9. 附錄
9.2 模具補償最佳化分析系統測試結果
為了對建構完成的最佳化分析系統進行測試，以曲率半徑分別為 10mm 與 15mm 之初始模具外型，對形狀分別為球面、拋物面以及雙曲面之目標玻璃外 型，進行模具補償最佳化取得最佳的模具形狀。圖 71 表示目標為曲率半徑 10mm 之球面透鏡時，圖 72 比較模具的初始形狀，以及分別透過經驗補償與最佳化補 償之結果；則比較玻璃未受補償之熱壓結果，透過經驗補償、最佳化補償後之結 果，以及期望之理想形狀。圖 73 至圖 76 則是不同非球面目標形狀下，對於模 具、玻璃進行與前述相同方式之比較。透過以上結果將誤差整理於表7。
圖 71 模具外型 (R=10mm，球面)
圖 72 玻璃外型(R=10mm，球面)
圖 73 模具外型(R=10mm，拋物面)
圖 74 玻璃外型(R=10mm，拋物面)
圖 75 模具外型(R=10mm，雙曲面)
.
圖 76 玻璃外型(R=10mm，雙曲面)
表7 誤差修正結果比較(R=10mm) 球面(k=0)
誤差(mm) 誤差消除(%)
未補償 0.06425 0.00
經驗補償 0.01479 76.98 模具補償最佳化系統0.00214 96.67 拋物面(k=-1)
誤差(mm) 誤差消除(%)
未補償 0.06194 0.00
經驗補償 0.01217 80.35 模具補償最佳化系統0.00108 98.26 雙曲面(k=-3)
誤差(mm) 誤差消除(%)
未補償 0.06144 0.00
經驗補償 0.01522 75.23 模具補償最佳化系統0.00332 94.60
表示目標曲率半徑為10mm 時，球面與不同非球面形狀下補償後之誤差與誤 差修正值。透過經驗補償誤差消除約為75.23%~80.35%，而透過模具補償最佳化 系統，誤差的消除可達94.60%~98.26%。
圖77 至圖 82 表示目標曲率半徑 15mm，球面與不同非球面形狀下，對模具 與玻璃進行前述相同之比較結果。計算以上結果將誤差整理於表8。
圖77 模具外型(R=15mm，球面)
圖78 玻璃外型(R=15mm，球面)
圖79 模具外型(R=15mm，拋物面)
圖80 玻璃外型(R=15mm，拋物面)
圖81 模具外型(R=15mm，雙曲面)
圖82 玻璃外型(R=15mm，雙曲面)
表8 誤差修正結果比較(R=15mm) 球面(k=0)
誤差(mm) 誤差消除(%) 未補償 0.06542 0.00 經驗補償 0.01335 79.59 模具補償最佳化系統 0.00343 94.76 拋物面(k=-1)
誤差(mm) 誤差消除(%) 未補償 0.06461 0.00 經驗補償 0.01976 69.46 模具補償最佳化系統 0.00244 96.27 雙曲面(k=-3)
誤差(mm) 誤差消除(%) 未補償 0.04910 0.00 經驗補償 0.01289 73.74 模具補償最佳化系統 0.00185 96.22
表示在目標曲率半徑為 15mm 之情況下，透過經驗補償誤差消除約為 69.46%~79.59%，而透過模具補償最佳化系統，誤差的消除可達 94.76%~96.27%。
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 751–754
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j m a t p r o t e c
Glass material model for the forming stage of the glass molding process
Yu-Chung Tsaia, Chinghua Hunga,∗, Jung-Chung Hungb
aDepartment of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan, ROC
bDepartment of Mechanical Engineering, National Chin-Yi Institute of Technology, 35 Lane 215, Section 1, Chung-Shan Road, Taiping City, Taichung, Taiwan, ROC
a r t i c l e i n f o
The aim of this research is to obtain an accurate material model for glass that can be used in finite element (FE) analysis of the glass molding process. A thorough understanding of the deformation behavior of the glass specimens was acquired by performing uniaxial compres-sion tests. The elasto-viscoplastic model was utilized for the glass material at the molding temperature to construct the FE model, and a suitable set of parameters for this material model was verified by comparing the simulation results to the experimental data. As a result, the feasibility of the elasto-viscoplastic model for glass at the molding temperature was con-firmed; this material model can be used in FE analysis of the prediction and modification of properties of the final lens products.
© 2008 Published by Elsevier B.V.
1. Introduction
In recent years, glass molding technology has been widely used to produce the small scale optical lenses used in 3C products. A feature of this technology is that glasses are heated to a temperature above the glass transition temper-ature (Tg) or even the yield point (At) and are formed by replication from the same mold in high numbers (Meden-Pielinger, 1983; Taniguchi, 1999; Firestone et al., 2005; Yi et al., 2006). The ability to produce large numbers of replicas and the imprint characteristic make this glass molding tech-nology an ideal choice, more preferable to the conventional glass grinding/polishing technology used to make aspherical lenses.
There are three stages of the glass molding process: heat-ing, molding and annealing. During the heating stage, both molds and glass are heated to the molding temperature, and a fixed displacement is then applied in order to proceed with
∗Corresponding author. Tel.: +886 3 5712121x5516; fax: +886 3 5720634.
open/closed die forming in the forming stage. In the subse-quent annealing stage, the molds are held in the final position of the forming stage and cooled along with the glass until the mold-releasing temperature is reached; the glass is then separated from the molds.
Glass is a temperature-sensitive material, and both the forming and annealing stages, in which the glass undergoes high temperature variation, will greatly affect the precise shape and dimensions of glass lenses. Consequently, defects in the optical properties of glass lenses will be affected by the deviations in shape and dimension. In addition, the life-time of the molds used in the forming stage is another critical problem that is encountered in mass production. Therefore, this study focuses on the forming stage of the glass molding process.
It is known that low temperature processes help to lengthen the operating lifetime of the mold material (SCHOTT, in press). In the molding stage, the higher the molding
tem-752 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 751–754
perature, the lower the pressure, and vice versa. The molding temperature currently used by the industry is between 30◦C and 40◦C above At, i.e., the molding temperature is high, and the operating lifetime of the molds is shortened. If the mold-ing temperature is lowered, the pressure increases, which also shortens the operating lifetime of the molds. In order to retain a good operating lifetime for the molds, a com-promise between temperature and pressure was made in this study, with the molding temperature set to 30–50◦C above Tg. Uniaxial compression tests were performed at this molding temperature and the stress–strain relationships were observed in the first part of this study. A finite element (FE) model of the uniaxial compression tests was then constructed;
analyses were performed and the simulation results were compared to the experimental data. Attempts were made to find an accurate material model for the FE analysis. After the feasibility of the material model was verified, it could then be introduced into the FE analysis of the glass molding process.
2. Material model
Several studies have regarded glass as a viscoelastic mate-rial and have focused on its stress relaxation behavior (Scherer, 1986; Rekhson, 1986; Gy et al., 1994; Duffre‘ne et al., 1997; Duffre‘ne and Gy, 1997). Jain et al. (2005)not only focused on the measurement of the viscosity of glass at the molding temperature but also utilized FE analysis for the glass molding process; this study regarded glass as a viscoelastic material (Jain and Yi, 2005; Jain et al., 2006).
When discussing the bottle formation of glass at a high temperature, glass is regarded as behaving as a Newto-nian fluid, where the viscosity is temperature-dependent, and the material model is rigid-viscoplastic (Hyre, 2002;
MSC, 2005).Yi and Jain (2005)also attempted to utilize the rigid-viscoplastic model in FE analysis of the glass molding process.
In order to fully understand the material behavior of glass in the forming stage, and to develop an accurate material model which not only can be used in FE analysis of the glass molding process, but also in the microstructure imprinting procedure, the elastic properties of glass should be consid-ered. In this research, the elasto-viscoplastic model (Cristescu and Suliciu, 1982) was introduced to investigate the deformed behavior of glass in the molding stage. This model is described by
= Eε, if < Y
= 3(T)˙ε, if ≥ Y
(1)
where is the stress, (T) the temperature (T) dependent vis-cosity, and ˙ε is the strain rate. This function shows that the material behaves as a linear elastic material before the flow stress (Y) is reached, and as a strain rate-dependent vis-coplastic material after the flow stress is reached. Although the viscosity varies with temperature, it will be regarded as
3. Experiments
In order to find a material property of the glass that can be used in FE analysis of the glass molding process, uniaxial com-pression tests on the glass material S-FPL52 (with Tg equal to 445◦C), fabricated by the OHARA company, were performed at the chosen molding temperature (475◦C). The strain rate was held at 0.00667 s−1, and the experiments were conducted with-out lubricant. Cylindrical specimens of 10 mm in diameter and 6 mm in height were used. The FE model of the uniaxial com-pression test at the molding temperature was then built using a commercial FE program, MSC.MARC, as shown inFig. 1. Both the upper and lower molds were set as rigid bodies, and the glass specimen was set as an elasto-viscoplastic material. The parameters of the material model were adjusted using the trial and error method to achieve the best-fitting simulation results in comparison with the experimental data.
The friction model, used to model the interfacial friction conditions between the glass and molds, is described by
= mkm (2)
where is the frictional stress of the interface, m the shear fac-tor (0 < m < 1), and kmis the shear yield stress of the glass near the interface. A shear friction factor of 1.0 was used, which assumes complete sticking between the glass and molds (Yi and Jain, 2005).
4. Results and discussion
The comparison results of the experiment and simulation are shown inFigs. 2 and 3. A set of parameters for the material model was obtained from these trial and error attempts such that Young’s modulus was equal to 1300 MPa and viscosity was equal to 1010P (1000 MPa s). The simulation results fitted with the experimental data quite well, and show that this set of parameters is feasible under the condition of a strain rate of 0.00667 s−1.
To verify whether or not the elasto-viscoplastic model con-sisting of this set of parameters is feasible for FE analysis under different strain rates, further comparisons between simulation results and experimental data were made. Uni-axial compression tests with strain rates of 0.00833 s−1 and
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 751–754 753
Fig. 2 – Comparison of force–displacement curves between experimental and simulation results at a strain rate of 0.00667 s−1.
0.01 s−1 were performed, and the flow stresses under each strain rate were found to be 24.9 MPa and 30 MPa, respectively.
Comparisons of the simulation results and experimental data are shown inFigs. 4 and 5, from which it can be seen that the simulation results using the previously obtained material parameters fitted to the experimental data quite well. There-fore, the elasto-viscoplastic model is feasible for describing the deformation behavior of the glass in the molding stage with different strain rates.
The final shape of the glass specimen after compression is shown inFig. 6and the simulation result is shown inFig. 7.
Due to the limitations of the apparatus, some parallel devi-ations exist between the upper and the lower molds, which may cause the nonuniform deformation of the glass specimen;
temperature control of the environment and both molds also have some discrepancies. For glass material, a small differ-ence in temperature or pressure could change the final shape of the product. It can be seen from these two figures that
Fig. 4 – Comparison of force–displacement curves between experimental and simulation results at strain rates of 0.00667 s−1, 0.00833 s−1and 0.01 s−1.
Fig. 5 – Comparison of stress–strain curves between experimental and simulation results at strain rates of 0.00667 s−1, 0.00833 s−1and 0.01 s−1.
754 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 751–754
Fig. 7 – Simulation results of the final shape of the glass specimen.
the glass ends were not deformed as evenly as was shown in the simulation results. Nevertheless, this study can still pro-vide a reference for a material model that can be used in FE analysis of glass molding. More precise investigations will be performed when the precision of the apparatus is improved.
5. Conclusion
Research on the deformation behavior of glass at a specific molding temperature (30◦C above Tg) was performed in this work, and the feasibility of the elasto-viscoplastic model for glass material in the molding stage was verified by comparing the simulation results to the experimental data. Some conclu-sions from this work can be made as follows:
(1) The elasto-viscoplastic model can be introduced into FE analysis of the glass molding process during the molding stage.
(2) The investigations performed in this work are within the molding stage. However, annealing is also a key stage in the glass molding process and will also affect the precision of the final product shape. In order to perform FE anal-ysis more precisely, and to reduce the residual stress of the products to improve the optical properties, the stress relaxation characteristic of the viscoelastic property of the glass material should be considered in the annealing stage.
Also, thermal properties in the annealing stage such as heat conduction between the molds and glass, convec-tion between the environment and the glass and molds, and change in the thermal expansion coefficient should be considered thoroughly.
(3) Molds were assumed to be rigid bodies in this work, but in the glass molding process, elastic recovery of the molds will affect the prediction of the final product shape.
There-fore, consideration of the elastic property of the molds should be included in the FE analysis in order to pre-compensate for the molds in advance and to predict the final shape of the glass lens more precisely.
Acknowledgements
The authors would like to thank the National Science Council of Taiwan, ROC for the grant NSC 95-2221-E-009-176, under which the investigation was undertaken. The authors would also like to thank the National Center for High-Performance Computing for its facility support.
r e f e r e n c e s
Cristescu, N., Suliciu, I., 1982. Viscoplasticity. Martinus Nijhoff.
Duffre‘ne, L., Gy, R., 1997. Viscoelastic constants of a soda-lime-silica glass. J. Non-Cryst. Solids 211, 30–38.
Duffre‘ne, L., Gy, R., Burlet, H., Piques, R., 1997. Viscoelastic behavior of a soda-lime-silica glass: inadequacy of the KWW function. J. Non-Cryst. Solids 215, 208–217.
Firestone, G.C., Jain, A., Yi, A.Y., 2005. Precision laboratory apparatus for high temperature compression molding of glass lenses. Rev. Sci. Instrum. 76.
Gy, R., Duffre‘ne, L., Labrot, M., 1994. New insights into the viscoelasticity of glass. J. Non-Cryst. Solids 175, 103–117.
Hyre, M., 2002. Numerical modeling of glass forming and conditioning. J. Am. Ceram. Soc. 85, 1047–1056.
Jain, A., Yi, A.Y., 2005. Numerical modeling of viscoelastic stress relaxation during glass lens forming process. J. Am. Ceram.
Soc. 88, 530–535.
Jain, A., Firestone, G.C., Yi, A.Y., 2005. Viscosity measurement by cylindrical compression for numerical modeling of precision lens molding process. J. Am. Ceram. Soc. 88, 2409–2414.
Jain, A., Yi, A.Y., Xie, X., Sooryakumar, R., 2006. Finite element modeling of stress relaxation in glass lens moulding using measured temperature-dependent elastic modulus and viscosity data of glass. Model. Simul. Mater. Sci. Eng. 14, 465–477.
Meden-Pielinger, G.A.A., Van de Heuvel, J.H.P., 1983. Precision pressed optical components made of glass and glass suitable modeling, US Patent 4,391,915.
MSC, 2005. MSC. Marc User’s Guide. MSC Software.
Rekhson, S., 1986. In: Uhlmann, D.R., Kreidl, N.J. (Eds.), Glass Science and Technology. Academic Press Inc., Florida, USA.
Scherer, G.W., 1986. Relaxation in Glass and Composites. Wiley, New York.
SCHOTT Technical Information, Optical glass for precision molding, SCHOTT, in press.
Y. Taniguchi, 1999. Mold for molding optical element, US Patent 5,855,641.
Yi, A.Y., Jain, A., 2005. Compression molding of aspherical glass lenses–a combined experimental and numerical analysis. J.
Am. Ceram. Soc. 88, 579–586.
Yi, A.Y., Huang, C., Klocke, F., Brecher, C., Pongs, G.,
Winterschladen, M., Demmer, A., Lange, S., Bergs, T., Merz, M., Niehaus, F., 2006. Development of a compression molding process for three-dimensional tailored free-form glass optics.
Appl. Optics 45, 6511–6518.
中國機械工程學會第二十四屆全國學術研討會論文集 中原大學 桃園、中壢 中華民國九十六年十一月二十三日、二十四日 論文編號：D17-0019
Die Shape Optimization on Molding Process of Optical Glass Lens
Tsung-Chun Wu, Yu-Chung Tsai, Chinghua HungDepartment of Mechanical Engineering, National Chiao Tung University NSC Project No.: NSC-95-2221-E-009-176
Abstract
Demand of optical glass lens is progressively increasing with the development of optical and electrical products. As far as the optical glass material is concerned, lens molding technique, compared with the conventional glass lens grinding and polishing process, has lots of advantages, like much simplified manufacture process and dramatically reduction of cost and waste. However, there still exist several difficulties needed to be overcome, such as the shape deviations of the final lens products that may influence the qualities of optical image. This paper utilized FEA on the glass lens molding process and constructed a die shape optimization design system in order to compensate the shape deviations of the lens products so that the errors can be reduced efficiently. Once the deviations of the lens products have been minimized, the aim of mass production for lens molding of optical glass can be accomplished.
Keywords：glass molding, optimization, FEA.
1. Introduction
The fabrication processes of optical lenses comprise casting, hot embossing forming, injection molding, grind-polishing and so on. But as far as optical glass material is concerned, grind-polishing and glass molding are the only two ways to manufacture optical glass lenses for the time being.
Compared with the grind-polishing fabrication process of optical glass lens, glass molding serves as a more economical one. Glass molding is also called hot embossing forming of optical glass lens since the quality of the die surface can be translated onto the lens surface. There are several merits of glass molding, like easiness for mass production, cost reduction of labor and time, and simplified steps of process. Fabrication process of glass lens molding can be generalized to three stages:
(1) Heating: After the dies and glass gob were put into the hot forming working machine, both the top and bottom dies and the glass gob were then heated to the desired temperature (the forming temperature) which is slightly higher than the transition temperature (Tg) of
(1) Heating: After the dies and glass gob were put into the hot forming working machine, both the top and bottom dies and the glass gob were then heated to the desired temperature (the forming temperature) which is slightly higher than the transition temperature (Tg) of