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 REFERENCES [1] E. Brinksmeier, O. Riemer: Metal cutting of microstructures. Proc. of First International Conference on Multi-Material Micro Manufacture. Elsevier, 2005. [2] E. Brinksmeier, 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. Annals of the CIRP. 2006; Vol. 55/2: pp. 745-768.