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1 한국정밀공학회지제 3 권 12 호 pp J. Korean Soc. Precis. Eng., Vol. 3, No. 12, pp ISSN (Print), ISSN (Online) December 213 / 대면적미세패턴롤금형가공용초정밀롤선반개발 An Ultra-precision Lathe for Large-area Micro-structured Roll Molds 오정석 1, 송창규 1, 황주호 1, 심종엽 1, 박천홍 1, Jeong Seok Oh 1, Chang Kyu Song 1, Jooho Hwang 1, Jong Youp Shim 1, and Chun Hong Park 1, 1 한국기계연구원첨단생산장비연구본부 (Advanced Manufacturing Systems Research Division, Korea Institute of Machinery & Materials) Corresponding author: pch657@kimm.re.kr, Tel: Manuscript received: / Accepted: We report an ultra-precision lathe designed to machine micron-scale features on a large-area roll mold. The lathe can machine rolls up to 6 mm in diameter and 2,5 mm in length. All axes use hydrostatic oil bearings to exploit the high-precision, stiffness, and damping characteristics. The headstock spindle and rotary tooling table are driven by frameless direct drive motors, while coreless linear motors are used for the two linear axes. Finite element method modeling reveals that the effects of structural deformation on the machining accuracy are less than 1 µm. The results of thermal testing show that the maximum temperature rise at the spindle outer surface is approximately.5 C. Finally, performance evaluations of the error motion, micro-positioning capability, and fine-pitch machining demonstrate that the lathe is capable of producing opticalquality surfaces with micron-scale patterns with feature sizes as small as 2 µm on a large-area roll mold. Key Words: Hydrostatic oil bearings ( 유정압베어링 ), Optical Films ( 광학필름 ), Single-point Diamond Cutting ( 다이아몬드선삭 ), Ultra-precision Roll Lathe ( 초정밀롤선반 ) 1. Introduction Large-surface micromachining systems include equipment and processes for manufacturing micropatterned products with a large surface using mechanical machining. These micromachining systems rely on ultraprecision machines, which are becoming increasingly larger to handle the increasing demand for large-surfacearea micro-patterned products, especially for applications in flat-panel display technologies. The backlight unit (BLU) of liquid crystal displays (LCDs) is composed of several large-surface-area micropatterned optical elements, and is one of the most important markets for large-surface micromachining systems. Examples of the large-surface-area micropatterned elements in BLUs include light guide plates (LGP) and optical films. 1,2 The required feature pitch in these optical films is typically as small as 2 µm, which must be patterned over a width of 2, mm. Fig. 1 illustrates the evolution of micromachining systems according to the surface size of the micropatterned products. 3 Even 15 years ago, the major target products of the micromachining systems were small LGP molds for mobile phones and notebooks, or precision molds for optical devices. These products are less than 5 mm in size and were machined by using an ultraprecision lathe or ultra-precision 5-axis milling machine. As LCD TVs have become larger, the size of the BLUs

2 한국정밀공학회지 제 3 권 12 호 pp Injection molding Injection or Direct machining Precision/Medical devices, Notebook, Fuel cell parts Optical devices 3 (12 ) Ultra-precision Lathe Toyoda AHN5 FANUC Robonano Kugler Micro gentry Roll embossing LCD BLU parts, Solar heat condensing lens 5 (2 ) Ultra-precision 5-axis Milling Grooving Machine NACHI Nano Groover Toshiba UMP December 213 / 134 Optical film Ultra high luminance reflecter 1, (4 ) Roll(Drum) Lathe Toshiba ULR Moore VDTM Fig. 1 Trends in micromachining systems according to the surface size of the related products UV Curable Resin Micropatterned Film Base Film (PET) Curing by UV Light Fig. 2 Continuous forming process for manufacturing optical films and related molds has increased. Ultra-precision grooving machines a specialized version of a milling machine are typically used for flat-mold or direct-machining applications. For optical films, which can be larger than 1, mm, the manufacturing process using a flat mold is no longer suitable and continuous forming processes using a micro-patterned roll mold are being applied for mass production. Fig. 2 presents the concept of a typical continuous forming process used to produce optical films. An ultraviolet (UV) curable resin is coated on a polyethylene terephthalate (PET) film, and the micro-pattern on the roll mold is transferred to the coating layer. The transferred pattern is cured using UV light. In this continuous forming process, a precisely machined roll mold is essential. The ultra-precision roll lathe is a machine tool that can be used to produce optical quality surfaces or complex micro-structures on a large roll mold using single-point diamond-cutting tools. In this article, we present the design and analysis of an ultra-precision horizontal roll lathe that is able to machine large rolls with a diameter of 6 mm and a length of 2,5 mm (with a pattern length of up to 2, mm). We also report the results of its performance in terms of error motion, micro-positioning tolerance, thermal behaviors, and fine-pitch machining. 2. Design and analysis 2.1 Design of the ultra-precision roll lathe The minimum required pitch is 2 µm, and the pitch variation should be less than ±.2 µm. The required form error of the roll mold is about 5 µm. To satisfy the required accuracy over a 2,-mm machining length, several strict requirements must be considered in the design of the machine. First, thermal stability is very important, because machining can take a long time typically from half a day to several days to machine an entire roll surface. For example, an optical prism pattern is usually produced from several repetitive machinings to meet the required pattern depth and surface quality. The relative thermal deformation between the diamond tool and the roll mold during machining can cause pattern shift between each machining step.4 If we consider that a temperature variation of 1 C in a 2,-mm steel roll causes a thermal deformation of about 23 µm, thermal sources in the roll lathe and surrounding environment should be carefully controlled to minimize relative thermal deformation. Second, error motion in the Z-axis, which is the axis parallel to the centerline of the roll, should be less than 2 µm to ensure good form accuracy. Additionally, the radial error motion of the spindle holding the workpiece should be less than 1 µm. Third, the positioning stability of the X-axis (the tool-feed axis) is critical to guarantee an optical-quality surface roughness. Fourth, high stiffness and load capacity is essential for both the headstock and tailstock spindle to support heavy rolls. Fig. 3 illustrates the structural layout of the machine, and Table 1 lists the specifications. The machine has a roll-diameter capacity of 6 mm and a capacity of 6 kg. The headstock, tailstock, and Z-axis slide are mounted on the machine bed, which is made of cast iron. The two ends of the roll are mounted on the headstock and tailstock, respectively. The roll is rotated and controlled by the headstock spindle (C-axis). The B-axis precisely indexes the cutting tool, while the X-axis controls the cutting depth. The Z-axis moves the cutting tool in the direction parallel to the centerline of the roll. The working strokes of Z- and X-axis are 2,32 mm and 26 mm, respectively. The position of the tailstock can be adjusted manually to fit rolls with different lengths.

3 한국정밀공학회지제 3 권 12 호 pp December 213 / 135 Cooling Jacket Thrust B/R Chuck C Encoder DD Motor Journal B/R Linear Scale Horizontal B/R Cooling Plate Linear Motor Z B Vertical B/R X Fig. 3 Layout of the ultra-precision roll lathe Table 1 Specifications of the roll lathe Term Specifications Machine Size 4,91(L) x 1,57(W) x 1,425(H) mm Maximum Roll Size φ6 x 2,5 mm Effective Pattern Length 2, mm Maximum Roll Weight 6 kg Motor coreless linear motor, direct drive rotary motor Bearing Hydrostatic oil bearing Rotation Speed ~ 6 rpm Resolution ~.18 arcsec C-axis 3,58 N/μm (radial), Bearing Stiffness 2,83 N/μm (axial) Resolution ~.18 arcsec B-axis 36 N/μm (radial), Bearing Stiffness 88 N/μm (axial) Stroke 2,32 mm Speed 2 m/min Z-axis Resolution ~ 1 nm Bearing Stiffness 2,3 N/μm (ver.), 1,15 N/μm (hor.) Stroke 26 mm Speed 1 m/min X-axis Resolution ~ 1 nm Bearing Stiffness 1,81 N/μm (ver.), 95 N/μm (hor.) To implement these precision requirements, constantpressure hydrostatic oil bearings were used in all axes, including the tailstock spindle. Compared with aerostatic bearings, hydrostatic oil bearings have a higher degree of stiffness and more damping, which is very important in machining heavy rolls with high-precision surface features. The headstock spindle and the tool index table were driven using frameless direct-drive motors, while coreless linear motors were used for the two linear axes. C W Fig. 4 Thermal distortion of the machine structure by the over-constraint design of the tailstock To obtain nanometer positioning capability, linear scales with 1-nm resolution were used for the linear axes. The resolution of the C-axis was.18 arcsec, which corresponds to.26 µm for a roll with a diameter of 6 mm. Cooling jackets were installed in the headstock spindle to dissipate the heat generated from the hydrostatic oil bearings and the spindle motor. Additionally, the temperature of the oil supplied to the hydrostatic oil bearings was controlled at ±.1 C using a precision oil cooler. In the Z- and X-axes, box-type hydrostatic slides were constructed to provide a high level of structural rigidity; the table was equipped with double-sided hydrostatic bearings in the vertical and horizontal directions. In particular, two linear motors were used in the Z-axis to reduce the heat generated during high-speed transverse machining processes. The amount of heat generated in the Z-axis motor was halved compared with a single motor design. A cooling plate was installed at the upper part of two linear motors for additional heat dissipation. One of the most critical issues in the design of the tailstock is thermal deformation of the spindle and roll. Although most of the heat generated at the bearings and motors is removed via cooling, any temperature increase can result in expansion of the spindle and roll. If the tailstock cannot accommodate this expansion, it can result in an overall distortion of the machine structure, as illustrated in Fig. 4. Four types of tailstock design were investigated to accommodate this thermal expansion, as illustrated in Fig. 5. The thrust bearings were removed in the hydrostatic type 2 design, and spring and sliding mechanisms were used in the other three designs. To provide a reference position when mounting the roll, a roll-centering mechanism that fixes the spindle shaft at the center position between two journal bearings was implemented in the hydrostatic type 2 design. Section 3.4

4 한국정밀공학회지제 3 권 12 호 pp December 213 / 136 Spring Spring 72.8 µm Sliding Surface Spring Sliding Surface Roll Centering 9.2 µm 6.5 µm (c) (d) Fig. 5 Four tailstock designs: dead center, live center, (c) hydrostatic type 1, and (d) hydrostatic type 2 Table 2 Physical properties of the materials used in the FEM analysis Material Density (kg/m 3 ) Young s Possion s Modulus Ratio (GPa) Thermal Conductivity (W/m C) Thermal Expansion (µm/m C) Specific Heat (J/kg C) GC3 7, S45C 7, SS4 7, discusses the results of the comparison between the thermal behaviors of these tailstocks; briefly, following the evaluation of these four systems, the hydrostatic type 2 design was selected for the prototype machine. 2.2 Structural analysis Table 2 lists the physical properties of the materials used for finite element method (FEM) modeling. The FEM model included 272,329 node points, 1,218,882 solid elements, and 1,8 matrix elements. The stiffness and the pad pressure of the hydrostatic oil bearings were also taken into account. Fig. 6 shows the total simulated structural deformation when the Z- and X-axis were located in the middle of the range of motion. Even though the maximum deformation of the roll was about 73 µm in the vertical direction, the effect on the machining accuracy was minimal because the cutting action occurred at the side of the roll. The deformation of the roll in the X-direction is more important. Fig. 6 shows that the deformation of -1.9 µm Fig. 6 FEM structural analysis: total structural deformation (Max µm., Min. µm); structural deformation in the X-direction (Max. 9.2 µm, Min µm) Deformation (µm) , ,2 Z-axis position (mm) X-direction :.93 µm Y-direction :.27 µm Z-direction :.44 µm Fig. 7 FEM-simulated data showing the variation in the tool position depending on the Z-axis translation the roll in the X-direction was 6.5 µm; however, it was quite uniform over the full length of the roll. Because machining accuracy depends on the variation in the distance between the roll and the cutting tool, deformation at the tool position should be taken into account. The mean deformation at the tool position merely acts as a DC offset: the deformation itself does not limit machining accuracy, but the variation in the

5 한국정밀공학회지제 3 권 12 호 pp December 213 / 137 Fig. 9 Photograph of the prototype ultra-precision lathe (c) Fig. 8 Modal analysis data: 1st mode (67.8 Hz), 3rd mode (73.9 Hz), (c) 4th mode (75.1 Hz), and (d) 5th mode (85.2 Hz) deformation with translation in the Z-axis does. To observe this variation in deformation at the tool position, FEM calculations were carried out for a number of positions of the tool along the Z-axis, as shown in Fig. 7. The variations in the deformation at the tool position were.93 µm in the X-direction,.27 µm in the Y- direction, and.44 µm in the Z-direction. The effects of structural deformation on the machining accuracy resulted in an error of less than 1 µm. Fig. 8 shows the results of modal analyses. The first and second modes appear at 67.8 Hz and 71. Hz, respectively. These modes are horizontal and vertical vibrations of the roll coupled with the spindle. Because the size and weight of the roll can change with the application, these frequencies will also change. The third, fourth and fifth modes are roll, pitch and yaw motions of the Z-axis slide, respectively. These modes are affected by the stiffness of the hydrostatic oil bearings. The frequency of these modes is in the range Hz. Because the main excitation frequency of the roll lathe is in the range 5 1 Hz (the maximum rotation speed of the spindles holding the workpiece is typically in the range 3 6 rpm), the modal analysis results imply that the stiffness of the roll lathe is sufficient to avoid these modes being excited. 3. Performance evaluation of the roll lathe 3.1 Evaluation of the headstock spindle (d) Load (N) Measured : 4 N/µm FEM : 446 N/µm Displacement (µm) Fig. 1 Measured nose stiffness and comparison with the FEM data Fig. 9 presents a photograph of the prototype machine. The journal bearing of the headstock spindle must support the weight of the spindle itself (3 kg) and that of half the roll (3 kg). Because most of the weight is supported by the front journal bearing, the load capacity of the front journal bearing was 6 kgf with an eccentricity ratio of.2. The stiffness of the front journal bearing under this design condition was 1,79 N/µm. The nose stiffness of the headstock spindle was then estimated from the FEM data. Fig. 1 presents the measured nose stiffness. A load cell and a capacitive displacement sensor (Micro sense 341, 2.5 µm/v) were used for these measurements. The nose stiffness of the headstock spindle was 446 N/µm from the FEM data, and the measured stiffness was 4 N/µm. Fig. 11 and 11 show the measured spindle error motions in the radial and axial directions, respectively. A precision master ball (Lion Precision, roundness: 2.9 nm) and capacitive displacement sensors were used to characterize the spindle error motions. Synchronous error

6 한국정밀공학회지제 3 권 12 호 pp December 213 / 138 Axial Error Motion (µm) Radial Error Motion (µm) Radial error motion Displacement (nm) Time (sec) Fig. 12 Micro-step response in the X-axis (5 nm/step) the X-axis at nanometer level, the micro-step response of the X-axis which has a resolution of 1 nm was measured using a capacitive displacement sensor. A lowpass filter with a cutoff frequency of 5 Hz was used to eliminate the effect of floor vibrations at 26 Hz. Figure 11 presents the 5-nm micro-step response in the X-axis. The results indicate that the X-axis has good micromotion capability at the nanometer level Axial error motion Fig. 11 Measured error motions of the headstock spindle motion in the radial direction was.53 µm, while asynchronous error motion was.12 µm. The total radial error motion of the spindle was.58 µm. The sources of the spindle error motion in the radial direction were attributed to cogging of the spindle motor and imperfect machining of the spindle shaft. If these errors resulted from cogging, the spindle error motion would be reduced if the stiffness of the journal bearings is increased by increasing the oil supply pressure. 5 However, doing so resulted in little change in the spindle error motion. It follows that the spindle error motion in the radial direction mainly resulted from imperfect machining of the spindle shaft. The axial error motion of the spindle was very small: the total axial error motion of the spindle was.4 µm and the asynchronous error motion was.3 µm. 3.2 Fine motion response in the X-axis To obtain optical-quality surface roughness of the patterns, the positioning stability of the X-axis during machining is very important. To investigate control over Characterization and compensation of Z- axis error motion Form error of the roll mold is dominated by Z-axis slide error motion, which is composed of a straightness error component and an axis misalignment error component. The straightness error component is mainly introduced by the form error of the hydrostatic guideway of the Z-axis, and is directly transferred to the roll mold. The axis misalignment error is introduced by misalignment between the Z-axis translation and the axis of rotation of the spindle holding the workpiece. The axis misalignment error component generates a taper-shaped form error of the roll mold. Because the form error of the roll mold must be less than 5 µm, measuring and compensating for the error motion of the Z-axis is critical for the fabrication of an accurate roll mold. To measure the error motion of the Z-axis, we used a measurement method based on the error separation technique. 6 In this method, a roll workpiece, which is cut by the roll lathe itself, is employed as a specimen for the measurement. Fig. 13 shows the experimental setup for measuring the error motion of the Z-axis slide. The error motion in the Z-axis was measured using two capacitive displacement sensors placed at the two sides of the roll workpiece. The capacitive sensors were first moved by

7 한국정밀공학회지제 3 권 12 호 pp December 213 / 139 X A Y B Spindle Z C Probe B Fixture B Large-scale roll workpiece Probe A Fixture A Fig. 13 Experimental setup to measure the error motion of the Z-axis slide Error Motion (µm) Error Motion (µm) st measurement 2 nd measurement 3 rd measurement 1 st measurement 2 nd measurement 3 rd measurement , 1,25 1,5 1,75 Position (mm) Fig. 14 Measurement and compensation of error motion in the Z-axis: before compensation; after compensation the Z-axis motor to scan the stationary roll workpiece from the starting position to the end position of the Z-axis travel range before and after a 18 rotation of the workpiece about the axis of rotation of the spindle. The straightness error component can be accurately evaluated using the reversal method. The two capacitive sensors were then kept stationary at the start and end positions of the Z-axis travel range, to scan the rotating roll workpiece over multiple rotations. The axis misalignment error component can be evaluated using an averaging operation of the sensor outputs over one or multiple rotations, m) Displacement (µ Live Center Hydrostatic Type 1 Hydrostatic Type Time (hour) Fig. 15 Thermal behavior of the tailstocks which removes the influence of the roundness error of the roll workpiece as well as the spindle error motion. Fig. 14 shows the measured error motion in the Z- axis without compensation. A total of three measurements were carried out, and the time elapsed for each measurement was 6 minutes. The average of the three peak-to-valley (PV) error motions was 8.6 µm over the 1,7-mm travel range. The PV deviation, i.e., the repeatability, was.2 µm. The error motion in the Z-axis was compensated for, using the measured data. This compensation was carried out by moving the X-axis with a command motion, which had the same amplitude but opposite sign as the error motion of the Z-axis. The compensated error motion is shown in Fig. 14; the error motion in the Z-axis was reduced to.8 µm with a repeatability of.2 µm. Further details of these measurements and compensation schemes can be found in Ref Effect of tailstock design on thermal behavior The tailstock design is important to accommodate thermal expansion of the workpiece and spindle during high-speed rotation. To compare the thermal behavior depending on the tailstock design, a commercial heterodyne laser interferometer (Agilent 5529A) was installed to measure the relative displacement of headstock and tailstock during high-speed rotation (3 rpm). With a dead-center type tailstock (see Fig. 5), it was impossible to rotate the roll due to excessive friction. Therefore, comparisons were carried out using the other three types of tailstock. Fig. 15 presents the measured relative displacement between headstock and tailstock over 4 hours. The refractive index of air was compensated for, using the

8 한국정밀공학회지제 3 권 12 호 pp December 213 / 131 Edlén formula. 7 The relative displacement was approximately 34 µm with the live center tailstock, and was approximately 25 µm for the hydrostatic type 1 tailstock. In both designs, the relative displacements did not stabilize even after 4 hours. In contrast, the relative displacement with the hydrostatic type 2 tailstock was less than 5 µm, and stabilized quickly. These results demonstrate that the hydrostatic type 2 tailstock is far more effective in accommodating thermal expansion of the roll and spindle. 3.5 Cooling the bearings Cooling jackets were installed at the headstock and the tailstock to dissipate heat generated from the spindle motor and the hydrostatic oil bearings during high-speed rotation. To evaluate the effects of bearing cooling, the temperature rise at the headstock and the tailstock at a rotation of 3 rpm was measured using T-type thermocouples. Each thermocouple was attached to the outer surface of the journal bearing, as shown in Fig. 16. Fig. 16 shows the temperature rise at the headstock. Without cooling, the temperature rise at thermocouple 2 was.85 C, and was.52 C at thermocouple 1. The difference in the temperature rise at the two positions was mainly the result of heat generated at the spindle motor, which was installed near thermocouple 2. With cooling, the temperature rise at thermocouple 2 was.52 C, and was.13 C at thermocouple 1. Fig. 16(c) shows the temperature rise at the tailstock. Without cooling, the temperature rise at thermocouples 3 and 4 was 1.13 C; these results were almost identical because no spindle motor had been installed in the tailstock. The average temperature rise was greater at the tailstock than at the headstock, possibly because the bearing clearance of the tailstock spindle was smaller than that of headstock spindle. With cooling, the average temperature rise at the tailstock was.4 C and the temperature stabilized within 1 hour. These results demonstrate that bearing cooling effectively reduced the temperature rise. 4. Evaluation of machining performance Testing involved a copper-plated roll with a length of & % ' ( 1.2 C) o Temperature Rise ( C) o Temperature Rise ( No. 2 (No Cooling) No. 2 (Cooling) No. 1 (No Cooling) No. 1 (Cooling) Time (hour) No. 4 (No Cooling) No. 4 (Cooling) No. 3 (Cooling) No. 3 (No Cooling) Time (hour) (c) Fig. 16 Position of the thermocouples, temperature profiles at the headstock with and without cooling, and (c) temperature profiles at the tailstock with and without cooling 2,333 mm (of which the machining face had a length of 1,8 mm) and a diameter of 32 mm. The surface of the copper-plated roll surface was not perfectly cylindrical, and rough cutting using a cubic boron nitride (CBN) tool was carried out, followed by machining using a roundshaped diamond tool to achieve a mirror-like surface. Finally, a prism pattern was generated using a V-shaped diamond tool. The speed of the spindle was 3 rpm. To generate a 2-µm-pitch prism pattern, the speed of the Z- axis was set to 2 µm/rev. Fig. 17 presents scanning electron microscope (SEM) images of the machined prism patterns. For the SEM measurements, the patterns on the roll mold were transferred using a UV-curable resin. As shown in the

9 한국정밀공학회지 제 3 권 12 호 pp December 213 / 1311 (c) Fig. 17 Machined 2-µm-pitch prism pattern (with normal spiral cutting): near the headstock, at the center, and (c) near the tailstock (c) Fig. 18 Machined 45 prism pattern with a 3-µm pitch: near the headstock, at the center, and (c) near the tailstock image, the 2-µm-pitch patterns with an optical-quality surface were successfully machined regardless of the roll positions. For some applications, optical film manufacturers require a 45 prism pattern as well as normal spiral pattern. Because the speed and position of the C-axis and the Z-axis must be carefully synchronized to machine 45 prism patterns, the control performance of the roll lathe can be evaluated accurately. Fig. 18 presents SEM pictures of the machined 45 prism patterns. The rotation speed of the C-axis was set to rpm, and the Z-axis translation speed was 1 m/min. As with spiral cutting, clear 45 prism patterns with a 3-µm pitch were generated regardless of the roll position. This demonstrates good control of the roll lathe. 5. Conclusions We designed, fabricated, analyzed, and evaluated an ultra-precision horizontal roll lathe capable of machining cylindrical rolls with a diameter of up to 6 mm and a length of 2,5 mm. Hydrostatic bearings were used in all axes to provide high levels of precision and stiffness. Additionally, non-contact driving was realized using coreless linear motors and direct-drive rotary motors. Structural analysis using FEM simulations revealed that the structural deformation of the machining accuracy can be maintained below 1 µm. FEM modal analysis revealed that the main vibrational modes (other than the vibration modes of the roll) were Z-axis slide, roll, pitch, and yaw. The resonant frequencies of these vibrational modes were higher than 7 Hz. Major performance parameters were evaluated, such as the nose stiffness of the spindle, micro-motion capability in the X-axis, error motion of the Z-axis, and thermal behavior of the roll lathe. The measured nose stiffness of the headstock spindle matched very well with the FEM data. The radial error motion of the spindle was less than.6 µm; this may be reduced further by improving the machining accuracy of the spindle shaft, which was identified as the limiting factor. The error motion of the Z-axis, which is directly transferred to the form of the roll, was measured using a recently developed error separation method. Following compensation, Z-axis error motion was reduced to less than 1 µm. The maximum temperature rise at the spindle outer surface was less than.5 C and the temperature stabilized within one hour, due to the bearing cooling. Additionally, we compared four tailstock designs by analyzing the relative displacement between headstock and tailstock, and identified a hydrostatic design with significant performance enhancements. The micron-scale patterns were machined over the whole area of the roll and analyzed using SEM. The roll lathe was capable of producing optical-quality surface micro-patterns with features of 2 µm, and demonstrated excellent synchronization control in the fabrication of 45 prism patterns. ACKNOWLEDGEMENT This research was supported by the Industrial Core Technology Development Program funded by the Korea Ministry of Knowledge Economy (MKE) (No ).

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