Skip to main content
Log in

Simultaneous optimization of cast part and parting direction using level set method

  • Industrial Application
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Parting direction is one of the main parameters that significantly affect mouldability and manufacturing costs of a cast part. In conventional optimal design of cast part, a parting direction is pre-selected by a designer and fixed throughout the optimization. However, when the optimization is performed with a different parting direction, the resulting design will also be different, and more importantly it will end up with different working performance. Therefore, we take the parting direction as a design variable in the optimization of a cast part so that the working performance can be optimized as much as possible. With these goals, a level set based method is proposed for the simultaneous optimization of cast part and parting direction. In each iteration, an optimal parting direction is first computed for the current structure, then the boundary of the current structure is updated by a design velocity that guarantees the design be moldable with the optimal parting direction. Therefore, although the parting direction may be changed during the optimization, the structure will always be moldable in the current parting direction. Numerical examples are provided in 3D.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Allaire G, Jouve F (2006) Coupling the level set method and the topological gradient in structural optimization. In: Bends\({\o}\)e MP, Olhoff, N, Sigmund O (Eds) IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, vol 137. pp 3–12

  • Allaire G, Jouve F, Toader AM (2002) A level-set method for shape optimization. C.R., Acad, Sci. Paris, Serie I 334:1–6

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Baumgartner A, Harzheim L, Mettheck C (1992) SKO (Soft Kill Option): the biological way to find an optimum structure topology. Int J Fatigue 14:387–393

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology Optimization: Theory, Methods and Applications. Springer-Verlag, Berlin

    Google Scholar 

  • Burger M (2003) A framework for the construction of level set methods for shape optimization and reconstruction. Interfaces Free Bound 5:301–329

    Article  MATH  MathSciNet  Google Scholar 

  • Burger M, Hackl B, Ring W (2004) Incorporating topological derivatives into level set methods. J Comput Phys 194:344–362

    Article  MATH  MathSciNet  Google Scholar 

  • Céa J, Garreau S, Guillaume P, Masmoudi M (2000) The shape and topological optimizations connection. Computer Methods in Applied Mechanics and Engineering. 188:713–726

    Article  MATH  MathSciNet  Google Scholar 

  • Chen LL, Chou SY, Woo TC (1993) Parting directions for mould and die design. Computer-Aided Design 25:762–768

    Article  MATH  Google Scholar 

  • Eschenauer HA, Kobelev HA, Schumacher A (1994) Bubble method for topology and shape optimization of structures. Struct Optim 8:142–151

    Article  Google Scholar 

  • Fu MW, Fuh JYH, Nee, AYC (1999) Generation of optimal parting direction based on undercut features in injection molded parts. IIE Trans 31:947–955

    Google Scholar 

  • Fu MW, Nee AYC, Fuh JYH (2002) The application of surface visibility and moldability to parting line generation. Journal of Computer-Aided Design 34:469–480

    Article  Google Scholar 

  • Gournay FD (2006) Velocity extension for the level-set method and multiple eigenvalues in shape optimization. SIAM J Control Optim 45:343–367

    Article  MATH  MathSciNet  Google Scholar 

  • Harzheim L, Graf G (1995) Optimization of engineering components with the sko method. In: the ninth international conference on vehicle structural mechanics and CAE, pp 235–243

  • Harzheim L, Graf G (2002) Topshape: an attempt to create design proposals including manufacturing constraints. Int J Veh Des 28:389–408

    Article  Google Scholar 

  • Harzheim L, Graf G (2005) A review of optimization of cast parts using topology optimization: I—topology optimization without manufacturing constraints. Struct Multidiscipl Optim 30:491–497

    Article  Google Scholar 

  • Harzheim L, Graf G (2006)A review of optimization of cast parts using topology optimization: II—topology optimization with manufacturing constraints. Struct Multidiscipl Optim 31:388–399

    Article  Google Scholar 

  • He L, Kao CY, Osher S (2007) Incorporating topological derivatives into shape derivative based level set methods. J Comput Phys 225:891–909

    Article  MATH  MathSciNet  Google Scholar 

  • Leiva JP, Watson BC, Kosaka I (1999) Modern structural optimization concepts applied to topology optimization. In: 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference. St. Louis, MO

  • Leiva JP, Watson BC, Kosaka I (2004) An analytical directional growth topology parameterization to enforce manufacturing requirements. In: 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference. Palm Springs, CA

  • Leiva JP, Watson BC, Kosaka I (2004) An analytical bi-directional growth parameterization to obtain optimal castable topology designs. In: 10th AIAA/ISSMO symposium on multidisciplinary analysis and optimization. Albany, NY

  • Li WS, Martin RR, Langbein FC (2007) Generating smooth parting lines for mold deisgn for meshes. In: ACM symposium on Solid and Physical Modeling. Beijing, China, pp 193–204

    Chapter  Google Scholar 

  • Mattheck C (1990) Design and growth rule for biological structures and their application in engineering. Fatigue Fract Eng Mater Struct 13:535–550

    Article  Google Scholar 

  • Nee AYC, Fu MW, Fuh JYH, Lee KS, Zhang YF (1997) Determination of optimal parting direction in plastic injection mold design. annals of the. Annals of CIRP 46:429–432

    Article  Google Scholar 

  • Nocedal J, Wright SJ (1999) Numerical Optimization. Springer

  • Osher S, Fedkiw R (2002) Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York

    Google Scholar 

  • Osher S, Santosa F (2001) Level-set methods for optimization problems involving geometry and constraints: frequencies of a two-density inhomogeneous drum. J Comput Phys 171:272–288

    Article  MATH  MathSciNet  Google Scholar 

  • Osher S, Sethian JA (1988) Front propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J Comput Phys 78:12–49

    Article  MathSciNet  Google Scholar 

  • Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4:250–254

    Article  Google Scholar 

  • Sethian JA (1999) Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge Monographs on Applied and Computational Mathematics, 2nd edn. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163:489–528

    Article  MATH  MathSciNet  Google Scholar 

  • Sokolowski J, Zochowski A (1999) On the topological derivative in shape optimization. SIAM J Control Optim 37:1251–1272

    Article  MATH  MathSciNet  Google Scholar 

  • Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization. Comput. Methods Appl Mech Eng 192:227–246

    Article  MATH  Google Scholar 

  • Wang SY, Wang MY (2005) A moving superimposed finite element method for structural topology optimization. Comput. Methods Appl Mech Eng 65:1892–1922

    Google Scholar 

  • Weinstein M, Manoochehri S (1996) Geometric influence of a molded part on the draw direction range and parting line locations. J Mech Des 118:29–C39

    Article  Google Scholar 

  • Weinstein M, Manoochehri S (1997) Optimum parting line design of molded and cast parts for manufacturability. Journal of manufacturing Systems 16:1–12

    Article  Google Scholar 

  • Xia Q, Shi TL, Wang MY, Liu SY (2010) A level set based method for the optimization of cast part. Comput. Methods Appl Mech Eng 41:735–747

    Google Scholar 

  • Xia Q, Wang MY (2008) Topology optimization of thermoelastic structures using level set method. Comput Mech 42:837–857

    Article  MATH  Google Scholar 

  • Zhou M, Shyy YK, Thomas HL (2001) Topology optimization with manufacturing constraints. In: 4th world congress of structural and multidisciplinary optimization. Dalian, China

    Google Scholar 

Download references

Acknowledgments

This research work is partly supported by the Fundamental Research Funds for the Central Universities, HUST, (Grant No. Q2009009), the Natural Science Foundation of Hubei province (Grant No. 2009CDB321), the National Fundamental Research Programme of China (Grant No. 2009CB724204), which the authors gratefully acknowledge. The insightful comments of the reviewers’ are cordially appreciated.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tielin Shi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, Q., Shi, T., Wang, M.Y. et al. Simultaneous optimization of cast part and parting direction using level set method. Struct Multidisc Optim 44, 751–759 (2011). https://doi.org/10.1007/s00158-011-0690-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-011-0690-3

Keywords

Navigation