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Electrolytic-abrasive mirror finishing
Electrolytic-abrasive mirror finishing H. Maehata, H. Kamada and M. Yamamoto* Using the electrolytic-abrasive mirror finishing method, large workpieces of stainless and ordinary carbon steel can be easily mirror-finished in a short time and with high etficiency, resulting in a surface roughness of up to 0.01 0.02 l~m Rz This method is based on the fact that the electrolytic effect is assisted by the removal action of abrasive grains within an appropriate current density range by the use of neutral salt-type electrolytes. In the past, the actual implementation of this method in the field of high-precision machining was not clearly defined and many unsolved technical problems remained. This paper clarifies the combined effects of the electrolytic dissolution and polishing action of abrasive grains in this method. It also describes the results of the experimental analysis of the surface roughness formation mechanism and the process for forming the required surface shape.
Keywords: electrochemical machining, mirror finishing
An ultimate target of production machining technologies is the realization of high-precision machining that has high performance and reliability at low cost. To attain this, machining methods capable of removing and machining extremely small amounts of material stably and effectively with minimal heat or vibration disturbance are required. One of the methods to realize these aims is an electrochemical machining method capable of removing metal in the form of ion particles. In practice, however, this method is not able to produce a smoothfinished, high-precision surface because of nonuniform dissolution due to material composition or defects. On the other hand, it is expected that rendering this dissolution action uniform will provide a faster method of high-precision machining, making it possible to achieve high-precision finished surfaces of near atomic order. The electrolytic-abrasive mirror finishing method combines electrolysis, capable of removing extremely small amounts of metal, with an abrasive grain action on highly elastic minute cuts, as a way to achieve the aims set out above. It is a new mirror finishing method providing stable removal action and capable of finishing a large surface area to mirror smoothness in a short time, thanks to the highly efficient eliminating properties of electrolytic products. 1 Applications of this method include inner surface finishing for chemical vessels and mirror finishing for atomic power-related equipment, as well as parts of marine diesel engines and stainless steel substrate for amorphous silicon solar cells. 1 The application of this method to mould processing or electronic equipment parts is also under study. The required surface roughness hasa wide range of 0.01 0.21~mRz, and * Techmcal Research Inshtute, Hitachi Zosen Corporation, 3 22. Sakurajlma l-chome, Konohana l~u, Osaka 554, Japan
PRECISION ENGINEERING
materials appropriate for application are various, ranging from stainless and ordinary steel to nonferrous metals such as aluminium, titanium and copper. However, this finishing technology has many unsolved problems, including tool electrode design, establishment of proper machining conditions for mirror finishing of free curved surfaces or planes of large surface area, development of technologies for mirror finishing very hard material and nonferrous metals, as well as perfection of technologies for high-precision machining of worked shapes. This paper aims mainly to describe the solution of these problems associated with high-precision machining mechanisms. In electrolytic-abrasive mirror finishing, the machining effects from the combined actions of electrolysis and abrasive grains are first explained, followed by an analysis of the generaton mechanism of worked surface roughness and the formation process of worked shapes; the experiments conducted to study the suitability of this method are described.
Machining effects from the combination of electrolysis and abrasive grains Application of direct current voltage to two facing metals in an electrolytic solution causes the anode metal to be dissolved in an ionic unit. An amount of the dissolved metal W is proportional to an applied quantity of electricity / x t (current x time) from Faraday's law, and represented by
W=qklt
(g)
(1)
where k is the electrochemical equivalent intrinsic to an anode material, and ~1is the current efficiency used for dissolution and affected by oxygen generation or oxide film formation. ~1is a ratio of a theoretical value kdt and an actual amount of metal removed W and has the characteristics shown in Fig 1:~1 is low in the
0141 6359/87/010031 13/$0300 q 1987 Butterworth & Co (Publishers) Ltd
31
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing 300 $45C(2 cm 2
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means of mirror finishing because of the generation of oxide film or pits on the dissolved surface. Fig 2 shows the machining results of abrasive grain action w h i c h was combined with electrolysis in order to eliminate the electrolytic products, as well as to continuously maintain the ground metal surface and to remove metal uniformly over the entire surface area In the machining experiments, # 3000 polishing abrasive was applied to the face of a hollow Cu cathode of ~/)20 (h12 mm and rotated while pressing to the face of a $ 4 5 C anode. A 2 0 % aqueous solution of passivation-type sodium nitrate f l o w e d out from the centre of the cathode face. It is apparent from Fig 2 that, due to the combination of grain action, the amount of removed metal W is nearly proportional to the working time t and that the current efficiency ~1 has a constant of approximately 60°,/,,, independent of t. A comparison of worked surfaces w h e n electrolysis alone is used and w h e n abrasive is combined with it, is s h o w n in Fig 3. The worked surface by the electrolytic-abrasive method has a uniform metal mirror finish with no film or pits generated. The abrasive used should have elastic abrasive grain action, as well as water permeability and insulation in order to create a homogeneous smooth surface by the uniform pressing force of the grains with minute cuts. As mentioned above, it has been confirmed that the combination of grain action with electrolysis provides an efficient method of metal removal (subject to Faraday's law) while simultaneously generating a lustrous metal surface. The electrolytic-abrasive mirror finishing method. a new mirror finishing method, aims to provide these combined machining effects. This is achieved through developing the appropriate shape or movement path for tool electrodes optimal to large-surface areas, and to various shapes and materials, applied under the
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Fig 1 Characteristics of electrolytic dissolution. (a) effect of current density, J, and (b) influence of working time, t current density region of less than 10 A cm 2 but rises as J increases and becomes nearly 1 0 0 % at several 1 0 A c m 2 . Studies of the relationship between r/and working time t, however, s h o w t/ has a tendency to decrease sharply immediately after initiation of application of electricity w h e n the value of ~1 is less than 20 % at about 1 00 s. This is because of the growth of oxide film or electrolytic products 2, making it difficult to control the amount of metal removal by electrolysis alone. In addition, this is not an efficient 32
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~
~
Electrolytic abrasive
200 1
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,60 cc E
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W ~
,
L 100
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~ 200
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Working time it), s
Fig 2 Comparison of electrolytic abrasive with electrolysis J A N U A R Y 1987 VOL 9 NO !
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing
~ f
Fig 3 Comparison of worked surface." (a) with electrolysis only and (b) with the electrolytic-abrasive method
proper conditions of electrolysis and grain action, depending upon the unevenness of the ground and the desired worked surface roughness. In the following, the machining characteristics of this finishing method are described and the generating mechanisms of worked surface roughness and the formation process of worked shapes are analysed. Machining
characteristics
Fig 4 shows the outline of a revolving disk-type tool electrode used in the machining method. The tool electrode consists of a disk electrode (cathode) with numerous holes for the electrolytic solution, to the face of which an abrasive (unwoven nylon cloth impregnated with resin grains) is applied. The machining is carried out by pressing a tool electrode to a workpiece (anode) and spinning it with a speed of revolution N to give v~. Electrolytic and abrasive conditions are selected according to the unevenness of the ground and finish level desired 1. For example, an initial surface of 5-- 10HmRzis finished to the worked surface roughness of 0.1 - I l~mRz with # 240 #600 abrasive by applying a current density of J - 0 . 5 1 A c m 2. This worked surface is then further machined to a mirror surface of 0.01 0.1 Hm Rz with #800 - # 4 0 0 0 abrasive under the condition of J - 0. An appropriate balance of the two actions gives this result. In rough machining, high-speed metal
~
N
E,~c~oIv,~~.\~tk~,'q~ ' ~ ~q / /
"
""
,.;///7/'/',,"/'/'//// Workpiece
Fig 4 Basic diagram of the electrolytic-abrasive mirror finishing method using a disk-type tool electrode PRECISION ENGINEERING
removal is carried out by employing a high current density, as well as large abrasive grains. For mirror finishing, small grains and low current density are selected. Any break in this balance, particularly by use of excessively strong electrolysis, deteriorates the worked surface by forming pits, destroying the mirror surface. The primary machining factors of the electrolyticabrasive finishing method are the pressing force of abrasive P, the speed of revolution of tool electrode N and relative feed velocity vf in addition to the abovementioned current density J and working time t. The basic machining characteristics of each factor are shown in Fig5(a) (d), where machining is performed using # 3 2 0 abrasive, J = 1 A cm 2, and SUS304 is machined by an electrode of tool diameter DE = d~70mm. The removed depth d c is a value at the position where the centre of a tool electrode makes one pass and the worked surface roughness R s is a ten-point height of irregularities. The initial surface is a 0.05 l~mRz mirror. It is clear from Fig 5 that the removed depth dc is proportional to J even though the amount of metal removed by the # 3 2 0 abrasive is added and is inversely proportional to the feed velocity vf corresponding to t. However, dc is proportional to the tool speed of revolution N and has an increasing value as the pressing force P becomes larger. This is because the mirror cutting action of the abrasive grain and the grain action increase the combined efficiency ~1". In the experiments, ~1= 100%, is obtained at P = 10kgf cm 2 (981 kPa) or above. On the other hand, R s has a high value under the conditions of large J and low P because of the formation of micropits, and has a tendency to be proportional to vf and inversely proportional to N, both of which are independent of the formation of the pits. Fig 6(a) shows the pattern of scratches on the abrasive-worked surface. Concentric scratches are formed immediately below the tool. After the tool is passed over, however, regular scratches nearly equal to the radius of the outer circumference of the tool appear on the worked surface. This may be explained * Actually current efficiency, but referred to as c o m b i n e d efficiency, o w i n g to the c o m b i n e d abrasive action
33
Maehata, Kamada and Yamamoto---electrolytic-abrasive mirror finishing 5
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--1
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Fig 5 Characteristics of removed depth and worked surface roughness with the electrolytic-abrasive method. Influence of (a) current density, J, (b) pressing force, P, (c) tool revolutions per minute, N, and (d) feed velocity, vf
34
JANUARY
1 9 8 7 V O L ~-~ r'4(~
Maehata, Kamada and Yamamoto --electrolytic-abrasive mirror finishing ! 0 f~
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Fig 6 Sketch of scratches on the abrasive-worked surface having used (a) the disk-type tool and (b) the ring-type tool
104
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,1
by the fact that the abrasive grain action of the outer circumference of the tool is the action that forms the surface. The scratches made by a ring-type tool shown in Fig 6(b) also prove this fact. The regularity of the scratches on the abrasive-worked surface is subject to tool feed determined by vf N and the continuous surface of the scratches becomes the worked surface roughness.
10-'
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L )) ~ ' ~ L ~ . / " ~ / ' ~ J ~ ' ~
Analysis of mechanism of worked surface roughness generation In this section, the dynamic properties of an abrasive containing grains and the role played by machining factors in roughness generation are quantified and the generation mechanism of the worked surface roughness is analysed.
~~l t
10 °
0
01
4
5
6
7
8
Compression of abrasive (,~), mm
Fig 7 Spring constant of abrasive buffs
Dynamic properties of abrasives
The abrasives used, usually called buffs, and made by impregnating resin containing grains (AI203, SiC) in unwoven nylon cloth, have highly elastic and viscoelastic properties. The pressing force of abrasive P is a logarithm of the compression of abrasive ;.. The coefficient of variation of the pressing force AP/A). is, as shown in Fig 7, four to five orders smaller than that of a rigid vitrified grinding wheel and has high elasticity. Therefore, the abrasive grain action is hardly affected by the precision of the machining device. For example, the pressing force variation AP is several 10 gf cm 2 to the variation of A).-- 1/100 mm, thereby resulting in a variation of the pressing force of a grain AP/m:~ of about 0.01 gf, where m g is the number density of abrasive grains acting on the worked surface and, if the pressing force P is equally divided among each abrasive grain, the pressing force of grain PG is calculated by Pc, = P/mq
=240
2 Q.
=1500 5~
0
l
5;o
1000
( m q ) number crrl :'
I
(2)
Fig 8 shows the relationship between )., P and mg by measuring the number density of abrasive grains mg from the mirror cutting scratches by a scratch transfer method. From this figure, the pressing force of a grain PG iS calculated to be 30-80gf from #240 abrasive, 5 9gffrom # 3 2 0 a n d 2 4gffrom #1 500, each of which has an approximately c o n s t a n t PG3. If the grain shape is assumed to be a core of the edge angle 0, the cutting depth h to the worked surface PRECISION ENGINEERING
1000
E
_-S,.<
::240
:;320 ~1500
I0
Fig 8 Relationship between ~., P and mg
35
Maehata, Kamada and Yamamoto--electrolytic-abrasive
mirror finishing
Table 1 Measurement results of the edge angle of abrasive grains Edge angle of abrasive grains 0h (deg) Abrasive h = 0.21~m
h = 0.41zm
h =. 0.75l~m
h = 1.5 f~m
Average (i (deg)
#240
167
154
144
140
152
#320
164
160
148
142
155
(material hardness: Hv) by the pressing force of a grain PG is represented by
,f P _coslO/2) I' (3)
0.8
where h is decided by the edge angle 8 if PG is constant. Table 1 gives the measurement results of h and/). (The edge angle is read by each average cutting depth /~ from the section shape profile of mirror cutting scratches and ~h is an average of 20 measured values.)
0.6
h = [ H v 7z tan(fl/2) ~
F
','1
0.4
Grain m o t i o n a n d m i r r o r c u t t i n g scratches
The grain motion of a revolving disk-type tool is given by the tool speed of revolution N and relative feed velocity vf as shown in Fig 4. Fig 9 shows the approximate loci made by the motion of one grain of radius r on a tool and the equation at time t is represented by f(x.v, tl = (X ..... vft)2 + y2 _ / 2
= 0
'°> Fig 1 0 s h o w s the relationship b e t w e e n the feed f at the width direction g / r from Eq (5), and the distance b e t w e e n scratches A f , where m = 1 w h e n a single grain
rt
Af
1"2
]
06
08
'~,
0
0.2
0.4
1
(4)
tf vft in Eq (4) is assumed to be the feed of the revolution centre f ( = vf/N), the distance Af (in the radial direction) between circular scratches is calculated by
Y
f 02
Fig 10 Relationship between v/r and Af/f
is used and m = 5 and 50 when multiple grains are aligned at equal distances on a circle with radius r From this calculation, the larger m is and the closer y/r is to 1, the smaller Af becomes. The number of working grains M, on a circle with radius r is calculated from the following equation, assuming that the grains are in a regular lattice alignment: M, :: 2~.r/Xg = 2.=r/~(m~, 1'' ~ 212m~, I ;')/2'. = 1.66~rm~ '2
(6>
where Xg is the average distance between grains. The scratches occurring with the passing of the tool are determined by grain groups on the outermost circumference of the tool, as shown in Fig 6. If M a is substituted for M, in Eq (6) by using a tool radius a and f / M a for f in Eq (5), then a general equation of the distance Af between scratches generated is given by i
cos(s,o "~'f =
1/2
d
z[amg
[0'0"tcos'("n
]
11. 1
~2a2mg
f-
1.'2
a,,
t7i
On the centre y/a = 0, the equation is represented by --f
f ~ u~/N
Fig 9 Circular motion of the abrasive gram
36
Af =
0.6f 0.6vf - 1~,amq = ~aNm~ 1 2
(8i
JANUARY 1987 VOL 9 NO 1
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing Theoretical equation of roughness The relationship "between the tool feed f and the distance between scratches Af is considered by using the scratch section models shown in Fig 11, in order to establish an equation for roughness generation. Fig 11 (a) shows a single g~ain model and scratches of cutting depth h and edge angle 0 formed at the feed point f. The scratch width 2x is 2h tan(()/2) if ~ =/L Fig 11 (b) is a multiple grain model under the condition A f < 2x. In this case, the scratches of cutting depth h interfere with each other to form continuous scratches and the unevenness of scratch Rth has a smaller value than h. Rth is the roughness of the worked surface. A geometrical calculation for the condition Af < 2x gives Af tan ~ R'h = (tan ~/ tan fl) + 1
Rth = 21 Aftan ~= 2 Aftan 90 -
(10)
Therefore, the theoretical roughness Rm is represented by Eq (11) below by substituting Af from Eq (8) in basic Eq (10) and using the number density of abrasive grain mh by the cutting depth h and the edge angle Oh. 0.6f tan(90 -- 0h/2) 2~am~,.2
0.6Vf tan(90
.....
• 0h/2 )
2~aNmlh-~
(h
E
(cm)
(11 )
Eq (11 ) is effected under f < 3.3~a~m~ ''2 tan(igh/2) because of the condition A f < 2x and if the condition is f _>_3.3~a/~m~h'2 tan(0h/2) (1 2)
Rth(h ) = h
a
15/Jm)
/ //
1
//
&
0
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J
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.
°~0- o
0
•
t~
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o
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/
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005
f,)
/
/ i
001
0.05
•
/
,/"l f,
,
01
f,.,
05
I
Feed (i,, N). cnm
(9)
If the grain edge is perpendicular and the cut becomes =/~+, a basic equation of the roughness of the worked surface is represented by
Rth(R / =
SUS304 P - I kgf cm 2 (98.1 kPa)
Fig 12 Comparison of calculated results with the experimental results
Fig 12 shows a comparison of results of the theoretical roughness Rth calculated from Eq (11) with the experimental results for # 320 abrasive and a disk-type tool of radius a = 35 mm, giving good mutual agreement at an order level. The number of abrasive grains Ma used for the calculation under the condition of P = 1 kgf cm 2 (98.1 kPa) is as follows: h = 0.2/~m: Ma = 105, h = 0.4 l~m: M a = 41, h = 0.75/~m : Ma = 18 - 4 5 and h = 1.51~m: M a = 1 8 - 26. Fig 13 shows a comparison of the disk-type tool with the ring-type in order to study the relationship between the presence of the central part of the disktype tool and the roughness of the worked surface. It is apparent from Fig 13 that the worked surface roughness R s is independent of the presence of the central part of the tool but is finally determined by the abrasive grain action at the outer tool circumference. As stated above, the mechanism of the generation of worked surface roughness in the electrolyticabrasive mirror finishing method depends largely on the grain groups which act in the final stage of the passing of the tool. The grain groups achieve the mirror finishing by virtue of their mirror cutting motion conditions, ie, the feed vf/N, under the highly elastic abrasive grain action. As for highly elastic abrasives, the number of abrasive grains and the edge angle rather
I
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1
SUS304 =320
t, . j ~ ,
b
33 ~ f/m
Fig 11 Section models of typical scratches by abrasive grain in the case of (a) single grain, ~: face angle, fl: chamfer angle and (b) multiple grains
0.5 C
==
°
O
°o ~ "
o o3 0.1
+ Because the abrasive grains are supported by an ultraelastic spring system, serf-ad/ustment (operational balance) to the upright position ~s induced when they cut into the surface to be worked Therefore, it is permissible to assume ~ - ft. M o s t scratched sections are V-shaped
PRECISION ENGINEERING
f
0.05
0.1
0.5 1 Feed (uJN), mm
Fig 13 Comparison of disk-type tool (o, ~/~70mm) with ring-type tool (o, ~fi70 50mm) 37
Maehata, Kamada and Yamamoto---electrolytic-abrasive mirror finishing than the grain size are likely to be major factors in determining the roughness.
Analysis of worked shape formation process The electrolytic dissolution of metal at low current density is not subject to Faraday's law. However, as mentioned above, the electrolytic-abrasive mirror finishing method, with added auxiliary abrasive grain action, can give controllable machining characteristics. The machined pattern under the face of a revolving disk-type tool electrode (which is practicable for plane machining) with respect to determining the formation process of the worked shape is discussed in this section.
Current density a n d r e m o v e d d e p t h d i s t r i b u t i o n on the t o o l electrode surface The holes for the electrolytic solution on the disk electrode face are dispersed over the entire surface, as shown in Fig 4, so that the solution is supplied sufficiently to the machining gap. However, the current density does not become uniform because of the tool electrode revolution, and as shown in Fig 14, concentrates at the outer circumference of the tool in a conical distribution. On the other hand, because of the number of abrasive grains, proportional to the radius as represented by Eq (6), and the large value of
the pressing force distributed at the outer circumference of the t o o l 34, greater abrasive action occurs at the outer circumference. Accordingly it can be expected that patterns will appear for which the removed depth is also larger at the outer circumference Fig 15 shows the profile of the worked surface machined by a tool electrode only, with revolution and results of the profile measured by an electric micrometer. The worked shape obtained is as expected, and the outer circumference is well machined. In other words, the machining action of the tool electrode face has a conical distribution. No is the number of tool revolutions. The machined patterns under the face of the tool are approximated by straight, angular lines d - - N o ~ r (where ~ is a proportional constant changing according to machining conditions) shown by broken lines in Fig 1 5, and the worked shape resulting from the passing of the toot electrode having this machining distribution is presumed in the next section
P r e s u m p t i o n o f w o r k e d shape by w o r k i n g process mode/ Fig 16 shows a working process model explaining the formation process of the worked shape and the removed depth dy in the machining width direction y. which is the integrated result of the action at each point of the tool face. The removed surface pattern per revolution of the tool can be expressed as d . ~r
(r'_:a)
113!
Therefore the removed surface patterns ~n the ~, direction at coordinates x o, x.. x:~.. on the x axes are represented by
N
F7
d(x o, y):. ~(x 2 t y:')~ •
d(x!,
y) = ~ ( x 2 + y2) I '; : ~i(
x-. y)
d(x 2, y ) : : ~(x~ , y'!)~ ~ - ,.tl
x:,. ~)
¢14;
'rV
1.0
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,0,0
]
T00 T0
,o ,0,,,,,,,,
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0.5
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,,. ,
,'
~
,.
~/ V
0.25
10
,
'.
~J~
~ No ~ 380 , N o - 620 No - 8 5 0
#320, J = 1 A cm 2
N = 380 rpm O=31mi n 1 D, - ~70 mm
t =60s Uf-0
"~J 0
J Fig 14 Current density distribution on electrode surface 38
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15
Fig 15 Approximate curve and profile of the worked surface JANUARY 1987 VOL 9 NO 1
Maehata, Kamada and Yamamoto- electrolytic-abrasive m#ror finishing y '
a
a ..--. . . . . . . . . .
o-,----.-:.---_--
oa
d (x0 .y) :e~,"xg + y2 "..~. d (xl, y) = 2a~/'x~
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-~" d
+ y2
d (x~, y) = 2a~/"x2 + y2
Workpiece
d y = a E v " x 2 + y2
Fig 16 Working process model by the disk-type tool electrode Thus, the removed depth dy in the m a c h i n i n g w i d t h direction is calculated by integrating Eq (1 4) and is represented by
d y - ~ % ( x ~ d y2)12
•
/
,,
/
/
, ,
~
,
/
/ , ,
'
/
t . , ' ' / / / / / Tool electrode / / / / / / J V, ,'.,','//.,',,1.,,.1 i i .. . / / / / / , / A 50 A
(15)
40
30
20
10
0
10
20
30 40
50 (r) mm
where
a
J-1Acm
2 ~320, P-
1 kgf cm -p (98.1 kPa)
(d)/Jm ~ 3 4 0 m m m i n N = 620 rpm
a
1
(r) turn o
50
50
Comparison w i t h experimental results The removed depth d c s h o w n in Fig 5 is the result of examining the position where the centre of the tool passes and these experimental results are represented by the worked shapes s h o w n in Fig 18. A c c o r d i n g to
1 2 3
y/a 1.0 0.8 0.6 0.4 0.2
0
0.2 0.4 0.6 0.8 1.0
6 c~1
u~ = 1 5 0 m m rain -1
b
(d)/Jrn
320, J= 1Acre N = 620 rpm
(r) mm 50
~2
0
5O
~3
N = 620 rpm
c~4
5 C
dy
Fig 17 Simulated results of the worked shape PRECISION ENGINEERING
=320, J = 1 A cm 2 vt = 340 mm min 1
(d) ,urn
Fig 18 Experimental results of the worked shape showing the influence of (a) the current density, J, (b) feed velocity, W, and (c) tool revolutions per minute, N 39
Maehata, Kamada and Yamamoto---electrolytic-abrasive mirror finishing Fig 18, the simulated results shown in Fig 17 accurately explain actual worked shapes. Both the simulated and actual curves have convex centre shapes. Normalization of the worked shape by the ratio dv/d c (shape coefficient) 5 to the removed depth dc at the centre gives nearly equal patterns regardless of machining conditions and removed depth, as shown in Fig 19. This is also explained by the fact that the ratio of d c = =~(x~n) 1/2 to Eq (15) is dvld c = ~ (X'~n+ y2)1,,'2/~(x2) 1/2 which is independent of ~. The comparison of normalized simulated results also shows nearly average values of experimental results. The results shown in Fig 19 contain tool-worked shapes with diameter 2a = 50 - 120 mm, in addition to the experimental results shown in Fig 18. From the above analysis and experimental results, the approximation of the machined pattern of the revolving disk-type tool electrode increasing linearly in the direction of the outer circumference with the tool centre as zero is appropriate. Thus the formation of the convex centre worked shape is made clear. The worked shape is represented by a constant shape coefficient dv/d c which is not affected by machining conditions.
Discussion of analytical results Shape accuracy Plane machining using a disk-type tool generates a worked shape similar to that shown in Fig 19, giving this type of machining a limited use when applied to machining requiring a good plane degree. For example, for a worked face larger than the tool diameter, a tool path overlapping 1 0 % of the worked width is required. For small parts, machining should be implemented within 7 0 % (y/a < 0.7) of the central part of the tool. However, in either case, according to Fig 19, the plane degree S is
S - - i d v l d c - 11 x d c - 0 . 1 d ~
b e d c < 1 0 l l m in the case o f S : l l ~ m a n d de< 1,m~ in the case of S = 0.1/~m. An addition of motion by which the tool feed Js vibrated horizontally is recommended as a method to improve machined patterns by a disk-type tool. Machining cylindrical workpieces with a concave tool is also highly recommended because the machined patterns under the tool face are uniformly distributed and the working time on each part of the worked surface by passing the tool is the same. Fig 20 shows a measurement result of a machining accuracy check of cylindrical work machining, with an accuracy of 1 l~m or b e l o w / 1 0 0 m m
Cylindrical work machining mechanism by concave face too/ Fig 21 shows a schematic diagram of a cylindrical workpiece being machined. The machining is carried out by giving constant-speed feed vf in the axial direction by using a concave face tool electrode of a nearly equal diameter to the workpiece diameter D. In this case, the workpiece rotates and an electrolytic solution is supplied into an abrasive through the face of the electrode. vf/N is a major factor for the achieving of a worked surface roughness similar to that of plane machining The tool shape factor largely depends on the tool height H e, independent of the tool width WE, thereby H E corresponds to the outer circumference of the disk-type tool and WE to the central part. An equation for generation of roughness by the cylindrical work machining method is obtained as 0.6vf tan(90 - i)h/21
RTh -
:17~
HeNm~ ?
As can be seen, this is similar to the equation for plane roughness, Eq (11).
(16)
In order to ensure accuracy, the removed depth should ~ d
0
0.2
0.4
06
0
0.8
1.0 T- --
' - -
02
I
-~lb
I
o
^ •
I I
ol
% J 04 I I
i
i
;
i
-
i
J
i
i
i
l
1
i
,
: . ~ - ,
i
100 mm
i
,
;
,
I
-
Fig 20 Machining accuracy of cyhndrical work machining
06
Simulated 08
~
Work piece:
/~ H.
_
_ _
=320 2a = 50-120 mm d,: = 12-85 #m on
~ eH:clr
od~t
1.2[
Fig 19 Normafization of the worked shape 40
Fig 21 Schematic diagram of cyhndrica/ work machining JANUARY 1987 VOL 9 NO 1
Maehata, Kamada and Yamamoto--.electrolytic-abrasive mirror finishing
The removed depth d is determined by the amount of facing time used with tool t and J because of uniform distribution of the current density J and the number of abrasive grains on the worked surface facing the concave face tool, and is represented by
HE WEplkJn
d=
nD vf
p
(1 8)
- Kt~lkJn/p
where p is the density of a workpiece, n is the number of tool passes and K the tool facing ratio (WE/~D). In Eq (18), each part of the worked surface is uniform and theoretically the worked shape (roundness or machining accuracy) is maintained. The accuracy of the machine, if less than 5/100mm, will have no influence on the worked shape. On the assumption of setting removed depth as d o and n - 1, the working time t is as follows from Eq (18):
12 are approximated by J=lAcm J=0
Fig 22 shows the results of a confirmation experiment comparing workpieces between diameter D = 030, 96 and 800 mm, wherein K is kept constant and t is independent of the workpiece D. Eq (19) demonstrates one of the characteristics of the electrolytic-abrasive mirror finishing method, representing the improvement of productivity as the workpieces become larger in diameter. 6
Rs-O.95(vf/N)O25
(l~m)'~
R s - O . 5 4 ( v f / N ) °4
(iLm) J
(20) and if the distance between scratches of Eq (8) is arranged by Af s vt/(2aN ) = vf/ND E and vt/N in Eq (20) is substituted by vf/NDE, then J=lAcm
2.
J ---0:
R~ - 2.77(vf/NDL) °25
R:, / P 13
(22)
Eq (21) is an experimental equation at P = 1 kgf cm 2 (98.1 kPa). Thus R l h i l ) = 1 is set and roughness ratios ;' = Rt~,(m,,'Rth(1) are ntroduced ~' = P 1 3from Eq (22) and (,'vf/NDE) are used relating to the machining condition of Eq (21) and then ; becomes •
J=lAcm
2.
Vf
. 0 25
R s=2.771 1 ~ k ND~P 3 3
J=0:
The theoretical roughness Rth represented by Eq (11 ) can explain experimental results at an order level, but the setting of machining conditions with accuracy is difficult if R~,~ is applied to actual machining without modification. The experimental results shown in Fig
/ cm :' 5 kgf(:m ? (4903 kPa)
J - 2 A
P
/
,/
E o
0
E
!
GI
101
(/,m)
(llm)
(24)
Fig 24 shows an application example of Eq (24) to mirror finishing of a large surface area by a tool
•
o/.
ID
)o 4
resulting in successful substitution of the practical machining equation for the theoretical Eq (11).6 The units of the machining conditions in Eq (23) arevf (mm min 1 ) , N ( r e v m i n 1), DE (mm) a n d P (kgf cm 2), respectively. Fig 23 shows a comparison between the practical Eq (23) and experimental values, proving that Eq (23) adequately explains the experimental results. The above discussion is for # 3 2 0 abrasive. Furthermore, a similar equation to Eq (21) is calculated for # 1500 abrasive used for mirror finishing. If J - 0, then the equation is represented by Rs = 0.66(vf/NDE) °4
o/
20
Rs : 3OSt, NDEv "
(/~m)
(23)
Practical equation for the w o r k e d surface roughness and generating of mirror finish
30,
(Pm) l (l~m)~ (21)
Rs = 3.03(vf/NDF) °4
where D E is the tool electrode diameter. The pressing force of abrasive P determines the number density of abrasive grains Mg. They are in a relationship of m g / p2.3, which is substituted into theoretical Eq (11) to obtain
(1 9)
t - do~/K~ikJ
2:
#320, SUS304
I.
/
E ~
0.5
Calculated 1
0
0
20
i
40
I
l
I
60
80
100
0.2 120
Working time (t) s
Fig 22 Relationship between D and d of cylindrical workpieces • D = 030ram, 0 D = ~h96mm, × D ~- ~/~800mm
PRECISION ENGINEERING
0.1
i
o
ooo2
o
o&
oo08
o.o,o
0.O12
0014
t~f / (NDE)1/3 Fig 23 Proof for experimental equation
41
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing Exp. equation: R, = 0.07 (ujN) °4
0.15
I
i
I. . . .
,
I
.J"
"~ C'~
-4
Fig 26 Mirror finishing using free-state abrasive grams
0.05 =1500, SUS304 D. = 0 3 5 0 mm
0
............... 0
500
1000 1500 2000 Feed velocity II~) mm rnin 1
Conclusions
2500
Fig 24 Mirror finishing of a large surface area
The following summarizes the analyses of the machining mechanism and experimental results for the electrolytic-abrasive mirror finishing method: •
electrode of D E = ~#350 mm. The worked surface roughness of Rs = 0.05 --- 0.08 HmRz is obtained at v~- 500mm min 1 Fig 25 shows an example of mirror finishing of a cylindrical workpiece (SKD-11:~h96 mm) with 6 s finish and a worked surface roughness of 0.01 0.03 l~mRz. Fig 26 shows the machining result 7 from using free-state abrasive grains in which very small abrasive grains are mixed into an electrolytic solution and the worked surface has a generated physical mirror surface of 0.0021~m
Action factors in machining mechanism and highprecision machining The electrolytic-abrasive mirror finishing method has excellent capacity as a method of generating mirror levels of up to 0.1/~m Rz in a short time. In order to establish it as a high-precision machining method, however, further study on shapes and motions of tool electrodes is required, as well as a review of the viscoelastic behaviour of abrasive grains. 8 Fig 27 shows a summary of the action factors participating in the mechanism of electrolytic-abrasive mirror finishing, as discussed above.
•
•
The removal of metal is performed mainly by electrolytic dissolution with the aid of grain action and is proportional to working current and time i.e. subject to Faraday's law. The worked shape is determined by the distribu tion of the removed depth under the face of the tool electrode and by the tool feed. Revolving disk-type tools can be approximated by a conical machined pattern, and the worked shape has a centre convex shape, represented by a constant ratio independent of machining conditions or removed depth. An electrolytic-abrasive machining method using a concave-faced tool with uniform machining distribution applied to cylindrical work achieves results very close to high-precision machining. The generation of worked surface roughness ~s accomplished mainly by grain action. The electrolysis becomes a reducing factor because of the formation of pits, thereby requiring a proper balance with the abrasive grain action. The mechanism of generation of roughness largely depends on the grain groups which act in the final stage of the passing of the tool and on their motion conditions under the highly elastic abrasive grain action with an extremely small spring constant. The roughness is determined by the number of grains and the edge angle rather than by the grain size.
Abrasive
( G....... i
grain size
_ ,~ ................
bet (nl,/~_~_.
(~ Edge angle of gta,rl,:~ r-- ----~Pre~sing f .... (P)
,'. ) ,
j
shape
'
I! ( Current density (J) El~tfoWteno~,,a~e~OI
~ > ~ "~
.....
Pr :mjr~' ac~k;r, Sul~plecnerl~lr~"Jchon
Fig 2 7 Machining factors and effect in electrolyt¢c
Fig 25 Example of 0.01 0.03 llm Rz mirror finishing 42
abrasive finishing JANUARY 1987 VOL 9 NO
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing •
The equations for plane machining by a revolving disk-type tool and for cylindrical work machining by a concave faced tool, respectively,
helpful guidance and encouragement of Dr Keiji
are obtained as follows:
References (in Japanese)
0.6vf tan(90 - (~/2) Rth = -2~a--lVm~ ~ -- (cm) 0.6vf tan(90 - ~t/2) Rth = -. HE~Im~, ~ -- (cm) Furthermore, the above equations are modified to
empirical equations applicable to practical machining. The equations obtained are J=lAcm
2:
Rs=A
ND
1/3) Vf
J = 0:
Rs = B NDEPI,, 3
(F~m)
)0 4
(tim)
where A and B are constants determined by the abrasive used and are confirmed in their agreement with actual values.
Acknowledgments The authors wish to express their gratitude for the
PRECISION ENGINEERING
Okushima, Professor Emeritus of Kyoto University.
1 T a m i y a K. et al. MLrror finishing of metals using the electrolyhc-abras=ve mirror finishing method. The Hitachi Zosen Technical Review, 1981, 42 (3) 2 Sugie Y. Y o s h i z a w a S. et al. The relationship between current density and machining characteristics in the electrochemical machining for various steels The Electrochemical Society of Japan, 1978, 46 (3) 3 M a e h a t a H., Kamada H. and Y a m a m o t o , M. Studies on mirror finishing by buffing (1 st and 2nd Reports). Collection of Papers No. 427, 428, "82 Autumnal Meeting of the Japan Society of Prec. Engg., 1982 4 Kamada H. and Maehata, H. Studies on electrolytic-abrasive mirror finishing (5th Report). Collection of Papers No. 334, "83 Autumnal Meeting of the Japan Society of Prec. Engg., 1983 5 Maehata, H. Kamada H. et al. Study on electrolytic-abrasive mirror finishing of a cylindrical work (1 st Report). Collection of Papers No, 325, 79 Autumnal Meeting of the Japan Society of Prec Engg, 1979 6 M a e h a t a H. and Kamada H. Studies on electrolytic-abrasive mirror finishing (4th Report). Collection of Papers No. 333, "83 Autumnal Meeting of the Japan Society of Prec. Engg., 1983 7 Kamada H. et al. A study on electrolytic-abrasive mirror finishing Bull Japan Society of Prec. Engg., June 1982, 16 (2) 8 Kurobe T., Imanaka O. and O m u r a M. Finishing characteristics in extrude hone process. J. Japan Society of Prec Engg, 1982, 48 (8)
43
Keywords: electrochemical machining, mirror finishing
An ultimate target of production machining technologies is the realization of high-precision machining that has high performance and reliability at low cost. To attain this, machining methods capable of removing and machining extremely small amounts of material stably and effectively with minimal heat or vibration disturbance are required. One of the methods to realize these aims is an electrochemical machining method capable of removing metal in the form of ion particles. In practice, however, this method is not able to produce a smoothfinished, high-precision surface because of nonuniform dissolution due to material composition or defects. On the other hand, it is expected that rendering this dissolution action uniform will provide a faster method of high-precision machining, making it possible to achieve high-precision finished surfaces of near atomic order. The electrolytic-abrasive mirror finishing method combines electrolysis, capable of removing extremely small amounts of metal, with an abrasive grain action on highly elastic minute cuts, as a way to achieve the aims set out above. It is a new mirror finishing method providing stable removal action and capable of finishing a large surface area to mirror smoothness in a short time, thanks to the highly efficient eliminating properties of electrolytic products. 1 Applications of this method include inner surface finishing for chemical vessels and mirror finishing for atomic power-related equipment, as well as parts of marine diesel engines and stainless steel substrate for amorphous silicon solar cells. 1 The application of this method to mould processing or electronic equipment parts is also under study. The required surface roughness hasa wide range of 0.01 0.21~mRz, and * Techmcal Research Inshtute, Hitachi Zosen Corporation, 3 22. Sakurajlma l-chome, Konohana l~u, Osaka 554, Japan
PRECISION ENGINEERING
materials appropriate for application are various, ranging from stainless and ordinary steel to nonferrous metals such as aluminium, titanium and copper. However, this finishing technology has many unsolved problems, including tool electrode design, establishment of proper machining conditions for mirror finishing of free curved surfaces or planes of large surface area, development of technologies for mirror finishing very hard material and nonferrous metals, as well as perfection of technologies for high-precision machining of worked shapes. This paper aims mainly to describe the solution of these problems associated with high-precision machining mechanisms. In electrolytic-abrasive mirror finishing, the machining effects from the combined actions of electrolysis and abrasive grains are first explained, followed by an analysis of the generaton mechanism of worked surface roughness and the formation process of worked shapes; the experiments conducted to study the suitability of this method are described.
Machining effects from the combination of electrolysis and abrasive grains Application of direct current voltage to two facing metals in an electrolytic solution causes the anode metal to be dissolved in an ionic unit. An amount of the dissolved metal W is proportional to an applied quantity of electricity / x t (current x time) from Faraday's law, and represented by
W=qklt
(g)
(1)
where k is the electrochemical equivalent intrinsic to an anode material, and ~1is the current efficiency used for dissolution and affected by oxygen generation or oxide film formation. ~1is a ratio of a theoretical value kdt and an actual amount of metal removed W and has the characteristics shown in Fig 1:~1 is low in the
0141 6359/87/010031 13/$0300 q 1987 Butterworth & Co (Publishers) Ltd
31
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing 300 $45C(2 cm 2
t=60s 20% NaNO3
~, 20O
/ //
o
E &)
/
100 W 80 ~o >.
6O
~
e
E
100
#
4o
/ /
20
,Z 0
~ 0
~ 0 2 4 6 8 Current density (J) A cm ~
10
a
300
/
~' 200
, /
e
$45C (2 cm 2) J=3Acm 2 20% NaNO3
8O
#
I d
0
100
6o { ._~
l
~b
E <
means of mirror finishing because of the generation of oxide film or pits on the dissolved surface. Fig 2 shows the machining results of abrasive grain action w h i c h was combined with electrolysis in order to eliminate the electrolytic products, as well as to continuously maintain the ground metal surface and to remove metal uniformly over the entire surface area In the machining experiments, # 3000 polishing abrasive was applied to the face of a hollow Cu cathode of ~/)20 (h12 mm and rotated while pressing to the face of a $ 4 5 C anode. A 2 0 % aqueous solution of passivation-type sodium nitrate f l o w e d out from the centre of the cathode face. It is apparent from Fig 2 that, due to the combination of grain action, the amount of removed metal W is nearly proportional to the working time t and that the current efficiency ~1 has a constant of approximately 60°,/,,, independent of t. A comparison of worked surfaces w h e n electrolysis alone is used and w h e n abrasive is combined with it, is s h o w n in Fig 3. The worked surface by the electrolytic-abrasive method has a uniform metal mirror finish with no film or pits generated. The abrasive used should have elastic abrasive grain action, as well as water permeability and insulation in order to create a homogeneous smooth surface by the uniform pressing force of the grains with minute cuts. As mentioned above, it has been confirmed that the combination of grain action with electrolysis provides an efficient method of metal removal (subject to Faraday's law) while simultaneously generating a lustrous metal surface. The electrolytic-abrasive mirror finishing method. a new mirror finishing method, aims to provide these combined machining effects. This is achieved through developing the appropriate shape or movement path for tool electrodes optimal to large-surface areas, and to various shapes and materials, applied under the
% 40
loo
~
300
.... $45C(2
"" .,,
o
w ~ -
cm 2 )
J = 3 A cm-2
b
0
100 200 Working time (t), s
300
Fig 1 Characteristics of electrolytic dissolution. (a) effect of current density, J, and (b) influence of working time, t current density region of less than 10 A cm 2 but rises as J increases and becomes nearly 1 0 0 % at several 1 0 A c m 2 . Studies of the relationship between r/and working time t, however, s h o w t/ has a tendency to decrease sharply immediately after initiation of application of electricity w h e n the value of ~1 is less than 20 % at about 1 00 s. This is because of the growth of oxide film or electrolytic products 2, making it difficult to control the amount of metal removal by electrolysis alone. In addition, this is not an efficient 32
/
20
r/ 0
W
~
~
Electrolytic abrasive
200 1
100 80
~; p-
,60 cc E
E 40 (_;
~
0 " 0
Electr?lysis
W ~
,
L 100
,
~ 200
2o
L
0 300
Working time it), s
Fig 2 Comparison of electrolytic abrasive with electrolysis J A N U A R Y 1987 VOL 9 NO !
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing
~ f
Fig 3 Comparison of worked surface." (a) with electrolysis only and (b) with the electrolytic-abrasive method
proper conditions of electrolysis and grain action, depending upon the unevenness of the ground and the desired worked surface roughness. In the following, the machining characteristics of this finishing method are described and the generating mechanisms of worked surface roughness and the formation process of worked shapes are analysed. Machining
characteristics
Fig 4 shows the outline of a revolving disk-type tool electrode used in the machining method. The tool electrode consists of a disk electrode (cathode) with numerous holes for the electrolytic solution, to the face of which an abrasive (unwoven nylon cloth impregnated with resin grains) is applied. The machining is carried out by pressing a tool electrode to a workpiece (anode) and spinning it with a speed of revolution N to give v~. Electrolytic and abrasive conditions are selected according to the unevenness of the ground and finish level desired 1. For example, an initial surface of 5-- 10HmRzis finished to the worked surface roughness of 0.1 - I l~mRz with # 240 #600 abrasive by applying a current density of J - 0 . 5 1 A c m 2. This worked surface is then further machined to a mirror surface of 0.01 0.1 Hm Rz with #800 - # 4 0 0 0 abrasive under the condition of J - 0. An appropriate balance of the two actions gives this result. In rough machining, high-speed metal
~
N
E,~c~oIv,~~.\~tk~,'q~ ' ~ ~q / /
"
""
,.;///7/'/',,"/'/'//// Workpiece
Fig 4 Basic diagram of the electrolytic-abrasive mirror finishing method using a disk-type tool electrode PRECISION ENGINEERING
removal is carried out by employing a high current density, as well as large abrasive grains. For mirror finishing, small grains and low current density are selected. Any break in this balance, particularly by use of excessively strong electrolysis, deteriorates the worked surface by forming pits, destroying the mirror surface. The primary machining factors of the electrolyticabrasive finishing method are the pressing force of abrasive P, the speed of revolution of tool electrode N and relative feed velocity vf in addition to the abovementioned current density J and working time t. The basic machining characteristics of each factor are shown in Fig5(a) (d), where machining is performed using # 3 2 0 abrasive, J = 1 A cm 2, and SUS304 is machined by an electrode of tool diameter DE = d~70mm. The removed depth d c is a value at the position where the centre of a tool electrode makes one pass and the worked surface roughness R s is a ten-point height of irregularities. The initial surface is a 0.05 l~mRz mirror. It is clear from Fig 5 that the removed depth dc is proportional to J even though the amount of metal removed by the # 3 2 0 abrasive is added and is inversely proportional to the feed velocity vf corresponding to t. However, dc is proportional to the tool speed of revolution N and has an increasing value as the pressing force P becomes larger. This is because the mirror cutting action of the abrasive grain and the grain action increase the combined efficiency ~1". In the experiments, ~1= 100%, is obtained at P = 10kgf cm 2 (981 kPa) or above. On the other hand, R s has a high value under the conditions of large J and low P because of the formation of micropits, and has a tendency to be proportional to vf and inversely proportional to N, both of which are independent of the formation of the pits. Fig 6(a) shows the pattern of scratches on the abrasive-worked surface. Concentric scratches are formed immediately below the tool. After the tool is passed over, however, regular scratches nearly equal to the radius of the outer circumference of the tool appear on the worked surface. This may be explained * Actually current efficiency, but referred to as c o m b i n e d efficiency, o w i n g to the c o m b i n e d abrasive action
33
Maehata, Kamada and Yamamoto---electrolytic-abrasive mirror finishing 5
1.5
1.5
dc
4 E
E
1.0
:::L. ,.-:
3
E
1.0
E
::t
aE
£
c_
£
2
'"c
o
0.5
o
~,
n-
rr
Rs
/'
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-o "o
0.5 i
SUS304, D E =2~70 P = 1 kgf c m (98.1 kPa) #320 m
0.5 Current
I
~
1.0
1.5
density
(J), A cm
SUS304, D~ ,= ~70 =320, J= 1Acm 0
A
&
i
100
2.0 -2
"2
I
200
Pre~ingforce(P),kPa
a
b
SUS304, D( = q~70 N = 6 2 0 rpm ;-'320, J : 1 A cm 2
14
5,
1.5
1,5
SUS304, D~ = ~)70
12
mm rain- 1 #320. J = 1 Acm -2
uf = 340
E
E
::&
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E o.
E
1.0
::L dc
..c
e::
£
1.0
c
t~
==
c
"o "o
o
o
nr
0.5
rr
0
i 200
A 400
i 600
i 800
Rs
t3
~
0.5
0 1000
L
200
Tool revolution per minute (N), rpm ( m i n - 1 )
C
,~
&
A
J
A
400
0
600
Feed v e l o c i t y (Uf), m m rain
--1
d
Fig 5 Characteristics of removed depth and worked surface roughness with the electrolytic-abrasive method. Influence of (a) current density, J, (b) pressing force, P, (c) tool revolutions per minute, N, and (d) feed velocity, vf
34
JANUARY
1 9 8 7 V O L ~-~ r'4(~
Maehata, Kamada and Yamamoto --electrolytic-abrasive mirror finishing ! 0 f~
Vf~
~
V,=
- "Y'
Vitrified .qrindmg wheel
10 S
a
b
Fig 6 Sketch of scratches on the abrasive-worked surface having used (a) the disk-type tool and (b) the ring-type tool
104
E
,1
by the fact that the abrasive grain action of the outer circumference of the tool is the action that forms the surface. The scratches made by a ring-type tool shown in Fig 6(b) also prove this fact. The regularity of the scratches on the abrasive-worked surface is subject to tool feed determined by vf N and the continuous surface of the scratches becomes the worked surface roughness.
10-'
,'1
102
101
L )) ~ ' ~ L ~ . / " ~ / ' ~ J ~ ' ~
Analysis of mechanism of worked surface roughness generation In this section, the dynamic properties of an abrasive containing grains and the role played by machining factors in roughness generation are quantified and the generation mechanism of the worked surface roughness is analysed.
~~l t
10 °
0
01
4
5
6
7
8
Compression of abrasive (,~), mm
Fig 7 Spring constant of abrasive buffs
Dynamic properties of abrasives
The abrasives used, usually called buffs, and made by impregnating resin containing grains (AI203, SiC) in unwoven nylon cloth, have highly elastic and viscoelastic properties. The pressing force of abrasive P is a logarithm of the compression of abrasive ;.. The coefficient of variation of the pressing force AP/A). is, as shown in Fig 7, four to five orders smaller than that of a rigid vitrified grinding wheel and has high elasticity. Therefore, the abrasive grain action is hardly affected by the precision of the machining device. For example, the pressing force variation AP is several 10 gf cm 2 to the variation of A).-- 1/100 mm, thereby resulting in a variation of the pressing force of a grain AP/m:~ of about 0.01 gf, where m g is the number density of abrasive grains acting on the worked surface and, if the pressing force P is equally divided among each abrasive grain, the pressing force of grain PG is calculated by Pc, = P/mq
=240
2 Q.
=1500 5~
0
l
5;o
1000
( m q ) number crrl :'
I
(2)
Fig 8 shows the relationship between )., P and mg by measuring the number density of abrasive grains mg from the mirror cutting scratches by a scratch transfer method. From this figure, the pressing force of a grain PG iS calculated to be 30-80gf from #240 abrasive, 5 9gffrom # 3 2 0 a n d 2 4gffrom #1 500, each of which has an approximately c o n s t a n t PG3. If the grain shape is assumed to be a core of the edge angle 0, the cutting depth h to the worked surface PRECISION ENGINEERING
1000
E
_-S,.<
::240
:;320 ~1500
I0
Fig 8 Relationship between ~., P and mg
35
Maehata, Kamada and Yamamoto--electrolytic-abrasive
mirror finishing
Table 1 Measurement results of the edge angle of abrasive grains Edge angle of abrasive grains 0h (deg) Abrasive h = 0.21~m
h = 0.41zm
h =. 0.75l~m
h = 1.5 f~m
Average (i (deg)
#240
167
154
144
140
152
#320
164
160
148
142
155
(material hardness: Hv) by the pressing force of a grain PG is represented by
,f P _coslO/2) I' (3)
0.8
where h is decided by the edge angle 8 if PG is constant. Table 1 gives the measurement results of h and/). (The edge angle is read by each average cutting depth /~ from the section shape profile of mirror cutting scratches and ~h is an average of 20 measured values.)
0.6
h = [ H v 7z tan(fl/2) ~
F
','1
0.4
Grain m o t i o n a n d m i r r o r c u t t i n g scratches
The grain motion of a revolving disk-type tool is given by the tool speed of revolution N and relative feed velocity vf as shown in Fig 4. Fig 9 shows the approximate loci made by the motion of one grain of radius r on a tool and the equation at time t is represented by f(x.v, tl = (X ..... vft)2 + y2 _ / 2
= 0
'°> Fig 1 0 s h o w s the relationship b e t w e e n the feed f at the width direction g / r from Eq (5), and the distance b e t w e e n scratches A f , where m = 1 w h e n a single grain
rt
Af
1"2
]
06
08
'~,
0
0.2
0.4
1
(4)
tf vft in Eq (4) is assumed to be the feed of the revolution centre f ( = vf/N), the distance Af (in the radial direction) between circular scratches is calculated by
Y
f 02
Fig 10 Relationship between v/r and Af/f
is used and m = 5 and 50 when multiple grains are aligned at equal distances on a circle with radius r From this calculation, the larger m is and the closer y/r is to 1, the smaller Af becomes. The number of working grains M, on a circle with radius r is calculated from the following equation, assuming that the grains are in a regular lattice alignment: M, :: 2~.r/Xg = 2.=r/~(m~, 1'' ~ 212m~, I ;')/2'. = 1.66~rm~ '2
(6>
where Xg is the average distance between grains. The scratches occurring with the passing of the tool are determined by grain groups on the outermost circumference of the tool, as shown in Fig 6. If M a is substituted for M, in Eq (6) by using a tool radius a and f / M a for f in Eq (5), then a general equation of the distance Af between scratches generated is given by i
cos(s,o "~'f =
1/2
d
z[amg
[0'0"tcos'("n
]
11. 1
~2a2mg
f-
1.'2
a,,
t7i
On the centre y/a = 0, the equation is represented by --f
f ~ u~/N
Fig 9 Circular motion of the abrasive gram
36
Af =
0.6f 0.6vf - 1~,amq = ~aNm~ 1 2
(8i
JANUARY 1987 VOL 9 NO 1
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing Theoretical equation of roughness The relationship "between the tool feed f and the distance between scratches Af is considered by using the scratch section models shown in Fig 11, in order to establish an equation for roughness generation. Fig 11 (a) shows a single g~ain model and scratches of cutting depth h and edge angle 0 formed at the feed point f. The scratch width 2x is 2h tan(()/2) if ~ =/L Fig 11 (b) is a multiple grain model under the condition A f < 2x. In this case, the scratches of cutting depth h interfere with each other to form continuous scratches and the unevenness of scratch Rth has a smaller value than h. Rth is the roughness of the worked surface. A geometrical calculation for the condition Af < 2x gives Af tan ~ R'h = (tan ~/ tan fl) + 1
Rth = 21 Aftan ~= 2 Aftan 90 -
(10)
Therefore, the theoretical roughness Rm is represented by Eq (11) below by substituting Af from Eq (8) in basic Eq (10) and using the number density of abrasive grain mh by the cutting depth h and the edge angle Oh. 0.6f tan(90 -- 0h/2) 2~am~,.2
0.6Vf tan(90
.....
• 0h/2 )
2~aNmlh-~
(h
E
(cm)
(11 )
Eq (11 ) is effected under f < 3.3~a~m~ ''2 tan(igh/2) because of the condition A f < 2x and if the condition is f _>_3.3~a/~m~h'2 tan(0h/2) (1 2)
Rth(h ) = h
a
15/Jm)
/ //
1
//
&
0
0.5
J
1 Acre
.
°~0- o
0
•
t~
/
"~oo
I
o
(h - 0 . 2 , u r n )
/
/ 0.1
,/ - 0 Calculated (f.
005
f,)
/
/ i
001
0.05
•
/
,/"l f,
,
01
f,.,
05
I
Feed (i,, N). cnm
(9)
If the grain edge is perpendicular and the cut becomes =/~+, a basic equation of the roughness of the worked surface is represented by
Rth(R / =
SUS304 P - I kgf cm 2 (98.1 kPa)
Fig 12 Comparison of calculated results with the experimental results
Fig 12 shows a comparison of results of the theoretical roughness Rth calculated from Eq (11) with the experimental results for # 320 abrasive and a disk-type tool of radius a = 35 mm, giving good mutual agreement at an order level. The number of abrasive grains Ma used for the calculation under the condition of P = 1 kgf cm 2 (98.1 kPa) is as follows: h = 0.2/~m: Ma = 105, h = 0.4 l~m: M a = 41, h = 0.75/~m : Ma = 18 - 4 5 and h = 1.51~m: M a = 1 8 - 26. Fig 13 shows a comparison of the disk-type tool with the ring-type in order to study the relationship between the presence of the central part of the disktype tool and the roughness of the worked surface. It is apparent from Fig 13 that the worked surface roughness R s is independent of the presence of the central part of the tool but is finally determined by the abrasive grain action at the outer tool circumference. As stated above, the mechanism of the generation of worked surface roughness in the electrolyticabrasive mirror finishing method depends largely on the grain groups which act in the final stage of the passing of the tool. The grain groups achieve the mirror finishing by virtue of their mirror cutting motion conditions, ie, the feed vf/N, under the highly elastic abrasive grain action. As for highly elastic abrasives, the number of abrasive grains and the edge angle rather
I
E
1
SUS304 =320
t, . j ~ ,
b
33 ~ f/m
Fig 11 Section models of typical scratches by abrasive grain in the case of (a) single grain, ~: face angle, fl: chamfer angle and (b) multiple grains
0.5 C
==
°
O
°o ~ "
o o3 0.1
+ Because the abrasive grains are supported by an ultraelastic spring system, serf-ad/ustment (operational balance) to the upright position ~s induced when they cut into the surface to be worked Therefore, it is permissible to assume ~ - ft. M o s t scratched sections are V-shaped
PRECISION ENGINEERING
f
0.05
0.1
0.5 1 Feed (uJN), mm
Fig 13 Comparison of disk-type tool (o, ~/~70mm) with ring-type tool (o, ~fi70 50mm) 37
Maehata, Kamada and Yamamoto---electrolytic-abrasive mirror finishing than the grain size are likely to be major factors in determining the roughness.
Analysis of worked shape formation process The electrolytic dissolution of metal at low current density is not subject to Faraday's law. However, as mentioned above, the electrolytic-abrasive mirror finishing method, with added auxiliary abrasive grain action, can give controllable machining characteristics. The machined pattern under the face of a revolving disk-type tool electrode (which is practicable for plane machining) with respect to determining the formation process of the worked shape is discussed in this section.
Current density a n d r e m o v e d d e p t h d i s t r i b u t i o n on the t o o l electrode surface The holes for the electrolytic solution on the disk electrode face are dispersed over the entire surface, as shown in Fig 4, so that the solution is supplied sufficiently to the machining gap. However, the current density does not become uniform because of the tool electrode revolution, and as shown in Fig 14, concentrates at the outer circumference of the tool in a conical distribution. On the other hand, because of the number of abrasive grains, proportional to the radius as represented by Eq (6), and the large value of
the pressing force distributed at the outer circumference of the t o o l 34, greater abrasive action occurs at the outer circumference. Accordingly it can be expected that patterns will appear for which the removed depth is also larger at the outer circumference Fig 15 shows the profile of the worked surface machined by a tool electrode only, with revolution and results of the profile measured by an electric micrometer. The worked shape obtained is as expected, and the outer circumference is well machined. In other words, the machining action of the tool electrode face has a conical distribution. No is the number of tool revolutions. The machined patterns under the face of the tool are approximated by straight, angular lines d - - N o ~ r (where ~ is a proportional constant changing according to machining conditions) shown by broken lines in Fig 1 5, and the worked shape resulting from the passing of the toot electrode having this machining distribution is presumed in the next section
P r e s u m p t i o n o f w o r k e d shape by w o r k i n g process mode/ Fig 16 shows a working process model explaining the formation process of the worked shape and the removed depth dy in the machining width direction y. which is the integrated result of the action at each point of the tool face. The removed surface pattern per revolution of the tool can be expressed as d . ~r
(r'_:a)
113!
Therefore the removed surface patterns ~n the ~, direction at coordinates x o, x.. x:~.. on the x axes are represented by
N
F7
d(x o, y):. ~(x 2 t y:')~ •
d(x!,
y) = ~ ( x 2 + y2) I '; : ~i(
x-. y)
d(x 2, y ) : : ~(x~ , y'!)~ ~ - ,.tl
x:,. ~)
¢14;
'rV
1.0
I/S, - - f -
[ Toolelectro~ 0.75
E f.; < ~.
,0,0
]
T00 T0
,o ,0,,,,,,,,
> C Q~ %;
0.5
• s
,,. ,
,'
~
,.
~/ V
0.25
10
,
'.
~J~
~ No ~ 380 , N o - 620 No - 8 5 0
#320, J = 1 A cm 2
N = 380 rpm O=31mi n 1 D, - ~70 mm
t =60s Uf-0
"~J 0
J Fig 14 Current density distribution on electrode surface 38
SoI
E ~
15
Fig 15 Approximate curve and profile of the worked surface JANUARY 1987 VOL 9 NO 1
Maehata, Kamada and Yamamoto- electrolytic-abrasive m#ror finishing y '
a
a ..--. . . . . . . . . .
o-,----.-:.---_--
oa
d (x0 .y) :e~,"xg + y2 "..~. d (xl, y) = 2a~/'x~
U,
X
I
0
-~" d
+ y2
d (x~, y) = 2a~/"x2 + y2
Workpiece
d y = a E v " x 2 + y2
Fig 16 Working process model by the disk-type tool electrode Thus, the removed depth dy in the m a c h i n i n g w i d t h direction is calculated by integrating Eq (1 4) and is represented by
d y - ~ % ( x ~ d y2)12
•
/
,,
/
/
, ,
~
,
/
/ , ,
'
/
t . , ' ' / / / / / Tool electrode / / / / / / J V, ,'.,','//.,',,1.,,.1 i i .. . / / / / / , / A 50 A
(15)
40
30
20
10
0
10
20
30 40
50 (r) mm
where
a
J-1Acm
2 ~320, P-
1 kgf cm -p (98.1 kPa)
(d)/Jm ~ 3 4 0 m m m i n N = 620 rpm
a
1
(r) turn o
50
50
Comparison w i t h experimental results The removed depth d c s h o w n in Fig 5 is the result of examining the position where the centre of the tool passes and these experimental results are represented by the worked shapes s h o w n in Fig 18. A c c o r d i n g to
1 2 3
y/a 1.0 0.8 0.6 0.4 0.2
0
0.2 0.4 0.6 0.8 1.0
6 c~1
u~ = 1 5 0 m m rain -1
b
(d)/Jrn
320, J= 1Acre N = 620 rpm
(r) mm 50
~2
0
5O
~3
N = 620 rpm
c~4
5 C
dy
Fig 17 Simulated results of the worked shape PRECISION ENGINEERING
=320, J = 1 A cm 2 vt = 340 mm min 1
(d) ,urn
Fig 18 Experimental results of the worked shape showing the influence of (a) the current density, J, (b) feed velocity, W, and (c) tool revolutions per minute, N 39
Maehata, Kamada and Yamamoto---electrolytic-abrasive mirror finishing Fig 18, the simulated results shown in Fig 17 accurately explain actual worked shapes. Both the simulated and actual curves have convex centre shapes. Normalization of the worked shape by the ratio dv/d c (shape coefficient) 5 to the removed depth dc at the centre gives nearly equal patterns regardless of machining conditions and removed depth, as shown in Fig 19. This is also explained by the fact that the ratio of d c = =~(x~n) 1/2 to Eq (15) is dvld c = ~ (X'~n+ y2)1,,'2/~(x2) 1/2 which is independent of ~. The comparison of normalized simulated results also shows nearly average values of experimental results. The results shown in Fig 19 contain tool-worked shapes with diameter 2a = 50 - 120 mm, in addition to the experimental results shown in Fig 18. From the above analysis and experimental results, the approximation of the machined pattern of the revolving disk-type tool electrode increasing linearly in the direction of the outer circumference with the tool centre as zero is appropriate. Thus the formation of the convex centre worked shape is made clear. The worked shape is represented by a constant shape coefficient dv/d c which is not affected by machining conditions.
Discussion of analytical results Shape accuracy Plane machining using a disk-type tool generates a worked shape similar to that shown in Fig 19, giving this type of machining a limited use when applied to machining requiring a good plane degree. For example, for a worked face larger than the tool diameter, a tool path overlapping 1 0 % of the worked width is required. For small parts, machining should be implemented within 7 0 % (y/a < 0.7) of the central part of the tool. However, in either case, according to Fig 19, the plane degree S is
S - - i d v l d c - 11 x d c - 0 . 1 d ~
b e d c < 1 0 l l m in the case o f S : l l ~ m a n d de< 1,m~ in the case of S = 0.1/~m. An addition of motion by which the tool feed Js vibrated horizontally is recommended as a method to improve machined patterns by a disk-type tool. Machining cylindrical workpieces with a concave tool is also highly recommended because the machined patterns under the tool face are uniformly distributed and the working time on each part of the worked surface by passing the tool is the same. Fig 20 shows a measurement result of a machining accuracy check of cylindrical work machining, with an accuracy of 1 l~m or b e l o w / 1 0 0 m m
Cylindrical work machining mechanism by concave face too/ Fig 21 shows a schematic diagram of a cylindrical workpiece being machined. The machining is carried out by giving constant-speed feed vf in the axial direction by using a concave face tool electrode of a nearly equal diameter to the workpiece diameter D. In this case, the workpiece rotates and an electrolytic solution is supplied into an abrasive through the face of the electrode. vf/N is a major factor for the achieving of a worked surface roughness similar to that of plane machining The tool shape factor largely depends on the tool height H e, independent of the tool width WE, thereby H E corresponds to the outer circumference of the disk-type tool and WE to the central part. An equation for generation of roughness by the cylindrical work machining method is obtained as 0.6vf tan(90 - i)h/21
RTh -
:17~
HeNm~ ?
As can be seen, this is similar to the equation for plane roughness, Eq (11).
(16)
In order to ensure accuracy, the removed depth should ~ d
0
0.2
0.4
06
0
0.8
1.0 T- --
' - -
02
I
-~lb
I
o
^ •
I I
ol
% J 04 I I
i
i
;
i
-
i
J
i
i
i
l
1
i
,
: . ~ - ,
i
100 mm
i
,
;
,
I
-
Fig 20 Machining accuracy of cyhndrical work machining
06
Simulated 08
~
Work piece:
/~ H.
_
_ _
=320 2a = 50-120 mm d,: = 12-85 #m on
~ eH:clr
od~t
1.2[
Fig 19 Normafization of the worked shape 40
Fig 21 Schematic diagram of cyhndrica/ work machining JANUARY 1987 VOL 9 NO 1
Maehata, Kamada and Yamamoto--.electrolytic-abrasive mirror finishing
The removed depth d is determined by the amount of facing time used with tool t and J because of uniform distribution of the current density J and the number of abrasive grains on the worked surface facing the concave face tool, and is represented by
HE WEplkJn
d=
nD vf
p
(1 8)
- Kt~lkJn/p
where p is the density of a workpiece, n is the number of tool passes and K the tool facing ratio (WE/~D). In Eq (18), each part of the worked surface is uniform and theoretically the worked shape (roundness or machining accuracy) is maintained. The accuracy of the machine, if less than 5/100mm, will have no influence on the worked shape. On the assumption of setting removed depth as d o and n - 1, the working time t is as follows from Eq (18):
12 are approximated by J=lAcm J=0
Fig 22 shows the results of a confirmation experiment comparing workpieces between diameter D = 030, 96 and 800 mm, wherein K is kept constant and t is independent of the workpiece D. Eq (19) demonstrates one of the characteristics of the electrolytic-abrasive mirror finishing method, representing the improvement of productivity as the workpieces become larger in diameter. 6
Rs-O.95(vf/N)O25
(l~m)'~
R s - O . 5 4 ( v f / N ) °4
(iLm) J
(20) and if the distance between scratches of Eq (8) is arranged by Af s vt/(2aN ) = vf/ND E and vt/N in Eq (20) is substituted by vf/NDE, then J=lAcm
2.
J ---0:
R~ - 2.77(vf/NDL) °25
R:, / P 13
(22)
Eq (21) is an experimental equation at P = 1 kgf cm 2 (98.1 kPa). Thus R l h i l ) = 1 is set and roughness ratios ;' = Rt~,(m,,'Rth(1) are ntroduced ~' = P 1 3from Eq (22) and (,'vf/NDE) are used relating to the machining condition of Eq (21) and then ; becomes •
J=lAcm
2.
Vf
. 0 25
R s=2.771 1 ~ k ND~P 3 3
J=0:
The theoretical roughness Rth represented by Eq (11 ) can explain experimental results at an order level, but the setting of machining conditions with accuracy is difficult if R~,~ is applied to actual machining without modification. The experimental results shown in Fig
/ cm :' 5 kgf(:m ? (4903 kPa)
J - 2 A
P
/
,/
E o
0
E
!
GI
101
(/,m)
(llm)
(24)
Fig 24 shows an application example of Eq (24) to mirror finishing of a large surface area by a tool
•
o/.
ID
)o 4
resulting in successful substitution of the practical machining equation for the theoretical Eq (11).6 The units of the machining conditions in Eq (23) arevf (mm min 1 ) , N ( r e v m i n 1), DE (mm) a n d P (kgf cm 2), respectively. Fig 23 shows a comparison between the practical Eq (23) and experimental values, proving that Eq (23) adequately explains the experimental results. The above discussion is for # 3 2 0 abrasive. Furthermore, a similar equation to Eq (21) is calculated for # 1500 abrasive used for mirror finishing. If J - 0, then the equation is represented by Rs = 0.66(vf/NDE) °4
o/
20
Rs : 3OSt, NDEv "
(/~m)
(23)
Practical equation for the w o r k e d surface roughness and generating of mirror finish
30,
(Pm) l (l~m)~ (21)
Rs = 3.03(vf/NDF) °4
where D E is the tool electrode diameter. The pressing force of abrasive P determines the number density of abrasive grains Mg. They are in a relationship of m g / p2.3, which is substituted into theoretical Eq (11) to obtain
(1 9)
t - do~/K~ikJ
2:
#320, SUS304
I.
/
E ~
0.5
Calculated 1
0
0
20
i
40
I
l
I
60
80
100
0.2 120
Working time (t) s
Fig 22 Relationship between D and d of cylindrical workpieces • D = 030ram, 0 D = ~h96mm, × D ~- ~/~800mm
PRECISION ENGINEERING
0.1
i
o
ooo2
o
o&
oo08
o.o,o
0.O12
0014
t~f / (NDE)1/3 Fig 23 Proof for experimental equation
41
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing Exp. equation: R, = 0.07 (ujN) °4
0.15
I
i
I. . . .
,
I
.J"
"~ C'~
-4
Fig 26 Mirror finishing using free-state abrasive grams
0.05 =1500, SUS304 D. = 0 3 5 0 mm
0
............... 0
500
1000 1500 2000 Feed velocity II~) mm rnin 1
Conclusions
2500
Fig 24 Mirror finishing of a large surface area
The following summarizes the analyses of the machining mechanism and experimental results for the electrolytic-abrasive mirror finishing method: •
electrode of D E = ~#350 mm. The worked surface roughness of Rs = 0.05 --- 0.08 HmRz is obtained at v~- 500mm min 1 Fig 25 shows an example of mirror finishing of a cylindrical workpiece (SKD-11:~h96 mm) with 6 s finish and a worked surface roughness of 0.01 0.03 l~mRz. Fig 26 shows the machining result 7 from using free-state abrasive grains in which very small abrasive grains are mixed into an electrolytic solution and the worked surface has a generated physical mirror surface of 0.0021~m
Action factors in machining mechanism and highprecision machining The electrolytic-abrasive mirror finishing method has excellent capacity as a method of generating mirror levels of up to 0.1/~m Rz in a short time. In order to establish it as a high-precision machining method, however, further study on shapes and motions of tool electrodes is required, as well as a review of the viscoelastic behaviour of abrasive grains. 8 Fig 27 shows a summary of the action factors participating in the mechanism of electrolytic-abrasive mirror finishing, as discussed above.
•
•
The removal of metal is performed mainly by electrolytic dissolution with the aid of grain action and is proportional to working current and time i.e. subject to Faraday's law. The worked shape is determined by the distribu tion of the removed depth under the face of the tool electrode and by the tool feed. Revolving disk-type tools can be approximated by a conical machined pattern, and the worked shape has a centre convex shape, represented by a constant ratio independent of machining conditions or removed depth. An electrolytic-abrasive machining method using a concave-faced tool with uniform machining distribution applied to cylindrical work achieves results very close to high-precision machining. The generation of worked surface roughness ~s accomplished mainly by grain action. The electrolysis becomes a reducing factor because of the formation of pits, thereby requiring a proper balance with the abrasive grain action. The mechanism of generation of roughness largely depends on the grain groups which act in the final stage of the passing of the tool and on their motion conditions under the highly elastic abrasive grain action with an extremely small spring constant. The roughness is determined by the number of grains and the edge angle rather than by the grain size.
Abrasive
( G....... i
grain size
_ ,~ ................
bet (nl,/~_~_.
(~ Edge angle of gta,rl,:~ r-- ----~Pre~sing f .... (P)
,'. ) ,
j
shape
'
I! ( Current density (J) El~tfoWteno~,,a~e~OI
~ > ~ "~
.....
Pr :mjr~' ac~k;r, Sul~plecnerl~lr~"Jchon
Fig 2 7 Machining factors and effect in electrolyt¢c
Fig 25 Example of 0.01 0.03 llm Rz mirror finishing 42
abrasive finishing JANUARY 1987 VOL 9 NO
Maehata, Kamada and Yamamoto--electrolytic-abrasive mirror finishing •
The equations for plane machining by a revolving disk-type tool and for cylindrical work machining by a concave faced tool, respectively,
helpful guidance and encouragement of Dr Keiji
are obtained as follows:
References (in Japanese)
0.6vf tan(90 - (~/2) Rth = -2~a--lVm~ ~ -- (cm) 0.6vf tan(90 - ~t/2) Rth = -. HE~Im~, ~ -- (cm) Furthermore, the above equations are modified to
empirical equations applicable to practical machining. The equations obtained are J=lAcm
2:
Rs=A
ND
1/3) Vf
J = 0:
Rs = B NDEPI,, 3
(F~m)
)0 4
(tim)
where A and B are constants determined by the abrasive used and are confirmed in their agreement with actual values.
Acknowledgments The authors wish to express their gratitude for the
PRECISION ENGINEERING
Okushima, Professor Emeritus of Kyoto University.
1 T a m i y a K. et al. MLrror finishing of metals using the electrolyhc-abras=ve mirror finishing method. The Hitachi Zosen Technical Review, 1981, 42 (3) 2 Sugie Y. Y o s h i z a w a S. et al. The relationship between current density and machining characteristics in the electrochemical machining for various steels The Electrochemical Society of Japan, 1978, 46 (3) 3 M a e h a t a H., Kamada H. and Y a m a m o t o , M. Studies on mirror finishing by buffing (1 st and 2nd Reports). Collection of Papers No. 427, 428, "82 Autumnal Meeting of the Japan Society of Prec. Engg., 1982 4 Kamada H. and Maehata, H. Studies on electrolytic-abrasive mirror finishing (5th Report). Collection of Papers No. 334, "83 Autumnal Meeting of the Japan Society of Prec. Engg., 1983 5 Maehata, H. Kamada H. et al. Study on electrolytic-abrasive mirror finishing of a cylindrical work (1 st Report). Collection of Papers No, 325, 79 Autumnal Meeting of the Japan Society of Prec Engg, 1979 6 M a e h a t a H. and Kamada H. Studies on electrolytic-abrasive mirror finishing (4th Report). Collection of Papers No. 333, "83 Autumnal Meeting of the Japan Society of Prec. Engg., 1983 7 Kamada H. et al. A study on electrolytic-abrasive mirror finishing Bull Japan Society of Prec. Engg., June 1982, 16 (2) 8 Kurobe T., Imanaka O. and O m u r a M. Finishing characteristics in extrude hone process. J. Japan Society of Prec Engg, 1982, 48 (8)
43