Precision machining and measurement of micro aspheric molds(Reprint from Proceedigns of ISUPEN2011)

H. Suzuki1,3, T. Moriwaki2, Y. Yamagata3, and T. Higuchi4
1

Chubu University, Kasugai, Aichi, Japan
Setsunan University, Neyagawa, Osaka, Japan
3
The Institute of Physical and Chemical Research, Wako, Saitama, Japan
4
University of Tokyo, Bunkyo, Tokyo, Japan
2

Abstract –Demands of micro aspheric optical components such as lenses and mirrors are increasing for installing to the digital

devices such as DVD, Digital camera, mobile phone and virtual reality system. As the devices become to be more compact
and complicated, the molds shapes of lens and mirrors would become smaller and complicated, and then would become moredifficult to be machined and measured. In this study, multi-axis controlled ultra precision machining/grinding/polishing andon-machine measurement technologies are developed for manufacturing of the complicated and micro molds. In this report,
our developed grinding method of the complicated mold, ultrasonic vibration method and contact type of multi axis controlled
on-machine measuring system are discussed.
Key Words: ceramic mold, ultraprecision grinding, ultrasonic vibration assisted polishing, on-measuring measurement

The grinding spindle was actuated in X, Y and Z axes by the linear

1. Introduction
Demands are increasing for installing of micro aspheric glass lenses

scale feedback system of 1 nm positioning resolutions. The grinding

to various digital devices, such as blue laser DVD pick-up systems,

and workpiece spindles were air bearings. The wheel was

digital cameras and optical transmission devices in order to improve

simultaneous 2-axes (Y, Z) controlled [1].

the optical performance. The micro aspheric glass lenses are generally

Wheel positioning (YNC, ZNC) is calculated as follows:press-molded using micro aspheric ceramic molds made of sinteredtungsten carbides or silicon carbides. These ultra-precision molds and

YNC=YW-R sinșdies are generally ground with micro diamond grinding wheels that

ZNC=ZW-R (1-cosș)(2)

are controlled in the positioning accuracy of 1 nm, and the groundmolds and dies are further polished using loose abrasives. They are

Where (YW, ZW) are workpiece coordinates and R is the wheel edge

finished through the compensation process based on the measured

radius.

form deviation profiles. As the optical system becomes more compact

The wheel rotates parallel to the direction of workpiece rotation at

and complicated and the high accuracy is required, the multi-axis

the grinding point. By scanning the sharp wheel edged, thecontrolled ultra precision machining/grinding technologies and theaxis-symmetric aspheric Fresnel workpiece could be generated1).

on-machine measurement technologies become important.

WorkpieceWorkspindle2. Micro Fresnel grinding

Coolant
nozzleFig. 1 shows a view and a schematic diagram of developed micro
Fresnel-grinding process. A disk shape of resinoid bonded diamondYwheel was trued on the machine, and the wheel edge was sharpened.

X

The wheel having a knife edge was scanned along the workpieceZradial position vertically.

Grinding
wheel

The Fresnel shape is expressed as follows:

Workpiece
Z
Fig. 1 Developed micro Fresnel grinding

Z(Y)=mod{g(Y),b}
Cv Y2

G(Y)=

n
+Ȉ Ci Y i
1+ 1-(K+1) Cv2 Y 2) i=1

Grinding
wheel
Y
X

(1)
2.2 Truing of grinding wheel by rare metal
In the conventional truing/dressing process of the resinoid bonded

Where, Cv is the radius curvature, K is the conic coefficient and b isdiamond wheel, the wheel is trued by a single crystalline diamond

the Fresnel depth.

truer and the trued diamond wheel is dressed by a green siliconcarbide (GC) stone. However, it is difficult to sharpen the wheel edge,

2.1 Vertically controlled Fresnel grinding method and system
A view of vertically controlled fresnel grinding is shown in Fig. 1.

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because the GC stone is not so hard compared with the diamondwheel.

1

In this study, rare metals are proposed to be used as a truer/dresserᴾof high precision and high performance. For the diamond wheel of theFresnel lens molds, the grinding wheel is rubbed and formed fortruing and dressing on the outer side surface and the bottom sidesurface of it, as shown in Fig. 2. Cylindrical diamond wheel was truedby each truer material in the conditions. Depth of cut was 1 ȝm and
500 times of cut was done. Fig. 3 shows changes of truing. A truing

300μ
μm

5mm

ratio is defined by the next equation:(a) Appearance
T = Ve / Vt

(3)(b) Nomarski micrographFig.4 Ground mold for diffractive optical elem ents (DOE)

Where, Ve is a volume of the trued diamond wheel and Vt is a volume
efficiency becomes higher.
Grinding wheel

Grinding wheel

Truer(a) Truing of wheel side surface

Depth ȝmof the worn truer. This value, T becomes larger when the truing

600μm

Truer
(b) Truing of wheel bottom surface

Fig.2 Proposed truing and dressing process of the resinoid bonded
Fig.5 Measured profile of ground DOE (Reference: base aspheric)diamond wheel for the grinding of the Fresnel lens mold.

50
40.1

40

㫆㫀
㫋㪸
㫉㩷 30
㪾
㫅㫀
㫆㫉
㪫20

33.7

SD400
SD12003. Micro lens array grinding

SD20003.1 Four-axes controlled grinding method
In micro lens array grinding, the grinding wheel moves
synchronously in the same direction and at the same speed as theworkpiece rotates, maintaining a constant distance between the

10 6.80Mo

workpiece rotation center to the machining point as shown in Fig. 6.

0.30
0.24
0.03

0.14
0.12
0.11

0.01
0.01
0.01

The workpiece rotates 180 degrees, yielding a precision concave

GC
stone
GC⎎⍹

SUS304

S50C

In four-axis controlled grinding (Fig. 7), the coordinates of the lensTruer
Fig. 3 Truing ratio
2.3 Grinding results

sphere. The lens array is produced by repeating this [2].
center (Xoij, Yoij) are positioned based on the turning radius rij on theworkpiece axis and rotation angle Coij are expressed as follows:r ij =As a mold material, glassy carbon was used for high temperature
glass molding. The grinding conditions are shown in Table 1. As a

X oij

2

+ Y oij

2(4)

C oij = tan − 1 ( Y oij / X oij )wheel, a resinoid bonded diamond wheel of #1200 in a grain size wasused and was trued to be sharp edge on the machine. Fig. 4(a) and (b)show views of the glassy carbon mold ground for the diffractive

After workpiece rotation of the angle Cșij, the coordinates, arbitrarylens center (Xșij, Yșij), are expressed as follows:

optical elem ents (DOE). Fig. 5 shows a form deviation profile
measured by Form Talysurf. Very sharp edges were generated and aform Form accuracy of 0.1 ȝm P-V was obtained.

Table 1 Grinding conditions
Grinding wheel
Grain size
Rotational rate

Resinoid bonded diamond
SD120025,000 min-1

Workpiece
Rotational rate

Glassy carbon
150 min-1

Depth of cut

0.5 ȝmFeed

0.3 mm/min

Coolant

Solution type

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X θ ij = r ij ⋅ cos( C oij − C θ )Y θ ij = r ij ⋅ sin( C oij − C θ )(5)

The grinding wheel is moved by simultaneous 4-axis (X, Y, Z, C) witha cut in Z direction to meet Eqs. (4), (5).

3.2 Grinding results
A micro lens array mold was ground having 15 concave 1.1 mm
radius spheres, spaced zigzag at 700 horizontally and vertically.

2ȝmP-V

Grinding conditions are shown Table 2. Fig. 8 shows a Nomarski
micrograph of ground mold made of glassy carbon. Fig. 9 shows a

Form accuracychange of the form accuracy of all 15 lenses and the form accuracy ofless than 0.2 ȝmP-V was obtained.

Wheel

Workpiece

Y X
Z

㪇㪅㪌
㪇㪅㪋
㪇㪅㪊
㪇㪅㪉
㪇㪅㪈
㪇

㪈 㪉 㪊 㪋 㪌 㪍 㪎 㪏 㪐 㪈㪇 㪈㪈 㪈㪉 㪈㪊 㪈㪋 㪈㪌

Lens No.
Fig.9 Changes of form accuracy

Feed
Feed

4. Precision cutting of ceramic molds by micro PCD milling tool
In order to machine micro aspheric molds and dies made ofYYceramics, micro milling tools made of polycrystalline diamond (PCD)Y

are developed. In this cutting method, the materials are removed by

X

X

X

interrupted cutting and the tool wear can be reduced. It is therefore
expected that the hard ceramic can be cut with micro milling tool [3].

GroundContact area

4.1 The PCD micro milling toolFig. 10 shows a PCD micro milling tool machined and theFig.6 Micro lens array grinding

Y-axisspecifications are shown in Table 3. The tools outer diameter is
ĭ1mm and 40 cutting edges are ground on the tool edge. The PCD

Y-axismicro milling tool was fabricated as shown in Fig. 11. At first theLens center

PCD wafer was bonded to a cemented carbide substrate and the(Xoij,Yoij)

rijbonded PCD plate was cut by wire EDM. The PCD chip was bonded

Coij

on to a cemented carbide shank. Finally, the end face and side face of

Cθ

0

0

X-AxisX Axisthe PCD chip was ground and polished with a diamond wheel, and thecutting edges were ground and polished with a sharp diamond wheel.

(b) After Cθ rotation(a) Initial position

Fig.7 Tool path calculation

Table 2 Grinding conditions
Grinding machine

4-axis controlled machine

Wheel

Resinoid bonded diamond

Grain size

㧏1200

Diameter

Ǟ0.8mm

Tip radius

㨞=0 mmRotational rate

60,000 min-㧝

Workpiece
Rotational rate(a) A view

720 degrees/min
5 µm

Feed rate

0.8 µm/min(b) SEM photographFig. 10 Photographs of PCD micro milling tool
Table 3 Specifications of milling tool

Glassy carbon

Depth of cut

100 μm

1 mm

Tool malParticle size
Diameter of cutting edge
Tip radius
Rake angle
Number of cutter

Polycrystalline diamond
0.5 ȝmɎ2 mm
0, 50, 100 ȝm-20 deg.
40

Wire
PCD wafer

EDM

DiamondAg

Ag alloy

Cemented carbide50ȝm
Fig.8 A micrograph of ground mold made of tungsten carbide

ISUPEN 2012(1)Bonding of PCD (2) Cutting ofto cemented carbide
PCD chip bysubstrate
wire EDM

Shank(3)Bonding of (4)Generating of
PCD chip to cutting edges withdiamond wheel
shankFig. 11 Machining process of PCD micro milling tool3

Fig. 12 shows a photograph and a Nomarski micrograph ofwere calculated based on the aspherical form and tool shape, and themachined micro array mold made of tungsten carbide. Fig. 10 shows a

NC program was generated by the PC. The B-axis tilting table couldchange of the workpiece surface roughness in machining the micro

be rotated from 10 to 100 degrees in order to control polishing angle

array mold. Tools with tool tip radius, r=0mm was used. The surfaceof the surface. Fig. 15 shows a structure of the developed two-axis

roughness profiles were measured with non-contact surface profiler,

controlled vibrator. The disk-shape actuators generate axial vibration

New View 6200. In machining 2400 molds of the tungsten carbide,and the half disk-shape actuators with anti-polarity generate flexural

very smooth surface roughness of less than 10 nm Rz was obtained.

vibration. This composite vibration is expected to improve workpiece

Fig. 13 shows a tool wear changes of the PCD tool in machining

surface roughness [4].

the micro array mold made of tungsten carbide. Tools with 3 kinds oftool tip radius, r were used. The tool tip radius became smaller, the

5.2 Polishing results

tool wear was reduced. In the case of using the tool with tool tip

The tungsten carbide mold was tested under the conditions of Table

radius r=0.1 mm, tool wear was 10 ȝm. From the experiments, the4. The aspherical workpiece was polished with the developed

tool wear of the PCD milling tool was 1/10th smaller than that of theultrasonic two-axis vibration polishing machine. Fig.16 shows

resinoid bonded diamond wheel.

Nomarski micrographs of the removal function, and (a) is that by theconventional vibration and (b) is that by the proposed vibration. A
surface roughness was improved to 7 nmRz by the ultrasonic two-axis
vibration as shown in Fig.17.
Support point

Polishing load
adjusting screw

NC controller

PC
Ultrasonic vibrator

400 ȝm

5 mm

Z-axisPolisherX-axisFig.12 Photographs of machined micro array moldC-axisY-axisWorkpiece40

B-axisr=0mm

35Tool wear ȝm

30
25

Ultrasonic

r=0.05mm

vibrator

20
15

r=0.1mm10

Polisher

50C-axis

0

500

1000
Mold number

1500

2000
B-axisFig. 13 Tool wear of PCD tool in machining the micro array mold
Workpiece
Fig. 14 4-axes controlled polishing machine with ultrasonic two axis
vibration system

5. Micro aspheric polishing with ultrasonic two-axis vibration
Improvement aspheric molds and increasing high numericalElectrodeaperture (NA) or optics with steep angle, ultrasonic two-axes

Piezo-electric actuators

vibration assisted polishing system with piezo-electric actuators and4-axes (X,Y,Z,B) controlled was proposed and developed in order to

Axial

apply to the finishing of the steep molds3).
X

5.1 Four-axis controlled polishing machine with ultrasonic two axes
vibration system

Flexural

PolisherY

Fig. 14 shows a developed ultrasonic two axes vibration assisted
polishing system. The polishing head, attached to the polisher arm,

Fig. 15 Two-axis controlled ultrasonic vibrator with piezo-electric

was mounted on the X-Y-Z tables. The tool local scanning speeds

actuators

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the probe and workpiece surface is given by:

Table 4 Polishing conditions
Workpiece

fTungsten carbide

Polishern (a,b,c)= ( -Polyurethane

Tip radius

Diamond slurry
0.5 ȝ㨙

Grain size
Load
Vibrator-

X

1.0 mmAbrasive

f
,

(6)

The vector CO between the probe center O and the contact point C isgiven by:
a

20 mN

, 1)
Y

b
r,

CO = (

Piezoelectric

c
r,

l

l

r)

(7)

l

Axial

Frequency

26.5 kHz

Where, l =(a2+b2+c2)0.5, and rp is the ball probe radius respectively.

vibration

Applied voltage

100 V

When the probe is tilted at 45 degrees from the Y-Z plane, theFlexuralFrequency

21.8 kHz

directional vector of the probe p is given by p=(1,0,1). Fromvibration

Applied voltage

200 V

Equations (6) and (7), the following relation is obtained:

213μm

Y

146μm

168μm

Y

(8)

The contact point coordinate C (Xc,Yc,Zc) is expressed as follows:

100μm

X

b2 = 2ac

120μm

100μm

X

Xc = R·sin Ĳ
Yc = R·cos Ĳ(a) 1 axis vibration(b) Two-axis vibration
Fig. 16 removal functions(9)

Z = f(R)
Where, R is the workpiece radial position of and Ĳ is angle of the Cfrom Y axis.
From the Equations (6) and (9), the following relationship is obtained:n (a,b,c)= ( - f´(R)·cos Ĳ,

f´(R)·sin Ĳ, 1 )(10)From Equations (7) and (9), the angle Ĳ is given by:

213μm
100μm

120μm
100μm
200 ȝm
Y

X

146μm

Y

168μm

200 ȝm

1
+

f´(R)

100μm

45 nmRz(a) After grinding

1
sin Ĳ =

X

100μm

7 nmRz(b) After polishingsin Ĳ =

+1

; for convex shape(11.1)+1; for concave shape(11.2)

f´(R)

1

1
-

f´(R)

f´(R)

Fig. 17 Nomarski micrographs and surface roughness profiles ofpolished surface

In order to determine the probe scanning path, first, the angle Ĳ is
calculated at the radius position R as shown above, then the contact

6. Multi-axis controlled on-machine measurement system
The 45 degrees tilted multi-axis controlled on-machinemeasurement system was developed to measure aspheric optical parts
with steep surface angles for large numerical aperture (NA) 4).
6.1 45degrees tilted and new scanning method
In order to reduce the measurement errors caused by the probe
deformation, a new probe scanning method is proposed. The probe ispoint coordinate on the workpiece surface C(Xc,Yc,Zc) is calculated
yielding ball probe center coordinate O(Xo,Yo,Zo). The probe scans theworkpiece surface 3-dimentionally in the proposed method, while itscans 2-dimentionally in the X-Z plane in the conventional method.
Probe path of
proposedmethodProbe path ofconventional
methodntilted at 45 degrees from the workpiece axis on the X-Z plane and thepprobe scans 3-dimentionally so as to keep the contact angle betweenO

the probe axis and the contact surface constant in order to reduce the45°change in the friction force between the measuring probe andmeasured workpiece as shown in Fig. 18, while the probe scansconventionally in 2 dimensions on the Y-Z plane.

X-Y

WorkpieceZ(a) Probe path on

C

Probe

Trace of contact pointon the probe(b) Path of contact point

6.2 Probe path calculation

workpiece surface

The positional relationship between the ball probe and workpiece isshown in Fig. 18(b). The normal vector n at the contact point between

Fig. 18 Principle of 45 degrees tilted scanning principle

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on probe surface

55.3 45degrees tilted and new scanning method
Fig. 19 shows a schematic diagram of the developed air slider andthe measurement unit made of SIALON ceramics. The density is 1/2.5

Airbearing

HigherpressureLowerpressureAirbearing

and the thermal expansion coefficient of SIALON is 1/10 as
Pulling force
Pushing force

compared to steel. The air slider is supported by an air gap of 2 ȝm onboth sides of the air bearings. In the center of the slider, there is a gapof about 100 ȝm. The air is supplied through this port and released
through one side of the port while there is no release port at the otherAir
sliderHigherpressureside. The pushing force and the pulling force are generated byProbeadjusting the air pressure in both sides. Low contact force of 0.1 mN

Lower
pressure

Pushing air
supply port
Detectorhead

can be obtained by this mechanism. A small glass linear scale isattached to the rear end of the slider. The amount of its movement ismeasured with the detector of the linear glass scale in 0.14 nm
resolution [5].
Fig. 20 shows the form deviation profiles measured by the
proposed measurement method compared with the conventional one.

Air slider

In case of the conventional one, the measurement error increases as a

Glass scale

sweep angle increases up to 50 degrees because of the contact force
angle change of the probe. On the other hand, in case of the proposed
method, the form deviation profile is measured correctly.

Fig. 19 Schematic diagram and view of developed air slider formeasurement unit
Sweep angle

7. Summary
-50

-30

degrees

030

50

and mirrors are increasing and the molds shapes of lens andȝmDemands of micro aspheric optical components such as lenses
mirrors would become smaller and complicated. In this study,
controlled

polishingandultra-precision

on-machinemachining,measurement

grinding,

technologies

aredeveloped for manufacturing of the complicated and micro molds.
In this report, our developed grinding method of the complicatedDeviation

multi-axis

mold, ultrasonic vibration method and contact type of multi axis
controlled on-machine measuring system were discussed.

Radial position mm(a) Conventional scanning method

References
-50

[1]

- 30

Sweep angle

degrees

030

50

Y. Yamamato, H. Suzuki, T. Moriwaki, T. Okino and T.Higuchi:
report), Journal of Japan Society for Precision Engineering,ȝmPrecision Grinding of Micro Fresnel Lens Molding Die (2nd73(6), pp. 688-692 (2007) [in Japanese].
Y. Yamamato, H. Suzuki, T. Onishi, T. Okino and T. Moriwaki:
Precision Grinding of Microarray Lens Molding Die with
4-axes, Science and Technology of Advanced Materials, 8, pp.
173-176 (2007).

Deviation[2][3] Suzuki H., Moriwaki T., Yamamoto Y., Goto Y., 2007, Precision
Cutting of Aspherical Ceramic Molds with Micro PCD Milling
Tool, Annals of the CIRP, 56/1: 131-134.
[4]

H. Suzuki, T. Moriwaki, T. Okino, Y. Ando: Development ofRadial position mm(b) Proposed 45 degrees tilted method
Fig. 20 Measured form deviation profiles.

Ultrasonic Vibration Assisted Polishing Machine for Micro
Aspheric Die and Mold, Annals of the CIRP, 55(1), pp. 385-388(2006).
[5] H. Suzuki, T. Onishi, T. Moriwaki (1), M. Fukuta, J. Sugawara:
Development of 45 degrees tilted on-machine measuring system
for small optical parts, Annals of the CIRP, 57(1), M10 (2008).

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