The Influence of Viscosity Variation on the Oil Flowrate in Journal Bearing J.POROS 7 (4), Okt 2004
ISSN 1410- 6841
POROS
Jurna/1/miah Teknik Mesin
Volume 7 Nomor 4, Oktober 2004
TER...A:K.REI>IT ASI
No. 23a/DIKTI/Kep/2004
DEWAN REDAKSI
Pelindung
Dekan Fakultas Teknik
Ketua
Ir. Sofyan Djamil, M.Si.
Penyunting Ahli
Prof. Dr. lr. Eddy S.. Siradj, M.Sc. Eng.
Prof. Dr. Ir. I Made Kartika D., Dipl. Ing.
Dr. Ir. Erry Y. T. Adesta, C.Eng, MIMech E, IPM
Dr. Ir. Danardono AS.
Ir. Lamto Widodo, M.T.
Penyunting Pelaksana
Agustinus Puma Irawan, S.T., M.T.
Delvis Agusman, S.T., M.Sc.
Harto Tanujaya, S.T., M.T.
I Wayan Sukania, S.T., M.T.
Sekretariat
Endro Wahyono
Penerbit
Jurusan Teknik Mesin Fakultas Teknik
Universitas Tarumanagara
Alamat Redaksi
Jalan Let. Jend. S. Parman No. 1, Jakarta 11440
Telp. (021) 5638358- 5663124- 5672548, Fax. (021) 5663277
E-mail : ftmesin@cbn.net.id atau mesin@tarumanagara.ac.id
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melalui penelitian dan kajian teknologi dan science.
THE INFLUENCE OF VISCOSITY VARIATION ON
THE OIL FLOWRATE IN JOURNAL BEARING
Hasan Basri*)
Abstrak : Hasil yang disajikan da/am tu/isan ini merupakan kajian teoritis /aju a/iran minyak
pe/umas pada banta/anjurnal hidrodinamika yang mempunyai bentuk /a/uan aksial (axial groove).
Prediksi /aju a/iran minyak pe/umas dibawah kondisi beban tunak dan kekenta/an bervariasi da/am
arah leba/ film dise/esaikan dengan persamaan Reynold Prediksi unjuk kerja untuk model
kekenta/an bervariasi dibandingkan dengan so/usi kekenta/an konstan (iso-viskos) . Teori kekenta/an
konstan menunjukkan /aju a/iran tekan (feed pressure jlowrate) dan /aju a/iran kecepatan (induced
jlowrate) naik dengan rasio eksentrisitas sampai ke harga tertinggi, kemudian turun pada nilai rasio
eksentrisitas di atas 0, 75. Dengan demikian ter/ihat bahwa naiknya beban akan menghasi/kan
kenaikan atau penurunan laju a/iran berdasarkan ni/ai operasi rasio eksentrisitas. Hasi/ teoritis
untuk bantalanjurna/ pendek (bid= 0,5) menunjukkan bahwa, /aju a/iran kecepatan yang diprediksi
dengan model kekenta/an bervariasi jauh /ebih rendah dari pada yang diprediksi berdasarkan
kekenta/an konstan. Pengurangan /aju a/iran kecepatan naik dengan putaran, pada putaran tinggi
besarnya perbedaan laju a/iran tersebut turun menjadi 17% dari teori kekenta/an konstan.
Kata kunci: Pe/umasan hidrodinamika, Banta/an jurna/, Laju a/iran, kekenta/an.
INTRODUCTION
The basic design procedure for the prediction of journal bearing performance as shown in
Figure 1 (Basri, H., 1989) revolves around the ability to predict the operating temperature of the
bearing. Experience (Barnard, D.P., 1929; Wilcock, D.F. & Rosenblatt, M., 1952) has shown
that, for high speed bearings over 50 mm diameter, convection via the oil flow through the
bearing represents the primary flow of heat from the bearing. Thus oil flow rate is the key factor
determining the working temperature of larger bearings.
Originally, they (Wilcock, D.F. & Rosenblatt, M., 1952) predicted the oil flow through a
journal bearing on the basis of adding together the hydrodynamically induced flow and the
hydrostatic flow (stationary journal), and subsequently this method has been used by ESDU
84031 design procedure. There is evidence of poor agreement between actual flow rates in
journal bearings and those predicted on that basis (Cole, J.A. & Hughes, C.J., 1956).
In practice, the journal temperature lies between the maximum and minimum bearing
surface temperature. Considering the couette flow term, in the film inlet region the journal
temperature is generally higher tban the bearing temperature. Through the film thickness, the
viscosity increase from the journal to the bearing surface and the velocity gradient decreases as
shown in Figure 2a (Basri, H., 1989).
If we compare this with the constant viscosity case there will exist a reduced flow rate. In
the outlet film region (where dp/dx = 0), the journal temperature is lower than the bearing
surface temperature and the velocity gradient increases as the viscosity of lubricant film
decreases as shown in Figure 2b (Basri, H., 1989). Comparing with the constant viscosity case
there will exist an increased flow rate.
Thus, in comparison with the constant viscosity case, through the film thickness viscosity
variation is likely to lead to lower flow into the film, greater flow at the 'off end of the film
and, therefore reduced side flow of the bearing.
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basri)
251
Downstream
groove inlet
hole
1--t.:f=--Y U pstn1111
z
groove ｩｮｬｾｴ＠
hole
Figure 1. Journal bearing (Basri, H., 1989)
This study of oil flow in journal bearings arose from observations that the measured flow
rate was commonly lower than that of calculated as the assumption of a complete film and
constant viscosity. The need for a more comprehensive analysis of oil flow rate in journal
bearings should take account of the variation of viscosity through the film thickness.
Bearing
Tb Tj
decrease
h
-
Journal
U
Tj
u
Couette Flow: q < Uh I 2
Couette Flow: q > Uh I 2
(a) Film inlet region
(b) Film outlet region
Journal
Figure 2. Velocity profile (Basri, H., 1989)
THEORETICAL STUDY
The viscosity profile across the film thickness proposed in this study is shown in Figure 3.
The viscosity varies according to,
11
=
llj [ 1 + (C ylh) ]
(1)
where:
C = is viscosity factor
C = ( llb - llj ) I llj
252
POROS, Volume 7 Nom or 4, Oktober 2004, 251 -260
The modified Reynolds equation becomes,
hBp]+K ｾ｛ｨ
ｾ｛ｋ＠ ax
8X
I
Bp]=-U
Ｎ ｾ｛ｨｋ｝＠
8z
TJJ ax
Ｓ＠
3
I
8z
(2)
2
where;
1. For linear variation of viscosity, K 1 and K2 are given by;
1
1
1
K 1 -- - - - 2 + ＭＬＮｾ＠
2c C
{Cln(1 +c)}
1
= - -1 + ___,,-----,-
K
C
2
ln(1+C)
2. For parabolic variation of viscosity, K 1 and K2 are given by;
?c
Ir;:; {ln(I +C)}]
K 1 = _I [- 2 + ｾ＠ arctan JC + In(l +
-vC
arctan C 2-vC
2C
K2
=
I
JC
I
r;;
arctan C 2-vC
{ln(I +C)}
The finite difference of equation (2) becomes;
(3)
Pressure distribution
1lb
l___Ｏ｟ｾｸ］ｯ＠
0
11b
___[_\1lx=xl
11j
XL
(a) Pressure distribution
11j
(b) Parabolic form variation of viscosity
across the film thickness
Figure 3. Viscosity variation across the film thickness
Substituting the approximations into the Reynolds equation (3) gives a general
relationship between the pressure at each point and the pressures at the points adjacent to it.
A Pi-lj + B P;+Jj + C Pij-1 + D P;j+l + E P;j = F
(4)
Two bearings and journals are used in this investigation and the data is shown in Table 1.
The bearings have two axial grooves 30° circumferentially and 0.8 times bearing width, and
located 90° to the load line (see Figure 4).
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basri)
253
Table 1. Bearing dimensions (mm)
A
2 axial grooves
76.28
38.14 30.512
0.001-0.002
76.12
B
2 axial grooves
76.28
76.28 61.024
0.001-0.002
76.20
The lubricant temperature distribution
around the bearing is adapted from experimental
data (Basri, H., 1989) which is shown in Figure 5.
I
//--·::.. :ＮｾＺ
/
/
Ｍ ｾ Ｍ Ｍ ｾ Ｎ Ｂ＠
I
".
I
ANALISYS OF JOURNAL BEARING
I
'·
'-, Ｇﾷ Ｌ Ｍｾ
ＢＧﾷ
Ｍｾ＠
I
I
The lubricant was assumed to supplied at
ambient pressure via a full width line groove in
the upstream groove. The Reynolds equation was
solved using the Gauss-Seidel iterative method
with over relaxation factor.
,.
Ｍ ﾷ Ｎ Ｏ＠
....-/
.
The boundary conditions required were at
the bearing edges and at the lubricant supply line.
The lubricant was assumed to cavitate at ambient
pressure. Thus;
Pcavitation = Pambient = 0
Figure 4. Bearing and groove geometry
7" ,----,.----r..,..::--.--:-O.J:---r--:-A-;;,_.::-:lk::;N-,
.
g
II.
::;::
{:!so
>
..l
II.
II.
;:l
Ill ••
Cdld • 0.001
Pr •l.OIIor
N
1.)1 kN
J.IHN
•
•
• U10,..
t
l.OnN
o
UHN
a) P = 0 at 9
j
::>
ｾ＠
c) P = dP/dX = dP/dZ = 0
at 9 = 82 = 1t + a
101
)0
d) P = 0
;.(
101
101
ｾ＠
;:l
ｾ＠
II.
10
90
110
Z1D
Angular co-ordinate 8
Figure 5. Typical bearing temperature
distribution (Basri, H., 1989)
254
at
z = ± b/2
zo
101
...ｾ＠
0
b) P = 0 at 9 = n/2 - \jJ,
and P = 0 at 9 = 3n/2- \jJ
!...
>
0
ｾ＠
u
For use with the Reynolds equation and
full-width film applied, the following boundary
conditions adopted were,
Approximations of the type representative
by equation (4) resulted in as many equations as
grid points and the solution of a system of
simultaneous linear equations in the pressure
variable was required.
The iterations were continue until the
following convergence criterion was satisfied;
POROS, Volume 7 Nomor4, Oktober2004, 251-260
A computer program flow chart which models the bearing behaviour is shown in Figure 6.
ｃ｡ｬｾｴ･＠
inlet position at centre line of the groove
A3 = 1t12- w+ aa12 +a,
Interpolation from input temperature data for mesh points
Calculate film thickness (h(i.j))
Calculate new starting
film angle
a,= a,·
Calculate Viscosity distribution
Calculate Pressure Distribution by solving
equation (4) for every node (i,j)
Locate Film Break Down Boundary (a2)
Yes
Locate Delayed Film Width Film Reformastion (a 1)
ｃ｡ｬｾｴ･＠
Load Capacity, Attitude Angle
A.= (7tl2- w'l + aa12 +a,
w' and
Calculate Lubricant Flowrates
Figure 6. Computer program flow chart
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basrl)
255
The dimensionless pressure P was given by;
ｾ＠
r:7r
0
m rectangular co-ord'mate,
•
p= [p h
and in polar co-ordinate, P = [ {
2
min ]
(5)
Uq 1 L
(p
q 1 N d /Cd
YJ]
(6)
The load capacity was determined by integration of the pressure distribution around the
bearing (Gross, W.A., et all., 1980). For the co-ordinate system represented in Figure 7, the
components of the resultant film pressure force along and perpendicular to the line of centres
respectively were,
I I
f
(7)
W1* =- 21t JP cosO dX dZ
00
I I
f
(8)
W2* = + 27t JP sinO dX dZ
00
where,
2
W*
W
= q Nbd [
1
Cd
d
(9)
]
The attitude angle was then determined from,
(10)
w
Figure 7. Orthogonal and resultant load (Gross, W.A., et all., 1980)
Lubricant Flow Rates
The computer program calculated the dimensionless flow rate from the sides of the
bearing (Q •5) and the flow rate into the cavitations region (Q \). The condition of the full-width
film reformation at the inlet region in journal bearing can be seen in Figure 8 (Basri, H., 1990).
256
POROS, Volume 7 Nomor 4, Oktober 2004, 251 - 260
Qs/2
ｴｶｬＢｩＺｊｮｾＷＣ＠
ba/2
ｾＮＭｲＢＷＧ＼Ｚ
b/2
---li--if.,j9'·-if /-"?'1-7(
Ttd
Figure 8. Fluid film region in journal bearing (Basri, H., 1990)
The circumferential flow rate across a bearing section of width (z 1) was given by,
(11)
The axial flow rate across the section of circumferential length (x 1) was determined from,
(12)
In dimensionless form, equation (11) and (12) were written as,
(13)
Q*
z
=.!.(d)2
8 b
f[K H3 az
aPJ drp
1
(14)
0
Where the flow rates were made dimensionless according to
Q*-
Q
CdNbd
(15)
RESULTS AND DISCUSSION
The non-dimensional feed flow factor (Martin, F.A. & Lee, C.S ., 1982) and the nondimensional side flow rate (iso-viscous theory) for two axial grooves journal bearing are shown
in Figure 9 and 10.
Constant viscosity theory for journal bearings leads us to expect feed pressure induced
flow rate and hydrodynamic induced flow rate to increase with eccentricity ratio to a peak value
and then to decrease for eccentricity ratio above about 0.75.
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan BasTl}
257
Thus it is to be expected that increase of load will result in increased or reduced flow rate
according to the operating eccentricity ratio value.
The results of the investigation for the influence of the variation of viscosity through the
film thickness on the velocity-induced flow rate are given for comparison with the iso-viscous
solution. Comparisons of these data are shown plotted in Figures 11 to 14.
Two -axial groove bearing each 90" to the load line
The groove circumferential extent is not more than 4011
•
•
g-
1.0
Ｗｾ＠
0.8
sA
.g
ｾ＠
0.6 .
u
: 0.4
0
2
0.2
ｏＬｔＭｾｲ＠
0.0
ＭｴＬＮｾ
0.2
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.4
0.8
0.6
Eccentric;ity ratio (£ )
Figure 10. Non-dimensional side flow rate
(iso-viscous theory)
Figure 9. Non-dimensional feed flow factor
bid
ｾｯＮｳ＠
Cdld
b.,lb
• 0.002
Pf
- 0.0 bar
• 2000 rpm
• 0.8
N
----...
lso-viscoustheory
------- Sl
P1r1bolic form variation
or viscosity across
the film thickness
·o.
E 0.6
ｾ＠
)! :-: Ｍｾ ］Ｍｾ＠
.!l
ｾ＠
Ｗｾ＠
Ｍ Ｍ Ｏｾ＠
ｾｰ
Ｍ
Ｚ｟ ｾ＠ Ｍｾ＠ Ｍ ｾ＠
----
Pf
N
(:!
ｾ＠
1.0
0
0.9
·o.
0.8
-1
2
--
_. !
I
ｾ＠
0.7
"''§
0.6
g
-------- - -
K
l
0.4
0.3
0.1
'iiｾ＠
0.2 -
0.0 .,.___,__+---+--+--4--+--4--+--+----f
ｾ＠
0.1 - -- - - - -- -
0.0
0.1
- - --- 1--
0.2
0.3
0.4
o.s
0.6
0.7
0.8
0.9
--
1.0
Eccentricity ratio (• )
M
0.0
Figure 11. Non-dimensional velocity
induced flow rate.
---a-lso -viscous theory
- • • • - o- • Parabolic form variation
or viscosity across
the film thickness
O.S
1...
r------ -- -
0.2
5
ｾ＠
Ｍ
-- - , - - - - - --- ----
0.3 ----- - - ---
Cdld
bjb
--r---- -- ---
0.7 - --- - ---
• O.S
-0.002
• 0.8
- 0.0 bar
4000 rpm
bid
!:: ｾ ｉＧ ＭＺ ｾﾷ ﾷｾ Ｍ ＺＭｾ ｲ｟Ｚ ＠ Ｍｾ＠ ＭｾＺＮ Ｍﾷ ﾷ Ｍ
1.0
Eccentricity ratio (t
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
r.
0.9
1.0
Figure 12. Non-dimensional velocity
induced flow rate.
It is evident that due to the viscosity variation through the film thickness, the velocityinduced flow rate is significantly less than that predicted on the basis of constant viscosity.
The reduction of velocity-induced flow rate increases with speed; the difference is of the
order of 17% at high speed from the iso-viscous theory. This result is consistent with what
would be expected. Since, through the film thickness, the viscosity of lubricant increases at the
258
POROS, Volume 7 Nomor 4, Oktober 2004, 251 - 260
film inlet and decreases at the film outlet from journal surface to the bearing surface, therefore
the oil side flow rate from the bearing would be reduced and the velocity-induced flow rate
would be reduced too.
b/d
Cd/d
bJb
= 0.5
= 0.002
______.
lso -viscous theory
0.8
--- -o
Parabolic form variation
=
Pf
= 0.0 bar
Two grooves
40
bid
Cd/d
bib
Pf
N
= 0.5
ｾ＠
0.7
-
=
-_=tl-- -j
I
]
0.4
I-
ｾ＠
E
l
-
Ｍ Ｍ Ｍ ＭＮ
Ｍｲ
0.2
- - - -
Ｗｾ
Ｍ｣ｾ
-
ｾ＠
- V I- -
ｾ＠
p-op
I
I
0.2
- --
I
I
I
20 ····-·0--·· ···-· --- --- ·- ··-·-- . -··- · --------- - -. ·-··---- · --·-·-
10 . - -- - - · ---- --
--·- ·----
··-- -·-- - - - · ---· - ---
0.3
0.4
0.5
'
I
·-··-· + -· ····0
0.1
Ｍ Ｍ Ｍｾ ﾷ Ｍｾ Ｍ +-ＡＮ＠ .......
.-----rv
I
-
I
L ;/ ｾ ｣ｲ＠
ｾＭ Ｍ ---- -- ----
ＭＫＱＮｪｾ＠
0.0
30 --·---
[
-- --
0.1 - - -1---- - -0.0
t ---,
-- -
8 0.5
""'li
the film thickness
ｾＭＮ＠
0.6
0.3
Ｍ Ｍｾ
Parabolic form variation
of viscosity across
-- ----- 0
8000 rpm
j
f
Ｍ
lso -viscous theory
= 0.002
= 0.8
= 0.0 bar
:: - ---Ｍ
ｾ＠
--.1.
of viscosity across
the film thickness
0.6
0.7
0.8
0.9
1.0
10
15
Load (kN)
Eccentricity ratio (£)
Figure 13. Non-dimensional velocity
induced flow rate
Figure 14. Velocity induced flow rate
in journal bearing
CONCLUSIONS AND SUGGESTIONS
•
Conclusions
The objective of the present journal bearing analysis was to carry out an investigation of
the oil flow rate allowing for the variation of viscosity through the film thickness. The
conclusions of such study can be summarized as follows:
1. For a given speed, it is expected that an increase of load will result in increased or reduced
flow rate according to the operating eccentricity ratio value.
2. In engineering terms, there is negligible difference between the results obtained from a
linear form and a parabolic form of variation of viscosity through the film thickness. It is the
magnitude rather than the manner of the variation that is important.
3. The effects of viscosity variation through the film thickness on the velocity-induced flow
rate is significant and the reduction of this flow rate has been achieved using this numerical
model.
4. The influence on the discrepancy of oil flow rates of viscosity variation model, incorporated
in the numerical model is greater at high speed than at low speed. As a result, a better
prediction is provided by this numerical model at high speed case than the case of low speed.
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basrt)
259
•
Suggestion for Future Work
It has been shown that there is a significant effect of variation of viscosity through the film
thickness upon the velocity-induced flow rates. From this findings, the suggestions for the future
work would be to study the precise manner and the magnitude of the delayed full width film
reformation at the inlet region of journal bearing.
NOMENCLATURE
B
Cd/d
c
D
h
: Bearing width
: Diametral clearance
:Clearance
: Bearing diameter
: Film thickness
N
p
Qx
Qz
Q
: Speed in rpm
: Film pressure
: Circumferential flow
: Axial flow rate
:Total flow rate
r : Radial clearance
R : Bearing radius
u : Tangential velocity
W : Load capacity
e : Angle of load line
lj1
a
'1
E
: Attitude angle
: Angle of cavitation
boundary
: Dynamic viscosity
: Eccentricity ratio
REFERENCES
Barnard, D.P., 1929, Oil Flow in Plain Bearing, Ind. Eng. Chern., 18,460.
Basri, H., 1989, Ph.D.
Sheffield, England.
Thesis, Mechanical Engineering Department, The University of
Basri, H., 1990, Oil Flow in Axial Groove Journal Bearing, Journal of The Institution of
Mechanical Engineers, 11, MEPLondon.
Cole, J.A., Hughes, C.J., 1956, Oil Flow and Film Extent in Complete Journal Bearings, Proc.
Inst. Mech. Engrs., 170, 499-510.
Dowson, D., 1962, A Generalized Reynolds Equation for Fluid Film Lubrication, Inst. J.
Mech. Sci., 4, 159-170.
Gross, W.A., et all., 1980, Fluid Film Lubrication, John Wiley & Sons, New York.
Martin, F.A., Lee, C.S., 1982, Feed Pressure Flow in Plain Journal Bearings, Trans. ASLE,
26, 3, 381-392.
So, H., Shieh, J.A., 1987, The Cooling Effects of Supply Oil on Journal Bearings for Varying
Inlet Conditions, Trib. Int., 20, 2, 79-89.
Wilcock, D.F., Rosenblatt, M., 1952, Oil Flow, Key Factor in Sleeve Bearing Performance,
Trans. ASME, 74, 849-866.
260
POROS, Volume 7 Nomor 4, Oktober 2004, 251 - 260
PETUNJUK PENULISAN NASKAH UNTUK
ｾｐｏｒｓＢ＠
JURNAL ILMIAH TEKNIK MESIN
0
;
1. Penyunting menerima naskah Hasil Penelitian atau Tinjauan Pustaka dalam Bahasa
Indonesia yang baku atau Bahasa lnggris, yang belum pernah dipublikasikan.
2. Naskah diketik dengan komputer menggunakan MS Word, di atas kertas ukuran A4 secara
rapi dengan jarak 1 (satu) spasi. Naskah dikirim sebanyak 2 eksemplar dengan disket ukuran
3,5" yang berisi file naskah; gambar; grafik dan tabel disertai keterangan yang diperlukan.
Jika ada foto harap dicetak hitam putih dan mengkilat.
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Nama (para) penulis ditulis lengkap disertai dengan keterangan lembaga/fakultas/institut
tempat bekerja dan bidang keahlian Gika ada) pada catatan kaki.
4. Sistematika penulisan naskah, untuk;
a. Naskah Hasil Penelitian ; terdiri dari 0 Abstrak/Abstract berisi masalah penelitian
yang diteliti, cara melaksanakannya, hasil dan kesimpulan), @ Kata kunci (di tulis
dibawah abstrak), @) Pendahuluan (berisi latar belakang permasalahan, tujuan dan ruang
lingkup), E).. Tinjauan Pustaka (berisi teori-teori yang dipergunakan untuk menyelesaikan
penelitian), 0 Tata Kerja (berisi tentang bahan, peralatan, metoda yang digunakan dan
cara pelaksanaan penelitian), 0 Hasil dan Pembahasan (hasil berupa data penelitian
yang telah diolah dan dituangkan dalam bentuk tabel, grafik atau foto/gambar.
Sedangkan pembahasan, berisi tentang analisa data-data hasil penelitian dengan
mengacu pada teori-teori yang ditulis dalam tinjauan pustaka dan pustaka-pustaka yang
diacu dalam penelitian), & Kesimpulan (menyimpulkan hasil-hasil penelitian yang
diperoleh) dan G) Daftar Pustaka.
b. Naskah Kajian Teknologi dan Science ; terdiri dari 0 Abstrak/ Abstract (berisi
masalah yang dikaji, cara melaksanakan, hasil dan kesimpulan), @ Kata Kunci, @)
Pendahuluan (berisi latar belakang, permasalahan, tujuan dan ruang lingkup ), 8
Tinjauan Pustaka (berisi tentang teori-teori yang mendukung pada kaji topik yang
dibahas), 0 Pembahasan (berisi tentang analisa terhadap teori-teori yang tertuang dalam
tinjauan pustaka, dengan mengetengahkan keunggulan dan kelebihannya), 0
Kesimpulan/Penutup dan & Daftar Pustaka.
5. Naskah yang ditulis dalam Bahasa Indonesia, abstraknya dalam Bahasa lnggris dan naskah
dalam Bahasa Inggris abstraknya dalam Bahasa Indonesia. Abstrak harus jelas dan ringkas,
maksimum 200 kata, diketik dalam satu alinea dengan huruf italik (miring) dengan jarak 1
(satu) spasi.
6. Daftar pustaka disusun menurut alfabet penulis.
Urutan penulisan : nama penulis, tahun, judul, penerbit, kota terbit, dan halaman. Nama
pengarang mendahulukan nama keluarga atau nama dibalik, tanpa gelar. Kutipan acuan
pustaka yang digunakan dinyatakan dengan menuliskan nama penulis, tahun dan halaman
dalam tanda kurung, contoh : (Madhukar et al, 1998: 31 0).
7. lsi tulisan bukan tanggung jawab Penyunting. Penyunting berhak mengedit redaksionalnya,
tanpa mengubah arti dan tidak diadakan surat menyurat kecuali tulisan yang disertai
perangko akan dikembalikan (karena tidak memenuhi persyaratan atau perlu diperbaiki).
8. Setiap artikel yang dimuat akan diberikan nomor bukti pemuatan dan cetak lepas masingmasing 3 (tiga) eksemplar.
POROS
Jurna/1/miah Teknik Mesin
Volume 7 Nomor 4, Oktober 2004
TER...A:K.REI>IT ASI
No. 23a/DIKTI/Kep/2004
DEWAN REDAKSI
Pelindung
Dekan Fakultas Teknik
Ketua
Ir. Sofyan Djamil, M.Si.
Penyunting Ahli
Prof. Dr. lr. Eddy S.. Siradj, M.Sc. Eng.
Prof. Dr. Ir. I Made Kartika D., Dipl. Ing.
Dr. Ir. Erry Y. T. Adesta, C.Eng, MIMech E, IPM
Dr. Ir. Danardono AS.
Ir. Lamto Widodo, M.T.
Penyunting Pelaksana
Agustinus Puma Irawan, S.T., M.T.
Delvis Agusman, S.T., M.Sc.
Harto Tanujaya, S.T., M.T.
I Wayan Sukania, S.T., M.T.
Sekretariat
Endro Wahyono
Penerbit
Jurusan Teknik Mesin Fakultas Teknik
Universitas Tarumanagara
Alamat Redaksi
Jalan Let. Jend. S. Parman No. 1, Jakarta 11440
Telp. (021) 5638358- 5663124- 5672548, Fax. (021) 5663277
E-mail : ftmesin@cbn.net.id atau mesin@tarumanagara.ac.id
Jurnal Ilmiah Poros terbit sejak bulan Januari 1998 dengan frekuensi 4 (empat) kali dalam
setahun (Januari, April, Juli dan Oktober) ini, diharapkan dapat menjadi salah satu sarana
para profesional (dari dunia usaha, pendidikan dan peneliti) untuk mengembangkan
profesi dan berpartisipasi serta menyebarluaskan perkembangan tentang iptek mesin
melalui penelitian dan kajian teknologi dan science.
THE INFLUENCE OF VISCOSITY VARIATION ON
THE OIL FLOWRATE IN JOURNAL BEARING
Hasan Basri*)
Abstrak : Hasil yang disajikan da/am tu/isan ini merupakan kajian teoritis /aju a/iran minyak
pe/umas pada banta/anjurnal hidrodinamika yang mempunyai bentuk /a/uan aksial (axial groove).
Prediksi /aju a/iran minyak pe/umas dibawah kondisi beban tunak dan kekenta/an bervariasi da/am
arah leba/ film dise/esaikan dengan persamaan Reynold Prediksi unjuk kerja untuk model
kekenta/an bervariasi dibandingkan dengan so/usi kekenta/an konstan (iso-viskos) . Teori kekenta/an
konstan menunjukkan /aju a/iran tekan (feed pressure jlowrate) dan /aju a/iran kecepatan (induced
jlowrate) naik dengan rasio eksentrisitas sampai ke harga tertinggi, kemudian turun pada nilai rasio
eksentrisitas di atas 0, 75. Dengan demikian ter/ihat bahwa naiknya beban akan menghasi/kan
kenaikan atau penurunan laju a/iran berdasarkan ni/ai operasi rasio eksentrisitas. Hasi/ teoritis
untuk bantalanjurna/ pendek (bid= 0,5) menunjukkan bahwa, /aju a/iran kecepatan yang diprediksi
dengan model kekenta/an bervariasi jauh /ebih rendah dari pada yang diprediksi berdasarkan
kekenta/an konstan. Pengurangan /aju a/iran kecepatan naik dengan putaran, pada putaran tinggi
besarnya perbedaan laju a/iran tersebut turun menjadi 17% dari teori kekenta/an konstan.
Kata kunci: Pe/umasan hidrodinamika, Banta/an jurna/, Laju a/iran, kekenta/an.
INTRODUCTION
The basic design procedure for the prediction of journal bearing performance as shown in
Figure 1 (Basri, H., 1989) revolves around the ability to predict the operating temperature of the
bearing. Experience (Barnard, D.P., 1929; Wilcock, D.F. & Rosenblatt, M., 1952) has shown
that, for high speed bearings over 50 mm diameter, convection via the oil flow through the
bearing represents the primary flow of heat from the bearing. Thus oil flow rate is the key factor
determining the working temperature of larger bearings.
Originally, they (Wilcock, D.F. & Rosenblatt, M., 1952) predicted the oil flow through a
journal bearing on the basis of adding together the hydrodynamically induced flow and the
hydrostatic flow (stationary journal), and subsequently this method has been used by ESDU
84031 design procedure. There is evidence of poor agreement between actual flow rates in
journal bearings and those predicted on that basis (Cole, J.A. & Hughes, C.J., 1956).
In practice, the journal temperature lies between the maximum and minimum bearing
surface temperature. Considering the couette flow term, in the film inlet region the journal
temperature is generally higher tban the bearing temperature. Through the film thickness, the
viscosity increase from the journal to the bearing surface and the velocity gradient decreases as
shown in Figure 2a (Basri, H., 1989).
If we compare this with the constant viscosity case there will exist a reduced flow rate. In
the outlet film region (where dp/dx = 0), the journal temperature is lower than the bearing
surface temperature and the velocity gradient increases as the viscosity of lubricant film
decreases as shown in Figure 2b (Basri, H., 1989). Comparing with the constant viscosity case
there will exist an increased flow rate.
Thus, in comparison with the constant viscosity case, through the film thickness viscosity
variation is likely to lead to lower flow into the film, greater flow at the 'off end of the film
and, therefore reduced side flow of the bearing.
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basri)
251
Downstream
groove inlet
hole
1--t.:f=--Y U pstn1111
z
groove ｩｮｬｾｴ＠
hole
Figure 1. Journal bearing (Basri, H., 1989)
This study of oil flow in journal bearings arose from observations that the measured flow
rate was commonly lower than that of calculated as the assumption of a complete film and
constant viscosity. The need for a more comprehensive analysis of oil flow rate in journal
bearings should take account of the variation of viscosity through the film thickness.
Bearing
Tb Tj
decrease
h
-
Journal
U
Tj
u
Couette Flow: q < Uh I 2
Couette Flow: q > Uh I 2
(a) Film inlet region
(b) Film outlet region
Journal
Figure 2. Velocity profile (Basri, H., 1989)
THEORETICAL STUDY
The viscosity profile across the film thickness proposed in this study is shown in Figure 3.
The viscosity varies according to,
11
=
llj [ 1 + (C ylh) ]
(1)
where:
C = is viscosity factor
C = ( llb - llj ) I llj
252
POROS, Volume 7 Nom or 4, Oktober 2004, 251 -260
The modified Reynolds equation becomes,
hBp]+K ｾ｛ｨ
ｾ｛ｋ＠ ax
8X
I
Bp]=-U
Ｎ ｾ｛ｨｋ｝＠
8z
TJJ ax
Ｓ＠
3
I
8z
(2)
2
where;
1. For linear variation of viscosity, K 1 and K2 are given by;
1
1
1
K 1 -- - - - 2 + ＭＬＮｾ＠
2c C
{Cln(1 +c)}
1
= - -1 + ___,,-----,-
K
C
2
ln(1+C)
2. For parabolic variation of viscosity, K 1 and K2 are given by;
?c
Ir;:; {ln(I +C)}]
K 1 = _I [- 2 + ｾ＠ arctan JC + In(l +
-vC
arctan C 2-vC
2C
K2
=
I
JC
I
r;;
arctan C 2-vC
{ln(I +C)}
The finite difference of equation (2) becomes;
(3)
Pressure distribution
1lb
l___Ｏ｟ｾｸ］ｯ＠
0
11b
___[_\1lx=xl
11j
XL
(a) Pressure distribution
11j
(b) Parabolic form variation of viscosity
across the film thickness
Figure 3. Viscosity variation across the film thickness
Substituting the approximations into the Reynolds equation (3) gives a general
relationship between the pressure at each point and the pressures at the points adjacent to it.
A Pi-lj + B P;+Jj + C Pij-1 + D P;j+l + E P;j = F
(4)
Two bearings and journals are used in this investigation and the data is shown in Table 1.
The bearings have two axial grooves 30° circumferentially and 0.8 times bearing width, and
located 90° to the load line (see Figure 4).
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basri)
253
Table 1. Bearing dimensions (mm)
A
2 axial grooves
76.28
38.14 30.512
0.001-0.002
76.12
B
2 axial grooves
76.28
76.28 61.024
0.001-0.002
76.20
The lubricant temperature distribution
around the bearing is adapted from experimental
data (Basri, H., 1989) which is shown in Figure 5.
I
//--·::.. :ＮｾＺ
/
/
Ｍ ｾ Ｍ Ｍ ｾ Ｎ Ｂ＠
I
".
I
ANALISYS OF JOURNAL BEARING
I
'·
'-, Ｇﾷ Ｌ Ｍｾ
ＢＧﾷ
Ｍｾ＠
I
I
The lubricant was assumed to supplied at
ambient pressure via a full width line groove in
the upstream groove. The Reynolds equation was
solved using the Gauss-Seidel iterative method
with over relaxation factor.
,.
Ｍ ﾷ Ｎ Ｏ＠
....-/
.
The boundary conditions required were at
the bearing edges and at the lubricant supply line.
The lubricant was assumed to cavitate at ambient
pressure. Thus;
Pcavitation = Pambient = 0
Figure 4. Bearing and groove geometry
7" ,----,.----r..,..::--.--:-O.J:---r--:-A-;;,_.::-:lk::;N-,
.
g
II.
::;::
{:!so
>
..l
II.
II.
;:l
Ill ••
Cdld • 0.001
Pr •l.OIIor
N
1.)1 kN
J.IHN
•
•
• U10,..
t
l.OnN
o
UHN
a) P = 0 at 9
j
::>
ｾ＠
c) P = dP/dX = dP/dZ = 0
at 9 = 82 = 1t + a
101
)0
d) P = 0
;.(
101
101
ｾ＠
;:l
ｾ＠
II.
10
90
110
Z1D
Angular co-ordinate 8
Figure 5. Typical bearing temperature
distribution (Basri, H., 1989)
254
at
z = ± b/2
zo
101
...ｾ＠
0
b) P = 0 at 9 = n/2 - \jJ,
and P = 0 at 9 = 3n/2- \jJ
!...
>
0
ｾ＠
u
For use with the Reynolds equation and
full-width film applied, the following boundary
conditions adopted were,
Approximations of the type representative
by equation (4) resulted in as many equations as
grid points and the solution of a system of
simultaneous linear equations in the pressure
variable was required.
The iterations were continue until the
following convergence criterion was satisfied;
POROS, Volume 7 Nomor4, Oktober2004, 251-260
A computer program flow chart which models the bearing behaviour is shown in Figure 6.
ｃ｡ｬｾｴ･＠
inlet position at centre line of the groove
A3 = 1t12- w+ aa12 +a,
Interpolation from input temperature data for mesh points
Calculate film thickness (h(i.j))
Calculate new starting
film angle
a,= a,·
Calculate Viscosity distribution
Calculate Pressure Distribution by solving
equation (4) for every node (i,j)
Locate Film Break Down Boundary (a2)
Yes
Locate Delayed Film Width Film Reformastion (a 1)
ｃ｡ｬｾｴ･＠
Load Capacity, Attitude Angle
A.= (7tl2- w'l + aa12 +a,
w' and
Calculate Lubricant Flowrates
Figure 6. Computer program flow chart
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basrl)
255
The dimensionless pressure P was given by;
ｾ＠
r:7r
0
m rectangular co-ord'mate,
•
p= [p h
and in polar co-ordinate, P = [ {
2
min ]
(5)
Uq 1 L
(p
q 1 N d /Cd
YJ]
(6)
The load capacity was determined by integration of the pressure distribution around the
bearing (Gross, W.A., et all., 1980). For the co-ordinate system represented in Figure 7, the
components of the resultant film pressure force along and perpendicular to the line of centres
respectively were,
I I
f
(7)
W1* =- 21t JP cosO dX dZ
00
I I
f
(8)
W2* = + 27t JP sinO dX dZ
00
where,
2
W*
W
= q Nbd [
1
Cd
d
(9)
]
The attitude angle was then determined from,
(10)
w
Figure 7. Orthogonal and resultant load (Gross, W.A., et all., 1980)
Lubricant Flow Rates
The computer program calculated the dimensionless flow rate from the sides of the
bearing (Q •5) and the flow rate into the cavitations region (Q \). The condition of the full-width
film reformation at the inlet region in journal bearing can be seen in Figure 8 (Basri, H., 1990).
256
POROS, Volume 7 Nomor 4, Oktober 2004, 251 - 260
Qs/2
ｴｶｬＢｩＺｊｮｾＷＣ＠
ba/2
ｾＮＭｲＢＷＧ＼Ｚ
b/2
---li--if.,j9'·-if /-"?'1-7(
Ttd
Figure 8. Fluid film region in journal bearing (Basri, H., 1990)
The circumferential flow rate across a bearing section of width (z 1) was given by,
(11)
The axial flow rate across the section of circumferential length (x 1) was determined from,
(12)
In dimensionless form, equation (11) and (12) were written as,
(13)
Q*
z
=.!.(d)2
8 b
f[K H3 az
aPJ drp
1
(14)
0
Where the flow rates were made dimensionless according to
Q*-
Q
CdNbd
(15)
RESULTS AND DISCUSSION
The non-dimensional feed flow factor (Martin, F.A. & Lee, C.S ., 1982) and the nondimensional side flow rate (iso-viscous theory) for two axial grooves journal bearing are shown
in Figure 9 and 10.
Constant viscosity theory for journal bearings leads us to expect feed pressure induced
flow rate and hydrodynamic induced flow rate to increase with eccentricity ratio to a peak value
and then to decrease for eccentricity ratio above about 0.75.
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan BasTl}
257
Thus it is to be expected that increase of load will result in increased or reduced flow rate
according to the operating eccentricity ratio value.
The results of the investigation for the influence of the variation of viscosity through the
film thickness on the velocity-induced flow rate are given for comparison with the iso-viscous
solution. Comparisons of these data are shown plotted in Figures 11 to 14.
Two -axial groove bearing each 90" to the load line
The groove circumferential extent is not more than 4011
•
•
g-
1.0
Ｗｾ＠
0.8
sA
.g
ｾ＠
0.6 .
u
: 0.4
0
2
0.2
ｏＬｔＭｾｲ＠
0.0
ＭｴＬＮｾ
0.2
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.4
0.8
0.6
Eccentric;ity ratio (£ )
Figure 10. Non-dimensional side flow rate
(iso-viscous theory)
Figure 9. Non-dimensional feed flow factor
bid
ｾｯＮｳ＠
Cdld
b.,lb
• 0.002
Pf
- 0.0 bar
• 2000 rpm
• 0.8
N
----...
lso-viscoustheory
------- Sl
P1r1bolic form variation
or viscosity across
the film thickness
·o.
E 0.6
ｾ＠
)! :-: Ｍｾ ］Ｍｾ＠
.!l
ｾ＠
Ｗｾ＠
Ｍ Ｍ Ｏｾ＠
ｾｰ
Ｍ
Ｚ｟ ｾ＠ Ｍｾ＠ Ｍ ｾ＠
----
Pf
N
(:!
ｾ＠
1.0
0
0.9
·o.
0.8
-1
2
--
_. !
I
ｾ＠
0.7
"''§
0.6
g
-------- - -
K
l
0.4
0.3
0.1
'iiｾ＠
0.2 -
0.0 .,.___,__+---+--+--4--+--4--+--+----f
ｾ＠
0.1 - -- - - - -- -
0.0
0.1
- - --- 1--
0.2
0.3
0.4
o.s
0.6
0.7
0.8
0.9
--
1.0
Eccentricity ratio (• )
M
0.0
Figure 11. Non-dimensional velocity
induced flow rate.
---a-lso -viscous theory
- • • • - o- • Parabolic form variation
or viscosity across
the film thickness
O.S
1...
r------ -- -
0.2
5
ｾ＠
Ｍ
-- - , - - - - - --- ----
0.3 ----- - - ---
Cdld
bjb
--r---- -- ---
0.7 - --- - ---
• O.S
-0.002
• 0.8
- 0.0 bar
4000 rpm
bid
!:: ｾ ｉＧ ＭＺ ｾﾷ ﾷｾ Ｍ ＺＭｾ ｲ｟Ｚ ＠ Ｍｾ＠ ＭｾＺＮ Ｍﾷ ﾷ Ｍ
1.0
Eccentricity ratio (t
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
r.
0.9
1.0
Figure 12. Non-dimensional velocity
induced flow rate.
It is evident that due to the viscosity variation through the film thickness, the velocityinduced flow rate is significantly less than that predicted on the basis of constant viscosity.
The reduction of velocity-induced flow rate increases with speed; the difference is of the
order of 17% at high speed from the iso-viscous theory. This result is consistent with what
would be expected. Since, through the film thickness, the viscosity of lubricant increases at the
258
POROS, Volume 7 Nomor 4, Oktober 2004, 251 - 260
film inlet and decreases at the film outlet from journal surface to the bearing surface, therefore
the oil side flow rate from the bearing would be reduced and the velocity-induced flow rate
would be reduced too.
b/d
Cd/d
bJb
= 0.5
= 0.002
______.
lso -viscous theory
0.8
--- -o
Parabolic form variation
=
Pf
= 0.0 bar
Two grooves
40
bid
Cd/d
bib
Pf
N
= 0.5
ｾ＠
0.7
-
=
-_=tl-- -j
I
]
0.4
I-
ｾ＠
E
l
-
Ｍ Ｍ Ｍ ＭＮ
Ｍｲ
0.2
- - - -
Ｗｾ
Ｍ｣ｾ
-
ｾ＠
- V I- -
ｾ＠
p-op
I
I
0.2
- --
I
I
I
20 ····-·0--·· ···-· --- --- ·- ··-·-- . -··- · --------- - -. ·-··---- · --·-·-
10 . - -- - - · ---- --
--·- ·----
··-- -·-- - - - · ---· - ---
0.3
0.4
0.5
'
I
·-··-· + -· ····0
0.1
Ｍ Ｍ Ｍｾ ﾷ Ｍｾ Ｍ +-ＡＮ＠ .......
.-----rv
I
-
I
L ;/ ｾ ｣ｲ＠
ｾＭ Ｍ ---- -- ----
ＭＫＱＮｪｾ＠
0.0
30 --·---
[
-- --
0.1 - - -1---- - -0.0
t ---,
-- -
8 0.5
""'li
the film thickness
ｾＭＮ＠
0.6
0.3
Ｍ Ｍｾ
Parabolic form variation
of viscosity across
-- ----- 0
8000 rpm
j
f
Ｍ
lso -viscous theory
= 0.002
= 0.8
= 0.0 bar
:: - ---Ｍ
ｾ＠
--.1.
of viscosity across
the film thickness
0.6
0.7
0.8
0.9
1.0
10
15
Load (kN)
Eccentricity ratio (£)
Figure 13. Non-dimensional velocity
induced flow rate
Figure 14. Velocity induced flow rate
in journal bearing
CONCLUSIONS AND SUGGESTIONS
•
Conclusions
The objective of the present journal bearing analysis was to carry out an investigation of
the oil flow rate allowing for the variation of viscosity through the film thickness. The
conclusions of such study can be summarized as follows:
1. For a given speed, it is expected that an increase of load will result in increased or reduced
flow rate according to the operating eccentricity ratio value.
2. In engineering terms, there is negligible difference between the results obtained from a
linear form and a parabolic form of variation of viscosity through the film thickness. It is the
magnitude rather than the manner of the variation that is important.
3. The effects of viscosity variation through the film thickness on the velocity-induced flow
rate is significant and the reduction of this flow rate has been achieved using this numerical
model.
4. The influence on the discrepancy of oil flow rates of viscosity variation model, incorporated
in the numerical model is greater at high speed than at low speed. As a result, a better
prediction is provided by this numerical model at high speed case than the case of low speed.
The influence of viscosity variation on oil flowrate
in journal bearing (Hasan Basrt)
259
•
Suggestion for Future Work
It has been shown that there is a significant effect of variation of viscosity through the film
thickness upon the velocity-induced flow rates. From this findings, the suggestions for the future
work would be to study the precise manner and the magnitude of the delayed full width film
reformation at the inlet region of journal bearing.
NOMENCLATURE
B
Cd/d
c
D
h
: Bearing width
: Diametral clearance
:Clearance
: Bearing diameter
: Film thickness
N
p
Qx
Qz
Q
: Speed in rpm
: Film pressure
: Circumferential flow
: Axial flow rate
:Total flow rate
r : Radial clearance
R : Bearing radius
u : Tangential velocity
W : Load capacity
e : Angle of load line
lj1
a
'1
E
: Attitude angle
: Angle of cavitation
boundary
: Dynamic viscosity
: Eccentricity ratio
REFERENCES
Barnard, D.P., 1929, Oil Flow in Plain Bearing, Ind. Eng. Chern., 18,460.
Basri, H., 1989, Ph.D.
Sheffield, England.
Thesis, Mechanical Engineering Department, The University of
Basri, H., 1990, Oil Flow in Axial Groove Journal Bearing, Journal of The Institution of
Mechanical Engineers, 11, MEPLondon.
Cole, J.A., Hughes, C.J., 1956, Oil Flow and Film Extent in Complete Journal Bearings, Proc.
Inst. Mech. Engrs., 170, 499-510.
Dowson, D., 1962, A Generalized Reynolds Equation for Fluid Film Lubrication, Inst. J.
Mech. Sci., 4, 159-170.
Gross, W.A., et all., 1980, Fluid Film Lubrication, John Wiley & Sons, New York.
Martin, F.A., Lee, C.S., 1982, Feed Pressure Flow in Plain Journal Bearings, Trans. ASLE,
26, 3, 381-392.
So, H., Shieh, J.A., 1987, The Cooling Effects of Supply Oil on Journal Bearings for Varying
Inlet Conditions, Trib. Int., 20, 2, 79-89.
Wilcock, D.F., Rosenblatt, M., 1952, Oil Flow, Key Factor in Sleeve Bearing Performance,
Trans. ASME, 74, 849-866.
260
POROS, Volume 7 Nomor 4, Oktober 2004, 251 - 260
PETUNJUK PENULISAN NASKAH UNTUK
ｾｐｏｒｓＢ＠
JURNAL ILMIAH TEKNIK MESIN
0
;
1. Penyunting menerima naskah Hasil Penelitian atau Tinjauan Pustaka dalam Bahasa
Indonesia yang baku atau Bahasa lnggris, yang belum pernah dipublikasikan.
2. Naskah diketik dengan komputer menggunakan MS Word, di atas kertas ukuran A4 secara
rapi dengan jarak 1 (satu) spasi. Naskah dikirim sebanyak 2 eksemplar dengan disket ukuran
3,5" yang berisi file naskah; gambar; grafik dan tabel disertai keterangan yang diperlukan.
Jika ada foto harap dicetak hitam putih dan mengkilat.
3. Judul naskah singkat, dengan kata-kata atau frasa kunci yang mencerminkan isi tulisan.
Nama (para) penulis ditulis lengkap disertai dengan keterangan lembaga/fakultas/institut
tempat bekerja dan bidang keahlian Gika ada) pada catatan kaki.
4. Sistematika penulisan naskah, untuk;
a. Naskah Hasil Penelitian ; terdiri dari 0 Abstrak/Abstract berisi masalah penelitian
yang diteliti, cara melaksanakannya, hasil dan kesimpulan), @ Kata kunci (di tulis
dibawah abstrak), @) Pendahuluan (berisi latar belakang permasalahan, tujuan dan ruang
lingkup), E).. Tinjauan Pustaka (berisi teori-teori yang dipergunakan untuk menyelesaikan
penelitian), 0 Tata Kerja (berisi tentang bahan, peralatan, metoda yang digunakan dan
cara pelaksanaan penelitian), 0 Hasil dan Pembahasan (hasil berupa data penelitian
yang telah diolah dan dituangkan dalam bentuk tabel, grafik atau foto/gambar.
Sedangkan pembahasan, berisi tentang analisa data-data hasil penelitian dengan
mengacu pada teori-teori yang ditulis dalam tinjauan pustaka dan pustaka-pustaka yang
diacu dalam penelitian), & Kesimpulan (menyimpulkan hasil-hasil penelitian yang
diperoleh) dan G) Daftar Pustaka.
b. Naskah Kajian Teknologi dan Science ; terdiri dari 0 Abstrak/ Abstract (berisi
masalah yang dikaji, cara melaksanakan, hasil dan kesimpulan), @ Kata Kunci, @)
Pendahuluan (berisi latar belakang, permasalahan, tujuan dan ruang lingkup ), 8
Tinjauan Pustaka (berisi tentang teori-teori yang mendukung pada kaji topik yang
dibahas), 0 Pembahasan (berisi tentang analisa terhadap teori-teori yang tertuang dalam
tinjauan pustaka, dengan mengetengahkan keunggulan dan kelebihannya), 0
Kesimpulan/Penutup dan & Daftar Pustaka.
5. Naskah yang ditulis dalam Bahasa Indonesia, abstraknya dalam Bahasa lnggris dan naskah
dalam Bahasa Inggris abstraknya dalam Bahasa Indonesia. Abstrak harus jelas dan ringkas,
maksimum 200 kata, diketik dalam satu alinea dengan huruf italik (miring) dengan jarak 1
(satu) spasi.
6. Daftar pustaka disusun menurut alfabet penulis.
Urutan penulisan : nama penulis, tahun, judul, penerbit, kota terbit, dan halaman. Nama
pengarang mendahulukan nama keluarga atau nama dibalik, tanpa gelar. Kutipan acuan
pustaka yang digunakan dinyatakan dengan menuliskan nama penulis, tahun dan halaman
dalam tanda kurung, contoh : (Madhukar et al, 1998: 31 0).
7. lsi tulisan bukan tanggung jawab Penyunting. Penyunting berhak mengedit redaksionalnya,
tanpa mengubah arti dan tidak diadakan surat menyurat kecuali tulisan yang disertai
perangko akan dikembalikan (karena tidak memenuhi persyaratan atau perlu diperbaiki).
8. Setiap artikel yang dimuat akan diberikan nomor bukti pemuatan dan cetak lepas masingmasing 3 (tiga) eksemplar.