Simulation of Precision Glass Molding for Aspherical Cylindrical Microlens Arrays

Qilin Wang; Peng Yao; Yifan Wang; Wanying He; Chuanzhen Huang

doi:10.3788/CJL240466

Chinese Journal of Lasers, Volume. 51, Issue 20, 2002104(2024)

Simulation of Precision Glass Molding for Aspherical Cylindrical Microlens Arrays

Qilin Wang¹, Peng Yao^1、*, Yifan Wang¹, Wanying He¹, and Chuanzhen Huang²

Author Affiliations

¹School of Mechanical Engineering, Shandong University, Jinan 250061, Shandong , China

²School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei , China

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Abstract Get PDF(in Chinese)

Figures & Tables(19)

Fig. 1. Schematics of creep test. (a) Traditional creep test; (b) minimal uniaxial creep test

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Fig. 2. Common constitutive models of viscoelastic material. (a) Generalized Kelvin model; (b) generalized Maxwell model

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Fig. 3. MUCT experiment of fused silica

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Fig. 4. Test results of fused silica at different temperatures. (a) Creep displacement; (b) creep compliance

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Fig. 5. Curves of test and fitting. (a) Creep compliance curves (1380 ℃); (b) calculated shear modulus curves at different temperatures

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Fig. 6. Time-temperature equivalent model. (a) Fitting result of WLF equation; (b) fitting results of shear modulus based on WLF equation

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Fig. 7. Simulation of MUCT of fused silica. (a) 3D simulation model; (b) comparison of simulation and experiment results at different temperatures

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Fig. 8. Simulation of ACMA molding. (a) 2D simulation model; (b) parameters of ACMA mold

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Fig. 9. Results of molding simulation. (a) Stress distribution in glass after molding at 1400 ℃; (b) maximum stress values at different temperatures

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Fig. 10. Maximum stress values at different molding velocities

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Fig. 11. Simulation results at different friction coefficients. (a) 0.1; (b) 0.9; (c) total curve

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Fig. 12. Simulation results at different molding pressures. (a) Displacement of upper mold; (b) maximum stress

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Fig. 13. Simulation results at different holding pressures. (a) Displacement of upper mold; (b) maximum stress

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Fig. 14. Maximum stress at different holding time

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Table 1. MUCT parameters of fused silica
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Table 1. MUCT parameters of fused silica
Parameter Value
Temperature /℃ 1360， 1380， 1400
Heating velocity /（℃/min） 10
Soaking time /min 10
Load /N 0.3
Holding time /s 1800

Table 2. Shear moduli at different temperatures
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Table 2. Shear moduli at different temperatures
Temperature /℃ Shear modulus /MPa
$G_{1}$ $G_{2}$ $G_{3}$ $G_{4}$ $G_{5}$ $G_{\infty}$ $G_{0}$
1360 33232.4 8.8983 3.3847 1.39760 1.47700 0.30523 33247.9
1380 33232.7 8.5011 5.4713 0.96765 0.18940 0.02445 –
1400 33238.8 4.4211 3.5548 0.61510 0.36446 0.09304 –

Table 3. Relaxation time at different temperatures
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Table 3. Relaxation time at different temperatures
Temperature /℃ Relaxation time /s
$τ_{1}$ $τ_{2}$ $τ_{3}$ $τ_{4}$ $τ_{5}$
1360 0.0017669 8.1360 15.138 48.9730 212.900
1380 0.0006799 7.6960 16.986 84.8860 452.830
1400 0.0003928 0.5906 1.629 2.2495 54.995

Table 4. Thermomechanical properties of glass and mold materials

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Table 4. Thermomechanical properties of glass and mold materials

Material property	Fused silica	Glassy carbon
Young modulus /GPa	77.8	35
Poisson’s ratio	0.17	0.17
Density /（g/cm³）	2.20	1.42
Thermal conductivity /［W/（m·K）］	1.42	6.30
Thermal expansion /（10^-6/K）	0.54	2.60

Table 5. Molding simulation process parameters

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Table 5. Molding simulation process parameters

Group	Molding temperature /℃	Molding velocity /（μm/s）	Coefficient of friction	Molding force /N	Holding force /N	Holding time /s
1	1360， 1380， 1400， 1420， 1440	5	0.3	–	–	–
2	1400	1， 2， 5， 10， 20	0.3	–	–	–
3	1400	5	0.1， 0.3， 0.5， 0.7， 0.9	–	–	–
4	1400	–	0.3	500， 750， 1000， 1250， 1500	–	–
5	1400	–	0.3	1000	100， 200， 300， 400， 500	100
6	1400	–	0.3	1000	400	50， 100， 150， 200， 250

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Qilin Wang, Peng Yao, Yifan Wang, Wanying He, Chuanzhen Huang. Simulation of Precision Glass Molding for Aspherical Cylindrical Microlens Arrays[J]. Chinese Journal of Lasers, 2024, 51(20): 2002104

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