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Fabrication of aspheric surface using ultraprecision cutting and BMG molding
Journal of Materials Processing Technology 209 (2009) 5014–5023
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Fabrication of aspheric surface using ultraprecision cutting and BMG molding Cheng-Tang Pan a , Tsung-Tien Wu a , Yung-Tien Liu b,∗ , Y. Yamagata c , J.C. Huang d a
Department of Mechanical and Electro-Mechanical Engineering, and Center for Nanoscience & Nanotechnology, National Sun Yat-Sen University, Kaoshiung 804, Taiwan, ROC Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, Kaoshiung 811, Taiwan, ROC c VCAD System Research Program Applied Fabrication Team, the Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako, Saitama 351-0198, Japan d Institute of Materials Science and Engineering; Center for Nanoscience and Nanotechnology, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, ROC b
a r t i c l e
i n f o
Article history: Received 13 August 2008 Received in revised form 7 January 2009 Accepted 28 January 2009 Keywords: Oxygen free copper Aspheric surface Metallic glass
a b s t r a c t A new process to replicate an aspheric lens is presented in this study. A mold of oxygen free copper (OFC) is fabricated using ultraprecision machining, which is a popular material for machining due to its good machinability. But OFC has a very low hardness of 1.606 GPa, it is not suitable for the subsequent molding process. Then, this OFC mold (known as the first mold) is used to hot emboss on Mg58 Cu31 Y11 amorphous alloy to form a secondary mold which is one kind of metallic glass. The hardness of the secondary mold is as high as 3.445 GPa, whereas the glass transition temperature (Tg ) of the Mg58 Cu31 Y11 metallic glass is as low as 413 K (140 ◦ C), at which the Mg58 Cu31 Y11 metallic glass shows a good glassforming ability (GFA). In order to perform superplastic microforming, the working temperature must be close to the glass temperature around 413 K. Therefore, in this study, the temperatures of the hot embossing experiments to fabricate the secondary mold are set at 423 K (150 ◦ C). It shows experimentally that the working temperature is dependent on the applied stress level. Since the Mg58 Cu31 Y11 metallic glass has superplastic property at the supercooled liquid region, it can be easily formed by the master die. This embossing process on the Mg58 Cu31 Y11 metallic glass makes molding process faster and more diverse applications. Next, the secondary mold is used to emboss on polymethylmethacrylate (PMMA) sheets for replication process. The Mg58 Cu31 Y11 metallic glass is not only a good material for hot embossing process to fabricate micro-structure directly, but also an excellent fast-molding material for hot embossing process. It is expected that the machining processes described in this paper could be applied to the related fields to fabricate precision components required of micro, sub-micro, or nano order of dimensional accuracy. © 2009 Elsevier B.V. All rights reserved.
1. Introduction With the ongoing technological improvement in 3C (computer, consumer, and communication) products, it caused high requirements of precise optical components (Brinksmeier et al., 2006). For example, it has become very usual that a digital camera with a miniaturized optical lens is integrated into a cell phone. To obtain a high-quality of camera image, an aspheric lens with a specially designed curvature has become one of the key components of the optical device (Syoji, 2004). For providing attractive prices of the 3C products, most of the precise components were produced by massproduction based on ultraprecision molds and dies which were fabricated by using ultraprecision machine tools (Muranaka, 2003; Dornfeld et al., 2006). However, since the ultraprecision machining process is extremely expensive and the test of a new mold for mass-production is time-consuming, how to provide a process of
∗ Corresponding author. Tel.: +886 7 6011000x2220; fax: +886 7 6011066. E-mail address: [email protected] (Y.-T. Liu). 0924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2009.01.025
both time-saving and cost-effective is the current issue in the manufacturing industry, especially, for the rapid growth of diverse 3C products. Therefore, a new process to fabricate an aspheric surface of bulk metallic glass (BMG) is proposed in this paper. BMG is referred to as an amorphous metallic alloy. The materials show very high strength at room temperature and excellent viscous flow property at temperatures between the glass transition temperature (Tg ) and crystallization temperature (Tx ). The maximum diameter of glass formation (Dc ), temperature interval of the supercooled liquid region (Tx ), melting temperature (Tm ), liquidus temperature (Tl ) as well as heats of crystallization (Hx ) and melting (Hm ) were reported for Ga-based (Senkov et al., 2006) and Mg-based bulk amorphous alloys (Liu et al., 2005). Glass transition and crystallization behavior of Mg–Ni–Nd metallic glass have been systematically studied by temperature-modulated differential scanning calorimetry (TMDSC). That provided a clear observation of glass transition and crystallization micro-mechanism (Lu et al., 2004). The application of melt-spinning process of Mg85 Cu5 Zn5 Y5 alloy was studied, which was found to cause the formation of a mixed structure consisting of nanoscale crystalline particles embedded in an amorphous matrix (Yuan et al., 2004). Yuan and
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Inoue (2005) reported that an appropriate substitution of Cu by Ni in Mg65 Cu25 Gd10 significantly improved its mechanical properties, especially improved the ductility of Mg-based bulk metallic glass. The viscous flow behavior of the Mg58 Cu31 Y11 bulk amorphous rods in the supercooled viscous region was investigated (Chang et al., 2007). It was found that the appropriate working temperature for microforming was about 460–474 K. Furthermore, the Mg58 Cu31 Y11 BMGs showed physical properties of good glass forming. It is known that BMG alloys can exhibit not only the unique physical properties such as excellent elasticity and strength, but also the significant plasticity occurred in the supercooled liquid region, Tx (=Tx − Tg ), due to a drastic drop in viscosity during glass transition upon heating (Busch et al., 1998). Several researchers have reported the mechanical properties by using uniaxial tensile testing (Yuan and Inoue, 2005; Pérez et al., 2005; Pérez et al., 2004) and uniaxial compression testing (Chang et al., 2007; Liu et al., 2005; Yuan and Inoue, 2005; Zheng et al., 2007; Wolff et al., 2004). However, there were only few studies on imprinting or hot embossing process of BMG material. Saotome et al. (2001) used imprint process to fabricate a silicon mold with nano-patterns. With this die, the nano-forming ability of Pd-based amorphous alloy was examined. Chu et al. (2007) reported the fabrication of a siliconbased grating die to imprint on Pd40 Ni40 P20 BMG plate, which was then used as a mold to imprint on polymer material. The advantages of aspheric lenses over spherical lenses are well recognized. Manufacturing methods of aspheric lenses have been reported, such as grinding aspheric ceramic mirrors (Kuriyagawa et al., 1996), large depth-to-diameter ratio aspheric surfaces (Chen et al., 2002), and diamond turning of large off-axis aspheric mirrors (Kim et al., 2004). Properly manufactured aspheric lenses were reported by using diamond grinding, lapping, and polishing on a CNC machining centre (Ligten et al., 1985; Zhong and Venkatesh, 1995). In addition, semi-ductile grinding obtained by using conventional CNC machining centers and commercial grinding wheels were very promising and helpful to reduce manufacturing costs. Semi-ductile grinding for aspheric surface has been observed on glass, silicon and germanium (Venkatesh, 2003). Conventional grinding in many optical industries is highly successful. The manufacture of plastic lenses for ophthalmic purposes was gaining in popularity with decreasing costs brought about by low-cost
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manufacture of glass moulds. Also, ductile mode grinding gains worldwide attention in industries for low-cost manufacture; for instance, oxygen free copper (OFC) presented in this study shows a good machinability. Another method of generating aspheric profiles was reported using more advanced technologies of CAD/CAM, which showed that the use of general-purpose machine can give flexible output in terms of variety of lenses without using any special purpose machine (Venkatesh et al., 2005). In recent years, micro-lens array has been attracting much attention for a variety of applications. For display field, it is used to enhance the brightness of illumination and simplify the light guide module construction. Both higher accuracy and lower cost of micro-lens fabrication methods are needed to meet the rapid growth of commercial devices. It is an important issue to make a high accuracy and strong mold to replicate micro-lens array. The selection of BMG is based on the fact that amorphous alloys contain no dislocation that can be responsible for yielding in crystalline materials, and are therefore expected to be strong and hard. The objective of this study is to fabricate an aspheric lens of OFC mold, as the first mold. OFC is a popular material for machining due to its good machinability. First, it is initially machined by a four-axis desktop ultraprecision machine (Uehara et al., 2005) as the first mold. Then, hot embossing process is employed to transfer the pattern of OFC onto BMG, as a secondary mold. Then the BMG mold is used to replicate aspheric surface on the polymethylmethacrylate (PMMA) sheets. A modified molding process using the Mg58 Cu31 Y11 BMG as a secondary mold to replicate aspheric surface is attempted in this study. The schematic illustration is shown in Fig. 1. Before hot embossing process, the thermo-mechanical properties of Mg-based Mg58 Cu31 Y11 system are investigated using differential scanning calorimetry (DSC) and thermo-mechanical analyzer (TMA). The working temperature for superplastic microforming is the one close to the glass temperature around 413 K (140 ◦ C). It shows experimentally that the working temperature is dependent on the applied stress level. Since the BMG material has superplastic property at the supercooled liquid region, it can be easily formed by the master die. After cooling, the material has very high mechanical strength to be a secondary mold. The embossing feasibility and degree of forming ability of the OFC (the first mold), BMG (the secondary mold), and PMMA replica are compared and discussed.
Fig. 1. Schematic of hot embossing process for (a) the first and secondary mold and (b) the secondary mold and final product.
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Fig. 2. Results of temperature dependence of relative displacement (Chang et al., 2007).
2. Ultraprecision cutting for the first mold 2.1. Machine code To describe an aspheric lens with a symmetrical optical axis of z, the curved surface of the lens with respect to the position axis x, which is perpendicular to the optical path, is expressed as Eq. (1).
z=
1+
cx2
1 − c 2 (k + 1)x2
+
12
ci xi
(1)
i=2
If the radius curvature at the vertex of the aspheric surface is defined as r0 and the eccentricity is e, then c = 1/r0 , and k = 1 − e2 , ci is an aspheric coefficient. Based on Eq. (1), the G-code is generated for CNC ultraprecision machine to perform the cutting process. In the G-code generating algorithm, several operational parameters have to be considered. They include the radius and position of the diamond tool, the surface error due to linear interpolation, and the allowable surface roughness affected by feed rate. The G-code is generated by a package language LabVIEW instead of the tradition CAM (computeraided machining) method. 2.2. Experimental facilities The first mold of OFC is machined by a desktop four-axis ultraprecision machine (Trider-X, from Nexsys inc.). The travel range along each linear axis (x-, y-, z-axis) is 100 mm long, and the rotational range of C-axis is 360◦ . Each axis is driven by a servomotor coupled with a ball-screw transmission mechanism. The feeding resolution along linear axes and rotational axis are 0.1 m and 0.0225◦ , respectively. To avoid disturbance from operational circumstances, a passive vibration air table is equipped at the bottom of the machine tool. A single crystal diamond tool with a nose radius of 0.2 mm is used to machine the raw material of OFC with a dimension of Ø5 × 20 mm2 . In the machining process, a CCD device is used to monitor the cutting conditions.
Fig. 3. A cylinder OFC is manufactured follow the (a) tool path in G-code and (b) the OFC first mold having mirror surface is observed.
3. Hot embossing for the secondary mold Mg58 Cu31 Y11 BMGs in the form of rod with a diameter of 4 mm were prepared by a copper mold injection casting technique, through the induction melting of pure Mg and pre-alloyed Cu–Y ingots in an argon atmosphere. The basic thermal properties were measured in a continuous heating mode by DSC, TA Instruments DSC 2920 and TMA, Perkin Elmer Diamond. The applied heating rate was 10 K/min. The Tg , Tx and Tm (solidus temperature) are 413 K (140 ◦ C), 479 K (206 ◦ C), and 711 K (438 ◦ C), respectively, which are obtained by DSC. The bulk amorphous Mg58 Cu31 Y11 alloys are measured by using TMA operated in the compression mode at various stress levels and a fixed heating rate of 10 K/min (Chang et al., 2007). The maximum displacement (Lmax ) occurred in the supercooled liquid region reaches 60.9, 162.6, 265.3, 748.8, and 923.3 m under the applied compressive load of 0.8, 2.4, 7.1, 117.8, and 318.5 kPa, respectively. The results of the temperature dependence of the relative displacement of the bulk amorphous Mg58 Cu31 Y11 alloys are collected in Fig. 2. Such displacements correspond to engineering strains Lmax /L0 (where L0 is the original specimen height 4 mm) of 1.52%, 4.07%, 6.63%, 18.72%, and 23.08%. The relative displacements become pronounced at temperatures greater than Tg , indicating
Table 1 Parameters used for G-code generation. Nose radius of tool
Diameter of lens
Aspheric coefficient
Radius of curvature
Escaped distance zesc
0.2 mm
3.6 mm
k = −6.44
r0 = 4.72
1 mm
resc 1, 0 mm
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the high deformability of the glassy alloy in the supercooled liquid region. The first mold (OFC) is used to fabricate a secondary mold of Mg58 Cu31 Y11 (BMG) amorphous alloy. Then, the secondary mold is then employed to emboss on PMMA sheets. The embossing process of BMG requires much lower pressure level for than that of PMMA. The deformability at different pressure degree is explored.
4. Experimental results and discussions 4.1. Aspheric lens of OFC mold G-code generation mentioned in Section 2.1 is listed in Table 1. The starter position of the diamond tool is set at zesc = 1 mm and resc = 1 mm, and the end position of the diamond tool is set as zesc = 1 mm and resc = 0 mm after machining process. The feeding step of 0.010 mm in the G-code program is calculated based on the given conditions. The nose radius of diamond tool is 0.2 mm and the error caused by linear interpolation is within 0.05 m. According to these working parameters, the tool path generated by LabVIEW program is shown in Fig. 3(a). The arrow signs shown in the figure indicate the moving direction of the cutting tool. During the cutting process, the feeding speed along x-axis is set at 5 mm/min determined by the operational conditions. The revolution of main spindle (z-axis) is 500 rpm and the length segment of linear interpolation is 0.010 mm. The cylinder-shaped OFC is manufactured into a convexshaped OFC mold with a diameter of 5 mm. The cutting process is lubricated by kerosene mist, and the machined result is shown in Fig. 3(b).
Fig. 5. Measured result of the aspheric surface of the OFC first mold.
Fig. 4(a) shows that the ring marks on the area “A” of the OFC mold is caused by cutting tool during CNC ultraprecision machining. Fig. 4(b) shows a scanning dimension 100 × 100 m2 of the area “B” in Fig. 4(a) by using nano indenter system (From Nano Indenter XP System, MTS inc.). Fig. 4(b) also reveals the roughness of the scanned area “B”. The roughness of OFC mold can be observed roughly. In this study, only rough cutting is performed due to the objective issue of examining the proposed fabrication process. Furthermore, ␣-step system (Talyscan 150) is used to measure the roughness and the measurement range is set at x = ±0.5 mm. Fig. 5 shows the measured result of the OFC mold by Talyscan 150. The roughness of curved surface is about Ra = 331 nm. 4.2. Hot embossing onto BMG and PMMA The hardness of the OFC mold and Mg58 Cu31 Y11 BMGs alloy measured by using nano indenter system is shown in Fig. 6(a) and (b), respectively. OFC shows a good machinability but very low hardness (HOFC ) of 1.606 GPa, which is not suitable for direct molding process.
Fig. 4. The tool marks caused by cutting tool of CNC ultraprecision machine for performing cutting process (a) area “A” of OFC mold and (b) image is measured by nano indenter system (From Nano Indenter XP System, MTS co.) and the images for the dimension 100 × 100 m2 of the area “B” is presented for roughness.
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Fig. 6. Hardness (an average of testing 1–16 from point M to N) of (a) the OFC mold of HOFC 1.606 GPa and (b) the Mg58 Cu31 Y11 BMGs alloy of HMg58Cu31Y11 3.445 GPa.
Fig. 7. The profiles of the Mg58 Cu31 Y11 BMGs lens which are embossed by the convex OFC mold with lens of 5 mm in diameter for a constant hot embossing time.
The secondary mold is a BMG material with hardness (HMg58Cu31Y11 ) of 3.445 GPa as shown in Fig. 6(b), which is suitable for molding process. The Tg of BMG is about 140 ◦ C (413 K). Therefore, a temperature of 150 ◦ C is chosen for the hot embossing experiment. The concave profiles of the Mg58 Cu31 Y11 BMGs lens which are embossed by the convex OFC mold at a constant time of 10 min are shown in Fig. 7. The larger the pressure is applied, and the deeper the embossed depth is reached. In addition, for a constant pressure of 500 kPa, it is shown in Fig. 8, which shows the same trend; the longer the embossed time is applied, the deeper the embossed depth is
obtained. The hot embossing parameters are listed in Table 2. Fig. 9 reveals that tool marks on the OFC mold are transferred clearly onto the Mg58 Cu31 Y11 BMGs under different pressures of 100, 250, 500 kPa for a constant time of 10 min, respectively. It means that the embossing process is applicable to the replication. For different embossing times of 1, 5, 10 min under a constant pressure of 500 kPa, respectively, the result is shown in Fig. 10. It demonstrates that the BMG surfaces are molded well under a higher pressure. It can be seen clearly that a higher pressure results in a larger embossed area of lens. Furthermore, the measured roughness (Ra) of the Mg58 Cu31 Y11 BMGs lens is shown in Fig. 11. Based on Eq. (2), the value of Ra can be calculated and arranged in Table 2. Under a constant pressure for different hot embossing times, it is shown in Fig. 12, the Ra decreases with increasing hot embossing time significantly; it means that the profile of lens can be embossed better for a longer hot embossing time. In addition, for a constant time under different hot embossing pressures, it is shown in Fig. 13. The Ra also decreases with increasing hot embossing pressure; it means that the profile of lens can be improved better under a higher hot embossing pressure. It is worth noticing that the relaxing rate shown in Fig. 13 is faster than that in Fig. 12. It indicates that the hot embossing time has a noticeable influence on the deformation of the Mg58 Cu31 Y11 BMGs lens under a specific pressure. 1 Ra = L
L
|z 2 (x)|dx
(2)
0
The OFC mold with a very low hardness (HOFC ) of 1.606 GPa has been transferred successfully to the BMG Mg58 Cu31 Y11 amorphous alloy with hardness (HMg58Cu31Y11 ) of 3.445 GPa. In addition, another OFC mold with smaller micro-lens array of 140 m in Table 2 The Ra of the Mg58 Cu31 Y11 BMGs lens (concave) for different hot embossing condition using the OFC aspheric surface mold. Hot embossing condition
Fig. 8. The profiles of the Mg58 Cu31 Y11 BMGs lens which are embossed by the convex OFC mold with lens of 5 mm in diameter for a constant hot embossing pressure.
Ra (m)
500 kPa, 150 ◦ C
10 min 5 min 1 min
1.5905 2.2107 2.8469
10 min, 150 ◦ C
250 kPa 100 kPa
1.7222 2.3297
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Fig. 9. The convex OFC mold with lens of 5 mm in diameter is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 100 kPa for 10 min; (b) at 150 ◦ C under pressure of 250 kPa for 10 min; and (c) at 150 ◦ C under pressure of 500 kPa for 10 min.
diameter is fabricated. A micro-lens array is designed in order to observe its forming behavior and viscous flow clearly. Since the OFC mold with micro-lens array of 140 m in diameter has a smaller diameter than that of the convex OFC lens mold (5 mm in diameter). The micro-lens array on the OFC mold is also
transferred onto Mg58 Cu31 Y11 BMGs alloy using hot embossing process. The embossed patterns on Mg58 Cu31 Y11 BMGs alloy is shown in Fig. 14. In figures from 14(a), (b) to (c), the hot embossing processes are operated at 150 ◦ C under different pressures of 10, 5, and 1 MPa for 10 min, respectively. Obviously, the higher the applied
Fig. 10. The convex OFC mold with lens of 5 mm in diameter is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 500 kPa for 1 min; (b) at 150 ◦ C under pressure of 500 kPa for 5 min; and (c) at 150 ◦ C under pressure of 500 kPa for 10 min.
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Fig. 11. Roughness of these Mg58 Cu31 Y11 BMGs lens.
Fig. 12. Ra is compared for constant pressure with different hot embossing time.
pressure is applied, the better the surface quality is for the same hot embossing time. In figures from 15(a), (b) to (c), the hot embossing is operated at 150 ◦ C under a constant pressure of 10 MPa for different times of 10, 5, and 1 min, respectively. The results show that the longer the holding time, the better the surface quality. However,
Fig. 13. Ra is compared for a constant time with different hot embossing pressures.
Fig. 14. Micro-lens array on the OFC mold is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 10 MPa for 10 min; (b) at 150 ◦ C under pressure of 5 MPa for 10 min; and (c) at 150 ◦ C under pressure of 1 MPa for 10 min.
the temperature can not be too high; neither can the embossing time be too long due to the limitation of thermal properties of Mg58 Cu31 Y11 . When the embossing time is too long, Mg58 Cu31 Y11 might be crystallized and become brittle, which is prone to breaking at high pressure conditions. Therefore, an appropriate embossing temperature and time are key parameters to the hot embossing process. For a better understanding, a comparison between these molds is made. The OFC mold with a micro-lens array of 140 m in diameter is shown in Fig. 16(a), which is served as the first mold. Fig. 16(b) is the replicated patterns on the BMG material by using the first mold (OFC). Excellent replicated patterns can be obtained on Mg58 Cu31 Y11 BMGs alloy under a pressure of 5 MPa for 10 min. Before the embossing process, there are some obvious defects on the surface of a BMG raw material, which is created during its casting process. To improve this, the surface was polished with abrasive papers of No. 2000, but some polishing marks are visible in Fig. 16(b). Though these marks are present on the BMG prior to hot embossing, the marks are improved obviously after hot emboss-
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Fig. 15. Micro-lens array on the OFC mold is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 10 MPa for 10 min; (b) at 150 ◦ C under pressure of 10 MPa for 5 min; and (c) at 150 ◦ C under pressure of 10 MPa for 1 min.
ing process as shown in Fig. 17(a), which is a scanning electron microscopy (SEM) picture. The concave Mg58 Cu31 Y11 BMG mold is used to emboss on PMMA to form a convex micro-lens at 120 ◦ C under a pressure of about 138.3 MPa for 5 min. Fig. 16(c) is a picture of a PMMA with micro-lens array. The PMMA sheet with 1 mm in thickness is purchased from Hsintou Company in Taiwan. The glass transition temperature of PMMA is around 105 ◦ C. Fig. 16(c) shows that similar defects on BMG mold are replicated on the surface of the PMMA sheets. PMMA requires much higher embossing pressure than that of Mg58 Cu31 Y11 material. It means that Mg58 Cu31 Y11 is more deformable material than PMMA. The result also shows that the patterns on BMG are transferred completely on the PMMA. They exhibit optical characteristics because clear focused spots are observed. In order to realize optical function of a curve surface, refraction has to be explained. The refractive index of a medium is a measure for how much the speed of light is reduced inside the medium. Two common properties of transparent materials are directly related to
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Fig. 16. Micro-lens array on (a) the OFC mold is used for hot embossing onto (b) Mg58 Cu31 Y11 BMGs alloy at 150 ◦ C under pressure of 5 MPa for 10 min, and then (c) micro-lens array is transferred to PMMA at 120 ◦ C under pressure of 138.3 MPa for 5 min.
their refractive index. First, light rays change direction when they cross the interface from air to the material, an effect that is used in lenses. Second, light reflects partially from surfaces that have a refractive index different from that of their surroundings. The refractive index, n, of a medium is defined as the ratio of the phase velocity, v, of a wave phenomenon such as light in a vacuum to the phase velocity, vp , in the medium itself: n=
v vp
(3)
By Snell’s law: n1 sin 1 = n2 sin 2
(4)
In Fig. 17(b) and (c), light changes direction when it crosses the interface from air to the material. From Snell’s law, for a same medium, the refractive angle ( 2 , see Fig. 17 (b) or (c)) is a constant. Nevertheless, different curvature surfaces result in different refractive directions ( 3 and 4 , see Fig. 17(b) and (c), respectively).
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6 × 10−6 m/m K for the crystalline Mg2 Cu intermetallic phase, and for quartz (common standard optical material) 5.5 × 10−7 m/mK. Above Tg , significant viscous deformation occurred as a result of applied compressive load, and the deformation strain increases with increasing applied load. Such a high level of induced displacements (or strains) as shown in Fig. 2 can no longer be regarded as the linear thermal expansion, because the alloy readily deformed by the compressive load from the probe at temperatures above Tg . At a temperature above Tg , the thermal expansion of the soft viscous glass (probably in the order of ∼10−4 m/mK (Myung et al., 2001) is expected to be overshadowed by the large viscous compressive strain ranging from 1% to 25%. Therefore, when working temperature is greater than Tg , the BMG-based lens loses its accuracy in dimension and fails its optical function. It follows from what has been said that L(T+T) below or above Tg of the Mg58 Cu31 Y11 BMG can be calculated as following: Below Tg of the Mg58 Cu31 Y11 BMG: L(T +T ) = {1 + [(3 ± 1) × 10−6 ] × T }L(T )
(6)
Above Tg of the Mg58 Cu31 Y11 BMG: L(T +T ) = (1 + 10−4 × T )L(T )
Fig. 17. (a) SEM picture of a BMG sample with micro-lens; for optical function, light refracted from the same angle of incidence through different lenses has an induced angle of (b) 3 and (c) 4 with material surface.
In addition, curvature of an aspheric lens can be affected by the molding process, which influences refraction in lenses as shown in Fig. 17(b) and (c). Thus, it is necessary to discuss the thermal expansion of BMG. Thermal expansion and contraction are important issues in lens molding because they greatly influence the form accuracy of the lens. In general, thermal expansion and contraction are strongly temperature dependent. For metallic glass material, glass-forming ability (GFA) is an important basis for thermal expansion or shrinkage in molding process. A conceptual approach to evaluate GFA for various glass-forming systems has been proposed from a physical metallurgy point of view. It was found that the GFA for noncrystalline materials was related mainly to two factors, i.e., 1/(Tg + Tl ) and Tx (wherein Tx is the onset crystallization temperature, Tg the glass transition temperature, and Tl the liquidus temperature), and could be predicated by a unified parameter ␥ defined as Tx /(Tg + Tl ) (Lu and Liu, 2002, 2003). This approach was confirmed and validated by experimental data in various glass-forming systems including oxide glasses, cryoprotectants, and metallic glasses. The value of the Mg58 Cu31 Y11 BMG (Tx = 479 K, Tg = 413 K, Tl = 754 K (Chang et al., 2007)) is 0.410, having a good GFA. Besides, the coefficient of thermal expansion (˛) of the Mg58 Cu31 Y11 BMG is an important issue when it is used for optical material. According to the thermal linear expanded model, L(T +T ) = (l + ˛T )L(T )
(5)
where L is the length, i.e., diameter, aperture radius, or curvature radius of optical lens, etc., T is the room temperature, T is the difference in temperature, and ˛ is the thermal expansion coefficient. For the Mg58 Cu31 Y11 BMG, below the glass transition temperature, Tg , a linear thermal expansion coefficient (˛) of (3 ± 1) × 10−6 m/mK is obtained (Chang et al., 2007). This can be compared with the ˛ = 26 × 10−6 m/m K for the pure Mg,
(7)
Similarly, thermal expansion of PMMA can be discussed. For the PMMA, below the glass transition temperature, Tg , a linear thermal expansion coefficient (˛) of (75 ± 25) × 10−6 m/mK is obtained (Papanicolaou et al., 1998); above the glass transition temperature, Tg , a linear thermal expansion coefficient (˛) of ∼5 × 10−4 m/mK is obtained (Manabe et al., 1971). Though the recommended refractive index of PMMA is about 1.489, the curvatures of lenses on BMG or PMMA sheet would be different from OFC mold due to their thermal expansion properties, which influences the refraction in PMMA sheet. The micro-lens array on OFC, Mg58 Cu31 Y11 BMGs alloy, and PMMA is shown in Fig. 16(a)–(c), respectively. The convex OFC mold is 140 m in width, the concave BMG mold is 129.93 m in width, and the convex PMMA product is 127.21 m in width. The shrinkage between the first and secondary mold shows 7.19% in shrinkage, whereas the shrinkage between the secondary mold and PMMA replica shows 2.09%. 5. Conclusion This study presents a new process to fabricate an aspheric lens. The process includes the contents of the formula expression of aspheric curves, the brief descriptions of ultraprecision machining process and the operation processes of rough cutting to fabricate an OFC mold as the first mold. The roughness of the first mold is measured as Ra = 0.331 m, and Rz = 1.466 m. Then, this first mold is employed to hot emboss on Mg–Cu–Y amorphous alloy to form a secondary mold. The secondary mold is BMG-based material, whose glass transition temperature of BMG is around 413 K. Therefore, the hot embossing experiments are set at 423 K. This embossing process on BMG material makes molding process faster and more diverse applications. In addition, the secondary mold is used to emboss on PMMA sheets. Molding process by using BMG material as a secondary mold can be more cost-effective and timesaving than the traditional manufacturing process does. BMG is not only a good material for hot embossing process to fabricate microstructure directly, but also fast-molding material for hot embossing process. A practical examination for the ultraprecision cutting and molding was performed in this study. It is expected that the machining methods described in this paper could be applied to relative fields to fabricate precise components with micro or sub-micro order of dimensional accuracy.
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Acknowledgements The authors would like to thank the National Science Council (NSC) for their financial supports to the project (granted number: 95-2221-E-110-093-MY2, 95-2221-E-110-141, and 94-2622-E-110017-CC3). Also, the authors would like to thank the Center for Micro/Nano Technology Research, National Cheng Kung University, Tainan, Taiwan, for equipment access and technical support. References Brinksmeier, E., Riemer, O., Glabe, R., 2006. Merging technologies for optics. In: Proceedings of the 11th International Conference on Precision Engineering, Tokyo, Japan, pp. 16–18. Busch, R., Bakke, E., Johnson, W.L., 1998. Viscosity of the supercooled liquid and relaxation at the glass transition of the Zr46.75 Ti8. 25 Cu7.5 Ni10.0 Be27.5 bulk metallic glass forming alloy. Acta Mater. 46, 4725–4732. Chang, Y.C., Hung, T.H., Chen, H.M., Huang, J.C., Nieh, T.G., Lee, C.J., 2007. Viscous flow behavior and thermal properties of bulk amorphous Mg58 Cu31 Y11 alloy. Intermetallics 15, 1303–1308. Chen, M.J., Li, D., Dong, S., 2002. Research on a large depth-on-diameter ratio ultraprecision aspheric grinding system. J. Mater. Process. Technol. 129, 91–95. Chu, J.P., Wijaya, H., Wu, C.W., Tsai, T.R., Wei, C.S., Nieh, T.G., Wadsworth, J., 2007. Nanoimprint of gratings on a bulk metallic glass. Appl. Phys. Lett. 90, 034101. Dornfeld, D., Min, S., Takeuchi, Y., 2006. Recent advances in mechanical micromachining. Ann. CIRP 55, 745–768. Kim, H.S., Kim, E.J., Song, B.S., 2004. Diamond turning of large off-axis aspheric mirrors using a fast tool servo with on-machine measurement. J. Mater. Process. Technol. 146, 349–355. Kuriyagawa, T., Zahmaty, M.S.S., Syoji, K., 1996. A new grinding method for aspheric ceramic mirrors. J. Mater. Process. Technol. 62, 387–392. Liu, W.Y., Zhang, H.F., Hua, Z.Q., Wang, H., 2005. Formation and mechanical properties of Mg65 Cu25 Er10 and Mg65 Cu15 Ag10 Er10 bulk amorphous alloys. J. Alloy. Compd. 397, 202–206. Lu, Z.P., Liu, C.T., 2002. A new glass-forming ability criterion for bulk metallic glasses. Acta Mater. 50, 3501–3512. Lu, Z.P., Liu, C.T., Li, Y., 2004. Glass transition and crystallization of Mg–Ni–Nd metallic glasses studied by temperature-modulated DSC. Intermetallics 12, 869– 874. Lu, Z.P., Liu, C.T., 2003. Glass formation criterion for various glass-forming systems. Phys. Rev. Lett. 91, 115505.
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Manabe, S., Murakami, R., Takayanagi, M., Uemura, S., 1971. Glass-transition temperature and thermal expansion coefficient of a tow-phase system of polymers. Int. J. Polymer. Mater. 1, 47–73. Muranaka, M., 2003. Technology and Application of Plastic Lens System. CMC Publishing Co., Ltd., Tokyo, Japan, pp. 3–16 (In Japanese). Myung, W.N., Hwang, I.S., Bae, H.Y., Kim, H.G., Masumoto, T., Greer, A.L., 2001. Viscous-flow behavior of amorphous Co69 Fe4.5 Nb1.5 Si10 B15 alloys. Mater. Sci. Eng. A 304–306, 467–471. Papanicolaou, G.C., Bakos, D., Imielinska, K., 1998. Effect of interfacial phenomena on the thermal expansion behavior of rubber-toughened PMMA composites. J. Macromol. Sci. Phys. 37, 201–217. ´ Pérez, P., Eddahbi, M., Garces, G., Sommer, F., Adeva, P., 2004. Mechanical properties of crystallised amorphous Mg–23.5Ni(wt%) alloy. Scripta Mater. 50, 1039–1043. ´ Pérez, P., Garces, G., Sommer, F., Adeva, P., 2005. Mechanical properties of amorphous and crystallized Mg–35 wt% Ni. J. Alloy. Compd. 396, 175–181. Saotome, Y., Itoh, K., Zhang, T., Inoue, A., 2001. Superplastic nanoforming of Pd-based amprphous alloy. Scripta Mater. 44, 1541–1545. Senkov, O.N., Scott, J.M., Miracle, D.B., 2006. Composition range and glass forming ability of ternary Ca–Mg–Cu bulk metallic glasses. J. Alloy. Compd. 424, 394–399. Syoji, K., 2004. Ultraprecision Machining and Aspheric Machining. NTS Inc., Tokyo, Japan, pp. 191–198 (In Japanese). Uehara, Y., Naruse, T., Mitsuishi, N., Kuriyagawa, T., Lin, W., Ohmori, H., Miura, T., 2005. Development of desktop 4-axes machine tools. In: Proceedings of JSPE Semestrial Meeting, Japan, pp. 845–846. van Ligten, R.F., Venkatesh, V.C., 1985. Diamond grinding of aspheric surfaces on a CNC 4-axis machining centre. Ann. CIRP 34, 295–298. Venkatesh, V.C., Izman, S., Vichare, P.S., Mon, T.T., Murugan, S., 2005. The novel bondless wheel, spherical glass chips and a new method of aspheric generation. J. Mater. Process. Technol. 167, 184–190. Venkatesh, V.C., 2003. Precision manufacture of spherical and aspheric surfaces on plastics, glass, silicon and germanium. Curr. Sci. 84, 1211–1219. Wolff, U., Pryds, N., Wert, J.A., 2004. Deformation characteristics of Mg60 Cu30 Y10 alloy at temperatures near Tg . Scripta Mater. 50, 1385–1388. Yuan, G., Inoue, A., 2005. The effect of Ni substitution on the glass-forming ability and mechanical properties of Mg–Cu–Gd metallic glass alloys. J. Alloy. Compd. 387, 134–138. Yuan, G., Zhang, T., Inoue, A., 2004. Structure and mechanical properties of Mg85Cu5Zn5Y5 amorphous alloy containing nanoscale particles. Mater. Lett. 58, 3012–3016. Zheng, Q., Cheng, S., Strader, J.H., Ma, E., Xu, J., 2007. Critical size and strength of the best bulk metallic glass former in the Mg–Cu–Gd ternary system. Scripta Mater. 56, 161–164. Zhong, Z., Venkatesh, V.C., 1995. Semi-ductile grinding and polishing of ophthalmic aspherics and spherics. Ann. CIRP 44, 339–342.
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Fabrication of aspheric surface using ultraprecision cutting and BMG molding Cheng-Tang Pan a , Tsung-Tien Wu a , Yung-Tien Liu b,∗ , Y. Yamagata c , J.C. Huang d a
Department of Mechanical and Electro-Mechanical Engineering, and Center for Nanoscience & Nanotechnology, National Sun Yat-Sen University, Kaoshiung 804, Taiwan, ROC Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, Kaoshiung 811, Taiwan, ROC c VCAD System Research Program Applied Fabrication Team, the Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako, Saitama 351-0198, Japan d Institute of Materials Science and Engineering; Center for Nanoscience and Nanotechnology, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, ROC b
a r t i c l e
i n f o
Article history: Received 13 August 2008 Received in revised form 7 January 2009 Accepted 28 January 2009 Keywords: Oxygen free copper Aspheric surface Metallic glass
a b s t r a c t A new process to replicate an aspheric lens is presented in this study. A mold of oxygen free copper (OFC) is fabricated using ultraprecision machining, which is a popular material for machining due to its good machinability. But OFC has a very low hardness of 1.606 GPa, it is not suitable for the subsequent molding process. Then, this OFC mold (known as the first mold) is used to hot emboss on Mg58 Cu31 Y11 amorphous alloy to form a secondary mold which is one kind of metallic glass. The hardness of the secondary mold is as high as 3.445 GPa, whereas the glass transition temperature (Tg ) of the Mg58 Cu31 Y11 metallic glass is as low as 413 K (140 ◦ C), at which the Mg58 Cu31 Y11 metallic glass shows a good glassforming ability (GFA). In order to perform superplastic microforming, the working temperature must be close to the glass temperature around 413 K. Therefore, in this study, the temperatures of the hot embossing experiments to fabricate the secondary mold are set at 423 K (150 ◦ C). It shows experimentally that the working temperature is dependent on the applied stress level. Since the Mg58 Cu31 Y11 metallic glass has superplastic property at the supercooled liquid region, it can be easily formed by the master die. This embossing process on the Mg58 Cu31 Y11 metallic glass makes molding process faster and more diverse applications. Next, the secondary mold is used to emboss on polymethylmethacrylate (PMMA) sheets for replication process. The Mg58 Cu31 Y11 metallic glass is not only a good material for hot embossing process to fabricate micro-structure directly, but also an excellent fast-molding material for hot embossing process. It is expected that the machining processes described in this paper could be applied to the related fields to fabricate precision components required of micro, sub-micro, or nano order of dimensional accuracy. © 2009 Elsevier B.V. All rights reserved.
1. Introduction With the ongoing technological improvement in 3C (computer, consumer, and communication) products, it caused high requirements of precise optical components (Brinksmeier et al., 2006). For example, it has become very usual that a digital camera with a miniaturized optical lens is integrated into a cell phone. To obtain a high-quality of camera image, an aspheric lens with a specially designed curvature has become one of the key components of the optical device (Syoji, 2004). For providing attractive prices of the 3C products, most of the precise components were produced by massproduction based on ultraprecision molds and dies which were fabricated by using ultraprecision machine tools (Muranaka, 2003; Dornfeld et al., 2006). However, since the ultraprecision machining process is extremely expensive and the test of a new mold for mass-production is time-consuming, how to provide a process of
∗ Corresponding author. Tel.: +886 7 6011000x2220; fax: +886 7 6011066. E-mail address: [email protected] (Y.-T. Liu). 0924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2009.01.025
both time-saving and cost-effective is the current issue in the manufacturing industry, especially, for the rapid growth of diverse 3C products. Therefore, a new process to fabricate an aspheric surface of bulk metallic glass (BMG) is proposed in this paper. BMG is referred to as an amorphous metallic alloy. The materials show very high strength at room temperature and excellent viscous flow property at temperatures between the glass transition temperature (Tg ) and crystallization temperature (Tx ). The maximum diameter of glass formation (Dc ), temperature interval of the supercooled liquid region (Tx ), melting temperature (Tm ), liquidus temperature (Tl ) as well as heats of crystallization (Hx ) and melting (Hm ) were reported for Ga-based (Senkov et al., 2006) and Mg-based bulk amorphous alloys (Liu et al., 2005). Glass transition and crystallization behavior of Mg–Ni–Nd metallic glass have been systematically studied by temperature-modulated differential scanning calorimetry (TMDSC). That provided a clear observation of glass transition and crystallization micro-mechanism (Lu et al., 2004). The application of melt-spinning process of Mg85 Cu5 Zn5 Y5 alloy was studied, which was found to cause the formation of a mixed structure consisting of nanoscale crystalline particles embedded in an amorphous matrix (Yuan et al., 2004). Yuan and
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Inoue (2005) reported that an appropriate substitution of Cu by Ni in Mg65 Cu25 Gd10 significantly improved its mechanical properties, especially improved the ductility of Mg-based bulk metallic glass. The viscous flow behavior of the Mg58 Cu31 Y11 bulk amorphous rods in the supercooled viscous region was investigated (Chang et al., 2007). It was found that the appropriate working temperature for microforming was about 460–474 K. Furthermore, the Mg58 Cu31 Y11 BMGs showed physical properties of good glass forming. It is known that BMG alloys can exhibit not only the unique physical properties such as excellent elasticity and strength, but also the significant plasticity occurred in the supercooled liquid region, Tx (=Tx − Tg ), due to a drastic drop in viscosity during glass transition upon heating (Busch et al., 1998). Several researchers have reported the mechanical properties by using uniaxial tensile testing (Yuan and Inoue, 2005; Pérez et al., 2005; Pérez et al., 2004) and uniaxial compression testing (Chang et al., 2007; Liu et al., 2005; Yuan and Inoue, 2005; Zheng et al., 2007; Wolff et al., 2004). However, there were only few studies on imprinting or hot embossing process of BMG material. Saotome et al. (2001) used imprint process to fabricate a silicon mold with nano-patterns. With this die, the nano-forming ability of Pd-based amorphous alloy was examined. Chu et al. (2007) reported the fabrication of a siliconbased grating die to imprint on Pd40 Ni40 P20 BMG plate, which was then used as a mold to imprint on polymer material. The advantages of aspheric lenses over spherical lenses are well recognized. Manufacturing methods of aspheric lenses have been reported, such as grinding aspheric ceramic mirrors (Kuriyagawa et al., 1996), large depth-to-diameter ratio aspheric surfaces (Chen et al., 2002), and diamond turning of large off-axis aspheric mirrors (Kim et al., 2004). Properly manufactured aspheric lenses were reported by using diamond grinding, lapping, and polishing on a CNC machining centre (Ligten et al., 1985; Zhong and Venkatesh, 1995). In addition, semi-ductile grinding obtained by using conventional CNC machining centers and commercial grinding wheels were very promising and helpful to reduce manufacturing costs. Semi-ductile grinding for aspheric surface has been observed on glass, silicon and germanium (Venkatesh, 2003). Conventional grinding in many optical industries is highly successful. The manufacture of plastic lenses for ophthalmic purposes was gaining in popularity with decreasing costs brought about by low-cost
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manufacture of glass moulds. Also, ductile mode grinding gains worldwide attention in industries for low-cost manufacture; for instance, oxygen free copper (OFC) presented in this study shows a good machinability. Another method of generating aspheric profiles was reported using more advanced technologies of CAD/CAM, which showed that the use of general-purpose machine can give flexible output in terms of variety of lenses without using any special purpose machine (Venkatesh et al., 2005). In recent years, micro-lens array has been attracting much attention for a variety of applications. For display field, it is used to enhance the brightness of illumination and simplify the light guide module construction. Both higher accuracy and lower cost of micro-lens fabrication methods are needed to meet the rapid growth of commercial devices. It is an important issue to make a high accuracy and strong mold to replicate micro-lens array. The selection of BMG is based on the fact that amorphous alloys contain no dislocation that can be responsible for yielding in crystalline materials, and are therefore expected to be strong and hard. The objective of this study is to fabricate an aspheric lens of OFC mold, as the first mold. OFC is a popular material for machining due to its good machinability. First, it is initially machined by a four-axis desktop ultraprecision machine (Uehara et al., 2005) as the first mold. Then, hot embossing process is employed to transfer the pattern of OFC onto BMG, as a secondary mold. Then the BMG mold is used to replicate aspheric surface on the polymethylmethacrylate (PMMA) sheets. A modified molding process using the Mg58 Cu31 Y11 BMG as a secondary mold to replicate aspheric surface is attempted in this study. The schematic illustration is shown in Fig. 1. Before hot embossing process, the thermo-mechanical properties of Mg-based Mg58 Cu31 Y11 system are investigated using differential scanning calorimetry (DSC) and thermo-mechanical analyzer (TMA). The working temperature for superplastic microforming is the one close to the glass temperature around 413 K (140 ◦ C). It shows experimentally that the working temperature is dependent on the applied stress level. Since the BMG material has superplastic property at the supercooled liquid region, it can be easily formed by the master die. After cooling, the material has very high mechanical strength to be a secondary mold. The embossing feasibility and degree of forming ability of the OFC (the first mold), BMG (the secondary mold), and PMMA replica are compared and discussed.
Fig. 1. Schematic of hot embossing process for (a) the first and secondary mold and (b) the secondary mold and final product.
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Fig. 2. Results of temperature dependence of relative displacement (Chang et al., 2007).
2. Ultraprecision cutting for the first mold 2.1. Machine code To describe an aspheric lens with a symmetrical optical axis of z, the curved surface of the lens with respect to the position axis x, which is perpendicular to the optical path, is expressed as Eq. (1).
z=
1+
cx2
1 − c 2 (k + 1)x2
+
12
ci xi
(1)
i=2
If the radius curvature at the vertex of the aspheric surface is defined as r0 and the eccentricity is e, then c = 1/r0 , and k = 1 − e2 , ci is an aspheric coefficient. Based on Eq. (1), the G-code is generated for CNC ultraprecision machine to perform the cutting process. In the G-code generating algorithm, several operational parameters have to be considered. They include the radius and position of the diamond tool, the surface error due to linear interpolation, and the allowable surface roughness affected by feed rate. The G-code is generated by a package language LabVIEW instead of the tradition CAM (computeraided machining) method. 2.2. Experimental facilities The first mold of OFC is machined by a desktop four-axis ultraprecision machine (Trider-X, from Nexsys inc.). The travel range along each linear axis (x-, y-, z-axis) is 100 mm long, and the rotational range of C-axis is 360◦ . Each axis is driven by a servomotor coupled with a ball-screw transmission mechanism. The feeding resolution along linear axes and rotational axis are 0.1 m and 0.0225◦ , respectively. To avoid disturbance from operational circumstances, a passive vibration air table is equipped at the bottom of the machine tool. A single crystal diamond tool with a nose radius of 0.2 mm is used to machine the raw material of OFC with a dimension of Ø5 × 20 mm2 . In the machining process, a CCD device is used to monitor the cutting conditions.
Fig. 3. A cylinder OFC is manufactured follow the (a) tool path in G-code and (b) the OFC first mold having mirror surface is observed.
3. Hot embossing for the secondary mold Mg58 Cu31 Y11 BMGs in the form of rod with a diameter of 4 mm were prepared by a copper mold injection casting technique, through the induction melting of pure Mg and pre-alloyed Cu–Y ingots in an argon atmosphere. The basic thermal properties were measured in a continuous heating mode by DSC, TA Instruments DSC 2920 and TMA, Perkin Elmer Diamond. The applied heating rate was 10 K/min. The Tg , Tx and Tm (solidus temperature) are 413 K (140 ◦ C), 479 K (206 ◦ C), and 711 K (438 ◦ C), respectively, which are obtained by DSC. The bulk amorphous Mg58 Cu31 Y11 alloys are measured by using TMA operated in the compression mode at various stress levels and a fixed heating rate of 10 K/min (Chang et al., 2007). The maximum displacement (Lmax ) occurred in the supercooled liquid region reaches 60.9, 162.6, 265.3, 748.8, and 923.3 m under the applied compressive load of 0.8, 2.4, 7.1, 117.8, and 318.5 kPa, respectively. The results of the temperature dependence of the relative displacement of the bulk amorphous Mg58 Cu31 Y11 alloys are collected in Fig. 2. Such displacements correspond to engineering strains Lmax /L0 (where L0 is the original specimen height 4 mm) of 1.52%, 4.07%, 6.63%, 18.72%, and 23.08%. The relative displacements become pronounced at temperatures greater than Tg , indicating
Table 1 Parameters used for G-code generation. Nose radius of tool
Diameter of lens
Aspheric coefficient
Radius of curvature
Escaped distance zesc
0.2 mm
3.6 mm
k = −6.44
r0 = 4.72
1 mm
resc 1, 0 mm
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the high deformability of the glassy alloy in the supercooled liquid region. The first mold (OFC) is used to fabricate a secondary mold of Mg58 Cu31 Y11 (BMG) amorphous alloy. Then, the secondary mold is then employed to emboss on PMMA sheets. The embossing process of BMG requires much lower pressure level for than that of PMMA. The deformability at different pressure degree is explored.
4. Experimental results and discussions 4.1. Aspheric lens of OFC mold G-code generation mentioned in Section 2.1 is listed in Table 1. The starter position of the diamond tool is set at zesc = 1 mm and resc = 1 mm, and the end position of the diamond tool is set as zesc = 1 mm and resc = 0 mm after machining process. The feeding step of 0.010 mm in the G-code program is calculated based on the given conditions. The nose radius of diamond tool is 0.2 mm and the error caused by linear interpolation is within 0.05 m. According to these working parameters, the tool path generated by LabVIEW program is shown in Fig. 3(a). The arrow signs shown in the figure indicate the moving direction of the cutting tool. During the cutting process, the feeding speed along x-axis is set at 5 mm/min determined by the operational conditions. The revolution of main spindle (z-axis) is 500 rpm and the length segment of linear interpolation is 0.010 mm. The cylinder-shaped OFC is manufactured into a convexshaped OFC mold with a diameter of 5 mm. The cutting process is lubricated by kerosene mist, and the machined result is shown in Fig. 3(b).
Fig. 5. Measured result of the aspheric surface of the OFC first mold.
Fig. 4(a) shows that the ring marks on the area “A” of the OFC mold is caused by cutting tool during CNC ultraprecision machining. Fig. 4(b) shows a scanning dimension 100 × 100 m2 of the area “B” in Fig. 4(a) by using nano indenter system (From Nano Indenter XP System, MTS inc.). Fig. 4(b) also reveals the roughness of the scanned area “B”. The roughness of OFC mold can be observed roughly. In this study, only rough cutting is performed due to the objective issue of examining the proposed fabrication process. Furthermore, ␣-step system (Talyscan 150) is used to measure the roughness and the measurement range is set at x = ±0.5 mm. Fig. 5 shows the measured result of the OFC mold by Talyscan 150. The roughness of curved surface is about Ra = 331 nm. 4.2. Hot embossing onto BMG and PMMA The hardness of the OFC mold and Mg58 Cu31 Y11 BMGs alloy measured by using nano indenter system is shown in Fig. 6(a) and (b), respectively. OFC shows a good machinability but very low hardness (HOFC ) of 1.606 GPa, which is not suitable for direct molding process.
Fig. 4. The tool marks caused by cutting tool of CNC ultraprecision machine for performing cutting process (a) area “A” of OFC mold and (b) image is measured by nano indenter system (From Nano Indenter XP System, MTS co.) and the images for the dimension 100 × 100 m2 of the area “B” is presented for roughness.
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Fig. 6. Hardness (an average of testing 1–16 from point M to N) of (a) the OFC mold of HOFC 1.606 GPa and (b) the Mg58 Cu31 Y11 BMGs alloy of HMg58Cu31Y11 3.445 GPa.
Fig. 7. The profiles of the Mg58 Cu31 Y11 BMGs lens which are embossed by the convex OFC mold with lens of 5 mm in diameter for a constant hot embossing time.
The secondary mold is a BMG material with hardness (HMg58Cu31Y11 ) of 3.445 GPa as shown in Fig. 6(b), which is suitable for molding process. The Tg of BMG is about 140 ◦ C (413 K). Therefore, a temperature of 150 ◦ C is chosen for the hot embossing experiment. The concave profiles of the Mg58 Cu31 Y11 BMGs lens which are embossed by the convex OFC mold at a constant time of 10 min are shown in Fig. 7. The larger the pressure is applied, and the deeper the embossed depth is reached. In addition, for a constant pressure of 500 kPa, it is shown in Fig. 8, which shows the same trend; the longer the embossed time is applied, the deeper the embossed depth is
obtained. The hot embossing parameters are listed in Table 2. Fig. 9 reveals that tool marks on the OFC mold are transferred clearly onto the Mg58 Cu31 Y11 BMGs under different pressures of 100, 250, 500 kPa for a constant time of 10 min, respectively. It means that the embossing process is applicable to the replication. For different embossing times of 1, 5, 10 min under a constant pressure of 500 kPa, respectively, the result is shown in Fig. 10. It demonstrates that the BMG surfaces are molded well under a higher pressure. It can be seen clearly that a higher pressure results in a larger embossed area of lens. Furthermore, the measured roughness (Ra) of the Mg58 Cu31 Y11 BMGs lens is shown in Fig. 11. Based on Eq. (2), the value of Ra can be calculated and arranged in Table 2. Under a constant pressure for different hot embossing times, it is shown in Fig. 12, the Ra decreases with increasing hot embossing time significantly; it means that the profile of lens can be embossed better for a longer hot embossing time. In addition, for a constant time under different hot embossing pressures, it is shown in Fig. 13. The Ra also decreases with increasing hot embossing pressure; it means that the profile of lens can be improved better under a higher hot embossing pressure. It is worth noticing that the relaxing rate shown in Fig. 13 is faster than that in Fig. 12. It indicates that the hot embossing time has a noticeable influence on the deformation of the Mg58 Cu31 Y11 BMGs lens under a specific pressure. 1 Ra = L
L
|z 2 (x)|dx
(2)
0
The OFC mold with a very low hardness (HOFC ) of 1.606 GPa has been transferred successfully to the BMG Mg58 Cu31 Y11 amorphous alloy with hardness (HMg58Cu31Y11 ) of 3.445 GPa. In addition, another OFC mold with smaller micro-lens array of 140 m in Table 2 The Ra of the Mg58 Cu31 Y11 BMGs lens (concave) for different hot embossing condition using the OFC aspheric surface mold. Hot embossing condition
Fig. 8. The profiles of the Mg58 Cu31 Y11 BMGs lens which are embossed by the convex OFC mold with lens of 5 mm in diameter for a constant hot embossing pressure.
Ra (m)
500 kPa, 150 ◦ C
10 min 5 min 1 min
1.5905 2.2107 2.8469
10 min, 150 ◦ C
250 kPa 100 kPa
1.7222 2.3297
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Fig. 9. The convex OFC mold with lens of 5 mm in diameter is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 100 kPa for 10 min; (b) at 150 ◦ C under pressure of 250 kPa for 10 min; and (c) at 150 ◦ C under pressure of 500 kPa for 10 min.
diameter is fabricated. A micro-lens array is designed in order to observe its forming behavior and viscous flow clearly. Since the OFC mold with micro-lens array of 140 m in diameter has a smaller diameter than that of the convex OFC lens mold (5 mm in diameter). The micro-lens array on the OFC mold is also
transferred onto Mg58 Cu31 Y11 BMGs alloy using hot embossing process. The embossed patterns on Mg58 Cu31 Y11 BMGs alloy is shown in Fig. 14. In figures from 14(a), (b) to (c), the hot embossing processes are operated at 150 ◦ C under different pressures of 10, 5, and 1 MPa for 10 min, respectively. Obviously, the higher the applied
Fig. 10. The convex OFC mold with lens of 5 mm in diameter is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 500 kPa for 1 min; (b) at 150 ◦ C under pressure of 500 kPa for 5 min; and (c) at 150 ◦ C under pressure of 500 kPa for 10 min.
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Fig. 11. Roughness of these Mg58 Cu31 Y11 BMGs lens.
Fig. 12. Ra is compared for constant pressure with different hot embossing time.
pressure is applied, the better the surface quality is for the same hot embossing time. In figures from 15(a), (b) to (c), the hot embossing is operated at 150 ◦ C under a constant pressure of 10 MPa for different times of 10, 5, and 1 min, respectively. The results show that the longer the holding time, the better the surface quality. However,
Fig. 13. Ra is compared for a constant time with different hot embossing pressures.
Fig. 14. Micro-lens array on the OFC mold is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 10 MPa for 10 min; (b) at 150 ◦ C under pressure of 5 MPa for 10 min; and (c) at 150 ◦ C under pressure of 1 MPa for 10 min.
the temperature can not be too high; neither can the embossing time be too long due to the limitation of thermal properties of Mg58 Cu31 Y11 . When the embossing time is too long, Mg58 Cu31 Y11 might be crystallized and become brittle, which is prone to breaking at high pressure conditions. Therefore, an appropriate embossing temperature and time are key parameters to the hot embossing process. For a better understanding, a comparison between these molds is made. The OFC mold with a micro-lens array of 140 m in diameter is shown in Fig. 16(a), which is served as the first mold. Fig. 16(b) is the replicated patterns on the BMG material by using the first mold (OFC). Excellent replicated patterns can be obtained on Mg58 Cu31 Y11 BMGs alloy under a pressure of 5 MPa for 10 min. Before the embossing process, there are some obvious defects on the surface of a BMG raw material, which is created during its casting process. To improve this, the surface was polished with abrasive papers of No. 2000, but some polishing marks are visible in Fig. 16(b). Though these marks are present on the BMG prior to hot embossing, the marks are improved obviously after hot emboss-
C.-T. Pan et al. / Journal of Materials Processing Technology 209 (2009) 5014–5023
Fig. 15. Micro-lens array on the OFC mold is used for hot embossing onto Mg58 Cu31 Y11 BMGs alloy (a) at 150 ◦ C under pressure of 10 MPa for 10 min; (b) at 150 ◦ C under pressure of 10 MPa for 5 min; and (c) at 150 ◦ C under pressure of 10 MPa for 1 min.
ing process as shown in Fig. 17(a), which is a scanning electron microscopy (SEM) picture. The concave Mg58 Cu31 Y11 BMG mold is used to emboss on PMMA to form a convex micro-lens at 120 ◦ C under a pressure of about 138.3 MPa for 5 min. Fig. 16(c) is a picture of a PMMA with micro-lens array. The PMMA sheet with 1 mm in thickness is purchased from Hsintou Company in Taiwan. The glass transition temperature of PMMA is around 105 ◦ C. Fig. 16(c) shows that similar defects on BMG mold are replicated on the surface of the PMMA sheets. PMMA requires much higher embossing pressure than that of Mg58 Cu31 Y11 material. It means that Mg58 Cu31 Y11 is more deformable material than PMMA. The result also shows that the patterns on BMG are transferred completely on the PMMA. They exhibit optical characteristics because clear focused spots are observed. In order to realize optical function of a curve surface, refraction has to be explained. The refractive index of a medium is a measure for how much the speed of light is reduced inside the medium. Two common properties of transparent materials are directly related to
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Fig. 16. Micro-lens array on (a) the OFC mold is used for hot embossing onto (b) Mg58 Cu31 Y11 BMGs alloy at 150 ◦ C under pressure of 5 MPa for 10 min, and then (c) micro-lens array is transferred to PMMA at 120 ◦ C under pressure of 138.3 MPa for 5 min.
their refractive index. First, light rays change direction when they cross the interface from air to the material, an effect that is used in lenses. Second, light reflects partially from surfaces that have a refractive index different from that of their surroundings. The refractive index, n, of a medium is defined as the ratio of the phase velocity, v, of a wave phenomenon such as light in a vacuum to the phase velocity, vp , in the medium itself: n=
v vp
(3)
By Snell’s law: n1 sin 1 = n2 sin 2
(4)
In Fig. 17(b) and (c), light changes direction when it crosses the interface from air to the material. From Snell’s law, for a same medium, the refractive angle ( 2 , see Fig. 17 (b) or (c)) is a constant. Nevertheless, different curvature surfaces result in different refractive directions ( 3 and 4 , see Fig. 17(b) and (c), respectively).
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6 × 10−6 m/m K for the crystalline Mg2 Cu intermetallic phase, and for quartz (common standard optical material) 5.5 × 10−7 m/mK. Above Tg , significant viscous deformation occurred as a result of applied compressive load, and the deformation strain increases with increasing applied load. Such a high level of induced displacements (or strains) as shown in Fig. 2 can no longer be regarded as the linear thermal expansion, because the alloy readily deformed by the compressive load from the probe at temperatures above Tg . At a temperature above Tg , the thermal expansion of the soft viscous glass (probably in the order of ∼10−4 m/mK (Myung et al., 2001) is expected to be overshadowed by the large viscous compressive strain ranging from 1% to 25%. Therefore, when working temperature is greater than Tg , the BMG-based lens loses its accuracy in dimension and fails its optical function. It follows from what has been said that L(T+T) below or above Tg of the Mg58 Cu31 Y11 BMG can be calculated as following: Below Tg of the Mg58 Cu31 Y11 BMG: L(T +T ) = {1 + [(3 ± 1) × 10−6 ] × T }L(T )
(6)
Above Tg of the Mg58 Cu31 Y11 BMG: L(T +T ) = (1 + 10−4 × T )L(T )
Fig. 17. (a) SEM picture of a BMG sample with micro-lens; for optical function, light refracted from the same angle of incidence through different lenses has an induced angle of (b) 3 and (c) 4 with material surface.
In addition, curvature of an aspheric lens can be affected by the molding process, which influences refraction in lenses as shown in Fig. 17(b) and (c). Thus, it is necessary to discuss the thermal expansion of BMG. Thermal expansion and contraction are important issues in lens molding because they greatly influence the form accuracy of the lens. In general, thermal expansion and contraction are strongly temperature dependent. For metallic glass material, glass-forming ability (GFA) is an important basis for thermal expansion or shrinkage in molding process. A conceptual approach to evaluate GFA for various glass-forming systems has been proposed from a physical metallurgy point of view. It was found that the GFA for noncrystalline materials was related mainly to two factors, i.e., 1/(Tg + Tl ) and Tx (wherein Tx is the onset crystallization temperature, Tg the glass transition temperature, and Tl the liquidus temperature), and could be predicated by a unified parameter ␥ defined as Tx /(Tg + Tl ) (Lu and Liu, 2002, 2003). This approach was confirmed and validated by experimental data in various glass-forming systems including oxide glasses, cryoprotectants, and metallic glasses. The value of the Mg58 Cu31 Y11 BMG (Tx = 479 K, Tg = 413 K, Tl = 754 K (Chang et al., 2007)) is 0.410, having a good GFA. Besides, the coefficient of thermal expansion (˛) of the Mg58 Cu31 Y11 BMG is an important issue when it is used for optical material. According to the thermal linear expanded model, L(T +T ) = (l + ˛T )L(T )
(5)
where L is the length, i.e., diameter, aperture radius, or curvature radius of optical lens, etc., T is the room temperature, T is the difference in temperature, and ˛ is the thermal expansion coefficient. For the Mg58 Cu31 Y11 BMG, below the glass transition temperature, Tg , a linear thermal expansion coefficient (˛) of (3 ± 1) × 10−6 m/mK is obtained (Chang et al., 2007). This can be compared with the ˛ = 26 × 10−6 m/m K for the pure Mg,
(7)
Similarly, thermal expansion of PMMA can be discussed. For the PMMA, below the glass transition temperature, Tg , a linear thermal expansion coefficient (˛) of (75 ± 25) × 10−6 m/mK is obtained (Papanicolaou et al., 1998); above the glass transition temperature, Tg , a linear thermal expansion coefficient (˛) of ∼5 × 10−4 m/mK is obtained (Manabe et al., 1971). Though the recommended refractive index of PMMA is about 1.489, the curvatures of lenses on BMG or PMMA sheet would be different from OFC mold due to their thermal expansion properties, which influences the refraction in PMMA sheet. The micro-lens array on OFC, Mg58 Cu31 Y11 BMGs alloy, and PMMA is shown in Fig. 16(a)–(c), respectively. The convex OFC mold is 140 m in width, the concave BMG mold is 129.93 m in width, and the convex PMMA product is 127.21 m in width. The shrinkage between the first and secondary mold shows 7.19% in shrinkage, whereas the shrinkage between the secondary mold and PMMA replica shows 2.09%. 5. Conclusion This study presents a new process to fabricate an aspheric lens. The process includes the contents of the formula expression of aspheric curves, the brief descriptions of ultraprecision machining process and the operation processes of rough cutting to fabricate an OFC mold as the first mold. The roughness of the first mold is measured as Ra = 0.331 m, and Rz = 1.466 m. Then, this first mold is employed to hot emboss on Mg–Cu–Y amorphous alloy to form a secondary mold. The secondary mold is BMG-based material, whose glass transition temperature of BMG is around 413 K. Therefore, the hot embossing experiments are set at 423 K. This embossing process on BMG material makes molding process faster and more diverse applications. In addition, the secondary mold is used to emboss on PMMA sheets. Molding process by using BMG material as a secondary mold can be more cost-effective and timesaving than the traditional manufacturing process does. BMG is not only a good material for hot embossing process to fabricate microstructure directly, but also fast-molding material for hot embossing process. A practical examination for the ultraprecision cutting and molding was performed in this study. It is expected that the machining methods described in this paper could be applied to relative fields to fabricate precise components with micro or sub-micro order of dimensional accuracy.
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