DIAMOND MICRO CHISELING OF MOLDING INSERTS FOR OPTICAL
MICRO STRUCTURES
Christian Flucke, Ralf Gläbe, and Ekkard Brinksmeier
Laboratory for Precision Machining
University Bremen
Bremen, Germany
INTRODUCTION
Diamond Micro Chiseling (DMC) is a new
diamond cutting process developed for the
fabrication of micro structured precision optics. It
is designed to machine prismatic micro
structures onto surfaces of molding inserts for
the replication of polymer optics. The lateral
dimension of the structures ranges from 50 µm
to 500 µm with a structure depth from 5 µm to
500 µm. Of particular significance is that any
arbitrary geometry of V-grooves or pyramidal
cavities can be machined as the process is
much less limited by kinematics of the machine
tool or the diamond tool geometry in comparison
to other ultra precision cutting processes like
diamond milling, turning or planing [1]. This
feature gives the optic designer new degrees of
freedom for the design of micro structured optic
components. The range of possible applications
lies in components for micro spectroscopy
devices,
bio-chemical
photometry
and
fluorescence assays, optics for measuring
devices in production engineering, integrated
micro optics for LEDs, and micro structured
optics for illumination technologies e.g. in the
automotive industry.
This paper gives a brief introduction into the
kinematics of the DMC cutting process and
focuses then on the main developments which
are crucial to lead DMC to a future industrial
employment. The goal was to achieve sufficient
machining accuracy, tool life and acceptable
machining time for manufacturing of micro optic
arrays with macroscopic lateral extension.
KINEMATICS OF DMC
In DMC a CVD monocrystal diamond with an
opening angle of 50°, rake angle of 18° and
flank angle of 2° is utilized for the tool (cf. fig. 1).
The applied ultra precision machine tool is
comprised of three linear and two rotational
axes. A camera provides a resolution of
1.25 µm/pixel and is used to monitor the tool
positioning and cutting process [2]. The
alignment of the tool to the workpiece and the
workspace coordinate system is performed by
cutting test structures, measuring these in-situ
with a digital video microscope and generating
correcting summands for the coordinates.
Applying this method a setup deviation in [XYZ]
of less than one micrometer is achieved.
FIGURE 1. DMC tool geometry with DMC
specific location of faces and edges.
The cutting principle is illustrated in fig. 2 for a
three sided cavity. In combined movements of
axes X, Y and Z the tool enters the workpiece
and a sloped mirror edge is cut (cf. fig. 2a).
FIGURE 2. Cutting kinematics of DMC
demonstrated by cutting a three-sided cavity.
Then the tool is retracted in [-X Y -Z]-direction
cutting the second half of the micro mirror. By
rotating the workpiece two times and repeating
the process, three sided cavities can be
generated by aligning the generated micro
mirrors (cf. fig. 2b). A precise alignment within
the mentioned set-up accuracy is crucial otherwise the chip material does not come off.
Following this principle, cavities with up to six
sides and four-sided V-grooves are combined to
larger arrays such as cubic micro hexagon retro
reflectors (cf. fig 6 and 7, also [2]).
PARTITION OF UNDEFORMED CHIP CROSSSECTION
In practice, a structure cannot be machined with
only a single cut per side as depicted in fig. 2,
because the maximum thickness of cut,
bearable by the tool, would be exceeded.
Therefore, the cross-section of undeformed chip
has to be partitioned vertically or both, vertically
and laterally.
FIGURE 3. Vertical and lateral partition of
undeformed chip cross-section.
When only vertical partition of the cross-section
is applied the structure grows in depth and
lateral dimension (cf. fig. 3a). The thickness of
cut is constant but the cross-section increases
due to the increasing length t* = b, which is one
side of the V-groove. If the cross-section is still
beyond the acceptable maximum the length t* is
divided in n = t*/b segments which are cut one
after another. Here the cross-section is
(approximately) constant for each cut.
Cutting experiments with variation of b and h
were performed and the cutting force was
measured with a dynamometer (Kistler MiniDyn)
to quantify and characterize the load of the tool.
One set of experiments was performed under
normal conditions, with both, major and minor
cutting edge engaged. For the other set the
same cutting parameters were applied but the
contact of the minor cutting edge was avoided
by a modification of the V-groove design. As
workpiece materials electroless nickel and
OFHC copper were investigated to characterize
the influence of material strength.
FIGURE 4. Cutting forces dependent on
engagement of minor cutting edge. Cutting
parameters: vc = 750 µm/s, γ = 16°, b = 40 µm,
h = 4 µm (if not stated otherwise in the diagram).
Sample size of five, standard deviation Ø 0.02N.
Fig. 4 shows the data of the forces measured. If
h or b is raised, the cutting force increases for
both materials. As expected the material with the
higher strength, electroless nickel, shows
generally higher cutting forces. The increase of
the cutting force is due to the raised crosssection of undeformed chip nearly identical for
tool engagement with and without minor cutting
edge, but there is an offset between the curves
showing the amount of force generated at the
minor cutting edge. In the variation of b the
offset appears much stronger for both materials.
Considering these facts it is concluded that a
significant share of the cutting force is generated
at the minor cutting edge, even if the contact
length is small. This is plausible as the minor
rake angle is negative and the cutting edge
radius is considerably larger at the minor cutting
edge because the adjacent tool faces are not
polished.
A strategy for the design of cutting parameters
can be derived from these results to minimize
the cutting force per cross-sectional area and,
therefore, also the load of the tool. When h is
increased, the contact length of the major cutting
edge stays constant but the contact length of the
minor cutting edge increases proportional to h.
An increase of b represents directly the increase
of the main cutting edge contact length while the
contact length of the minor cutting edge remains
constant. The thickness of cut should be as low
as possible to minimize minor cutting edge
contact length, as long as the minimum
thickness of cut dependent on the cutting edge
radius is regarded (excellent overview in [3]). To
achieve a feasible cross-section of undeformed
chip the width of cut may be as large as
possible, ideally being t*. In this case the micro
mirror is finished with a single cut and there is
no effect of kinematic roughness. The surface
texture is only dependent on the cutting edge
quality and the accuracy of the ultra precision
machine tool.
calculated in dependency of the tool radius, the
inclination of the micro mirror to the workpiece
surface and the angles between the mirror facet
edges. A surplus of compensation leads to a bar
between the mirror facets (cf. bottom SEM
picture).
COMPENSATION OF TOOL TIP RADIUS
The ideal tool geometry for DMC is a sharp point
tool, which is in theory capable of cutting cavities
with infinitely sharp concave corners. In reality a
sharp point tool is too fragile and breaks upon
first use. Therefore, a radius of several
micrometer size is ground at the tip of the tool.
When cutting with a radius tool the utmost point
of the radius in contact with the workpiece,
which is defining the generated geometry of the
cavity,
changes
with
the
engagement
parameters and the structure geometry. When
generating the CNC-code for DMC machining
this point has to be determined and considered
when calculating the tool path.
Fig. 5 demonstrates the function of the radius
compensation at the example of a four-sided Vgroove machined with an 8 µm radius tool. None
or an insufficient compensation leads to
overlapping edges of the mirror facets as visible
in the SEM picture at top. In the middle picture
the edges are repositioned in [XYZ] such as they
meet with a deviation in position of less than one
micrometer. The values for the reposition are
FIGURE 5. Tool radius compensation for an
8 µm radius DMC tool at the example of a foursided V-groove.
Applying the radius compensation sharp mirror
facet edges are generated while keeping the
overall geometry at nominal dimensions. Only a
very small area (less than 0.1% of the total
mirror surface for a 3 µm radius finish machining
tool) in the concave corners of the cavities
remains undefined, as it cannot be reached by
the tool. Accordingly, with DMC machining
nearly 100% yield of efficient micro mirror
surface can be generated.
PRE- AND FINISH MACHINING WITH TOOL
EXCHANGE
For reducing the machining time and increasing
surface quality and dimensional accuracy DMC
machining is performed in three steps. During
pre-machining a robust DMC tool with a radius
of 8 - 12 µm is applied for high chip load
(h > 8 µm, b = t*) at high cutting speeds
vc ≥ 2000 µm/s. The first of two finish-machining
steps is done with the same tool at
vc < 500 µm/s and h = 4 µm to achieve
dimensional deviations below 1 µm of the
structures, which is a necessary preparation for
the final cut to be placed accurately in the premachined structure. Finally, the tool is
exchanged applying a 3 µm radius tool and
second step finish machining is performed with
h = 1.5 µm and vc ≤ 500 µm/s for optimized
surface quality. Mandatory for the tool exchange
is the precise setting-up described above. For
an array of 2,500 cubic hexagon retro reflectors
(cf. fig. 7) of 200 µm structure size (area approx.
8.84 x 10.3 mm²) the machining time (simulated
applying an analytical model) can be reduced
about 72% from impossible 437 hours to 79
hours, which is still very much, but feasible, if
the value of a micro structured master mold is
considered.
Conclusion
The process strategies described above were
tested by machining an electroless nickel
coating molding insert with several arrays of
optical micro structures. Fig. 6 shows an
example how V-grooves and four-sided small
cavities can be combined to form a riblet
structure. The second example (fig. 7) is an
array of cubic retro reflectors with hexagonal
aperture [2]. The surfaces are of optical quality
with a roughness Ra < 10 nm, flatness
PV < 50 nm and are free of artifacts. The effect
of tool radius compensation is clearly visible as
the edges and corners are sharp and only an
insignificant small area in concave corners
remains undefined.
mechanism of cutting force generation was used
when machining these samples to decrease the
amount of cutting force per cross-sectional area
of uncut chip. This allows lager cross-sections,
shorter machining time and increased tool life.
Better surface quality is gained as no effect of
kinematic roughness occurs when finish
machining micro mirror facets with a single cut
cutting width being b = t*. Also the concept of
pre and finish machining by utilizing two
dedicated tools reduces machining time and
quality, as the main load is taken by the robust
pre-machining tool. Nevertheless, the machining
time is quite high and future work will deal with
further reduction. The maximum cutting speeds
are not limited by the DMC process itself, but by
the dynamics of the machine tool and stiffness
of the DMC diamond tool. Here lies a large
potential for further optimization.
FIGURE 7. 100 µm cube corner retroreflectors
with hexagonal, 100%-effective aperture.
ACKNOWLEDGEMENTS
The authors like to thank the German Research
Foundation (DFG) for funding this work as a part
of the Transregional Collaborative Research
Center SFB/TR4.
FIGURE 6. Riblet structure of overlapping
V-grooves with cavities at the protruding ridges.
By reducing the contact length of the minor
cutting edge the better understanding of the
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R. Gläbe,
C. Flucke:
Manufacturing of molds for replication of
micro
cube
corner
retroreflectors.
Production Engineering. 2008; Vol. 2/1: 3338.
[3] D. Dornfeld, S. Min, Y. Takeuchi: Recent
Advances in Mechanical Micromachining.
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