Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 3,
March 20
16, pp. 627 ~ 6
3
4
DOI: 10.115
9
1
/ijeecs.v1.i3.pp62
7-6
3
4
627
Re
cei
v
ed O
c
t
ober 6, 20
15;
Revi
se
d Feb
r
ua
ry 2
2
, 201
6; Acce
pted
February 29,
2016
Design Front Rake Angle of PDC Bit Based on Solid
Works Simulation Method
Xiaoming Ha
n*, Chenx
u
Luo, Xing
y
u
Han
Schoo
l of Mechan
ical a
nd Po
w
e
r Eng
i
ne
eri
n
g, Hena
n Pol
y
t
e
chn
i
c Univ
ersi
t
y
Jiaoz
uo 4
540
0
0
, Chin
a
e
-ma
i
l
:
ha
nx
mr@
1
26
.co
m
A
b
st
r
a
ct
In ord
e
r to
solv
e the
bit
front r
a
ke
an
gle
par
a
m
eter
se
lectio
n
pro
b
le
m of
un
der
different
co
al r
o
ck,
it is pro
pose
d
i
n
po
lycrystall
i
n
e
di
a
m
on
d co
mp
act no c
o
re
bit as the
rese
arch o
b
ject, a
n
d
estab
lish
ed
a
bi
t
compact tw
o-di
me
nsi
ona
l stre
ss mod
e
l
of cu
tting teeth. T
h
e res
u
lt sh
ow
s
that
the
front rake ang
le is
t
h
e
factor of c
u
ttin
g
force
a
n
d
the
dri
lli
ng
efficie
n
cy. Appl
ic
ati
on
of Sol
i
d
W
o
rks
si
mu
latio
n
c
a
r
r
ies
out th
e fi
ni
te
ele
m
ent simul
a
tion an
alysis r
e
spectiv
e
ly to different fr
ont rake an
gle of bi
t mode
l un
der
the cond
itio
ns of
soft rock a
n
d
hard
rock. F
o
r
m
th
e s
i
mul
a
ti
on r
e
sults
it ca
n b
e
c
oncl
u
d
e
d
that
un
der
th
e co
nditi
on
of
soft
rock a
n
d
har
d r
o
ck, the
opti
m
al fro
n
t rak
e
a
n
g
le
is
10°
a
nd
15° r
e
spectiv
e
l
y
. It is o
b
tain
ed
that th
e stre
ng
t
h
of the bit is larg
est and the l
i
fe is lon
gest on th
e best front rake ang
le of bit.
Ke
y
w
ords
: PDC
；；
；
no core b
i
t
f
inite ele
m
ent
optimal front
rake an
gle
1. Introduc
tion
For ga
s d
r
ain
age drilli
ng at
mine, the bits mo
stly use
Polycrystalli
n
e
Diamo
nd Compa
c
t
(PDC) a
s
the cutting teeth. Be
cause the PDC ha
s some advanta
ges, such a
s
hardn
ess an
d
abra
s
io
n re
si
stan
ce of dia
m
ond, structu
r
al str
ength a
nd impa
ct re
sistan
ce of ce
mented carbi
de
material
s. It also
ca
n d
r
ill
ing qui
ckly the coal
and
has th
e lo
ng
er life u
nde
r the lo
w d
r
ill
ing
pre
s
sure and
high drilli
ng speed. So, this kind of bits
is widely use
d
in coal mini
ng
and oil drillin
g
[1-2]. In the drilling process, Wang
et al
[3] inve
stigat
ed the
change of interacti
on bet
ween the
cutting teeth
and coal fo
r the PDC b
y
the fi
nite
element sim
u
lation meth
od, and got
th
e
relation
shi
p
b
e
twee
n the
workin
g a
ngl
e an
d b
r
o
k
e
n
coal vol
u
m
e
from
the
re
sults.
Li et
al
[4]
studie
d
the chang
e of cru
s
hin
g
wo
rk
ratio,
when im
posed stati
c
load an
d dyn
a
mic lo
ad at the
surfa
c
e
of co
al and in
sid
e
the drilling
h
o
le, re
spe
c
tively, and obta
i
ned the inte
raction a
nd th
e
differen
c
e
when
crushing
co
al in
divid
ually an
d jo
i
n
tly. Li et al
[5] investig
ate the
wo
rking
mech
ani
sm o
f
cutter edge
of PDC, and pointed
out
that with th
e cutting co
a
l
depth beco
m
e
bigge
r, the
drilling
sp
ee
d of bit in
creased.
Th
ro
ugh
d
r
illing experim
ents on
different coal
sampl
e
s, Zh
o
u
et al [6-8]
got the influe
nce
of
the cu
tting
param
eters and coal protodya
k
o
n
o
v
coeffici
ent on
the st
re
ss
of PDC,
and th
e influen
ce
of
teeth di
stribu
tion pa
ramet
e
r of
cutter a
n
d
cutter
size on the drilling
efficiency. However, t
he previous work focused
m
o
stly
on the study
of
mechani
sm when
PDC cutting
teeth
drilling coal rock, the
report
s on design of
front rake angl
e
is few. So, this pape
r e
s
ta
blish
ed statics model
of bi
t by the finite element sim
u
lation metho
d
,
and for the
bit of different front rake
angle,
inve
stigated the
cha
nge of st
ress-st
rain a
nd
displ
a
cement
under the co
ndition of soft coal ro
ck
an
d hard
coal rock to get the corre
s
po
ndi
ng
optimal front rake a
ngle.
2. Main Geometr
y
Param
e
ters of PDC
As a ki
nd of
whol
e bits, P
DC
bit is the
most
wi
dely u
s
ed
bit. It is mostly used i
n
the soft
coal
rock
and
ha
rd
co
al
ro
ck.
The
ap
pe
aran
ce
an
d
structu
r
e
of P
D
C a
r
e
sh
own in fig
u
re 1.
It is
mainly made
up of bit body, PDC, junk
sl
ot, r
adius
rete
ntion, and no
zzl
e and oth
e
r
com
pon
ents.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 3, March 20
16 : 627 – 634
628
1. PDC, 2. Radiu
s
retentio
n, 3. Nozzle, 4. Jun
k
slot, 5. bit body
Figure 1. Structure of PDC
bit
PDC bit
cutting teeth
in
sp
atial di
rectio
n
are d
e
termi
n
ed by
front
ra
ke
angl
e
α
, as
sembly
angle
γ
and
side rake an
gle
β
, as sh
o
w
n in figure 2. Where, fro
n
t rake a
ngle
α
refers
to the
angle bet
wee
n
cutting plan
e and the axis of
the cutte
r of PDC; Assembly an
gle
γ
refers
to the
angle bet
wee
n
the axis of the cutting te
et
h and the p
l
ane of the bit; Side rake a
ngle
β
refe
rs
to
the angle b
e
twee
n cutting plane a
n
d
bit radius plane [9].
The above t
h
ree a
ngle
s
are
determi
ned
b
y
the structu
r
e of the P
D
C bit. Th
e
a
s
sembly
angl
e
is d
e
termi
n
e
d
by the
cro
w
n
sha
pe an
d the radial a
r
ran
gement of th
e bit, and fro
n
t rake angle
α
and si
de rake a
ngle
β
are
determi
ned b
y
the desig
n
of workin
g angle of
cutti
ng tooth, esp
e
cially cl
osel
y related to t
he
rationality of desi
gn of the front ra
ke an
gle and the d
r
illing efficien
cy.
Figure 2. PDC bit dire
ction
of
spatial structure pa
ram
e
ters
Becau
s
e th
e
r
e is
a ce
rta
i
n thickne
ss
of cutting te
eth, whe
n
ro
tating in the
cutting
groove,
The
rear pa
rt
will
have fri
c
tion
and
we
ar
bet
wee
n
the
ri
n
g
g
r
oove
s
an
d form
ation,
and
affect me
cha
n
ical
drillin
g speed, b
e
cau
s
e the cutting
edge i
s
p
a
rtly con
c
e
n
trated
in the fro
n
t p
a
rt
of PDC.
In o
r
der to
avoid
the a
bove
situ
ation,
rotate
t
he PDC i
n
a
certai
n a
ngle
alon
g
with th
e
cente
r
line,
so the
sid
e
rake a
ngle
β
is introdu
ce
d. The fri
c
tio
n
and
we
ar
part of the
rear
sup
portin
g
p
a
rt of the cutting teeth bet
wee
n
the
rock an
d hole th
e ro
ck l
a
yer i
s
re
du
ced.
With
the front
ra
ke
angl
e in
crea
sing, th
e fri
c
tion a
nd
wea
r
part b
e
twe
e
n
the rock
and
hole
the
ro
ck
layer will b
e
avoided. Wh
at’s mo
re, the side
ra
ke
a
ngle affect
s shape of bit bl
ade, so it is o
ften
ignored in the
actual de
sig
n
, and assum
ed to be ze
ro.
3. Force An
a
l
y
s
is of Bit Cutting Te
eth
PDC bit
und
er
the drillin
g
pressu
re, and she
a
r
coal un
der th
e actio
n
of
torque.
Acco
rdi
ng to analysi
s
of the pro
c
e
ss of
cutting
coal a
nd ro
ck
whe
n
cutting teeth are un
de
r sta
t
ic
pre
s
sure, we
can o
b
tain the cal
c
ul
atin
g formula
of the interaction
force
F
1
bet
wee
n
the cutt
ing
teeth of bits and the co
al ro
ck [10]:
cos
)
cos(
cos
1
Cbh
F
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
De
sign F
r
ont
Ra
ke Angle o
f
PDC Bit Based on Solid
Wo
rks Sim
u
lation Method
(Xiaom
ing HAN)
629
Whe
r
e,
C
i
s
cohe
sion
of th
e coal
ro
ck;
b
is cutting tee
t
h diam
eter;
h
is footag
e d
e
p
th pe
r
turn of bit;
θ
is friction a
ngl
e;
ψ
is angle betwe
en coal
rock sh
ea
r pl
ane an
d bit cutting teeth feed
dire
ction;
is friction an
gle
insid
e
the co
al.
As can
be
se
en fro
m
Eq
(1
), F
1
is
∞
or negative whe
n
α≥π
/2-(
ψ
+
θ
+
), If the front rake
angle i
s
too l
a
rge, T
he
co
ntact a
r
ea
bet
wee
n
the
cutting teeth of P
DC
and th
e coal ro
ck b
e
co
me
large
r
, and fo
rmed
a stron
g
extrusi
on to
the coal,
co
a
l
is una
ble to
she
a
r failu
re
at this time, so
its main failu
re mode
s a
r
e
cru
s
hi
ng. Th
e
comp
re
ssiv
e
stren
g
th of coal ro
ck is m
u
ch l
a
rg
er th
an
that of shea
r stren
g
th, so
coal crushing
need mo
re bi
gger d
r
illin
g p
r
essu
re a
nd tange
ntial force,
and the effici
ency is ve
ry low. The
r
efo
r
e, t
he effective rang
e of front ra
ke
an
gle is 0
≤α
≤π
/2
-
(
ψ
+
θ
+
).
When PDC
cutting teeth is drilling the
coal rock, besides the cutting force
F
C
and the
drilling pressure
W
, it is al
so
subj
ect to
the re
actio
n
o
f
coal
F
1
, and
there
are al
so fra
c
tion
F
3
and
positive pressure
P
2
at the interface of PDC
cutting te
eth and coal. as sho
w
n in figure 3.
Figure 3. Cutting Teeth Stress Analysi
s
Frictio
n
coefficient b
e
twe
e
n
co
al ro
ck a
nd wear
su
rface i
s
μ
,
so
F
3
=
μ
P
2
.
A
cco
rding t
o
Princi
ple of force b
a
lan
c
e,
we can get th
e followin
g
formula:
12
12
si
n(
)
co
s
(
)
c
WF
P
FF
P
(2)
Whe
r
e, The v
a
lue of
P
2
is related to the stre
ss distri
b
u
tion on the
wea
r
su
rfa
c
e.
)]
cos
6
.
0
(
3
1
cos
6
.
0
[
2
f
m
L
p
b
P
(3)
Whe
r
e,
ᇞ
L
f
i
s
cutting
teeth
we
ar length;
p
m
is
maximum value of
coal
r
o
ck s
t
ress
.
So
s
k
m
p
.
S
ubmitting Eq(1
) and Eq
(3
) to Eq(2), we
can obtai
n the followin
g
formula:
)]
cos
6
.
0
(
3
1
cos
6
.
0
[
)
sin(
cos
)
cos(
cos
)]
cos
6
.
0
(
3
1
cos
6
.
0
[
)
cos(
cos
)
cos(
cos
f
m
f
m
c
L
p
b
h
b
C
W
L
p
b
h
b
C
F
(4)
As can be
se
en from Eq(4
), The intera
ction force
W
and
F
C
of the PDC cutting
teeth is
related to the
factors su
ch
as the
cutting
fore-a
ngle
α
and the p
r
op
erties
of the coal. Th
erefo
r
e,
the cutting front ra
ke an
gl
e
and the
prop
ertie
s
of
the coal h
a
v
e a signifi
ca
nt influence
o
n
cutting fo
rce
and d
r
illing
efficien
cy of PDC. Wh
en
the f
r
ont rake an
gl
e be
come
s bi
gger, th
e thre
e
dire
ct
ion
com
p
re
ssiv
e
st
re
ss of
lo
we
r c
oal ro
c
k
increases, which
is une
asy to
form sh
eari
ng
failure of
bigg
er Volu
me. When the f
r
ont
rake a
ngl
e be
come
s small
e
r,
the
r
ear
pa
rt of the cuttin
g
teeth of PDC tends to be gentle, and cutting teeth
cannot dee
ply feed co
al ro
ck. Therefore,
the
bit has the op
timal front ra
ke angle.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 3, March 20
16 : 627 – 634
630
Accordi
ng to rel
e
vant
literature,
we can
obtai
n
coal
property parameters
and drilling
para
m
eters u
nder diffe
rent
solid coe
ffici
ents, as
sho
w
n in table 1.
T
able 1. Nature of Coal a
nd
Rock un
der Di
f
f
erent Coeffici
e
n
t and Dri
lli
ng
Parameters
Coal
propert
y
C
/mpa
θ
/°
φ
/°
ψ
/°
μ
/°
h
/mm
ᇞ
L
f
/mm
Soft coal
(
f
=1.5)
1.4 19
37
30
0.31
2
0.8
Hard coal
(
f
=4
）
6.2 23
34
30
0.40
1.1
1
S
ubmitting a
bove pa
rame
ters to Eq
(1)
and Eq(4),
we ca
n obtain
positive p
r
e
s
sure an
d
cutting fo
rce
of bit cutting
teeth
whe
n
the solid
co
e
fficient of
sof
t
coal
f
is 1.
5 an
d the
so
lid
coeffici
ent of hard
coal
f
is
4,as sho
w
n in
table 2.
T
able 2. Bit Cutting T
eeth Stress und
er Diffe
rent Coeffici
ent
f
=1.5
f
=4
F
1
/N
496 1672
F
C
/N
507 1681
4. Finite Element Simulation of PDC
Bit
Some simplifi
c
ation was u
s
ed to create
the bi
t model with Solid Wo
rks softwa
r
e due to
the little effect of bit su
rroundi
ng radi
us retenti
on strip,
corner roun
ding and
chamfe
r
of bit
s
t
rength.
(1)
Ignore cha
m
fer
and radi
us retention strip
c
haracte
ri
stics of the mo
d
e
l, which lead
to
uneven me
sh
easily.
(2)
Ignorin
g the internal th
rea
d
cha
r
a
c
teri
st
ics of the mo
del, whi
c
h ha
s the little impact on
the cal
c
ulatio
n results an
d easy to ca
use the grid divi
sion.
The a
c
tual
si
ze g
eomet
ric
modelin
g of t
he fro
n
t ra
ke
angle
com
p
o
s
ite bit of 0
°, 5°, 10
°,
15°, 20°, 25
° wa
s build
ed. As sho
w
n in
Figure 4.
Figure 4. Different To
oth F
o
re
-Angle
Co
mpact
Drill Bit Model
The el
asti
c m
odulu
s
of
pol
ycrystallin
e di
amond
comp
osite
sh
eet of
bit cutting te
eth was
setted to
790
Gpa, Poi
s
son
than 0.0
7
, the de
nsity of
2.9g/cm
3
; bit
body m
a
teri
als fo
r the
all
o
y
steel, the ela
s
tic mod
u
lu
s of the materi
al for
the 210
Gpa, Poisson
than 0.25, with a density of
7.8g/ cm
3
in the Solid Work
s
s
i
mulation s
o
ftware.
In the ca
se o
f
soft rock an
d hard ro
ck, the
value of the cutting fo
rce of the
cutting teeth
of different front ra
ke an
gl
e is sho
w
n in
Table
2. Th
e full con
s
traint wa
s appli
e
d
to the botto
m
surfa
c
e
of th
e bit, which
can n
o
t be
mo
ved with
out
e
l
astic defo
rm
ation. In thi
s
static
mod
e
l,
the
mes
h
parameters
are set to the "minimum unit s
i
z
e
".
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
De
sign F
r
ont
Ra
ke Angle o
f
PDC Bit Based on Solid
Wo
rks Sim
u
lation Method
(Xiaom
ing HAN)
631
5. Simulation Resul
t
s an
d Analy
s
is
5.1. Simulati
on Results Anal
y
s
is
in So
ft Rock
Und
e
r the co
ndition of soft rock, the stre
ss an
d
displa
ceme
nt imag
es of different
bits are
obtaine
d by static simul
a
tion of different front ra
ke an
gle, in whi
c
h
the stre
ss an
d displ
a
ceme
nt
of the
α
=1
0°
bit in soft rock are
sho
w
n i
n
Figure 5.
Figure 5. Bit
Stress and
Di
spla
cem
ent Image
s und
er
Soft Rock Propertie
s
As can
be
se
en fro
m
Fig
u
re 5, in th
e so
ft rock, the
bit in cutting
te
eth po
sition
a
nd the
stre
ss con
c
e
n
tration
suffe
r large
r
force
,
the bi
t suff
ering
maxim
u
m stress i
s
than 28
mpa.
Bit
lateral
cutting
teeth d
e
formation i
s
bi
g
gest, a
nd th
e
bigg
est
disp
lacem
ent
cha
nge
qua
ntity is
5.4
μ
m, whi
c
h
is in line wi
th the actual
drilling
bit wear
conditio
n
.
According t
o
the analysi
s
,
different fro
n
t ra
ke a
ngle
bit of maxim
u
m stress
σ
ma
x
and maxi
mum di
spla
cement
u
and
the
maximum strain
ξ
ma
x
values is sho
w
n in
Table 3 sho
w
s.
Table 3. Cal
c
ulation Analy
s
e Results of Different To
oth Fore
-an
g
le
Bits
α
/°
0
5
10 15 20
25
u
/
μ
m
9.1 6.3 5.4 6.9 9.3
13
σ
ma
x
/mpa
74 51 28 45 68
80
ξ
/
10
-4
2.2 1.7 0.9 1.4 2.4
2.9
The va
riation
tren
d of th
e
maximum
displacement
an
d the f
r
ont
ra
ke
angl
e of t
he bit i
n
the soft ro
ck
con
d
ition is
shown in Figu
re 6.
Figure 6. Displacement Chang
e Tre
nd
of Di
fferent Front Ra
ke Ang
l
e in Soft Rock
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IJEECS
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632
As can b
e
se
en from
Tabl
e 3 an
d Fig
u
re 6, front
ra
ke angl
e bit fro
m
0-1
0
° inte
rval of the
stre
ss de
cre
a
s
e
s
gradu
ally, indicating th
at in this
interval increa
sing
front ra
ke an
gle ca
n re
du
ce
friction an
d wea
r
, prolo
n
g
the servi
c
e
life of
the bit, enhance drilling efficien
cy; and in 10-25°
interval the st
ress g
r
ad
uall
y
incre
a
sed, indicating
that
in this interv
al red
u
ctio
n front ra
ke
ang
le
can i
n
crea
se
the se
rvice lif
e of the d
r
ill bit and imp
r
o
v
e drilling
efficien
cy. In Ta
ble 3 a
nd Fig
u
re
6 ca
n be
see
n
that the
α
=10° bit is th
e
maximum st
ress force a
n
d
displa
ce
men
t
is the lea
s
t, so
the optimal front rake angl
e of bit drilling in soft ro
ck
is
α
=1
0°.
5.2 Analy
s
is
of Simulation Resul
t
s in Hard
Rock
Und
e
r th
e
co
ndition
of ha
rd rock, the
st
ress and
di
splacement i
m
age
s of
different bits
are o
b
tained
by static si
mulation of
different
fron
t rake a
ngle
,
in which the stress a
n
d
displ
a
cement
of the
α
=15°
bit in hard rock are
sho
w
n i
n
Figure 7.
Figure 7. Bit
Stress and
Di
spla
cem
ent Image un
de
r Hard Ro
ck Propertie
s
As ca
n be
se
en from Fi
gure 7, PDC
bit in hard
coal a
nd ro
ck un
de
r stress i
s
larger tha
n
that in s
o
ft roc
k
under
s
t
res
s
,
at this
time, t
he bit subj
ected th
e ma
ximum stress is 12
2mp
a
, the
maximum displacement is
20.9
μ
m. In drilling hard rock,
because of the anti
shear st
rength of
the ha
rd
ro
ck is fa
r
gre
a
ter than th
e
soft strength
and
hard
ro
ck of
coal
ro
ck, d
r
il
l for
rea
c
tion
is
much l
a
rg
er
than that of the soft rock
drill for rea
c
tion, so the d
r
illing in ha
rd
rock bit of th
e
maximum stress is mu
ch
large
r
than t
hat of drilling
in soft rock
unde
r the m
a
ximum stre
ss.
Acco
rdi
ng to the analysis, different front
rake an
gl
e bits of maximum stre
ss
σ
ma
x
, t
he large
displ
a
cement
u
and the ma
ximum strain
ma
x
values are sho
w
n in ta
ble 4.
Table 4. Cal
c
ulation Results of Differe
nt Front Rake Angle Bits
α
/
°
0 5
10
15
20
25
u
/
μ
m
56.6
39.3 25.9 20.9 28.2
41.6
σ
ma
x
/mpa
201
183 143 122
135
160
ξ
/
10
-4
6.9
6.4 5.7 3.7 4.5
5.2
The va
riation
tren
d of th
e
maximum
displacement
an
d the f
r
ont
ra
ke
angl
e of t
he bit i
n
the hard
ro
ck
ca
se is
sho
w
n in Figure 8.
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IJEECS
ISSN:
2502-4
752
De
sign F
r
ont
Ra
ke Angle o
f
PDC Bit Based on Solid
Wo
rks Sim
u
lation Method
(Xiaom
ing HAN)
633
Figure 8. Displacement ch
ange tre
nd of
different fron
t rake a
ngle i
n
hard
ro
ck p
r
ope
rtie
s
It can be ob
tained a con
c
lu
sion from table 4:
in the hard ro
ck,
the front ra
ke angle
betwe
en 0
-
1
5
°, the big
g
e
st st
re
ss
a
nd di
spla
ce
ment of the
bit are
gra
dually de
cre
a
sin
g
,
indicating tha
t
in this inte
rval increa
sin
g
front
ra
ke
an
gle can im
prove the
servi
c
e life of th
e
bit,
increa
se
co
al
cru
s
hing
effi
cien
cy; But in
betw
een
15
-25° th
e m
a
ximum
stre
ss a
nd di
spl
a
cem
ent
of bit increa
ses, and the in
cre
a
se rate i
s
bigger a
nd bi
gger, indi
cati
ng the red
u
cti
on pinion a
n
g
l
e
is helpful to prolo
ng the service life
of the bit during
this interval. When
= 1
5
, t
he bigge
st
stre
ss an
d di
spla
cem
ent o
f
bit chan
ge
minimum.
Th
erefo
r
e, the o
p
timal front
rake
angl
e of
the
bit in drilling i
n
the hard
rock i
s
= 15
.
The re
ason
s for the above
phenom
eno
n are the in
crea
se of the
front ra
ke an
gle the
conta
c
t are
a
of the compo
s
ite and
coal
rock is
in
cre
a
sin
g
in the pro
c
e
ss of d
r
illing hard ro
ck
whe
n
α
=0-15
°
, the
stre
ss
area
of th
e
cutting teeth i
s
co
rrespon
din
g
ly larg
er, th
e bit i
s
m
a
inl
y
to
she
a
r
co
al ro
ck;
with th
e i
n
crea
se
of th
e front
ra
ke
a
ngle, the
co
ntact a
r
ea
bet
ween th
e cutting
teeth and the
coal ro
ck is
corre
s
p
ondin
g
ly large
r
wh
en
α
=1
5-2
5
°.
But at this time the bit broke
n
rock form
is g
r
adu
ally tra
n
sformed
into
b
r
oken
cru
s
hin
g
by
sh
ear
crushi
ng, a
n
d
the
com
p
re
ssi
v
e
stren
g
th of
co
al ro
ck i
s
m
u
ch l
a
rg
er tha
n
the
sh
ear st
rength, th
erefore,
the
maxi
mum
stre
ss a
nd
displ
a
cement
of the compo
s
ite ro
ck bit is chan
ging g
r
a
dually.
6. Conclusio
n
s
(1)
The
effect
ive rang
e of the front
ra
ke
angle i
s
0
≤α
≤
π
/2-(
ψ
+
θ
+
)
by the force
analysi
s
of the P
D
C bi
t’s cutting tee
t
h. The m
a
in
factors
affecti
ng the
cutting
force
and
dri
lling effici
en
cy
is cutting teet
h front ra
ke a
ngle.
(2) Usin
g Si
mulation finit
e
elem
ent
si
mulation,
the
static an
alysis of
different
front
ra
ke
angle bits in
soft and ha
rd
rock is ca
rri
e
d
out. The
re
sults
sho
w
that the optimal front rake a
n
g
le
of the bit in soft rock an
d
hard
ro
ck is
resp
ectively
α
=10
°
an
d
α
=1
5°, and th
e st
rength
of the
bit
is the la
rge
s
t
and lo
nge
st li
fe whe
n
the b
i
t is in the o
p
timum tooth a
ngle. It provid
es a
refe
ren
c
e
method for th
e desi
gn of compo
s
ite bit, and al
so prov
ides a theo
ret
i
cal ba
si
s for the sele
ction
of
PDC bit.
Ackn
o
w
l
e
dg
ements
The autho
rs are g
r
ateful for the fundin
g
of
this work by the Hen
an provin
ce
edu
catio
n
depa
rtment
applie
d re
se
arch p
r
oje
c
t
fund (1
5A4
4000
4, 16A4
6000
5) a
nd
Hen
an p
r
ovi
n
ce
sci
en
ce an
d tech
nolo
g
y project (1
621
02
2102
29).
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h
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etrical Para
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egu
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ao
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Vol.
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