilibrium equations on the plane H-G.
On the Metal Cutting Mechanism with the Built-up Edge 261
c. (Equilibrium equation of the force) With the curved portions of the two
boundary surfaces further approxiinated by straight planes as shown in Fig.
14, (1) the magnitude of the resultant cutting force, (2) the direction of the
resultant cutting force and (3) the resultant momentum of the cutting force
were analytically derived on both of the two boundaries as illustrated in Fig.
15 to 20 and were equated to each other according to the equilibrium theory.
1//t
lNN
x
/D
xNx s
A
-@
OSE.SOYny.-
'
foRcE;9
ojiRT.6,]N.VASY/or
po(bk
trsin, ¢
pRltvtARY
-t i"g'
/Zii Fi?-
FLOW
xG FCZFi)(2Er ew H-G
z3, ･Tim-, {}- - di
OT:;T2+th,.S2 (q3+Tse)-t"2nvfTylZi?Iil-E?M･cosl(tun-' f )- di]
@
stn-i
( ti
sin ip pm-h-of Tlj"T2+tiir(q}2+T;)+2ewT.tdiT.(73cusdi+q;sihdi)
Fig. 17. Resultant
B-H andequilibrium
H-G.equatlons on the plane
b⊃
ob⊃
翁・（伽曽・一磐「）
¢・乙
2蕨σ
一斗扉争・）
一・・ 阯﨟f薯・・）
一論（脚一卿の ’
o
ψ・3加（ど・・“要＋の
翠贋（聯α＋鵜）
跳’
．／1．＿静
． ，巧 ．＿．
／ 1 ε
垂
ノ
α
／
∠．
円＿＿＿⊥＿
②脚αrα催刀αv
をぎα・一’一集一・
伽1寄
②
③仰。妬ル昭M
の
⑦飛び棚上π班
∠／十一
∠樗乙・・瞬・一聯・）
・々・晦・…餌・ノ〃・）｝
θ
③
Fig．18。 Equilibrium equations on the plane D－E．
げ吋存
o ／
／
〆
｛
、ε
あη一1々
一 『一一rこ 一 、、 、
，、れ ／紀oo
，，σそ1て七
⑦贈
毒
ハ，．＿」＿
θ
舶9擁w殉〃
2．
9目．
oω
H
匹
虫
の
三
塁
o
oQO
同
⑦
③争（1・々2ル・
〃炉r／舜
Fig．1g。 Equilibr五um equations on the plane E－G．
On the Metal Cutting Mechanism with the Built-up Edge 263
B
z-(f-tda-i{.) +tati-t-:;}--tan-'le
-f+2fun"e-tati'k+a
@
-.tL-.-
t/lt
t
N
D /1
/
EN N s
'/=---h
-"
)`
C
- l--
-o.tx
f-tai'-{l--a
Lvfbii-Iil-ii
Z
(D roRCE rmGIV/IZIff
ufi-M- !iFi7
tan-' Z' -tan-ik'x
= (of+if) (L'+u2(1+fe')+2u･L,l71irJ5i'sin(2tan-'{I--ion-'le+a))
@ Ft]fi)CE DIMErC77(VV
g-taoJ'{-a-sin"tu/7-IiJeE-eas(2,tan-i{-tan-'fe+a)
lf+u'(1+k)+2･u･Lpm sin(2tan-'{;'-tan-tle+a)
Fig. 20. Resultant equilibrium equations on
the plane D-E and E-G.
d. (Computation of the force equilibrium) The derived equation contained
in its variables, the cutting geometries ¢, u, L, 7; ¢, the cutting parameterscr, ti and the stress ratios si, s2, and s3. The first seven variables were given
their values from experimental data, and the unknown stress ratios were de-
termined by a digital computer in such a way that the equilibrium equation
was satisfied at the best. The computation flow diagram is shown in Fig. 21,
and the computed values are presented in Table 4 and Table 5.
264 Koichi HOSHI and Tetsititaro HosHI
SMRT
1
f?El`ID 101
1'D. A, Tl, tc', u,
L, P. T
,[T?OM
P.4 ID, ALE, O /)ttLSE
WRITE20tirRUE
54EAtD0FRUAX
urR/IE201
ID,A,Tl,K,U,L,P,T
SIOP
,E?I=3.141592,K-k'/U,U--U/11,L=L/TlT=T/Tl,P=PNPV180.,A=AxPf/180.
va(RfrE202
K,U,l,
T
WRffE203
fABLEHbtlD/AtG
WM-0･,XIL4=O･,YIVI==0･,BXJf=O･,CM==O･,VMi=0･,VM2=0･,VM3=0･,RFM=0.Anv=0･,MFIVI=O･,Ma==0
Fig. 21. Computer bloc!< diagram
(continued)
On the Metal Ctitting Mechanism with the Built-up Edge
rr-----------------l1 Sl(2)=0.5+FLOATCJ'1-2)X,491
J
.t1
l-....--.--.---.m --..･DO 33
l
I S2(2)=a5+fltnTCJ2-2)X,49l Dl==0.15,D2==O,15,fbf?==o'･1 IQ=0, Ml=e, M2==O1
1
l
I
l I I I ' ' ' ' 1 I l 1 1 t l l l l l l I 1 1 ' 1 f I t I l l l l 1 1 1 ' 1 1 1 t l l , l 1 1FROMR3
DO33J1==1,3
fQ==va+1
DO 13J-- 1,3
-----":,.tib--ti
S1(J') = S1(2) + FZ(Z,1T(J'-2)X- D1
S2(J)=S2(2)+FZaAT(.J-2)xD2 e-----------
DD==le.xx3a
-- v--
l---m---ti---
DO20ll==1,3
DO20･f2=1,3
-1 I ' l 1 J l ' l--J
r--'-l
1
11
l l l l 1 1 1 1 I l l II
l l I l l l l l 1
A3
W=Sl(Jl), X=S2(l2),l
Y=1.-(W+V)x-2
F)t?0M
R3
,c )t?0M
(W !I O.)
OR (X ;!i D
y== sQl?T(r)
n- ,
oR(･vv>1,)qR(.rso-)/.)OR(YS0.)OR(Y->1･)
FAsEr
Tf?UE
'
(r),B=ATAIV(vaX)
Zl==,l2==,F2=.,F3=iElxx2+50.xE2xx2+2.-IC3xN2
52
'
(continued)
265
266 Koichi HosHI and Tetsutaro HOsHl
R2t
lllIll
･l
IlllIIlIll1Ill:;IllllllllllllJ
R2 2
t)I
,
lDIS;eDD TRUE
i EALSE
DD=DIS,V(1)==Fl,
Ml=ll,M2=l2,V(2)=iE2, V(3')==F3
lL-.--..-..
----- 2e
R2t
MM=MlXM2, SlC2)=S1(Ml), S2(2)=S2(M2),
IQ > 30 netLE
yci`ILSE
7]t?UE .MM-# 4'
,04LSE ,ma =ll)R +i
1or? }t･2
MLSE.
7)fVE
Dl=:Dl15', D2rhD2!51
32
Mt =Sl(2), )C==S2(2>, Y =SaRT(1,-(ldfjLX)xx2)B ==A])4N(W)X18a,/PI, C ==Al>4N(SeRr(1./rxx2-D)x.90.!Rr
RF=:SQRT(･･･,),,AF=: ,M,['==
v}eerre 2os
-Y; ,Y; K B, C,
(VaJll,J=1.oj,
RE AE MF;Ja
W/S,f= ww+;4t,- XM=:XM+X, W=:YM+Y, ･BM=BM+BCILf = CM +'C, uaX= vei'+ V-(l), ww2 =L,7Lf2+ V(2)l,7Ld3 === ua3 + V(3), Rnv == Rnv +RF, ,tlnv ==Aev +v4F
Mev ==Mev+MF, MO '= MQ+1
L-...--..-..----. -------
(II)
(continued)
On the Metal Cutting Mechanism with the Built-up Edge 267
Rl1
TRUE Me=o/[/ALSE
TP=Ma,,WM=ldtMITP,.¥M=XMIrP,YM=YMITP'
BM==BM/TP,CM==CtL7/TP,VMI==VMi/TP,'
VM2-VM2/rP.XiM3=VM3/TP,RFM=Rev/TPAnv=Atwlrp,Mev-=Mew!rp
rvRIrE2os,205
Ma
Mrvf,XM,/M,eM,cM,YMi,VM2,VM3.RFM,AFM,MFM,
'
RFM-RFM-VMI/2.AFM=SiN(AFMXPI/18a.)-VM2･!2.
AFM==180･/PlxAIA/VCSQRT(AFM･*,･･x-･2/(1-AFMx,･ti･2)))
MFM=MFM-VILd'3/2.
WRfTE207
RFM,AFM,'
MFM
268 Koichi HosHi and Tetsutaro HosHI
TABLE 4. Computed values of cutting force,
of force and momentum by change speed w.
direction
m cuttmg
Test
No.
(1)
(4)
(2)
(3)
(16)
(10)
(7)
(5)
.( 6)
(11)
(13)
(8)
(9)
(12)
(14)
(15)
(I7)
(18)
(20)
(19)
(21)
(22)
(23)
deg
B=tanmiLt af
5.33
16.83
23.02
23.51
15,82
21.06
20.05
20.55
15.29
24.94
26.56
26.79
22.05
30.54
27.25
10,39
4.00
18.09
21.30
17.57
22,62
16.64
deg
C=di,
29.86
29.73
33.48
34.24
31A5
32,76
32.43
32.09
32.76
34,24
35.05
35,05
34,24
36.91
35.93
31,45
33.73
32.76
36.91
33,48
38.03
38.03
Rtl Tf
3.702
2.728
2,309
2,232
2.969
2.491
2,598
2,804
2.394
2.139
1:979
2,059
2.041
1.587
1,852
3,305
2.828
3.024
2,289
3,138
2.206
2.523
deg Direction ofResultant Cutting Force
24,66
17.02
20.65
24.38
24,68
22.52
20,41
22,49
23,72
21,27
22,54
23.67
25,71
21.76
26.13
28,64
37,67
29,75
43,92
35,91
38.65
48,06
Mti Tf
6.628
2,998
2.423
2,389
3.858
2.682
3,023
3.376
2.707
2.084
1.887
2.024
2.037
1.365
1.776
4.766
3,702
3.610
2.519
3,140
2.164
1.987
4.3. Result of simulation.
For various cutting speeds and tool rake angles, the simulation presented
the stress ratio si=af!Tf: the normal to shear stress ratio which most probably
existed on the built-up edge boundary, and that on the start boundary of the
primary flow. Also the magnitude of the resultant cutting force, its direction
and the resultant momentum of the cutting force were predicted.
On the Metal Cutting Mechanism.with the
TABLE 5. Computed values of cutting t: , .. offorceandmomentumby ･ rakeanglecr. '
Built-up Edge
force, direction ,change in tool
269
Test
No.
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
(33)
(34)
(35)
(36)
(37)
(38)
(39)
(40)
(41)
(42)
(43)
(44)
deg
a
11,O
5.8
5,8
o
o
4,2
4.2
9.0
9.0
9.0
14,2
14.2
24.2
24.2
29.2
29.2
34.2
34.2
34.2
39.2
44.4
deg
B=tan-i-!l!tL
Tf
11.86
12:95
4.95
11.86
22.94
23.11
21.47
'18.09
17.22
27,02
15.64
12.77
14.39
11.13
13.31
17.37
19,79
4.38
20.30
21,06
deg
C= ip,
32.76
32,76
32.76
35,64
31.45
33.73
12.31
35.05
36,05
38,03
35,05
38,03
36,91
36,91
35.93
36,91
36.91
35.93
38.03
38.03
Rt! Tf
3.961
3.282
4.684
2,609
4.534
2.833
3.331
2.548
2.305
1.853
2,337
2,226
2.183
1873
2.050
1.515
1.465
1.975
1,641
1,481
deg Direction ofResultant Cutting Force
24.67
25.82
31.01
34,46
22.03
26.13
25.31
29,38
34,Ol
27,98
26,94
36,15
30.61
30.46
25.65
25.25
23.02
28.36
22.77
20.09
MtiTf
10.23
6.762
15.66
4,529
8.778
4.241
5.300
3,728
3.241
2.100
3,126
2.386
2.496
1,666
2.000
1.056
1.017
1.668
1,153
O.9249
The contact length between the built-up edge and the chip, in particular,
was found to corelate well with the resultant force magnitude, as shown in
Fig. 22, irrespective of the cutting speed and' the tool rake angle. This pre-
diction agrees with the well-known fact that the cutting force reduces with
the built-up edge, so that this fact ls possibly attributed to the reduced contact
length, instead of the increased effective rake angle as was formerly conceived.
270
6
KQichi HosHI and Tetsutaro HosHI
s}･J.
"x4eq
va
NEEI
s}28{g¥
o
.
7ZIS]IS AT uaR/Ous CUTIVAtG SAEEI)S wrJ7f I9'2e fl4zz 100L
7ES7:S wr11ef l4Al2tOus 70c2L E)4KE A/VeLE Ar 11 Mev SAEED
oo
o oo
JOI-O
ooo
ot
se
.
.
o
eeo o o
. o-ee
el.
oe o
o
.
l'-e.
.
.
B(nF-at7VPCewIJ4CTLE7VG71U/DEF)7ffCIFCUr t,/.E
Fig. 22. Predicted corelation of built-up edge-chip contact
length L to resultant cutting force R. (Result of
computer simulation)
References
1) W. Rosenhain and A. C, Sturney: Flow and Rupture of Metals during Cutting,
Proc, I.M.E. 1, 1925.
2) Diggs and Herbert: Proc. I.M.E, 1928.
3> H. Ernst and M. Martelotti: Die Bildung und Wirkung der "Aufbauschneide",
Werkzeugmaschine, Heft 18, 1936.
4) V. D. Prianishnilcoff: Am. Machinist, 180, 1936.
5) Rikichi Muranal<a: Research paper of Toyama University.
6) M. E Merchant: Tool Engineers Handbook, A.S.T.E,, 1949.
7) Koichi Hoshi: On the Built-up Edge and Counter-plot for it, J,S,M.E., Abst. 1937.
8) Koichi Hoshi: On the Characteristics in the Cutting Action of Steel and Cast Iron,
J,S,M.E., 1938.
Nomenclatures
(Cutting conditions)
cr : rake angle oi orthogonal cutting tool, deg
w : cutting speed, mpm (meters per minute)
ti : depth of cut in orthogonal cutting, mm
Hv: micro-Vickershardnessnumber
(Metal cutting geometries, refering to Fig. 6)
On the Metal Cutting Mechanism with the Built-up Edge 271
ze :
L:
¢:
gb :
h: T: t2 :
(Stress
Ts :
os :
Tf :
of :
thickness of built-up edge measured in the cutting direction at point
D, mrn contact length between built-up edge and chip measured parallel to
tool rake face, mm
angle of the start boundary of primary plastic flow to the cutting
direction, deg
over-cut depth, mm
depth of deformed layer, mm distance between point H and G, mm
chip thickness, mm
assumptions, refering to Fig. 13)
shear stress on the start boundary of primary flow
normal stress to the start boundary of primary flow
shear stress on the built-up edge boundary
normal stress to the built-up edge boundary
sl=of1Tf
s2=:as1Tf
s3=Tskf
//
/.t