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Generation of Sculptured Surfaces by Means of an Ultraprecision Milling Machine
Generation of Sculptured Surfaces by Means of an Ultraprecision Milling Machine Yoshimi Takeuchi (2), Kazuya Kato, Shinichiro Kawakita, T h e University of Electro-Communications/Japan; Kiyoshi Sawada, Fanuc Ltd./Japan; Toshio Sata ( I ) , Physical and Chemical Institute/Japan Received on January 15,1993 Summary: The srudy deals with the development of an ultra-precision milling machine. which allows the production of workpleces with sculptured surfaces. Until now, a vmety of precision pans have been produced by ultra-precision diamond turning machines. However, they can not cope with making sculptured surfaces, whlch have higher requirements. The ultra-precision milling machine developed consists of an air splndle with a milllng tool and a hreeaxis feed mechanism. As a milling tool. a pseudo ball-endmill is designed by slightly offsetting a conventional diamond tool having a nose radius. It is found that the ultra-precision milling machine can produce workpieces w i h sculptured surface in surface roughness of 70 nm Rmax. Key words: Ulaa-precision. hhlling Machine. Sculptured Surface
1. Introduction The ultra-precision cutting has been performed by use of ultra-precision tuming machines equipped with single crystal diamond tools, which result in the production of subsuates in magnetic discs, polygon mirrors in laser printers and so on [1,2.3]. p e ulrra-precision diamond turning machines can produce various axissymmetnc surfaces such as aspherical surfaces in addition to flat surface, sphencal surface and cylindrical surface. From now on, it is expected that the requirement of ultra-precision sculptured surfaces increases to cope with the production of X-ray mirror segments, metal molds for non-axis-symmenic lens and so on. However, it is difficult for current ulm-precision turning machines to generate sculptured surfaces. With regard to the generation of non-axis-symmetric surfaces, a study by USE of a precision diamond fly cutting machine was reported, where the tool cutting depth is dynamically controlled i n synchronizing to tool rotational angle [J]. However, even the newly developed machine can only cope with simple non-axissymmetric surfaces due to the fly cutting. Thus. it is intended to develop an ultra-precision milling machine to generate arbitrary sculptured surfaces. In the study, the concept of ultra-precision milling by pseudo ball-endmill and the development of an ulna-precision milling machine are reported together with the experimental results of sctilptured surface generation by it.
rotational axis. Figure 3 shows the control system configuration of the ultra-precision milling machine. A 16-bit personal computer controls the movement of each axis. The u h - p r e c i s i o n milling machine is placed in a vibration-proof room under h e tem-
2. S t r u c l u r e of Ultra-precision Milling Machine
Fig. 2 Whole view of ultra-precision milling machine
The ultra-precision milling machine is composed of three axes movements, ( x, y and z ) and a main spindle equipped with a pseudo ball-endmill, as illustrated in Fig. 1. The main spindle consists of air turbine and air bearing supporting radial and thrust loads. The rotation number is controllable by regulating air pressure, and the maximum rotation number is 3oooO rpm. The main spindle is mounted on the linear stage through a rotational a b l e ( B-axis ) to adjust the setting angle of tool. The x-axis ( feed direction ), consisting of air slider made i n ceramics, is driven by a linear motor having a linear scale with the resolution of 0.1 gm. The straightness of the x-axis is measured to be 0.04 p/20mm. As the y-axis ( pickfeed direction ), the linear stage driven by a stepping motor is used with the resolution of 0.5 p m and the straightness of 2 pm/5mm. With regard to the z-axis ( direction of depth of cut ). a micro tool servo is used which consists of a piezoelectric actuator [ 5 ] . The micro tool servo is developed to control the tool movement in an ultraprecision lathe [ 6 ] .The maximum stroke of the micro tool servo is 8.4 gm, and the resolution is about 0.02 pm. The micro tool servo is mounted on the air slider of the x-axis. The workpiece is attached to the top of the micro tool servo by a fixture. The whole view of the ultra-precision milling machine is shown in Fig. 2. . The pseudo ball-endmill as a milling tool is attached to the main spindle, taking account of the dynamic valance since the tool axis is slightly offset from the
Diamond tool / W orkuie ce Air spindle Rotational table \ Micro tool servo Linear motor Linear scale
perature control of 2 W. I "C . The workpiece IS roughly machined on the same milling machine to remove the alignment error by use of grinding wheel of 30 mm i n diameter with the grain size of #1W. The workpieces with the surface roughness of about 3 pm Rmax ) are in advance prepared.
3. Possibility of Ultra-precision Milling 3.1 Plunge cut by pseudo ball-endmill The ultra-precision milling is as same as the conventional one. That is, a milling tool is moved in the feed direction, while the tool position is controlled in the direction of depth of cut. After shifted by the amount of pickfeed, the tool is again moved in the feed direction. The movement of tool enables the generation of sculptured surfaces. The milling tool consists of a conventional diamond tool with a nose radius being slightly shifted from the rotational axis, as illustrated in Fig. 4. The shift of tool center is to avoid zero cutting speed since diamond ball-endmills are not commercially available. The devised milling tool is called a pseudo ball-endmill. The possibility of practical use of pseudo ball-endmill, whose amount of shift is about 50 p m and radius is 5 mm, is investigated. With the milling tool. an aluminium alloy is machined by plunge cut under the condition of depth of cut = 1 pm and spindle rotation = 100 rpm. The cross-sectional profile of the machmed surface measured by Form Talysurfis shown in Fig. 5. It is found that the tool shape is correctly transferred to the workpiece surface.
Personal computer (16bit)
3.
3.
3.
Motion [Counter] D/A controller converter
AD
3.
converter
1
motor
v
Fig. I Shucture of ulna-precision milling machine
Annals of the ClRP Vol. 42/1/1993
Feed mechanism (x-axis)
Micro tool servo (z-axis)
Linear stage (y-axis)
Fig. 3 Control system configuration
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f. 2 p mirev v'22920rpm p: 75 ,um R m a x = 122nm
=: c
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Fig. 4 Milling by pseudo ball-endmill
I
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a
f
L
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m
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o
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Length of workpiece , p m
Tool radius : 5mm Offset of tool mis : 1 9 9 m
Fig. 7 Surface roughness in plane milling ( pickfeed dirction )
c
Length , ,urn Fig. 5 Plunge cut by pseudo ball-endmill 3.2 Plane milling by pseudo ball-endmill The feed motion of the tool enables the plane surface generation. In the case. the nose radius of tool is 2 mm and the amount of shift is 50 pm. The cutting condition is as follows; spindle rotation number = 22920 rpm ( cutting speed = 7.2 m/min ), feed = 2 pm/rev, depth of cut = 1 pm and pickfeed = 75 pm. The workpiece is also an aluminium alloy. The surface roughness measured in the feed direction by Form Talysurf is 107 nm Rmax, as shown is Fig. 6. It is seen that the enlarged portion reveals cutter marks clearly. The undulation in cutter marks is due to the movement error of air slider. On the other hand, the surface roughness in the pickfeed direction is 122 nrn Rmax as shown in Fig. 7.
3.3 Plane milling by improved pseudo ball-endmill When the milling is camed out by a pseudo ball-endmill consisting of a diamond roo1 with a nose radius, only a half side of t w l concerns the cutting. The other side is rather unnecessary from the standpoint of chip removal. Thus, The
Fig. 8 Improved pseudo boll-endnill proved tool. 4. Milling Experiments
4.1 Parabolic surface A convex and concave parabolic surfaces are machined by use of the above improved tool under the same cutting condition as the plane milling. The micro tool servo driven by the piezoelectric actuator moves the tool in the direction of depth of cut, while fed in the feed direction. Since the piezoelecnic actuator has
half side is intended to be removed, which results in an improved pseudo ballendmill. The radius and the amount of shift of the improved tool are 2 m m and 100 pm respectively. The cutting condition is as same as the above pseudo ball-endmill except for the pickfeed. The pickfeed is set to be 25 pm in this case. Figure 8 shows the workpiece to be machined by the improved tool. The measured surface roughness in the feed direction and pickfeed direction is 78 n m Rmax and 92 nm Rmax respectively, as shown in Fig. 9. The result presents the effect of the im-
f: 2 ,umm/rev v : 22920 rpm
p: 75
p
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Length of workpiece , U , rn Fig. 6 Surface roughness in plane milling ( feed dirction )
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,
,
,
,
100
200
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Length of workpiece , ,U rn Fig. 9 Surface roughness obtained by improved pseudo ball-endmill ( upper : feed direction, lower : pickfeed direction )
4.3 Toroidal surface A toroidal surface is machined as another example of sculptured w e [oroidal surface is defined as follows: z=((
R1-R2 + ( R2’- Y ~ ) ” ) x’~ -)
A
’’
-4
8
A
0
2.0
4.0
6.0
8.0
Length of workpiece , mrn
6 -927 I U
Fig. 10 Profile of convex parabolic surface
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0.02
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1.57
hysteresis characteristics, it has to be considered in order to position the tool correctly. The computer converts the parabolic profile data into the corresponding control voltage for piezoelecuic actuator, taking account of the hysterisis characteristics. The cross-sectional shape of the machined workpiece is measured by Form Talysurf. Figure 10 shows the profile of the convex parabolic surface with the height of 8.2 pm against the distance of 10 m m . From the figure, it is seen that the profile is a parabolic curve. The surface roughness is 78 nm Rmax i n the feed direction and 87 nm Rmax in the pickfeed direction respectively. 4.2Elliptic Paraboloid As a sculptured surface. the generation of concave elliptic paraboloid surface is tried from the viewpoint of easy shape definition and offset surface. An elliptic paraboloid is defined as follows: z = axz + by’
’ b = 2.22xIO-’ is drawn in The elliptic paraboloid in case of a = 1 . 3 3 ~ 1 0and Fig. 1l(a). With the same t w l , a workpiece of an aluminium alloy is machined in the area of 3 mm x 3 rnm under the cutting condition of feed 2 gm and pickfeed 75 pm, The machined workpiece surface measured by Wyko interferometer is shown in Fig. 1l(b), which is similar to Fig. 1l(a). The profiles in the feed and picHeed djrection on the center line are shown in Fig. I l(c). The profile in the feed direction is better than that in the pickfeed direction. ?his is due to the relatively poor movement accuracy of the linear stage driven by the stepping motor. The surfoce roughness is 83 nm Rmax in the feed direction and 85 nm Rmax in the pickfeed direction respectively, as shown in Fig. 1l(d).
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Length of workpiece ,mm (c) Profile on the center line
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Length of workpiece , ,u m (a) Elliptic paraboloid surface f: 2
,u mfrev
Rmax = S5nm
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0
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p 1912 1984
Distance ( feed ) , p m
0
1
100
200
300
400
Length of workpiece , p m (d) S u r f x e roughness ( upper : feed direction , lower . pickfeed dlrechon )
(b) Measured elliptic paraboloid s u r f m
Fig. I 1 Milling of ellliptic paraboloid I
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i
f 2 5 LI, m/rev
Rmax = 66nm
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o
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wo
Length of workpiece , ,L( m (a) Toroidal surface
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100
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Length of workpiece , ,u m
p 1912 0
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(d) Surface roughness ( upper : feed direction , lower : pickfeed direction )
1984
Distance ( feed ) , p m
Fig. 12 Milling of toroidal surface roughness on two center lines respectively. The results are almost as same as those of elliptic panboloid. Althoumh the problem concerning the improvement of surface roughness still remains, it r s found that the ultra-precision sculptured surface generation is possible by means of the improved pseudo ball-endmill.
(b) Measured toroidal surface
5. Conclusion In order to realize. the production of sculptured mirror surface, the prototype of ulm-precision milling machine is developed together with the devised ballendmill. The improved pseudo ball-endmill consists of half part of a diamond tool with a nose radius, whose rotational axis is slightly shifted. From the experimental results, it is confirmed that the ultra-precision sculptured surface such as elliptic paraboloid and toroidal surfaces can be produced.
995
0.41
0.80
1.18
1.57
1.95
Acknowledgement The authors would like to express their sincere appreciation to Mr. Y. Fukushima for his earnest collaboration. and to Kuroda Seiko Co. Ltd. for the cooperation in the study.
References [l] Donaldson. R.R., Thompson, D.C., 1986, Design 3ndPerfomance of a Small Precision CNC Turning Machine, Annals of the CIRP.V01.3511: 373-?76
[2] Mckeown, P.A.. Wills-Moren. W.J., Read, R.F.I., Mdjarrad, H., 1983, The Design and Development of a Large Precision CNC Diamond Turning Machine, 1 lth NAMRC Proc.: 48-60
0.02
0.40
0.77
1.14
1.51
1.88
Length of workpiece ,mm (c) Profile on the center line ,where R1 and R2 are curvature radii in each axis direction respectively. Here, R1 and R2 are set to be 225 mm and 375 m m respectively. The cutting condinon is as same as that of elliptic pwnboloid. Figure 12(a) and (b) show calculated surface and the surface figure measured by Wyko interferometer respectively. Figure 12(c) and (d) are the profiles in the feed and pickfeed directions. and rhe surface
614
[3] Nishiguchi, T., Maeda, Y., Masuda. M., Sawa, M., 1988. Mechanism of Micro Chip Formation in Diamond Turning of A1-Mg Alloy. Annals of the CIRP, Vo1.37/1: 117.120 141 Uchida, F.,Moriyama, S., Seya, E., 1987, Aspheric Mirror Fabrication by Flycutting with Cutting Depth Control Synchronized to Tool Rotational Angle, Proc.6th Int. Conf. on Prod. Eng. O s k a : 551-556 [5] Shimizu, H., Takeuchi. Y..Inada, H., 1988, Devetopment of Piezoelectricdnven Twl Moving Device with High Positioning Accuracy, Proc. China-lapan Symp. on Mcchanonics: 58-62 [ 6 ] Takeuchi. Y., Shimizu, H., Yoshikawa, H., Inada, H.. Sata. T., Development of
Ultraprecision Lathe and Compensation of Machining Error, Tran. Japan SOC. Mech. Eng. (C). Vo1.57. No.542: 3269-3273
1. Introduction The ultra-precision cutting has been performed by use of ultra-precision tuming machines equipped with single crystal diamond tools, which result in the production of subsuates in magnetic discs, polygon mirrors in laser printers and so on [1,2.3]. p e ulrra-precision diamond turning machines can produce various axissymmetnc surfaces such as aspherical surfaces in addition to flat surface, sphencal surface and cylindrical surface. From now on, it is expected that the requirement of ultra-precision sculptured surfaces increases to cope with the production of X-ray mirror segments, metal molds for non-axis-symmenic lens and so on. However, it is difficult for current ulm-precision turning machines to generate sculptured surfaces. With regard to the generation of non-axis-symmetric surfaces, a study by USE of a precision diamond fly cutting machine was reported, where the tool cutting depth is dynamically controlled i n synchronizing to tool rotational angle [J]. However, even the newly developed machine can only cope with simple non-axissymmetric surfaces due to the fly cutting. Thus. it is intended to develop an ultra-precision milling machine to generate arbitrary sculptured surfaces. In the study, the concept of ultra-precision milling by pseudo ball-endmill and the development of an ulna-precision milling machine are reported together with the experimental results of sctilptured surface generation by it.
rotational axis. Figure 3 shows the control system configuration of the ultra-precision milling machine. A 16-bit personal computer controls the movement of each axis. The u h - p r e c i s i o n milling machine is placed in a vibration-proof room under h e tem-
2. S t r u c l u r e of Ultra-precision Milling Machine
Fig. 2 Whole view of ultra-precision milling machine
The ultra-precision milling machine is composed of three axes movements, ( x, y and z ) and a main spindle equipped with a pseudo ball-endmill, as illustrated in Fig. 1. The main spindle consists of air turbine and air bearing supporting radial and thrust loads. The rotation number is controllable by regulating air pressure, and the maximum rotation number is 3oooO rpm. The main spindle is mounted on the linear stage through a rotational a b l e ( B-axis ) to adjust the setting angle of tool. The x-axis ( feed direction ), consisting of air slider made i n ceramics, is driven by a linear motor having a linear scale with the resolution of 0.1 gm. The straightness of the x-axis is measured to be 0.04 p/20mm. As the y-axis ( pickfeed direction ), the linear stage driven by a stepping motor is used with the resolution of 0.5 p m and the straightness of 2 pm/5mm. With regard to the z-axis ( direction of depth of cut ). a micro tool servo is used which consists of a piezoelectric actuator [ 5 ] . The micro tool servo is developed to control the tool movement in an ultraprecision lathe [ 6 ] .The maximum stroke of the micro tool servo is 8.4 gm, and the resolution is about 0.02 pm. The micro tool servo is mounted on the air slider of the x-axis. The workpiece is attached to the top of the micro tool servo by a fixture. The whole view of the ultra-precision milling machine is shown in Fig. 2. . The pseudo ball-endmill as a milling tool is attached to the main spindle, taking account of the dynamic valance since the tool axis is slightly offset from the
Diamond tool / W orkuie ce Air spindle Rotational table \ Micro tool servo Linear motor Linear scale
perature control of 2 W. I "C . The workpiece IS roughly machined on the same milling machine to remove the alignment error by use of grinding wheel of 30 mm i n diameter with the grain size of #1W. The workpieces with the surface roughness of about 3 pm Rmax ) are in advance prepared.
3. Possibility of Ultra-precision Milling 3.1 Plunge cut by pseudo ball-endmill The ultra-precision milling is as same as the conventional one. That is, a milling tool is moved in the feed direction, while the tool position is controlled in the direction of depth of cut. After shifted by the amount of pickfeed, the tool is again moved in the feed direction. The movement of tool enables the generation of sculptured surfaces. The milling tool consists of a conventional diamond tool with a nose radius being slightly shifted from the rotational axis, as illustrated in Fig. 4. The shift of tool center is to avoid zero cutting speed since diamond ball-endmills are not commercially available. The devised milling tool is called a pseudo ball-endmill. The possibility of practical use of pseudo ball-endmill, whose amount of shift is about 50 p m and radius is 5 mm, is investigated. With the milling tool. an aluminium alloy is machined by plunge cut under the condition of depth of cut = 1 pm and spindle rotation = 100 rpm. The cross-sectional profile of the machmed surface measured by Form Talysurfis shown in Fig. 5. It is found that the tool shape is correctly transferred to the workpiece surface.
Personal computer (16bit)
3.
3.
3.
Motion [Counter] D/A controller converter
AD
3.
converter
1
motor
v
Fig. I Shucture of ulna-precision milling machine
Annals of the ClRP Vol. 42/1/1993
Feed mechanism (x-axis)
Micro tool servo (z-axis)
Linear stage (y-axis)
Fig. 3 Control system configuration
611
f. 2 p mirev v'22920rpm p: 75 ,um R m a x = 122nm
=: c
-
1
j0
Fig. 4 Milling by pseudo ball-endmill
I
I
a
f
L
-
m
5
I
o
100
200
400
300
Length of workpiece , p m
Tool radius : 5mm Offset of tool mis : 1 9 9 m
Fig. 7 Surface roughness in plane milling ( pickfeed dirction )
c
Length , ,urn Fig. 5 Plunge cut by pseudo ball-endmill 3.2 Plane milling by pseudo ball-endmill The feed motion of the tool enables the plane surface generation. In the case. the nose radius of tool is 2 mm and the amount of shift is 50 pm. The cutting condition is as follows; spindle rotation number = 22920 rpm ( cutting speed = 7.2 m/min ), feed = 2 pm/rev, depth of cut = 1 pm and pickfeed = 75 pm. The workpiece is also an aluminium alloy. The surface roughness measured in the feed direction by Form Talysurf is 107 nm Rmax, as shown is Fig. 6. It is seen that the enlarged portion reveals cutter marks clearly. The undulation in cutter marks is due to the movement error of air slider. On the other hand, the surface roughness in the pickfeed direction is 122 nrn Rmax as shown in Fig. 7.
3.3 Plane milling by improved pseudo ball-endmill When the milling is camed out by a pseudo ball-endmill consisting of a diamond roo1 with a nose radius, only a half side of t w l concerns the cutting. The other side is rather unnecessary from the standpoint of chip removal. Thus, The
Fig. 8 Improved pseudo boll-endnill proved tool. 4. Milling Experiments
4.1 Parabolic surface A convex and concave parabolic surfaces are machined by use of the above improved tool under the same cutting condition as the plane milling. The micro tool servo driven by the piezoelectric actuator moves the tool in the direction of depth of cut, while fed in the feed direction. Since the piezoelecnic actuator has
half side is intended to be removed, which results in an improved pseudo ballendmill. The radius and the amount of shift of the improved tool are 2 m m and 100 pm respectively. The cutting condition is as same as the above pseudo ball-endmill except for the pickfeed. The pickfeed is set to be 25 pm in this case. Figure 8 shows the workpiece to be machined by the improved tool. The measured surface roughness in the feed direction and pickfeed direction is 78 n m Rmax and 92 nm Rmax respectively, as shown in Fig. 9. The result presents the effect of the im-
f: 2 ,umm/rev v : 22920 rpm
p: 75
p
m
I o
b-t
3
m
I
100
2 0
300
400
Length of workpiece , p m
E C
40
g-401
I
3
0
100
200
300
Length of workpiece , U , rn Fig. 6 Surface roughness in plane milling ( feed dirction )
612
-
f 2 pni/rev v 22920 rprn p25pm
400
m
o
Rmax = 92nm
,
,
,
,
100
200
300
400
Length of workpiece , ,U rn Fig. 9 Surface roughness obtained by improved pseudo ball-endmill ( upper : feed direction, lower : pickfeed direction )
4.3 Toroidal surface A toroidal surface is machined as another example of sculptured w e [oroidal surface is defined as follows: z=((
R1-R2 + ( R2’- Y ~ ) ” ) x’~ -)
A
’’
-4
8
A
0
2.0
4.0
6.0
8.0
Length of workpiece , mrn
6 -927 I U
Fig. 10 Profile of convex parabolic surface
I
0.4 1
0.02
0.80
1.18
1.95
1.57
hysteresis characteristics, it has to be considered in order to position the tool correctly. The computer converts the parabolic profile data into the corresponding control voltage for piezoelecuic actuator, taking account of the hysterisis characteristics. The cross-sectional shape of the machined workpiece is measured by Form Talysurf. Figure 10 shows the profile of the convex parabolic surface with the height of 8.2 pm against the distance of 10 m m . From the figure, it is seen that the profile is a parabolic curve. The surface roughness is 78 nm Rmax i n the feed direction and 87 nm Rmax in the pickfeed direction respectively. 4.2Elliptic Paraboloid As a sculptured surface. the generation of concave elliptic paraboloid surface is tried from the viewpoint of easy shape definition and offset surface. An elliptic paraboloid is defined as follows: z = axz + by’
’ b = 2.22xIO-’ is drawn in The elliptic paraboloid in case of a = 1 . 3 3 ~ 1 0and Fig. 1l(a). With the same t w l , a workpiece of an aluminium alloy is machined in the area of 3 mm x 3 rnm under the cutting condition of feed 2 gm and pickfeed 75 pm, The machined workpiece surface measured by Wyko interferometer is shown in Fig. 1l(b), which is similar to Fig. 1l(a). The profiles in the feed and picHeed djrection on the center line are shown in Fig. I l(c). The profile in the feed direction is better than that in the pickfeed direction. ?his is due to the relatively poor movement accuracy of the linear stage driven by the stepping motor. The surfoce roughness is 83 nm Rmax in the feed direction and 85 nm Rmax in the pickfeed direction respectively, as shown in Fig. 1l(d).
%
8
I
-809 0.02
, 0.40
, 0.77
,
,
, 1.85
1.51
1.14
Length of workpiece ,mm (c) Profile on the center line
k
3
m
I o
I
100
200
300
400
Length of workpiece , ,u m (a) Elliptic paraboloid surface f: 2
,u mfrev
Rmax = S5nm
I m 1
0
496
992
1488
p 1912 1984
Distance ( feed ) , p m
0
1
100
200
300
400
Length of workpiece , p m (d) S u r f x e roughness ( upper : feed direction , lower . pickfeed dlrechon )
(b) Measured elliptic paraboloid s u r f m
Fig. I 1 Milling of ellliptic paraboloid I
613
i
f 2 5 LI, m/rev
Rmax = 66nm
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m
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o
I
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wo
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m 496
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1488
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100
200
300
400
Length of workpiece , ,u m
p 1912 0
I o
(d) Surface roughness ( upper : feed direction , lower : pickfeed direction )
1984
Distance ( feed ) , p m
Fig. 12 Milling of toroidal surface roughness on two center lines respectively. The results are almost as same as those of elliptic panboloid. Althoumh the problem concerning the improvement of surface roughness still remains, it r s found that the ultra-precision sculptured surface generation is possible by means of the improved pseudo ball-endmill.
(b) Measured toroidal surface
5. Conclusion In order to realize. the production of sculptured mirror surface, the prototype of ulm-precision milling machine is developed together with the devised ballendmill. The improved pseudo ball-endmill consists of half part of a diamond tool with a nose radius, whose rotational axis is slightly shifted. From the experimental results, it is confirmed that the ultra-precision sculptured surface such as elliptic paraboloid and toroidal surfaces can be produced.
995
0.41
0.80
1.18
1.57
1.95
Acknowledgement The authors would like to express their sincere appreciation to Mr. Y. Fukushima for his earnest collaboration. and to Kuroda Seiko Co. Ltd. for the cooperation in the study.
References [l] Donaldson. R.R., Thompson, D.C., 1986, Design 3ndPerfomance of a Small Precision CNC Turning Machine, Annals of the CIRP.V01.3511: 373-?76
[2] Mckeown, P.A.. Wills-Moren. W.J., Read, R.F.I., Mdjarrad, H., 1983, The Design and Development of a Large Precision CNC Diamond Turning Machine, 1 lth NAMRC Proc.: 48-60
0.02
0.40
0.77
1.14
1.51
1.88
Length of workpiece ,mm (c) Profile on the center line ,where R1 and R2 are curvature radii in each axis direction respectively. Here, R1 and R2 are set to be 225 mm and 375 m m respectively. The cutting condinon is as same as that of elliptic pwnboloid. Figure 12(a) and (b) show calculated surface and the surface figure measured by Wyko interferometer respectively. Figure 12(c) and (d) are the profiles in the feed and pickfeed directions. and rhe surface
614
[3] Nishiguchi, T., Maeda, Y., Masuda. M., Sawa, M., 1988. Mechanism of Micro Chip Formation in Diamond Turning of A1-Mg Alloy. Annals of the CIRP, Vo1.37/1: 117.120 141 Uchida, F.,Moriyama, S., Seya, E., 1987, Aspheric Mirror Fabrication by Flycutting with Cutting Depth Control Synchronized to Tool Rotational Angle, Proc.6th Int. Conf. on Prod. Eng. O s k a : 551-556 [5] Shimizu, H., Takeuchi. Y..Inada, H., 1988, Devetopment of Piezoelectricdnven Twl Moving Device with High Positioning Accuracy, Proc. China-lapan Symp. on Mcchanonics: 58-62 [ 6 ] Takeuchi. Y., Shimizu, H., Yoshikawa, H., Inada, H.. Sata. T., Development of
Ultraprecision Lathe and Compensation of Machining Error, Tran. Japan SOC. Mech. Eng. (C). Vo1.57. No.542: 3269-3273