Multi-objective optimization of glass multi-station bending machining for smartphone curved screen

  • Wenbin He
  • Zhijun Chen
  • Wuyi MingEmail author
  • Jinguang Du
  • Yang Cao
  • Jun Ma
  • Aiyun Wei
Technical Paper


Glass multi-station bending machining (GMBM) is a high-precision and efficient glass processing technique for smartphone curved screen in 3C industry. In this paper, simulation model of the GMBM of smartphone curved screen was researched by using MSC Marc software. The stress relaxation and structural relaxation models of glass material were used in the numerical model to accurately predict the forming process of the glass component. The effects of process parameters of GMBM, namely heating rate (HR), holding time, bending temperature (BT), bending pressure and cooling rate (CR), on the product quality characteristics (residual stress and shape deviation) and energy efficiency were analyzed based on orthogonal experiments. It can be found that the BT, CR and HR have extremely important effects on product residual stress, shape deviation and energy efficiency. Furthermore, a multi-objective optimization method based on NSGA-III (a non-dominant sorting genetic algorithms based on reference points) was applied to efficiently solve the optimization problem between glass product quality and energy efficiency. The optimal parameter schemes with high quality and low energy efficiency were obtained by the Pareto front of multi-objective, and the average prediction errors of the numerical results by the optimized schemes are no more than 20% through confirm experiments. The optimized schemes improve the stability of the process of GMBM, which can deal with the challenge of green manufacturing.


Glass multi-station bending machining (GMBM) Simulation Multi-objective optimization Residual stress Shape deviation Energy efficiency 



This research is supported by the Natural Science Foundation of Guangdong Province (2018A030313679) and the Natural Science Foundation of Henan Province (Grant No. 182300410215). In addition, this research is also supported by Natural Science Foundation (Grant No. 11602230), by Local Innovative and Research Team Project of Guangdong Pearl River Talents Program (Grant No. 2017BT01G167) and by the development program (2017B030314146) of Guangdong Provincial Key Laboratory.


  1. 1.
    Blair G, Clarence C (1974) Method for molding glass lens. U.S. Patent. 3833347Google Scholar
  2. 2.
    Cha DH, Park HS, Hwang Y (2011) Experimental study of glass molding process and transcription characteristics of mold surface in molding of aspheric glass lenses. Opt Rev 18(2):241–246CrossRefGoogle Scholar
  3. 3.
    Nieto D, Flores-Arias MT, O’Connor G, Gomez-Reino C (2010) Laser direct-write technique for fabricating microlens arrays on soda-lime glass with a Nd:YVO4 laser. Appl Opt 49(26):4979–4983CrossRefGoogle Scholar
  4. 4.
    Yi AY, Jain A (2005) Compression molding of aspherical glass lenses—a combined experimental and numerical analysis. J Am Ceram Soc 88(3):579–586CrossRefGoogle Scholar
  5. 5.
    Ananthasayanam B, Joseph PF, Joshi D (2012) Final shape of precision molded optics: part I—computational approach, material definitions and the effect of lens shape. J Therm Stress 35(6):550–578CrossRefGoogle Scholar
  6. 6.
    Yan J, Zhou T, Masuda J (2009) Modeling high-temperature glass molding process by coupling heat transfer and viscous deformation analysis. Precis Eng 33(2):150–159CrossRefGoogle Scholar
  7. 7.
    Jain A, Yi AY, Xie X (2006) Finite element modelling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass. Model Simul Mater Sci 14(3):465–477CrossRefGoogle Scholar
  8. 8.
    Zhou T, Yan J, Kuriyagawa T (2007) Evaluating the viscoelastic properties of glass above transition temperature for numerical modeling of lens molding process. Proc SPIE 6624:175–182Google Scholar
  9. 9.
    Zhou T, Yan J, Masuda J (2009) Investigation on the viscoelasticity of optical glass in ultraprecision lens molding process. J Mater Process Technol 209(9):4484–4489CrossRefGoogle Scholar
  10. 10.
    Saotome Y, Imai K, Sawanobori N (2003) Microformability of optical glasses for precision molding. J Mater Process Technol 140(1–3):379–384CrossRefGoogle Scholar
  11. 11.
    Jain A, Firestone GC, Yi AY (2005) Viscosity measurement by cylindrical compression for numerical modeling of precision lens molding process. J Am Ceram Soc 88(9):2409–2414CrossRefGoogle Scholar
  12. 12.
    Jain A, Yi AY (2005) Numerical modeling of viscoelastic stress relaxation during glass lens forming process. J Am Ceram Soc 88(3):530–535CrossRefGoogle Scholar
  13. 13.
    Jain A, Yi AY (2006) Finite element modeling of structural relaxation during annealing of a precision-molded glass lens. J Manuf Sci Eng 128(3):683–690CrossRefGoogle Scholar
  14. 14.
    Zhou J, Shi T, Hu Y (2013) Numerical simulation in compression molding of glass lens. In: CASE, IEEE, pp 669–674Google Scholar
  15. 15.
    Nielsen JH, Olesen JF, Poulsen PN (2010) Finite element implementation of a glass tempering model in three dimensions. Comput Struct 88(17–18):963–972CrossRefGoogle Scholar
  16. 16.
    Ananthasayanam B (2008) Computational modeling of precision molding of aspheric glass optics. Mechanical Engineering, Doctorate of Philosophy, Clemson UniversityGoogle Scholar
  17. 17.
    Zhou T, Yan J, Masuda J (2011) Investigation on shape transferability in ultraprecision glass molding press for microgrooves. Precis Eng 35(2):214–220CrossRefGoogle Scholar
  18. 18.
    Zhou TF, Yan JW, Masda J (2009) Investigation on ultraprecision molding process for microgrooves on glass plate. In: the 3rd international conference of Asian society for precision engineering and nanotechnology, kitakyushu, Japan, pp 65–68Google Scholar
  19. 19.
    Jain A (2006) Experimental study and numerical anslysis of compression molding process for manufacturing precision aspherical glass lenses. The Ohio State University, ColumbusGoogle Scholar
  20. 20.
    Anurag Jain (2004) Numerical simulation of compression molding of aspherical glass lenses. AIP 712:239–244Google Scholar
  21. 21.
    Aronen A (2012) Modelling of deformations and stresses in glass tempering. Tampereen teknillinen yliopisto. Julkaisu-Tampere University of Technology. Publication, p 1036Google Scholar
  22. 22.
    Aronen A, Karvinen R (2018) Effect of glass temperature before cooling and cooling rate on residual stresses in tempering. Glass Struct Eng 3(1):3–15CrossRefGoogle Scholar
  23. 23.
    Schneider J, Hilcken J, Aronen A (2016) Stress relaxation in tempered glass caused by heat soak testing. Eng Struct 122:42–49CrossRefGoogle Scholar
  24. 24.
    Scherer GW (1986) Relaxation in glass and composites. Wiley, New YorkGoogle Scholar
  25. 25.
    Kurkjian C (1963) Relaxation of torsional stress in transformation range of soda-lime-silica glass. Phys Chem Glasses 4(4):128–36Google Scholar
  26. 26.
    Duffrene L, Gy R (1997) Viscoelastic constants of a soda-lime-silica glass. J Non Cryst Solids 211(1):30–38CrossRefGoogle Scholar
  27. 27.
    Hoque A, Fischer CE, Wu WT (2001) Simulation of glass pressing process using 3-dimensional large deformation finite element software. Scientific Forming Technologies Corporation, Columbus, pp 156–163Google Scholar
  28. 28.
    Druma C, Alam MK, Druma AM (2004) Finite element analysis of TV panel glass during cooling. Mater Manuf Process 19(6):1171–1187CrossRefGoogle Scholar
  29. 29.
    Zhao D, Liu P, He L (2016) Numerical and experimental investigation of the heating process of glass thermal slumping. J Opt Soc Korea 20(2):314–320CrossRefGoogle Scholar
  30. 30.
    Soules TF, Busbey RF, Rekhson SM (1987) Finite-element calculation of stresses in glass parts undergoing viscous relaxation. J Am Ceram Soc 70(2):90–95CrossRefGoogle Scholar
  31. 31.
    Narayanaswamy OS (1971) A model of structural relaxation in glass. J Am Ceram Soc 54(10):491–498CrossRefGoogle Scholar
  32. 32.
    Richet P, Bottinga Y, Tequi C (1984) Heat capacity of sodium silicate liquids. J Am Ceram Soc 67(1):6–8Google Scholar
  33. 33.
    Mann D, Field RE, Viskanta R (1992) Determination of specific heat and true thermal conductivity of glass from dynamic temperature data. Waerme-und Stoffuebertragung 27(4):225–231CrossRefGoogle Scholar
  34. 34.
    Sharp DE, Ginther LB (2010) Effect of composition and temperature on the specific heat of glass. J Am Ceram Soc 34(9):260–271CrossRefGoogle Scholar
  35. 35.
    Storck K, Karlsson M, Loyd D (1994) Analysis of the blank mould-a transient heat transfer problem in glass, forming. WIT Trans Eng Sci 5.
  36. 36.
    Su CH (2011) Mold shape compensation and residual stress analysis in molding process of aspherical glass lenes. National chiao Tung University, Hsinchu CityGoogle Scholar
  37. 37.
    Yi AY, Tao B, Klocke F (2011) Residual stresses in glass after molding and its influence on optical properties. Procedia Eng 19(1):402–406CrossRefGoogle Scholar
  38. 38.
    Pourmoghaddam N, Schneider J (2018) Finite-element analysis of the residual stresses in tempered glass plates with holes or cut-outs. Glass Struct Eng 3(1):17–37CrossRefGoogle Scholar
  39. 39.
    Tao B, He P, Shen L (2014) Quantitatively measurement and analysis of residual stresses in molded aspherical glass lenses. Int J Adv Manuf Technol 74(9–12):1167–1174CrossRefGoogle Scholar
  40. 40.
    He W, He S, Du J (2019) Fiber orientations effect on process performance for wire cut electrical discharge machining (WEDM) of 2D C/SiC composite. Int J Adv Manuf Technol 102(1–4):507–518CrossRefGoogle Scholar
  41. 41.
    Dumbhare PA, Dubey S, Deshpande YV (2018) Modelling and multi-objective optimization of surface roughness and kerf taper angle in abrasive water jet machining of steel. J Braz Soc Mech Sci Eng 40(5):259CrossRefGoogle Scholar
  42. 42.
    Harmesh K, Alakesh M, Rajesh K (2018) Modeling and desirability approach-based multi-response optimization of WEDM parameters in machining of aluminum metal matrix composite. J Braz Soc Mech Sci Eng 40(9):458CrossRefGoogle Scholar
  43. 43.
    Bouacha K, Terrab A (2016) Hard turning behavior improvement using NSGA-II and PSO-NN hybrid model. Int J Adv Manuf Technol 86(9–12):1–20Google Scholar
  44. 44.
    Chunrong W, Jing Z, Erdong X (2018) Multi-objective optimal design of a novel multi-function rescue attachment based on improved NSGA-II. J Braz Soc Mech Sci Eng 40(7):344CrossRefGoogle Scholar
  45. 45.
    Darvish Damavandi M, Safikhani H, Yahyaabadi M (2017) Multi-objective optimization of asymmetric v-shaped ribs in a cooling channel using CFD, artificial neural networks and genetic algorithms. J Braz Soc Mech Sci Eng 39(6):2319–2329CrossRefGoogle Scholar
  46. 46.
    Ming W, Zhang Z (2019) Comparative study of energy efficiency and environmental impact in magnetic field assisted and conventional electrical discharge machining. J Clean Prod 214:12–28CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Wenbin He
    • 1
  • Zhijun Chen
    • 1
  • Wuyi Ming
    • 1
    • 2
    • 3
    Email author
  • Jinguang Du
    • 1
  • Yang Cao
    • 1
  • Jun Ma
    • 1
  • Aiyun Wei
    • 1
  1. 1.Department of Electromechanical Science and EngineeringZhengzhou University of Light IndustryZhengzhouChina
  2. 2.State Key Lab of Digital Manufacturing Equipment Technology, School of Mechanical Science and EngineeringHuazhong University of Science TechnologyWuhanChina
  3. 3.Guangdong HUST Industrial Technology Research InstituteGuangdong Provincial Key Laboratory of Digital Manufacturing EquipmentDongguanChina

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