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Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization

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Abstract

Manufacturing methods using molds, such as casting and injection molding, are widely used in industries. A basic requirement when using such manufacturing methods is that design engineers must design products so that they incorporate certain geometrical features that allow the mold parts to be removed from the created solid object. In the present study, we propose a manufacturability evaluation method especially adapted for the use of molds. To evaluate the manufacturability, we introduce fictitious physical models that are described by steady-state anisotropic advection-diffusion equations. In these fictitious physical models, material domains have a virtual source term and the advection directions are aligned with the directions along which the mold parts are parted. Void regions, where the values of all fictitious physical fields are high, then represent either undercut geometries that would prevent the mold from being released, or interior voids that cannot be cast. Consequently, manufacturability can be evaluated using these fictitious physical fields. Furthermore, in the present study, we integrate this evaluation method with topology optimization and propose a scheme for imposing a molding constraint within the topology optimization procedure. This newly proposed topology optimization method can consider the position of mold parting lines prior to the detailed optimization procedure. Several numerical examples are provided to demonstrate the validity and effectiveness of the proposed method.

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References

  1. Xia Q, Shi T, Wang MY, Liu S (2010) A level set based method for the optimization of cast part. Struct Multidiscip Optim 41(5):735–747

    Article  Google Scholar 

  2. Boothroyd G, Dewhurst P, Knight WA (2002) Product design for manufacture and assembly, 2nd edn. CRC press,

  3. Joshi D, Ravi B (2010) Early castability evaluation using analytical hierarchy process. Int J Adv Manuf Technol 50(1):21–36

    Article  Google Scholar 

  4. Armillotta A, Fasoli S, Guarinoni A (2016) Cold flow defects in zinc die casting: prevention criteria using simulation and experimental investigations. Int J Adv Manuf Technol 85(1):605–622

    Article  Google Scholar 

  5. Hoque A, Halder P, Parvez M, Szecsi T (2013) Integrated manufacturing features and design-for-manufacture guidelines for reducing product cost under CAD/CAM environment. Comput Ind Eng 66(4):988–1003

    Article  Google Scholar 

  6. James BD, Spisak AB, Colella WG (2014) Design for manufacturing and assembly cost estimate methodology for transportation fuel cell systems. J Manuf Sci Eng 136(2):024,503

    Article  Google Scholar 

  7. Selvaraj P, Radhakrishnan P, Adithan M (2009) An integrated approach to design for manufacturing and assembly based on reduction of product development time and cost. Int J Adv Manuf Technol 42(1–2):13–29

    Article  Google Scholar 

  8. Lu C, Zhao W H, Yu S J (2012) Concurrent tolerance design for manufacture and assembly with a game theoretic approach. Int J Adv Manuf Technol 62(1–4):303–316

    Article  Google Scholar 

  9. Liu S G, Jin Q, Wang P, Xie R J (2014) Closed-form solutions for multi-objective tolerance optimization. Int J Adv Manuf Technol 70(9-12):1859–1866

    Article  Google Scholar 

  10. Salonitis K (2016) Design for additive manufacturing based on the axiomatic design method. Int J Adv Manuf Technol 87(1):989–996

    Article  Google Scholar 

  11. Prager W (1974) A note on discretized michell structures. Comput Methods Appl Mech Eng 3(3):349–355

    Article  MATH  Google Scholar 

  12. Svanberg K (1981) Optimization of geometry in truss design. Comput Methods Appl Mech Eng 28(1):63–80

    Article  MATH  Google Scholar 

  13. Pironneau O (1984) Optimal shape design for elliptic systems. Springer

  14. Sokolowski J, Zolesio JP (1992) Introduction to shape optimization. Springer

  15. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224

    Article  MathSciNet  MATH  Google Scholar 

  16. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202

    Article  Google Scholar 

  17. Yaji K, Yamada T, Yoshino M, Matsumoto T, Izui K, Nishiwaki S (2014) Topology optimization using the lattice boltzmann method incorporating level set boundary expressions. J Comput Phys 274:158–181

    Article  MathSciNet  MATH  Google Scholar 

  18. Otomori M, Yamada T, Izui K, Nishiwaki S, Andkjær J (2012) A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials. Comput Methods Appl Mech Eng 237:192–211

    Article  MathSciNet  MATH  Google Scholar 

  19. Noguchi Y, Yamada T, Otomori M, Izui K, Nishiwaki S (2017) An acoustic metasurface design for wave motion conversion of longitudinal waves to transverse waves using topology optimization. Appl Phys Lett 107 (22):221,909

    Article  Google Scholar 

  20. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654

    MATH  Google Scholar 

  21. Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J Comput Phys 79(1):12–49

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang M Y, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1):227–246

    Article  MathSciNet  MATH  Google Scholar 

  23. Allaire G, Jouve F, Toader A M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393

    Article  MathSciNet  MATH  Google Scholar 

  24. Bharanidaran R, Ramesh T (2017) A modified post-processing technique to design a compliant based microgripper with a plunger using topological optimization. Int J Adv Manuf Technol :1–10

  25. Liu J, Ma Y (2016) A survey of manufacturing oriented topology optimization methods. Adv Eng Softw 100:161–175

    Article  Google Scholar 

  26. Poulsen T A (2003) A new scheme for imposing a minimum length scale in topology optimization. Int J Numer Methods Eng 57(6):741–760

    Article  MathSciNet  MATH  Google Scholar 

  27. Guest J K, Prévost J H, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhou M, Lazarov BS, Wang F, Sigmund O (2017) Minimum length scale in topology optimization by geometric constraints. Comput Methods Appl Mech Eng 293:266–282

    Article  MathSciNet  Google Scholar 

  29. Guest J K (2009) Imposing maximum length scale in topology optimization. Struct Multidiscip Optim 37 (5):463–473

    Article  MathSciNet  MATH  Google Scholar 

  30. Chen S, Wang M Y, Liu A Q (2008) Shape feature control in structural topology optimization. Comput Aided Des 40(9):951–962

    Article  Google Scholar 

  31. Guo X, Zhang W, Zhong W (2014) Explicit feature control in structural topology optimization via level set method. Comput Methods Appl Mech Eng 272:354–378

    Article  MathSciNet  MATH  Google Scholar 

  32. Allaire G, Jouve F, Michailidis G (2016) Thickness control in structural optimization via a level set method. Struct Multidiscip Optim 53(6):1349–1382

    Article  MathSciNet  Google Scholar 

  33. Brackett D, Ashcroft I, Hague R (2011) Topology optimization for additive manufacturing. In: Proceedings of the solid freeform fabrication symposium. Austin, pp 348–362

  34. Leary M, Merli L, Torti F, Mazur M, Brandt M (2014) Optimal topology for additive manufacture: a method for enabling additive manufacture of support-free optimal structures. Mater Des 63:678–690

    Article  Google Scholar 

  35. Langelaar M (2016) Topology optimization of 3d self-supporting structures for additive manufacturing. Additive Manufacturing 12:60–70

    Article  Google Scholar 

  36. Gaynor AT, Guest JK (2016) Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design. Struct Multidiscip Optim:1–16

  37. Li Q, Chen W, Liu S, Tong L (2016) Structural topology optimization considering connectivity constraint. Struct Multidiscip Optim

  38. Zhou M, Fleury R, Shyy YK, Thomas H, Brennan J (2002) Progress in topology optimization with manufacturing constraints. In: Proceedings of the 9th AIAA MDO conference AIAA-2002-4901

  39. Allaire G, Jouve F, Michailidis G (2017) Molding direction constraints in structural optimization via a level-set method

  40. Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199(45–48):2876–2891

    Article  MathSciNet  MATH  Google Scholar 

  41. Li H, Li P, Gao L, Zhang L, Wu T (2017) A level set method for topological shape optimization of 3d structures with extrusion constraints. Comput Methods Appl Mech Eng 283:615– 635

    Article  MathSciNet  Google Scholar 

  42. Allaire G, De Gournay F, Jouve F, Toader A (2005) Structural optimization using topological and shape sensitivity via a level set method. Control Cybern 34(1):59

    MathSciNet  MATH  Google Scholar 

  43. Eschenauer H A, Kobelev V V, Schumacher A (1994) Bubble method for topology and shape optimization of structures. Struct Optim 8(1):42–51

    Article  Google Scholar 

  44. Otomori M, Yamada T, Izui K, Nishiwaki S (2014) Matlab code for a level set-based topology optimization method using a reaction diffusion equation. Struct Multidiscip Optim :1–14

  45. Allaire G (2002) Shape optimization by the homogenization method, vol 146. Springer, New York

    Book  MATH  Google Scholar 

  46. Sigmund O (1997) On the design of compliant mechanisms using topology optimization*. J Struct Mech 25 (4):493– 524

    Google Scholar 

  47. Nishiwaki S, Frecker M I, Min S, Kikuchi N (1998) Topology optimization of compliant mechanisms using the homogenization method. Int J Numer Methods Eng 42:535–559

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgment

The authors are grateful to co-researchers in the Mitsubishi Electric Corporation for helpful discussions. The authors also sincerely appreciate the support received from the research scholar of Toyota Physical & Chemical Research Institute.

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Correspondence to Yuki Sato.

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Sato, Y., Yamada, T., Izui, K. et al. Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization. Int J Adv Manuf Technol 92, 1391–1409 (2017). https://doi.org/10.1007/s00170-017-0218-0

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