Abstract

Numerical simulations for mold-flow analysis and experimental measurements of injection-molded plastic lenses have been conducted for investigation of optical qualities, residual birefringence, and form accuracy resulting from various pertinent process conditions. First, residual birefringence distributions on the lens have been predicted and verified experimentally. Furthermore, full-scale factorial design of experiments was conducted to comprehend the influences of qualities, such as shear stresses, form accuracy, and volumetric deviation, on the measured primary or Seidel aberrations. In conclusion, residual birefringence induced by stresses represented by photoelasticity measurements agrees well with the numerical predictions and the experimental results indicate that the residual birefringence is mainly generated during the mold-filling stage. In addition, spherical aberration of the injection-molded plastic lenses is more sensitive to the pertinent qualities as compared to coma and astigmatism.

© 2008 Optical Society of America

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References

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  1. X. H. Lu and L. S. Khim, “A statistical experimental study of the injection molding of optical lenses,” J. Mater. Process. Technol. 113, 189-195 (2001).
    [CrossRef]
  2. D. C. Montgomery, Design and Analysis of Experiments (Wiley, 2001).
  3. J. Antony and F. J. Antony, “Teaching the Taguchi method to industry engineers,” Work Study Manag. Services 50, 141-149 (2001).
  4. A. W. McFarland and J. S. Colton, “Production and analysis of injection molded micro-optic components,” Polym. Eng. Sci. 44, 564-579 (2004).
    [CrossRef]
  5. A. Bendell, J. Disney, and W. A. Pridmore, Taguchi Methods: Applications in World Industry (IFS, 1989).
  6. Y. Maekawa, M. Onishi, A. Ando, S. Matsushima, and F. Lai, “Prediction of birefringence in plastics optical elements using 3D CAE for injection molding,” Proc. SPIE 3944, 935-943(2000).
    [CrossRef]
  7. J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, 1991).
  8. K. Yoon, “An experimental study on precision injection molding of center-gated disks,” Korean J. Rheol. 7, 19-27 (1995).
  9. G. D. Shyu, A. I. Isayev, and H. S. Lee, “Numerical simulation of flow-induced birefringence in injection molded disk,” Korea-Australia Rheol. J. 15, 159-166 (2003).
  10. B. F. Fan, D. O. Kazmer, W. C. Bushko, R. P. Theriault, and A. J. Poslinski, “Birefringence prediction of optical media,” Polym. Eng. Sci. 44, 814-824 (2004).
    [CrossRef]
  11. C. A. Hieber and S. F. Shen, “Flow analysis of the non-isothermal two-dimensional filling process in injection molding,” Isr. J. Technol. 16, 248-254 (1978).
  12. S. Y. Kim, M. H. Rim, W. S. Lim, and W. Y. Kim, “A numerical approach for optical characteristics of injection-molded lens,” in Proceedings of ANTEC 1999 Plastics: Bridging the Millennia, (Society of Plastics Engineers, 1999), pp. 1491-1495.
  13. C. H. Chien, Y. Maekawa, H. Kishikawa, M. Onishi, and F. S. Lai, “Influence of processing conditions on the formation of birefringence of optical plastics lens by using 3D CAE,” in Proceedings of ANTEC 2001 Plastics: The Lone Star (Society of Plastics Engineers, 2001), pp. 1338 - 1342.
  14. R. Y. Chang and W. H. Yang, “Numerical simulation of mold filling in injection molding using a three-dimensional finite volume approach,” Int. J. Numer. Methods Fluids 37, 125-148(2001).
    [CrossRef]
  15. A. Y. Peng, W. H. Yang, and D. C. Hsu, “Enhanced structure CAE solution with molding effect for automotive parts,” in Proceedings of ANTEC 2005 Plastics (Society of Plastics Engineers, 2005), pp. 2787 - 2791.
  16. L. S. Turng, M. Peic, and D. K. Bradley, “Process simulation and optimization for injection molding-experimental verifications and field applications,” J. Inj. Molding Technol. 6, 143-155 (2002).
  17. P. J. Wang and H. E. Lai, “Study of optical characteristics for injection molded aspheric lenses,” in Proceedings of Asia Pacific Conference on Optics Manufacture (Asia Pacific Conference on Optics Manufacture, 2007).
  18. P. J. Wang and H. E. Lai, “Study of residual birefringence in injection molded lenses,” in Proceedings of Plastics Encounter at ANTEC 2007 (Society of Plastics Engineers, 2007), pp. 2494 - 2498.
  19. H. Janeschitz-Kriegl, Polymer Melt Rheology and Flow Birefringence (Spring-Verlag, 1983).
    [CrossRef]
  20. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, 1987).
  21. P. B. John, Runner and Gating Design Handbook (Hanser, 2004).
  22. J. C. Wyant, Applied Optics and Optical Engineering, Vol. XI (Academic, 1992).

2004

A. W. McFarland and J. S. Colton, “Production and analysis of injection molded micro-optic components,” Polym. Eng. Sci. 44, 564-579 (2004).
[CrossRef]

B. F. Fan, D. O. Kazmer, W. C. Bushko, R. P. Theriault, and A. J. Poslinski, “Birefringence prediction of optical media,” Polym. Eng. Sci. 44, 814-824 (2004).
[CrossRef]

2003

G. D. Shyu, A. I. Isayev, and H. S. Lee, “Numerical simulation of flow-induced birefringence in injection molded disk,” Korea-Australia Rheol. J. 15, 159-166 (2003).

2002

L. S. Turng, M. Peic, and D. K. Bradley, “Process simulation and optimization for injection molding-experimental verifications and field applications,” J. Inj. Molding Technol. 6, 143-155 (2002).

2001

R. Y. Chang and W. H. Yang, “Numerical simulation of mold filling in injection molding using a three-dimensional finite volume approach,” Int. J. Numer. Methods Fluids 37, 125-148(2001).
[CrossRef]

X. H. Lu and L. S. Khim, “A statistical experimental study of the injection molding of optical lenses,” J. Mater. Process. Technol. 113, 189-195 (2001).
[CrossRef]

J. Antony and F. J. Antony, “Teaching the Taguchi method to industry engineers,” Work Study Manag. Services 50, 141-149 (2001).

2000

Y. Maekawa, M. Onishi, A. Ando, S. Matsushima, and F. Lai, “Prediction of birefringence in plastics optical elements using 3D CAE for injection molding,” Proc. SPIE 3944, 935-943(2000).
[CrossRef]

1995

K. Yoon, “An experimental study on precision injection molding of center-gated disks,” Korean J. Rheol. 7, 19-27 (1995).

1978

C. A. Hieber and S. F. Shen, “Flow analysis of the non-isothermal two-dimensional filling process in injection molding,” Isr. J. Technol. 16, 248-254 (1978).

Int. J. Numer. Methods Fluids

R. Y. Chang and W. H. Yang, “Numerical simulation of mold filling in injection molding using a three-dimensional finite volume approach,” Int. J. Numer. Methods Fluids 37, 125-148(2001).
[CrossRef]

Isr. J. Technol.

C. A. Hieber and S. F. Shen, “Flow analysis of the non-isothermal two-dimensional filling process in injection molding,” Isr. J. Technol. 16, 248-254 (1978).

J. Inj. Molding Technol.

L. S. Turng, M. Peic, and D. K. Bradley, “Process simulation and optimization for injection molding-experimental verifications and field applications,” J. Inj. Molding Technol. 6, 143-155 (2002).

J. Mater. Process. Technol.

X. H. Lu and L. S. Khim, “A statistical experimental study of the injection molding of optical lenses,” J. Mater. Process. Technol. 113, 189-195 (2001).
[CrossRef]

Korea-Australia Rheol. J.

G. D. Shyu, A. I. Isayev, and H. S. Lee, “Numerical simulation of flow-induced birefringence in injection molded disk,” Korea-Australia Rheol. J. 15, 159-166 (2003).

Korean J. Rheol.

K. Yoon, “An experimental study on precision injection molding of center-gated disks,” Korean J. Rheol. 7, 19-27 (1995).

Polym. Eng. Sci.

A. W. McFarland and J. S. Colton, “Production and analysis of injection molded micro-optic components,” Polym. Eng. Sci. 44, 564-579 (2004).
[CrossRef]

B. F. Fan, D. O. Kazmer, W. C. Bushko, R. P. Theriault, and A. J. Poslinski, “Birefringence prediction of optical media,” Polym. Eng. Sci. 44, 814-824 (2004).
[CrossRef]

Proc. SPIE

Y. Maekawa, M. Onishi, A. Ando, S. Matsushima, and F. Lai, “Prediction of birefringence in plastics optical elements using 3D CAE for injection molding,” Proc. SPIE 3944, 935-943(2000).
[CrossRef]

Work Study Manag. Services

J. Antony and F. J. Antony, “Teaching the Taguchi method to industry engineers,” Work Study Manag. Services 50, 141-149 (2001).

Other

J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, 1991).

A. Bendell, J. Disney, and W. A. Pridmore, Taguchi Methods: Applications in World Industry (IFS, 1989).

D. C. Montgomery, Design and Analysis of Experiments (Wiley, 2001).

S. Y. Kim, M. H. Rim, W. S. Lim, and W. Y. Kim, “A numerical approach for optical characteristics of injection-molded lens,” in Proceedings of ANTEC 1999 Plastics: Bridging the Millennia, (Society of Plastics Engineers, 1999), pp. 1491-1495.

C. H. Chien, Y. Maekawa, H. Kishikawa, M. Onishi, and F. S. Lai, “Influence of processing conditions on the formation of birefringence of optical plastics lens by using 3D CAE,” in Proceedings of ANTEC 2001 Plastics: The Lone Star (Society of Plastics Engineers, 2001), pp. 1338 - 1342.

P. J. Wang and H. E. Lai, “Study of optical characteristics for injection molded aspheric lenses,” in Proceedings of Asia Pacific Conference on Optics Manufacture (Asia Pacific Conference on Optics Manufacture, 2007).

P. J. Wang and H. E. Lai, “Study of residual birefringence in injection molded lenses,” in Proceedings of Plastics Encounter at ANTEC 2007 (Society of Plastics Engineers, 2007), pp. 2494 - 2498.

H. Janeschitz-Kriegl, Polymer Melt Rheology and Flow Birefringence (Spring-Verlag, 1983).
[CrossRef]

R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, 1987).

P. B. John, Runner and Gating Design Handbook (Hanser, 2004).

J. C. Wyant, Applied Optics and Optical Engineering, Vol. XI (Academic, 1992).

A. Y. Peng, W. H. Yang, and D. C. Hsu, “Enhanced structure CAE solution with molding effect for automotive parts,” in Proceedings of ANTEC 2005 Plastics (Society of Plastics Engineers, 2005), pp. 2787 - 2791.

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Figures (15)

Fig. 1
Fig. 1

Schematic drawings of sample aspheric lens: (a) surface A is spherical in 70.35 mm with surface B being aspheric, (b) per spective view of the lens with 30 mm in diameter and 2 mm in thickness.

Fig. 2
Fig. 2

Geometric drawing of the (1) sprue, (2) runner, (3) gate, and (4) lens cavity modeled with tetrahedral and prism mesh employed for the simulations.

Fig. 3
Fig. 3

Three-dimensional shaded plots in cut-view of simulation results: (a) volumetric shrinkage and (b) warpage after ejection.

Fig. 4
Fig. 4

Schematic illustration of photoelasticity measurements: 1 is the light source; 2 is the polarizer; 3 is the first quarter-wave plate, where β is π / 4 ; 4 is the sample lens, where α is the principal-stress direction making an angle with the axis of polarization of the polarizer; 5 is the second quarter-wave plate; and 6 is the analyzer [7].

Fig. 5
Fig. 5

Comparisons between predicted shear stresses and fringe patterns: (a) shear stresses distribution versus fringe patterns, (b) locations of sensor nodes in the lens cavity, and (c) plots of shear stresses for sensor nodes at path 3 versus time during filling stage.

Fig. 6
Fig. 6

Comparisons of annealing effects, where annealing temperature was set at 125 ° C with annealing time being 12 h , on fringe orders before annealing and after annealing: (a) before annealing processes, fringe order is 6.5; and (b) after annealing processes, fringe order is 6.5.

Fig. 7
Fig. 7

Experimental results of linear shrinkage for sample plate at 125 ° C for 12 h : after annealing processes, linear shrinkage at side A, side B, side C, and side D are 8.34 × 10 2 % , 5.00 × 10 2 % , 1.67 × 10 2 % , and 7.50 × 10 2 % , respectively.

Fig. 8
Fig. 8

Experimental results of lenses being annealed at 153 ° C : (a) no annealing, (b) after 30 min annealing, (c) after 1 h annealing, (d) after 2 h annealing, (e) after 4 h annealing, and (f) after 8 h annealing.

Fig. 9
Fig. 9

Schematic drawings of the planoconvex spherical lens. The surface curvature is 70 mm with the diameter of 32 mm at thickness of 2 mm , while the gate is 0.80 mm in thickness.

Fig. 10
Fig. 10

Comparisons between shear stresses distributions and residual birefringence distributions on the plano-convex spherical lenses.

Fig. 11
Fig. 11

Shaded plots of predicted residual stresses in cut-view with enlarged insert in gapwise direction showing the high stresses near lens surfaces.

Fig. 12
Fig. 12

Schematic drawing for illustrating the layer-removal technique applied to molded lenses.

Fig. 13
Fig. 13

Photographs of residual birefringence on samples prepared by layer-removal technique: (a) lens without machining, (b) lens with 0.1 mm removed, (c) lens with 0.2 mm removed, (d) lens with 0.3 mm removed, and (e) lens with 0.4 mm removed.

Fig. 14
Fig. 14

Chart for percentile in removed birefringence versus thickness removed from the surface near the gate area.

Fig. 15
Fig. 15

Plots of average primary aberrations versus various process runs from the results of design of experiments.

Tables (5)

Tables Icon

Table 1 Pertinent Process Conditions for Computer-Aided Engineering Simulations and Experimental Verifications for Planoconvex Spherical Lenses

Tables Icon

Table 2 Control Factors and Settings for DOE Analysis on Form Accuracy

Tables Icon

Table 3 Relationships between Qualities and Process Conditions

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Table 4 Full-scale Factorial Design of Experiments for Studying Effects of Qualities on Seidel Aberrations

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Table 5 Contributions of Main Factors as Qualities on Seidel Aberrations

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

n 2 n 1 = c ( σ 1 σ 2 ) , n 3 n 2 = c ( σ 2 σ 3 ) , n 1 n 3 = c ( σ 3 σ 1 ) .
ρ t + . ρ u = 0 , t ( ρ u ) + . ( ρ u u σ ) = ρ g , σ = p I + η ( u + u T ) , ρ C p ( T t + u . T ) = ( k T ) + η γ ˙ 2 ,
σ + F = 0.
σ i j = C i j k l ( ε k l ε k l 0 α k l Δ T ) + σ i j F and ε ij = 1 2 ( u i , j + u j , i ) ,
S v = V c V V c = 1 V V c ,
E ax = k sin Δ 2 sin ( ω t + 2 α Δ 2 ) .
I = K sin 2 Δ 2 .
σ = [ P + σ 11 σ 12 σ 13 σ 21 P + σ 22 σ 23 σ 31 σ 32 P + σ 33 ] ,
σ = [ P + σ 11 σ 12 σ 21 P + σ 22 ] .
Δ n = c ( σ 1 σ 2 ) = c ( σ 11 σ 22 ) 2 + 4 σ 12 2 ,
Δ n = c ( σ 1 σ 2 ) = 2 c σ 12 .
SNR STB = 10 log ( 1 n i = 1 n y i 2 ) ,

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