Simulation for the Prediction of Surface-Accuracy in Magnetic Abrasive Machining

13 Pages·0.419 MB·English

by  Kim J., Choi M.

Journal of
Materials
Processing
Technology
ELSEVIER Journal of Materials Processing Technology 35 (1995) 036 246
Simulation for the prediction of surface-accuracy in magnetic
abrasive machining
Jeong-Du Kim*, Min-Seog Choi
Department of Precision Engineering & Mechatronics, Korea Advanced Institute of Science and Technology,
373-1, Kusong-dong, Yusong-yu, Taejon 305-701, South Korea
Received 12 March 1994
lairtsudnI yrammuS
A new machining technique, magnetic abrasive machining which uses magnetic force as
a machining pressure, has been developed recently for the efficient and precision finishing of
surfaces. The process si controllable because the machining pressure si controlled only by the
current that si input to the coil of solenoid, but it needs the monitoring of the surface roughness
for the automation of the process and for the achieving of machining efficiency by preventing
over-finishing of the surface. For this, in the present study, the surface roughness si predicted as
a function of finishing time by a model that has been derived from the removed volume of
material. Thus, it si possible, from the surface-roughness model, to predict the time when
existing scratches are completely removed. The simulation results are confirmed by comparing
them with the experimental results of previous papers.
:sdrowyeK Magnetic abrasive machining; Simulation, Surface roughness, Machining scratch
Nomenclature
~aA mA cross-sectional area of the air-gap and magnet
B magnetic flux density
sB saturated magnetic flux density
D mean diameter of the magnetic particles
F total force acting on the machining region
f force acting on a magnetic particle
H magnetic field strength of the magnetic abrasives
Ha magnetic field strength in the air gap
* Corresponding author.
0924-0136/95/$09.50 ;C( 1995 Elsevier Science S.A. llA rights reserved
SSDI 0924-0136(94~01 753-N
J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630-642 631
H c coercive force
workpiece hardness
Hmt
I input current
la, ml length of the air-gap and magnet
M total volume of material removed
m volume of material removal by a magnetic particle
N number of magnetic particles acting on the machining region simulta-
neously
the number of grain edges of a magnetic particle acting simultaneously
on the surface
number of turns of the coil
n c
P machining pressure supplied by the magnet
aR surface roughness
oR
initial surface-roughness
critical surface-roughness
Rcrl
t machining time
3/ speed of magnetic abrasives
w volume ratio of iron in a magnetic particle
Af force acting on a grain edge
mA volume of material removal by a grain edge
penetration depth of the abrasive grains
~crt
O2 mean angle of asperity of abrasive cutting edges
~02 mean angle of surface asperity
oP magnetic permeability in vacuum
relative permeability of the electromagnet
sr/~
relative permeability of pure iron
1. Introduction
A new finishing method, magnetic abrasive machining, has been developed recently
to produce, efficiently, good surface quality, which method is being applied to the
finishing of the internal and external surfaces of tube as well as to flat surfaces. One of
the merits of magnetic abrasive machining is that the machining pressure can be
controlled by input current only and thus the machining process simply by the current
1, 2. It can be applied to the internal as well as the external surfaces of bent or
long tubes, that are difficult to be finished by traditional finishing methods. Espe-
cially, in the finishing of internal surfaces, it is very difficult to test and monitor the
surface.
In this study, the aim is to predict the finishing time at which existing scratches are
removed completely by modelling of magnetic abrasive machining. Thus the finish-
ing efficiency is expected to be increased by reducing the time for the testing of
surfaces, and avoiding the over-finishing that can be excessive for the removal of
scratches.
632 J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630 246
/
w < /
/
/
m( j
T
Fig. .1 An example of a magnetic circuit, consisting of an electromagnet and an air gap.
2. Modelling
2.1. Modelling of the magnetic abrasive machining system
A simple typical magnetic circuit is shown in Fig. .1 The magnetic field is induced by
the input current to the coil of the electromagnet, and the gradient of the magnetic
field in the air-gap produces the machining pressure. It is assumed that leakage of the
magnetic field can be ignored and that the magnetic core is saturated uniformly
throughed the cross-section. Then, the magnetic field strength in the air-gap, the
machining region, is as follows 3 (Appendix A.1):
ncI
H. = (2.1)
aA/al(aA + lm/lArsAm)"
The magnetic abrasives that are in the above magnetic field are magnetized as follows:
3
H- 2Ha . (2.2)
The magnetization curve of the iron, which is a ferromagnetic material, is calculated
approximately using the hysteresis curve of the iron:
H+H~
B = sB tanh-- (2.3)
Hc '
whilst the magnetic permeability of the magnetic abrasives is the slope of the curve:
_ 1 dB 1 sB sech 2H+Hc (2.4)
ru, o~/ dH - #o Hc Hc
J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630-642 336
Magnetic equipotentia tines~
Lines "~o magne±ic Por'ce~
i"lagnet:ic pore ' ' I I
Fig. .2 Schematic view of internal finishing by magnetic abrasives 4.
The average of these two slopes (i.e. the two different slopes given by Eq. (2.4),
according to the positive and negative signs for quantity He) makes the permeability
curve of magnetic abrasives.
The magnetic abrasive process for internal finishing is shown in Fig. 2. The gradient
of the magnetic field produces the attraction force between the abrasives as well as the
machining pressure in the air-gap 5. The magnetic abrasives form the magnetic
brush -6 by the attraction force, and can finish the surface without the need for
splashing by the centrifugal force. The machining pressure between the abrasives and
the workpiece is:
H 2 A/(n3 r - 1)w
P = Po (2.5)
4 3(2 + )rP + n(pr- 1)w"
2.2. Modelling of surface accuracy
It was assumed that the surfaces of the workpiece have a uniform profile without
statistical distribution, that they have an initial surface-roughness R °, and that the
abrasives move in the length direction of the scratches. A model for the stock removal
based on the micro-cutting mechanism 7 was used:
Wl
V = K (2.6)
Hint n tan 0'
where K is a constant. In this study, the characteristics of the magnetic abrasives as
shown in Fig. 3 were considered in deriving the model for stock removal in magnetic
436 .D-.J Kim, .S-.M iohC / lanruoJ of slairetaM gnissecorP ygolonhceT 35 )5991( 036 246
sO£
direction of abrasive grain citengem evlsacolo pectlde
(b)
4R~t(~n sO
(AL9+ALs~A
.giF .3 Simplified surface geometry: )a( surface profile and magnetic abrasive particles; )b( shape of the
scratch machined.
f'¢~ 0
\..
i
:I rt
1
.giF .4 Penetration depth of magnetic abrasive grains.
abrasive machining (Appendix A.2). As the result, Eq. (2.7) was derived
( nNAfvt ~1/2
M = C H,~lw/ (R o) t/4. (2.7)
The averaged surface roughness (Ra) was derived from the stock removal as follows:
s/4 n_NAfvt \1/4
Ra= n ° -C'(R°)-l/s(lw) k Hmt~tanOlw| . (2.8)
J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630-642 536
A critical surface roughness (Rert) may exist in the given machining pressure because
of the indentation of the cutting edge into workpiece, such that the surface roughness
will no longer improve. In Fig. ,4 the indentation depth of a cutting edge having
a conical shape with slope angle 0 was calculated as follows:
r = 6~t tan ,0 (2.9)
Af: Hmt%r 2 = Hmt~(6cr t tan 0) .2 (2.10)
Thus
t,c6 tan0 X/Hm,~" )11.2(
-
3. Algorithm
The magnetic field strength and permeability in the air-gap are calculated for the
input data, after which the machining pressure si calculated using these values of
magnetic strength and permeability. Stock removal and improvement of the surface
roughness are progressive as the machining time increases. If the surface roughness
become the same as the critical surface roughness, the magnitude of the input current
is decreased to lower the machining pressure and, thus, the critical surface roughness.
The program ends if the surface roughness reaches the objective final surface-rough-
ness value. A schematic flow diagram for the algorithm is shown in Fig. .5
START >
,sevltcejbO:tupnI
Constroints L D~t~
.
noltaucioC For the system
H, P
CoLcuotion £or m~chlnin 9 process Change or
eR,M inpu± current
oN
DNE >
Fig. .5 Schematic flow diagram.
636 J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630 642
1.5
0,75-
o
3O
,_~- )b(
-= 0
o
-- --0.75-
1.5 i
--640 --J20 0 320 640
Field Strength, H AT/m
Fig. 6. Showing: (a), (b) hysteresis curves; and (c) a magnetization curve.
7500
jz \
\\x\
5625
\\
3750
E
2
1875
I
O 0 325 0.65 0.975 .5
Magnetic Induction, B iT
Fig. 7. Curve of permeability versus magnetic induction.
4. Simulation results and discussion
Magnetization and hysteresis curves of the iron included in the magnetic abrasives
are shown in Fig. 6, curves (a) and (b) showing the simulation result for the hysteresis
and curve (c) showing the magnetization curve of the iron, calculated from the mean
value of the two curves, i.e. (a) and (b). Fig. 7 shows the simulation result for the
relationship between the permeability and the magnetic flux density. It is noted that
J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630-642 736
1:I:-o:o%%OoOoOO 5
:£ i:__=°:°;::::°:°°7 '
1.5-
5: la =O.021Aa =O.O005~J"
c-
o
2~
g~
0.5
O 0 1 I 2 5 I 4
input Current, A
I
.giF .8 Magnetic induction B susrev tnerruc .I
55000
3~c 3t
-~ 41250- Experiment ~u
27500-
c
1375o-
0-
o 0.325 0.65 0.975 I .5
Mognetic /nductTon, B l T
Fig. .9 Machining erusserp P susrev citengam induction .B
the permeability has a maximum value at B = 0.6 T. Fig. 8 shows the magnetic flux
density produced in the air-gap by the input current. From Eqn. (2.1), the magnetic
flux density is seen to be affected significantly not by the cross-sectional area of the
air-gap but by its length. Therefore it should by noted, when the magnetic system is
designed, that as the length of the air-gap increases, the magnetic flux density increases
dramatically. Fig. 9 shows the simulation result of the relationship between the
836 J.-D. Kim, M.-S. Choi / Journal ~?'Materials Processing Technology 53 (1995) 630 642
25
18.75
E
Simulation --
6> 12.5 / ./
o
E
o2 /
/" / ~'" Experiment
q)
©
6.25-
/
/
0
0 1 5~ 3~0 4F5
60
Machining Time, t sec
.giF .01 Stock lavomer M susrev gninihcam emit .t
0.,3
E '\
0225
\
\
\i'
0.15-
3
8
~c
0.075-
~_ E x p e r i m e n t ~"~"~'~:::~ ~
0 5~1 0~5. 4~5 60
Machining Time, t sec
.giF .11 ecafruS ssenhguor ~R susrev gninihcam emit .t
magnetic flux density and the pressure that is produced between the magnetic brush
and the workpiece in the machining region. As the magnetic flux density increases, the
pressure increases slowly at first, but then increases rapidly. It is seen also from the
figure that the pressure has a maximum value in the vicinity of B = 1.2 T. It can be
said that the trend is similar to the experimental result of reference 5, but in the
latter the maximum pressure appeared close to B = 0.9 T. Fig. 10 shows the simulated
stock-removal of an SUS304 workpiece according to the machining time, where the
J.-D. Kim, M.-S. Choi / Journal of Materials Processing Technology 53 (1995) 630 642 639
0.5
Simulation
E \ ~- /o Experiment
0.225-
~
c o,15
o
B=O.6T
0.075- B=0 T
o s+s soo
Machining Time, t sec
.giF .21 tceffE fo eht citengam xulf ytisned no eht ecafrus .ssenhguor
experimental data, the lower line in the figure, is from reference 5. Fig. 11 shows the
simulation result for Eq. .)8.2( The simulated surface-roughness aR reduces by almost
the same trend as for the experimental data. In the simulation, the final objective value
of the surface roughness was 0.01 lain, and the finishing time in which the surface
roughness aR reduces to 0.01 maj from 0.27 maj was 571 s according to the algorithm of
the sequential reduction of the input current, as shown in Fig. .5 Fig. 21 shows the
effect of the magnetic flux density on the improvement of the surface roughness
compared with experimental data from reference 4. The finishing efficiency appears
to be very sensitive to the magnitude of the magnetic flux density, and the simulated
surface-roughness represents comparatively well the experimental data for low mag-
netic flux density, and thus for low pressure.
5. Conclusions
The modelling and simulation of the machining pressure and surface roughness in
magnetic abrasive machining has been performed, and the finishing time predicted. As
the result, the following were noted.
)1( The magnetic flux density in the air-gap is affected greatly by the length of the
air-gap, it increases as the length decreases.
)2( The machining pressure between the magnetic brush and the workpiece has its
maximum value at about B = 2.1 T.
)3( The simulation results for surface roughness agree better with the ex-
perimental data for low magnetic flux density than they do for high magnetic flux
density.