Analytical Prediction of Flank Wear of Carbide Tools in Turning Plain Carbon Steels (Part 1)

1. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/286911371
Analytical prediction of flank wear of carbide
tools in turning plain carbon steels (part 1) -
characteristics equation of flank wear
Article in Bulletin of the Japan Society of Precision Engineering · December 1988
CITATIONS
24
READS
28
4 authors, including:
Katsuhiro Maekawa
Ibaraki University
133 PUBLICATIONS 1,041 CITATIONS
SEE PROFILE
Available from: Katsuhiro Maekawa
Retrieved on: 14 October 2016

2. 8ull. Japan Soc. of Prec. Engg., Vol, 22, No. 4 (Dec. 1988)
r, Received 29th August, 1986 in Japanese
and 21st December, 1987 in English
** Faculty of Engineering, Kitani
Institute of Technology: 165 Koen-cho'
Kitani 090
*** Faculty of Engineering, Tokyo Inst!-
tute of Technology; 2-12-1 Ohokayana'
Meguro-ku, TokYo 152
Analytical Prediction of Flank Wear of Carbide Tools
in Turning Plain Carbon Steels (Part 1)x
- Characteristic Equation of FIank Wear
-
Takeaki KITAGAWAi' Katsuhiro MAEKAWA,'-
Takahiro SHIRAKASHI *i'* and Eiji USUI
t**
Flank wear characteristics of tungsten carbide tools in turning
plain carbon steels lrithout a built-up edge have been investigated by
neasuring temperature, norEal stress and vear rate on the flank wear
land. The crater wear characteristic equation which was derived fron an
adhesive wear model is able to describe the flank near as well'
Horever, the characteristic equation for flank wear consists of two
characteristic lines with different gradient which intersect at the
critical tempelature of around 1,150 K. Both lines are affected by
abrasives in the steels. This abrasion effect could be taken into
account by changing the constants involved in the wear characteristic
equation. On the other hand, an abrasive type wear equation could be
dirived so as to have the same expression as our wear equation'
Observation of the vear particles by Uehara et al'' honeve!' appears to
exclude the possibitity of this wear model.
Key words: cutting tool life, flank lrear, itear Eechanism' wear
characteristic equation, lrear test' abrasion
1. t ntrod uction
The vear nechanism of tungsten
carbide tools is dorninated by adheslon
and/or abrasion in continuous rnachining of
plain carbon steels vithout a built-up
"ag".
It is exPected, howeve!, that
adhesive ltear plays an important role
whereas abrasion by hard particles in
sceels, such as carbides and oxides like
SiOz or AlzOa, plays an auxiliary role'
Because of extreoely high pressure and
temDeratule on the tool/chiP contact
f""el) nutual diffusion of constitutive
atoms could easily occur at the interface
under practical cutting conditions '
Fioru this Point of view, discussions
of the crater vear have been made through
an adhesive wear nodeI, so ihat a wear
characteristic equation vhich invo lves
only two constants to be det,einined by
.*plri.ent has been proposedl' In this
pup"t
""
focus ort the flank vear in vhich
the temperature is experienced to be lower
than that of cratel wear, and investigate
the wear characteristics.
2. Discussion of Flank wear Mechanism
Fig. 1 dePicts the crater vear
characteristics of tungsten carbide tools
in nachining plain carbon steels, vhich
have already been rePorted in Reference
(l). The straight line in the figure is
vrlE[en as
dIl (1)
ヽ
１
／
■
ｏｔ
一
／
′
︲
ヽ
、=CexP
having been used for the analytical
orediJrion ot crater wear3) Here W is the
wear .roluoe per unit area of the worn
surafce, L the ltear distance, ot the
normal sttess on the worn surface, 0t the
absolute temPerature' and C and I are
characteristic constants dePending on the
combination of the tool aod uork
rnaterials. Eq. (1) well describes the
experimental results in the higher
temperature range, but is not conPatible
enough with those in the lor.'er temperature
range. The higher teoPerature range or
Fig. 1 contains nost of the clate! wear
reiults under plactical cutting conditions
of carbon steel s L'ith tungsten carblde
too1s. On the contrary, flank teoperature
is lower thao that on the rake face' This
oakes iE impossible to emPloy Eq' (1) for
the prediction of flank wear. Furthernore
the experirnenlaL points are not scaLtered
around the straight line, but the higher
the percentage of carbon content is, the
more the points are deviated froo the
1ine. Note that experiEental erlors are

3. work mate rial
a O.46ZC, tempered
o o.35Zc, lempe red
o O.25ZC, tcmpe red
o 0. 15ZC, lempe red
o 0.152C, annea 1ed
Too 1; carbide P20
(0,var,6,6, 15, 15,0.5)
Depth of cut i 2 o).n
-
Cutting fluid; dry
Takpaki KITACAWA, Katsuhrro MAEKAwA, Takahiro SHIRAKASHI and Eijt USUI
'10
e
1.0
0. 01
I /At K-r
Fig.l Crater wear characteristic of
carbide P20 for different plain
catbon steels.
exaggerated in the lower temperature range
because of using a logarithnic scale for
the ordinate.
Eq. (1) was based on an adhesive wea!
modelJ) On the other hand, it has been
pointed out that abrasive wear by hard
particl.es dispersed in carbon steels are
rnoie dorninant in the lower temperature
range?) This inplies that abrasive vear
might cause the- disagreemeot nentioned
above. As a matter of fact according to
Rabinowiczf) a characteristic equation of
abrasive wear is given by
dtir = K
j! dL e)Hr
where K is a constant depending on the
shape and size of abr:asive particles and
Hr is the hardness of a harder material
(i.e. a cuting tool). Then introducing the
same tempelatute effects as those in
Reference (1):
/Az / Bz
H'=A1 exp ( . J,K =Brexp[-
" J (3)
"t/ "t/
into Eq. (2), r.re obtain
being a sioilar expression to Eq. (1).
conbining Eq. (1) vith Eq. (4), the total
lrear rate may be given by
og dL
If the constants in the right-hand terBs
have different specific values, Eq. (5)
could describe the wear characteristics
Iike Fig. 6 which have a folded charac-
teristic 1ine.
However this idea is excluded by
observation of lrear particles. It is
vell-knorn'n that since stress states on the
rake face are very sevele1) nominal contact
area is nearly equal to the real one, and
developed plastic deforrnation like viscous
flow takes place ln the contact layers
owing to thermal softening, Under these
circuEstances, if abrasive wear is
predoEinant, wear particles caused by hard
particles on the chip surface scratching a
neakened diffused layer on the rake face
must be identified. According ro the
experinent by Uehara et al!) however, no
such large wear debris is discovered,
neither in flank vear nor in crater vear,
but only tiny r.'ear particles of 0.1.!1 uE
are observed.
Hence if abrasion doDinates the near
in the lower ternperature range of Fig. I
which is described by a sinilar wear
characteristic equation to Eq. (l), it is
a matter of discussion hov to exDlain the
difference in the constants of Eq. (l)
from those in the higher tenpeiature
range. Moreover consideration should be
given to the contribution of abrasive wear
to Eq. (1) because meaningfully different
qtear rates can be seen not onlv in the
louer temperature range but also in the
higher te&peraLure range, when compared
wrLh the cases beLween nore hard second
phase inclusions (0.462C steel) and less
inclusions (0.l5Zc steel). The first
question rf ill be answered in Section 3
fron the viewpoint of different Detallog-
raphy of diffused layers on the worn
surface in the lower and highe!
teDPerature ranges, respectively. The
second problen will experinentally be
investigated in Section 4 so that the
effect of abrasive wear appeats both in
the higher and lower temperature ranges,
resulting in the change of the
characteristic constants of Eq. (1).
3. Experimental Investigation of Flank
Wear C ha racteristics
It is foreseen fron the discussion so
that the wear characteristic equation
holds for flank wear as welI, but the
ヽ
、
′
′
Ｐ
一
鈍
′
↑
ヽ
ＰＸ＋
ヽ
、
１
ノ
上
ｏｔ
た
ヽｐＸｅＣ〓
〒
Ｚ
Σ
”
日
︵口
０
一
じ
︶
ヽ
〓
０
ヽ
、
′
／
だ
一
〇ｔ
一
／
１
ヽ
dW'
ｒ
ヽ
ノ
ａ
´︱
os dL
= Cr exp

4. ヽ
Z C Si Mn P S Cu Ni Cr Al
0.46ZC steel 0.46 0.23 0,72 0.026 0.016 0.01 0.01 0.01 0.020
0.47ZC steel 0.4フ 0.21 0。 フ4 0.022 0.017 0.01 0.02 0.10 0.025
0.25%C steel 0.25 0.24 0.51 0.020 0.022 0.01 0.03 0.02 0.020
Analytical Prediction of Flank Wear of Carbide Tools
in Turning Plain Carbon Steels (Part 1)
Table 1 chenical conposition of work oaterials.
appropriateness is to be experinentally
exaoined. 411 the experiments were
perforEed in senri-orthogonal turning of an
outer surface of plain carbon steeLs
(Ol50",2OO x 300 nn) with a carbide P20
grade cutting tool. Table 1 shows chemical
composition of the steels to be cut. The
tool geonetry was set in (0,0'6,6'
15,15,0.5), tool shank dimensions 30x30
om and its overhang 30 nn, which allosed a
stable cutting state vithout tool
v ibra t ion.
A special tool was used fo! oeasuring
flank tenperature. The tool consists of
tlro carbide tip Parts' between then is
held a Pt-wire (010 um) which is wrapped
vith a quartz glass tube (050 um) for
insulation. Fig. 2 shows the construction
and principle of the measurement. As soon
as t;rning begins a thermocouPle is formed
between the Pt-wire and sork nacerial'
Changing the exit position of the nire, it
is possible to measure the temPerature
anylrhere on the flank weal land. A worn
tool
"ith
artificial wear land initially
ground to -0.5 deg at the side clearaoce
iaae "as
used for the neasurement after
being pre-oachined enough to develop flank
r4'ear: Fig. 3 shovs the distribution of
flank temperature obtained by the use of
︾
Ｊ
︼
づ
一
。
●
。
。
日
ｏ
■
1200
1150
1100
1050
1000
950
0 0.5 1.0 1.5 2.O
Distance ,-s, ,-f , lc nm
Fig.3 Temperature dist!ibution on' tool
f ace.
Work; 0.462C stee1, Tool; carbide
P2O (0,0,6,6,15,15'0.5)
'
cutting
speed; I .67 a/s, Feed; 0.26 nm/rev,
Depth of cut; 2 mm, Cutting fluid;
dry.
︾
Ч
ｏ
０
，
っ
０
０
︼
①
Ｏ
Ｆ
Ｏ
い
Iflsulating material
Fig.2 Set-up for measur ing
flank vear 1and.
0246
cutting sPeed V n/s
Fig.4 Relation betr^teen temperature
center of flank weai and
speed.
Cutting conditions are the
those in Pig- 3.
8
at the
cutt rng
sane as
_::二 :Hpt:::l'vI[::メηh, 1[[￨:4mlm
a-Worn tool' I's=2.2 uun, t"=1 '4 nuu
Vg; width of flank wear land_-.9!{
鷺:]E:釜 pby_
thernocouple
:'CCき (♂
vr=: , ii"nt wear land
carbidc riP
Se tp late
Insu Lat ing
Iflsulating
os‐ Cs‐
0 -10° 15°
② 0 5
0 0 15
● 0 25
o 10 15
0 46スC
a O.46Zc ste€ I f=0.2
nn/:ev
O 0.252c s teel f=0.2
f; feed
os; side rake angle
Cs; side cut t ing edge
anSle
VB; sidlh of flank lrear
land (=0.6 mo)
telnperature on

5. 266 Takeaki KITAGAWA, Katsuhiro MAEKAWA, Takahiro SHIRAKASHI and Eiii USUI
the special tool. For compa!ison,
tenperature on the rake face of a sharp
tool is also shown. The attached figure
tells the difference among the individual
distribution curves. For the eidth of
flank wear land VB=0.4 @, the flank
tenperature 06 is found to be unifornly
distribured over the wear land. A similai
distribution vas obtained for changing Vg,
cutting speed and feed. Since 0g i;
regarded as a uniforql distribution, we
represent ef neasured at the center of the
wear land as the flank temperature. Fig. 4
shons how this Bf is affected by changing
work marerial and cutting conditions,
In terms of nornal stress on the
flank rdear 1and, it was difficult
precisely to measure the distribution in
the direction of the irear rridth by using a
divided tool6) because of the narrow width
of less than 0.6 nm. Accordinq to
preliminary rests and an analyiical
result ]) however, the oornal stress i.s
considered almost to be uniformly
distributed in the direction of the weai
vidth except in the vicinity of the
cutting edge. Hence assumiog the uniforn
distribution in rhe dilection of the
cutting edge as vel1, we measured the nean
stress by means of conparing cutting
forces between a sharp tool and a worn
tool having a!tificial wear on the
clearance facel) fig. 5 shows the effects
of cutting speed, feed and Lridth of wear
land on the mean normal stress 6-r. lt isfound from the figure that -5 d'ecreases
with increasing these paranerers. The
ざ
1
0.1 0.15 0.2 0.26
Feed f mn/rev
Fig.5 (b) Influence of feed.
滞錯垂鎌誓琲憮手
pf;宅
Ivalue is Only 1/5∼ 1/6 of the shear stress
::lili:il]:lilil::型 iI[lili:::i:ll;
area I:; ι[11lcli:[edr];e dw/dL per unit
#=十 静 ⑥
[1:reclttilgth[if』iaril:e f]ξle fFtt Tw::
”
“
目
∽
∽
０
ヽ
０
∽
”
自
ぽ
∽
∽日
あ
I 1.5 2 3 4
Cutting speed V m/s
(a) Influence of curting speed.
Fig.5 Experimental result of nean nornal
stress on flank wear land.
Cutting conditions are the same as
those in Fig. 3.
琴憂]菱
8::: い ＼● 0.8
0 1.0
0 46ZC steel
Cut ting speed;3.33 m/s
0 0.4 1… ミ」子、
0 0.6 1 ヽ ^｀く0、
:乳 :0●
6疑面
・
N=Feed; 0.2 rm/rev | ―-0-- 0.25%C steel
VB=0.6 1mll

6. Work material Feed
o0 46π C ―- 0 26 mm/rcv
o0 46%C ―- 0 2
o0 25ZC ―- 0 2
Tool, Carbidc P20
(0,0,6,6,15,15,0 5)
Depth Of cut, 2 mm
wiath of wcar land;
VB‐ 0 6 Fun
cutting Fluid, d
“
ω磁 品亜:
fi17-ひヾ●_ピ噂里
ヽ
ヽ
An6lytical Prediction of Flank Wear of Carbide Tools
in Turning Plain Carbon Steels (Part l)
，
Ｚ
目
Ｎ 日
︵口
●
Ч
Ｏ
︶
ヽ
〓
０
つ
０
１
１。
●
０
．
［，
Ｚ
，
Ｎ
ε
︵い
０
口
ｏ
︶
ヽ
〓
も
7.0 8.0 9.0
t /ot K
10.0 '10-q
(a) Conparison vith crater lrear.
by the same characteristics as crate!
wear, if the flank temPeratule goes uP !o
the higher teEperature range in case of
high speed Eachining. As to crater wear ln
which the experimental points doninate the
higher tenperature lange, the situation is
vice ve r sa.
In addition to the observation that a
wear chaiacteristic equation fike Eq. (1)
can be applied to the lower temperatule
range, it is further found from Fig. 6 (a)
tbat there seems to exist a significant
difference in flank wear !ates between the
trro sorts of the steels, because more
accurate experiments can be performed at
the lorrer temperature range as can be seen
in Fig. 6 (b). This Point will be
discussed in Section 4. Froro the viewpoint
of wear analysis or tool life prediction,
such a difference in the wear rates does
not introduce large errors in prediction
if a wear equation correspondent to the
broken line of Fig. 6 (a) is enployed'
This will be a subject of Pat 2.
It was pointed out in Section 2 that
the characteristic line in the louer
tenperature range of Fig. 6 was not caused
by abrasive wear, which is based on the
observation of vear particles:) Next the
explanation should be given to the
question why the gradient of the line is
different from that in the higher
tempeiature range, According to a static
diffusion experinent for the coulbination
between catbon steels and tungsten
carbides by Narutaki and Yanane f) not only
WC gtains disappear but also a fragile
Fe-l.l-Co carbide cornpund starts to form at
temperatures above 1,200 K. Moreover rhe
less carbon is contained in steels and
also the higher the temperature is, the
more cooplex conpound is produced. One of
the authorsr0) has perforned a sirnilar
diffusion experiment for: the cornbination
ot 0.467,C steel and a carbide P20 which
were used in the machining experiment,
confir(0ing Lhat the temPeratures at lthich
the comPlex compound apPeared were more
than 1.120.'. I,i7O K (1/O =8.59 xl0-a
1/K), This ternperature corresponds to the
critical temperature at which the two
characteristic lines intersect in Fig' 6'
though the agreenent is good -beyond
expectation since the concentratlon ot
diffused atoms and the vacancy density in
the actual chip are different from those
in the static diffusion exPeriment' Hence
such a different state of the diffused
layers between loter and higher
temperature ranges in Fig. 6 seems to
explain the difference in the wear
characteristic constants of Eq. (1).
4. contribution of Abrasive wear
0.02
7.0
t /€t K
(b) lnfluence of cutting speed V, feed
f, side rake angle crs, side cutting
edge angle Cs and width of flank
wear land VB.
Fig.6 Flank wear characteristic of carbide
P20 when cutting Plain carbon
steels.
mechanism: even the flank uear in vhich
the experioental points mainly occuPy the
lowe! teoPeratule range can be described
work nalerial; 0.462C sleel
O V=3. 33 m/s , f=0 2 nur/rev
'
os= 0 rad , Cs=0.262 rad,
vB=O.2 - 0.8 nm
a V=3.33 n/s, vB-o.6 nm,
0s= O rad , Cs=0.262 rad ,
f=0. I - 0. 26 il.n/rcv
AvB=0.6 nllll, f =0.2 nm/rev,
0s= 0 r:td, Cs=O.262 r3d,
V-].67 - 4.17 m/s
O v=2.5 n/s' f=0.2 nm/rcv
'
vB=O.6 ffr ,
os= -0.175 - 0 rad
'Cs‐ 0 087 - 0 436 rad

7. 258 Takeaki KITAGAWA, Katsuhiro MAEKAWA, Takahiro SHIRAKASHI and Eiii USUI
It may be concluded fron above
discussion that an adhesive vear mechanism
is still dominant over flank wear. Then
the effect of abrasive particles on the
wear characteristic equation (1) should
experimentally be examined. Since it is
difficult to mix and melt plenty of A12O:
particles in a steel natrix lrithout
changing its property, the following
technique was eutployed for conveniencers
sake: a unique V-shaped groove, the
surface width of which was 5 rDm, was
machined in the direction of the center
axis of a O.47ZC steel bar ({200 uun) as
shown in Fig. 7. lte groove was next
filled wfuh a mixture of bond containins
plastic glue (202), iron povder (802) anJ
AlzO3 powder ('l ,000 vt.ppn for the whole
steel !od) as an abrasive. We used tvo
kinds of parricle size of AlzOt with
diaEeter of 105., 149 pn and 53 tu74 ]ln, The
compressive fracture strength of the
mixture after solidificarion was lOO., 120
MPa. When turning an outer surface of this
steel bar, plenty of A1203 par:ticles in
the groove instantaDeously, once per
rotation, sciatch the diffused layer on
the worn surface which has been fonned
during cutting of the other steel natrix
part. Since the cutting distance on the
groove is 1/126 of the periphery of the
bar, the flank tenperature haidly drops
during cutting of the gr:oove part which
does not contain the mixturelD The
pressure on the flank wear land Eay be
mole or less decreased. A large drop
probably does not take place because the
state of contact betqeen the wear land and
rnachined surface is elastic as qras sho$n
in Reference (7). ttrese facts may allow us
to use the temperature and notBal stress
during cutting of the steel natrix part
for the discussi.on of the
""",characteristics.
In the case of tur:ning the steel lrith
a groove, it was inevitable that chipping
of the cutting edge occurred durins
cutting Lhe groove. part. As a result. the
flank wear rate rdas meaningfully different
between cutting the plain steel bar and
cutting the steel with a groove filled
only with the nixture of steel powder and
bond plastics. Therefore we evaluated the
diffeience in the wear rate between
turning the steel containing only steel
powder and bond plastics and turning that
added A1203, and then superinposed it on
fne uear rate in continuous turning of the
bar without a groove. Fig. g is the result
snowrng rhe effect of the abrasive
particles on the wear characteristic
diagran.'t The char:acte!istic lines are
translated paral1el to the axes bv the
addition of rhe hard particles. Ttris
Fig.7 Set-up for abrasion vear resE.
'10-e
1.0
０
→
ｚ日
ヽＥ
︵●
●
Ч
Ｏ
︶
ヽ
〓
一
0.01
8.0 9.0 10.0
1/Of K・
Fig.8 wear characterist■ c curve
effect of abrasion wear due
particles.
Work, 0.47ZC steel, Too l,
P20 (-5,-6,5,6,15,15,0.4),
cut, 2 mll, Feed: 0.2 mln/rev,
fluid; dry.
11 .0 'l o-r
showing
to A1203
carbide
Depth of
Cutting
,r T'he carbide tool used in the exDerinent
of Fig. 8 is a p20 grade produced bv a
Eool nanufacturer. As the chemical
composition of p20 had been alteled, the
old one used in Figs. I and 6 was not
obtainable. This is the reason why the
position of the characteristic linenithout Al zOr in Fig. g does not
coincide wirh that in Figs. 1 and 6.
Binding agent
Steel powder
AI20 3 Ponder
o WithOut A1203
0 A1203
105ヽ 149口 n,1000
0 A1203 Vt・ ppn
53∼ 7411m,1000 wt ppn
Width of flank vear
land; 0.6
V・ 3 33m/s
V=2.5 m/s
V‐ 1.25
ミ m/S

8. An6lytical Prediction of Flank Wear of Carbide Tools
in Tr-rrning Plain Carbon Steels (Psrt l)
suBgests that the abrasion effect could be
identified with the apparent difference in
the characteri.stic constants of Eq. (1).
As a eatter of fact, the difference in the
lower tenperatule lange of Fig.6 is so
sinilar to that of Fig. 8 rhar the
abrasion effect by hard palticles in
perlite should cause the di.fferent
characteristic constants. Note. that the
result of Fig. 8 is not direct
verification of the ablasion effect by
hard particles in the stee1, because A12O:
particles vele not uniforoly dispersed
over the steel rod but concentrated in a
groove with steel powder and bond
plastics.
5, conclusions
Flank rrear of tungsten carbide tools
in turning plain carbon steels at stable
cutting conditions I'ithout a built-up edge
has experiDentally been analysed and the
results obtained are as follovs:
(1) Flank lrear can be described by the
sat0e characteristic equation for crater
dt,l - / r
-=UexP{--}
ordl vtl
vhich is based on an adhesive wear model.
(2) Flank lrear consists of tuo
characteristic lines at the critical
telrperature of around ef'1'150 K despite
changing calbon content of lhe steels to
be cut, width of wear land and cutting
conditions. The folded characteristic line
is attributed to che fact that netallo-
graphic changes, such as genelation of
couplex carbide conpounds and disapPear-
ance of I,lC grains, take place in the tool
material at higher temperatures loore than
of=1 ,l50 K.
(3) Clater wear also obeys the same
characte!istic equation as that for flank
wear. The experiDental points for c!ater
wear usually 1ie on the line in the higher
teoperature range, whereas those for flank
wear are usually distributed around the
Iine in the lower tenperature lange.
(4) The effect of abrasive particles
dispersed in steels is correlated tith the
change in the constants of the sear
chalacteristic equation both in the higher
and lower tenperature ranges. The
influence is more ploninant in the lorter
tex0peratule range accompanied by a slight
difference in dw/ (ord],) depending on
changing carbon content of the steels to
be cut.
Acknow ledgements
T'tre authors vish to thank Messrs.
A.Kubo and Y.saeki, Kitani Institute of
Technology, for their dedicated assistance
to the experiruent. Thanks are also
extended to Sholra Denko Inc. for the
preparation of Alz0 r Powder.
References
l) T.Kitagawa, T.shirakashi and E.Usui:
J.JSPE, 42, 12 (1976) 1178. (in
J apanes e)
2) E.Usui, T,shirakashi and T.Kitagawa:
ibid., 43, 1O (1977) 1211 . (in
Japanese)
3) H. Takeyana and R.Murata: ibid., 27, 1
( 1961 ) 33. (in Japanese)
4) E.Rabinor,ricz, L.A.Dunn and P.G.Russel:
Wear, 4, ( 1961 ) 345.
5) K.Uehara, It.Takeshita, K.Nishina and
M.sakurai: Ploc. 2nd ICPE, TokYo
'(1976) 203.
6) S.Kato, K.Yauraguchi and M,Yanada:
J.JSME, 37, 298 (1971) 1228. (in
Japanes e)
7) E. Usui, T. Kit agawa
'
K,Maeka!'a,
T.Obikalta and T. Shirakashi: J.JSPE'
48, 9 (1982) 123'l ' (in JaPanese)
8) M,Okoshi and T.sata: ibid., 23, I
(1957) 404. (in Japanese)
9) N.Narutaki and Y'Yarnane: Proc. znd
ICPE, Tokyo, (1976) 190.
10) T.Kitagawa: Ph.D Thesis, Tokyo
Institute of Technology' (1978) 143.
(in Japanese)
11) T. Shirakashi, T.Ihara and E.Usui:
Proc, Annual Meetiog JsPE, SPring,
( 1986) 599. (in Japanese)