Abstract

This study focuses on injection molding process window determination for obtaining optimal imaging optical properties, astigmatism, coma, and spherical aberration using plastic lenses. The Taguchi experimental method was first used to identify the optimized combination of parameters and significant factors affecting the imaging optical properties of the lens. Full factorial experiments were then implemented based on the significant factors to build the response surface models. The injection molding process windows for lenses with optimized optical properties were determined based on the surface models, and confirmation experiments were performed to verify their validity. The results indicated that the significant factors affecting the optical properties of lenses are mold temperature, melt temperature, and cooling time. According to experimental data for the significant factors, the oblique ovals for different optical properties on the injection molding process windows based on melt temperature and cooling time can be obtained using the curve fitting approach. The confirmation experiments revealed that the average errors for astigmatism, coma, and spherical aberration are 3.44%, 5.62%, and 5.69%, respectively. The results indicated that the process windows proposed are highly reliable.

© 2014 Optical Society of America

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  1. R. O. Sánchez, A. Jorge, M. Arantza, and M. Daniel, “On the relationship between cooling step and warpage in injection molding,” Measurement 45, 1051–1056 (2012).
    [CrossRef]
  2. B. Ozcelik and I. Sonat, “Warpage and structural analysis of thin shell plastic in the plastic injection molding,” Mater. Des. 30, 367–375 (2009).
    [CrossRef]
  3. M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
    [CrossRef]
  4. M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).
  5. N. M. Mehat and S. Kamaruddin, “Optimization of mechanical properties of recycled plastic products via optimal processing parameters using the Taguchi method,” J. Mater. Process. Technol. 211, 1989–1994 (2011).
    [CrossRef]
  6. M. Altan, “Reducing shrinkage in injection moldings via the Taguchi, ANOVA and neural network methods,” Mater. Des. 31, 599–604 (2010).
    [CrossRef]
  7. J. Y. Shieh, L. K. Wang, and S. Y. Ke, “A feasible injection molding technique for the manufacturing of large diameter aspheric plastic lenses,” Opt. Rev. 17, 399–403 (2010).
    [CrossRef]
  8. P. J. Wang and H. E. Lai, “Study of residual birefringence in injection molded lenses,” in SPE ANTEC Conference Proceeding (SPE, 2007), paper 2498.
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    [CrossRef]
  10. H. Liu, Z. Lu, and F. Li, “Using diffractive optical element and ZYGO interferometer to test large-aperture convex surface,” Opt. Laser Technol. 37, 642–646 (2005).
    [CrossRef]
  11. T. J. Chen, “The error simulation and experiment analysis of Hartmann Shack wavefront sensor,” Master’s thesis (Yuan Ze University, 2007).
  12. P. Postawa and J. Koszkul, “Change in injection moulded parts shrinkage and weight as a function of processing conditions,” J. Mater. Process. Technol. 162–163, 109–115 (2005).
    [CrossRef]
  13. B. Ozcelik and T. Erzurumlu, “Comparison of the warpage optimization in the plastic injection molding using ANOVA, neural network model and genetic algorithm,” J. Mater. Process. Technol. 171, 437–445 (2006).
    [CrossRef]
  14. T. Erzurumlu and B. Ozcelik, “Minimization of warpage and sink index in injection-molded thermoplastic parts using Taguchi optimization method,” Mater. Des. 27, 853–861 (2006).
    [CrossRef]
  15. S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
    [CrossRef]
  16. L. Wua, K. L. Yick, S. P. Ng, J. Yip, and K. H. Kong, “Parametric design and process parameter optimization for bra cup molding via response surface methodology,” Exp. Syst. Appl. 39, 162–171 (2012).
    [CrossRef]
  17. E. Kilickap, “Modeling and optimization of burr height in drilling of Al-7075 using Taguchi method and response surface methodology,” Int. J. Adv. Manuf. Technol. 49, 911–923 (2010).
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  21. D. Bas and I. H. Boyaci, “Modeling and optimization I: usability of response surface methodology,” J. Food Eng. 78, 836–845 (2007).
    [CrossRef]
  22. D. J. Lizotte, R. Greiner, and D. Schuurmans, “An experimental methodology for response surface optimization methods,” J. Global Optim. 53, 699–736 (2012).
    [CrossRef]
  23. K. T. Chiang and F. P. Chang, “Analysis of shrinkage and warpage in an injection-molded part with a thin shell feature using the response surface methodology,” Int. J. Adv. Manuf. Technol. 35, 468–479 (2007).
  24. G. Wang, G. Zhao, H. Li, and Y. Guan, “Research on optimization design of the heating/cooling channels for rapid heat cycle molding based on response surface methodology and constrained particle swarm optimization,” Exp. Syst. Appl. 38, 6705–6719 (2011).
    [CrossRef]
  25. H. Kurtaran and T. Erzurumlu, “Efficient warpage optimization of thin shell plastics parts using response surface methodology and genetic algorithm,” Int. J. Adv. Manuf. Technol. 27, 468–472 (2006).
  26. C. C. Chen, P. L. Su, and Y. C. Lin, “Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology,” Int. J. Adv. Manuf. Technol. 45, 1087–1095 (2009).
  27. S. D. Wu and H. Zheng, “Interferogram analyses with microcomputer,” Acta Opt. Sin. 3, 815–820 (1983) (in Chinese).
  28. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering XI (Academic, 1992), Chap. 1.
  29. L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refr. Surg. 18, 652–665 (2002).
  30. J. M. Geary, Introduction to Lens Design: with Practical ZEMAX® Examples (Willmann-Bell, 2002).
  31. W. N. Charman, “Wavefront technology: past, present and future,” Cont. Lens Anterior Eye 28, 75–92 (2005).
  32. G. Taguchi, S. Chowdhury, and Y. Wu, Taguchi’s Quality Engineering Handbook (Wiley, 2005).
  33. G. S. Peace, Taguchi Methods (Addison-Wesley, 1993).

2013 (1)

M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
[CrossRef]

2012 (4)

R. O. Sánchez, A. Jorge, M. Arantza, and M. Daniel, “On the relationship between cooling step and warpage in injection molding,” Measurement 45, 1051–1056 (2012).
[CrossRef]

L. Wua, K. L. Yick, S. P. Ng, J. Yip, and K. H. Kong, “Parametric design and process parameter optimization for bra cup molding via response surface methodology,” Exp. Syst. Appl. 39, 162–171 (2012).
[CrossRef]

C. C. Tsao, “Evaluation of the drilling-induced delamination of compound core-special drills using response surface methodology based on the Taguchi method,” Int. J. Adv. Manuf. Technol. 62, 241–247 (2012).

D. J. Lizotte, R. Greiner, and D. Schuurmans, “An experimental methodology for response surface optimization methods,” J. Global Optim. 53, 699–736 (2012).
[CrossRef]

2011 (2)

G. Wang, G. Zhao, H. Li, and Y. Guan, “Research on optimization design of the heating/cooling channels for rapid heat cycle molding based on response surface methodology and constrained particle swarm optimization,” Exp. Syst. Appl. 38, 6705–6719 (2011).
[CrossRef]

N. M. Mehat and S. Kamaruddin, “Optimization of mechanical properties of recycled plastic products via optimal processing parameters using the Taguchi method,” J. Mater. Process. Technol. 211, 1989–1994 (2011).
[CrossRef]

2010 (5)

M. Altan, “Reducing shrinkage in injection moldings via the Taguchi, ANOVA and neural network methods,” Mater. Des. 31, 599–604 (2010).
[CrossRef]

J. Y. Shieh, L. K. Wang, and S. Y. Ke, “A feasible injection molding technique for the manufacturing of large diameter aspheric plastic lenses,” Opt. Rev. 17, 399–403 (2010).
[CrossRef]

K. M. Tsai, “Effect of injection molding process parameters on optical properties of lenses,” Appl. Opt. 49, 6149–6159 (2010).
[CrossRef]

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

E. Kilickap, “Modeling and optimization of burr height in drilling of Al-7075 using Taguchi method and response surface methodology,” Int. J. Adv. Manuf. Technol. 49, 911–923 (2010).

2009 (2)

B. Ozcelik and I. Sonat, “Warpage and structural analysis of thin shell plastic in the plastic injection molding,” Mater. Des. 30, 367–375 (2009).
[CrossRef]

C. C. Chen, P. L. Su, and Y. C. Lin, “Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology,” Int. J. Adv. Manuf. Technol. 45, 1087–1095 (2009).

2007 (3)

K. T. Chiang and F. P. Chang, “Analysis of shrinkage and warpage in an injection-molded part with a thin shell feature using the response surface methodology,” Int. J. Adv. Manuf. Technol. 35, 468–479 (2007).

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

D. Bas and I. H. Boyaci, “Modeling and optimization I: usability of response surface methodology,” J. Food Eng. 78, 836–845 (2007).
[CrossRef]

2006 (3)

B. Ozcelik and T. Erzurumlu, “Comparison of the warpage optimization in the plastic injection molding using ANOVA, neural network model and genetic algorithm,” J. Mater. Process. Technol. 171, 437–445 (2006).
[CrossRef]

T. Erzurumlu and B. Ozcelik, “Minimization of warpage and sink index in injection-molded thermoplastic parts using Taguchi optimization method,” Mater. Des. 27, 853–861 (2006).
[CrossRef]

H. Kurtaran and T. Erzurumlu, “Efficient warpage optimization of thin shell plastics parts using response surface methodology and genetic algorithm,” Int. J. Adv. Manuf. Technol. 27, 468–472 (2006).

2005 (3)

W. N. Charman, “Wavefront technology: past, present and future,” Cont. Lens Anterior Eye 28, 75–92 (2005).

H. Liu, Z. Lu, and F. Li, “Using diffractive optical element and ZYGO interferometer to test large-aperture convex surface,” Opt. Laser Technol. 37, 642–646 (2005).
[CrossRef]

P. Postawa and J. Koszkul, “Change in injection moulded parts shrinkage and weight as a function of processing conditions,” J. Mater. Process. Technol. 162–163, 109–115 (2005).
[CrossRef]

2002 (1)

L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refr. Surg. 18, 652–665 (2002).

1999 (1)

L. J. Moore and P. Sa, “Comparisons with the best in response surface methodology,” Stat. Probab. Lett. 44, 189–194 (1999).

1983 (1)

S. D. Wu and H. Zheng, “Interferogram analyses with microcomputer,” Acta Opt. Sin. 3, 815–820 (1983) (in Chinese).

Abdan, K.

M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
[CrossRef]

Altan, M.

M. Altan, “Reducing shrinkage in injection moldings via the Taguchi, ANOVA and neural network methods,” Mater. Des. 31, 599–604 (2010).
[CrossRef]

Applegate, R. A.

L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refr. Surg. 18, 652–665 (2002).

Arantza, M.

R. O. Sánchez, A. Jorge, M. Arantza, and M. Daniel, “On the relationship between cooling step and warpage in injection molding,” Measurement 45, 1051–1056 (2012).
[CrossRef]

Azaman, M.

M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
[CrossRef]

Bakir, B.

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

Bas, D.

D. Bas and I. H. Boyaci, “Modeling and optimization I: usability of response surface methodology,” J. Food Eng. 78, 836–845 (2007).
[CrossRef]

Boyaci, I. H.

D. Bas and I. H. Boyaci, “Modeling and optimization I: usability of response surface methodology,” J. Food Eng. 78, 836–845 (2007).
[CrossRef]

Chang, F. P.

K. T. Chiang and F. P. Chang, “Analysis of shrinkage and warpage in an injection-molded part with a thin shell feature using the response surface methodology,” Int. J. Adv. Manuf. Technol. 35, 468–479 (2007).

Charman, W. N.

W. N. Charman, “Wavefront technology: past, present and future,” Cont. Lens Anterior Eye 28, 75–92 (2005).

Chen, C. C.

C. C. Chen, P. L. Su, and Y. C. Lin, “Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology,” Int. J. Adv. Manuf. Technol. 45, 1087–1095 (2009).

Chen, T. J.

T. J. Chen, “The error simulation and experiment analysis of Hartmann Shack wavefront sensor,” Master’s thesis (Yuan Ze University, 2007).

Chiang, K. T.

K. T. Chiang and F. P. Chang, “Analysis of shrinkage and warpage in an injection-molded part with a thin shell feature using the response surface methodology,” Int. J. Adv. Manuf. Technol. 35, 468–479 (2007).

Chowdhury, S.

G. Taguchi, S. Chowdhury, and Y. Wu, Taguchi’s Quality Engineering Handbook (Wiley, 2005).

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering XI (Academic, 1992), Chap. 1.

Daniel, M.

R. O. Sánchez, A. Jorge, M. Arantza, and M. Daniel, “On the relationship between cooling step and warpage in injection molding,” Measurement 45, 1051–1056 (2012).
[CrossRef]

Erzurumlu, T.

B. Ozcelik and T. Erzurumlu, “Comparison of the warpage optimization in the plastic injection molding using ANOVA, neural network model and genetic algorithm,” J. Mater. Process. Technol. 171, 437–445 (2006).
[CrossRef]

T. Erzurumlu and B. Ozcelik, “Minimization of warpage and sink index in injection-molded thermoplastic parts using Taguchi optimization method,” Mater. Des. 27, 853–861 (2006).
[CrossRef]

H. Kurtaran and T. Erzurumlu, “Efficient warpage optimization of thin shell plastics parts using response surface methodology and genetic algorithm,” Int. J. Adv. Manuf. Technol. 27, 468–472 (2006).

Geary, J. M.

J. M. Geary, Introduction to Lens Design: with Practical ZEMAX® Examples (Willmann-Bell, 2002).

Greiner, R.

D. J. Lizotte, R. Greiner, and D. Schuurmans, “An experimental methodology for response surface optimization methods,” J. Global Optim. 53, 699–736 (2012).
[CrossRef]

Guan, Y.

G. Wang, G. Zhao, H. Li, and Y. Guan, “Research on optimization design of the heating/cooling channels for rapid heat cycle molding based on response surface methodology and constrained particle swarm optimization,” Exp. Syst. Appl. 38, 6705–6719 (2011).
[CrossRef]

Ismail, N.

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

Jorge, A.

R. O. Sánchez, A. Jorge, M. Arantza, and M. Daniel, “On the relationship between cooling step and warpage in injection molding,” Measurement 45, 1051–1056 (2012).
[CrossRef]

Kamaruddin, S.

N. M. Mehat and S. Kamaruddin, “Optimization of mechanical properties of recycled plastic products via optimal processing parameters using the Taguchi method,” J. Mater. Process. Technol. 211, 1989–1994 (2011).
[CrossRef]

Kamber, O. S.

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

Kaynak, Y.

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

Ke, S. Y.

J. Y. Shieh, L. K. Wang, and S. Y. Ke, “A feasible injection molding technique for the manufacturing of large diameter aspheric plastic lenses,” Opt. Rev. 17, 399–403 (2010).
[CrossRef]

Kilickap, E.

E. Kilickap, “Modeling and optimization of burr height in drilling of Al-7075 using Taguchi method and response surface methodology,” Int. J. Adv. Manuf. Technol. 49, 911–923 (2010).

Koklu, U.

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

Kong, K. H.

L. Wua, K. L. Yick, S. P. Ng, J. Yip, and K. H. Kong, “Parametric design and process parameter optimization for bra cup molding via response surface methodology,” Exp. Syst. Appl. 39, 162–171 (2012).
[CrossRef]

Koszkul, J.

P. Postawa and J. Koszkul, “Change in injection moulded parts shrinkage and weight as a function of processing conditions,” J. Mater. Process. Technol. 162–163, 109–115 (2005).
[CrossRef]

Kurt, M.

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

Kurtaran, H.

H. Kurtaran and T. Erzurumlu, “Efficient warpage optimization of thin shell plastics parts using response surface methodology and genetic algorithm,” Int. J. Adv. Manuf. Technol. 27, 468–472 (2006).

Lai, H. E.

P. J. Wang and H. E. Lai, “Study of residual birefringence in injection molded lenses,” in SPE ANTEC Conference Proceeding (SPE, 2007), paper 2498.

Li, F.

H. Liu, Z. Lu, and F. Li, “Using diffractive optical element and ZYGO interferometer to test large-aperture convex surface,” Opt. Laser Technol. 37, 642–646 (2005).
[CrossRef]

Li, H.

G. Wang, G. Zhao, H. Li, and Y. Guan, “Research on optimization design of the heating/cooling channels for rapid heat cycle molding based on response surface methodology and constrained particle swarm optimization,” Exp. Syst. Appl. 38, 6705–6719 (2011).
[CrossRef]

Lin, Y. C.

C. C. Chen, P. L. Su, and Y. C. Lin, “Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology,” Int. J. Adv. Manuf. Technol. 45, 1087–1095 (2009).

Liu, H.

H. Liu, Z. Lu, and F. Li, “Using diffractive optical element and ZYGO interferometer to test large-aperture convex surface,” Opt. Laser Technol. 37, 642–646 (2005).
[CrossRef]

Lizotte, D. J.

D. J. Lizotte, R. Greiner, and D. Schuurmans, “An experimental methodology for response surface optimization methods,” J. Global Optim. 53, 699–736 (2012).
[CrossRef]

Lu, Z.

H. Liu, Z. Lu, and F. Li, “Using diffractive optical element and ZYGO interferometer to test large-aperture convex surface,” Opt. Laser Technol. 37, 642–646 (2005).
[CrossRef]

Mehat, N. M.

N. M. Mehat and S. Kamaruddin, “Optimization of mechanical properties of recycled plastic products via optimal processing parameters using the Taguchi method,” J. Mater. Process. Technol. 211, 1989–1994 (2011).
[CrossRef]

Montgomery, D. C.

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2nd ed. (Wiley, 2002).

Moore, L. J.

L. J. Moore and P. Sa, “Comparisons with the best in response surface methodology,” Stat. Probab. Lett. 44, 189–194 (1999).

Mutlu, B.

M. Kurt, Y. Kaynak, O. S. Kamber, B. Mutlu, B. Bakir, and U. Koklu, “Influence of molding conditions on the shrinkage and roundness of injection molded parts,” Int. J. Adv. Manuf. Technol. 46, 571–578 (2010).

Myers, R. H.

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2nd ed. (Wiley, 2002).

Ng, S. P.

L. Wua, K. L. Yick, S. P. Ng, J. Yip, and K. H. Kong, “Parametric design and process parameter optimization for bra cup molding via response surface methodology,” Exp. Syst. Appl. 39, 162–171 (2012).
[CrossRef]

Ozcelik, B.

B. Ozcelik and I. Sonat, “Warpage and structural analysis of thin shell plastic in the plastic injection molding,” Mater. Des. 30, 367–375 (2009).
[CrossRef]

T. Erzurumlu and B. Ozcelik, “Minimization of warpage and sink index in injection-molded thermoplastic parts using Taguchi optimization method,” Mater. Des. 27, 853–861 (2006).
[CrossRef]

B. Ozcelik and T. Erzurumlu, “Comparison of the warpage optimization in the plastic injection molding using ANOVA, neural network model and genetic algorithm,” J. Mater. Process. Technol. 171, 437–445 (2006).
[CrossRef]

Peace, G. S.

G. S. Peace, Taguchi Methods (Addison-Wesley, 1993).

Postawa, P.

P. Postawa and J. Koszkul, “Change in injection moulded parts shrinkage and weight as a function of processing conditions,” J. Mater. Process. Technol. 162–163, 109–115 (2005).
[CrossRef]

Sa, P.

L. J. Moore and P. Sa, “Comparisons with the best in response surface methodology,” Stat. Probab. Lett. 44, 189–194 (1999).

Samin, R.

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

Sánchez, R. O.

R. O. Sánchez, A. Jorge, M. Arantza, and M. Daniel, “On the relationship between cooling step and warpage in injection molding,” Measurement 45, 1051–1056 (2012).
[CrossRef]

Sapuan, S. M.

M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
[CrossRef]

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

Schuurmans, D.

D. J. Lizotte, R. Greiner, and D. Schuurmans, “An experimental methodology for response surface optimization methods,” J. Global Optim. 53, 699–736 (2012).
[CrossRef]

Schweigerling, J. T.

L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refr. Surg. 18, 652–665 (2002).

Shieh, J. Y.

J. Y. Shieh, L. K. Wang, and S. Y. Ke, “A feasible injection molding technique for the manufacturing of large diameter aspheric plastic lenses,” Opt. Rev. 17, 399–403 (2010).
[CrossRef]

Sonat, I.

B. Ozcelik and I. Sonat, “Warpage and structural analysis of thin shell plastic in the plastic injection molding,” Mater. Des. 30, 367–375 (2009).
[CrossRef]

Su, P. L.

C. C. Chen, P. L. Su, and Y. C. Lin, “Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology,” Int. J. Adv. Manuf. Technol. 45, 1087–1095 (2009).

Sulaiman, S.

M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
[CrossRef]

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

Taguchi, G.

G. Taguchi, S. Chowdhury, and Y. Wu, Taguchi’s Quality Engineering Handbook (Wiley, 2005).

Tan, Y. J.

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

Tang, S. H.

S. H. Tang, Y. J. Tan, S. M. Sapuan, S. Sulaiman, N. Ismail, and R. Samin, “The use of Taguchi method in the design of plastic injection mould for reducing warpage,” J. Mater. Process. Technol. 182, 418–426 (2007).
[CrossRef]

Thibos, L.

L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refr. Surg. 18, 652–665 (2002).

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[CrossRef]

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J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering XI (Academic, 1992), Chap. 1.

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L. Wua, K. L. Yick, S. P. Ng, J. Yip, and K. H. Kong, “Parametric design and process parameter optimization for bra cup molding via response surface methodology,” Exp. Syst. Appl. 39, 162–171 (2012).
[CrossRef]

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[CrossRef]

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M. Azaman, S. M. Sapuan, S. Sulaiman, E. S. Zainudin, and K. Abdan, “Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding,” Mater. Des. 52, 1018–1026 (2013).
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[CrossRef]

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G. Wang, G. Zhao, H. Li, and Y. Guan, “Research on optimization design of the heating/cooling channels for rapid heat cycle molding based on response surface methodology and constrained particle swarm optimization,” Exp. Syst. Appl. 38, 6705–6719 (2011).
[CrossRef]

L. Wua, K. L. Yick, S. P. Ng, J. Yip, and K. H. Kong, “Parametric design and process parameter optimization for bra cup molding via response surface methodology,” Exp. Syst. Appl. 39, 162–171 (2012).
[CrossRef]

Int. J. Adv. Manuf. Technol. (6)

E. Kilickap, “Modeling and optimization of burr height in drilling of Al-7075 using Taguchi method and response surface methodology,” Int. J. Adv. Manuf. Technol. 49, 911–923 (2010).

C. C. Tsao, “Evaluation of the drilling-induced delamination of compound core-special drills using response surface methodology based on the Taguchi method,” Int. J. Adv. Manuf. Technol. 62, 241–247 (2012).

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C. C. Chen, P. L. Su, and Y. C. Lin, “Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology,” Int. J. Adv. Manuf. Technol. 45, 1087–1095 (2009).

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D. J. Lizotte, R. Greiner, and D. Schuurmans, “An experimental methodology for response surface optimization methods,” J. Global Optim. 53, 699–736 (2012).
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[CrossRef]

J. Refr. Surg. (1)

L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refr. Surg. 18, 652–665 (2002).

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T. Erzurumlu and B. Ozcelik, “Minimization of warpage and sink index in injection-molded thermoplastic parts using Taguchi optimization method,” Mater. Des. 27, 853–861 (2006).
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[CrossRef]

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J. Y. Shieh, L. K. Wang, and S. Y. Ke, “A feasible injection molding technique for the manufacturing of large diameter aspheric plastic lenses,” Opt. Rev. 17, 399–403 (2010).
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J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering XI (Academic, 1992), Chap. 1.

J. M. Geary, Introduction to Lens Design: with Practical ZEMAX® Examples (Willmann-Bell, 2002).

G. Taguchi, S. Chowdhury, and Y. Wu, Taguchi’s Quality Engineering Handbook (Wiley, 2005).

G. S. Peace, Taguchi Methods (Addison-Wesley, 1993).

P. J. Wang and H. E. Lai, “Study of residual birefringence in injection molded lenses,” in SPE ANTEC Conference Proceeding (SPE, 2007), paper 2498.

T. J. Chen, “The error simulation and experiment analysis of Hartmann Shack wavefront sensor,” Master’s thesis (Yuan Ze University, 2007).

R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2nd ed. (Wiley, 2002).

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Figures (7)

Fig. 1.
Fig. 1.

Flow chart for this study.

Fig. 2.
Fig. 2.

Dimensions of plano–convex lens.

Fig. 3.
Fig. 3.

Response graphs of S/N ratios for the optical properties of the lenses. (a) S/N ratios for astigmatism, (b) S/N ratios for coma, (c) S/N ratios for spherical aberration.

Fig. 4.
Fig. 4.

Response surface for the spherical aberration of the lens at a mold temperature of 85°C.

Fig. 5.
Fig. 5.

Contours for the astigmatism of the lens at a mold temperature of 70°C.

Fig. 6.
Fig. 6.

Process windows for a lens with astigmatisms of 0.382 and 0.39 μm at a mold temperature of 70°C.

Fig. 7.
Fig. 7.

Synthesized process windows for lenses with the three aberrations.

Tables (13)

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Table 1. Factors and Levels for the Taguchi Experiment

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Table 2. Experimental Data and S/N Ratios for L 18 ( 2 1 × 3 7 )

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Table 3. ANOVA of S/N Ratio for Astigmatisma

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Table 4. ANOVA of S/N Ratio for Comaa

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Table 5. ANOVA of S/N Ratio for Spherical Aberrationa

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Table 6. Results of Confirmation Experiment for Taguchi Method

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Table 7. Factors and Levels for 3 3 Full Factorial Experiment

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Table 8. Optical Properties for 3 3 Full Factorial Experiment

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Table 9. Regression Coefficients of Each Optical Property

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Table 10. Experimental Factor Levels after Adjustment

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Table 11. Coefficients and R 2 of the Fitted Ellipse for Process Windows

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Table 12. Best Optical Quality Values of Each Optical Property

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Table 13. Results of Confirmation Experiments for Process Windows of Lenses with Various Specified Optical Properties

Equations (7)

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

y = β 0 + i β i x i + i β i i x i 2 + i < j β i j x i x j + ε = β 0 + β 1 A + β 2 B + β 3 C + β 4 A B + β 5 A C + β 6 B C + β 7 A 2 + β 8 B 2 + β 9 C 2 + β 10 A B C + β 11 A 2 B + β 12 A 2 C + β 13 A B 2 + β 14 A C 2 + β 15 B 2 C + β 16 B C 2 + ε ,
R 2 = Regression sum of squares ( SSR ) Total sum of squares ( SST ) = 1 Error sum of squares ( SSE ) Total sum of squares ( SST ) ,
RMSE = i = 1 n ( y ^ i y i ) 2 n ,
Error ( % ) = | Experiment al results-Prediction s Experimental results | × 100 % ,
η STB = 10 lo g 10 ( 1 n i = 1 n y i 2 ) ( dB ) ,
y = β 0 + β 1 M O T + β 2 M T + β 3 C T + β 4 M O T M T + β 5 M O T C T + β 6 M T C T + β 7 M O T 2 + β 8 M T 2 + β 9 C T 2 + β 10 M O T M T C T + β 11 M O T 2 M T + β 12 M O T 2 C T + β 13 M O T M T 2 + β 1 4 M O T C T 2 + β 15 M T 2 C T + β 16 M T C T 2 ,
{ x = R x × cos t × cos θ R y × sin t × sin θ + C x y = R x × cos t × sin θ + R y × sin t × cos θ + C y ,

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