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Topology optimization for hybrid additive-subtractive manufacturing

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Abstract

Hybrid additive-subtractive manufacturing is gaining popularity by making full use of geometry complexity produced by additive manufacturing and dimensional accuracy derived from subtractive machining. Part design for this hybrid manufacturing approach has been done by trial-and-error, and no dedicated design methodology exists for this manufacturing approach. To address this issue, this work presents a topology optimization method for hybrid additive and subtractive manufacturing. To be specific, the boundary segments of the input design domain are categorized into two types: (i) Freeform boundary segments freely evolve through the casting SIMP method, and (ii) shape preserved boundary segments suppress the freeform evolvement and are composed of machining features through a feature fitting algorithm. Given the manufacturing strategy, the topology design is produced through additive manufacturing and the shape preserved boundary segments will be processed by post-machining. This novel topology optimization algorithm is developed under a unified SIMP and level set framework. The effectiveness of the algorithm is proved through a few numerical case studies.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  • Allaire G, Jouve F, Michailidis G (2013) Casting constraints in structural optimization via a level-set method. 10th World Congress Struct Multidisciplinary Optimization, Orlando, Florida, USA

  • Allaire G, Jouve F, Michailidis G (2016) Thickness control in structural optimization via a level set method. Struct Multidisc Optim 53:1349–4382

    Article  MathSciNet  Google Scholar 

  • Bendsoe MP, Sigmund O (2004) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  • Bracket D, Ashcroft I, Hague R (2011) Topology optimization for additive manufacturing. 22nd Annual International Solid Freeform Fabrication Symposium, Austin, TX

  • Chen JQ, Shapiro V, Suresh K, Tsukanov I (2007) Shape optimization with topological changes and parametric control. Int J Numer Methods Eng 71:313–346

    Article  MathSciNet  MATH  Google Scholar 

  • Chen JQ, Freytag M, Shapiro V (2008a) Shape sensitivity of constructively represented geometric models. Comput Aided Geom Des 25:470–488

    Article  MathSciNet  MATH  Google Scholar 

  • Chen SK, Wang MY, Liu AQ (2008b) Shape feature control in structural topology optimization. Comput Aided Des 40:951–962

    Article  Google Scholar 

  • Cheng GD, Mei YL, Wang XM (2006) A feature-based structural topology optimization method. IUTAM Symp Topologis Design Optimization Struct, Mach Mater, 505–514

  • Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidisc Optim 49:1–38

    Article  MathSciNet  Google Scholar 

  • Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54:331–390

    Article  Google Scholar 

  • Flynn JM, Shokrani A, Newman ST, Dhokia V (2016) Hybrid additive and subtractive machine tools – research and industrial developments. Int J Mach Tools Manuf 101:79–101

    Article  Google Scholar 

  • Gao HH, Zhu JH, Zhang WH, Zhou Y (2015) An improved adaptive constraint aggregation for integrated layout and topology optimization. Comput Methods Appl Mech Eng 289:387–408

    Article  MathSciNet  Google Scholar 

  • Garden N, Schneider A (2015) Topological optimization of internal patterns and support in additive manufacturing. J Manuf Syst 37:417–425

    Article  Google Scholar 

  • Gaynor AT, Meisel NA, Williams CB, Guest JK (2014) Multiple-material topology optimization of compliant mechanisms created via PolyJet three-dimensional printing. J Manuf Sci Eng 136:061015

    Article  Google Scholar 

  • Gersborg AR, Andreasen CS (2011) An explicit parameterization for casting constraints in gradient driven topology optimization. Struct Multidisc Optim 44:875–881

    Article  Google Scholar 

  • Gopalakrishnan SH, Suresh K (2008) Feature sensitivity: a generalization of topological sensitivity. Finite Elem Anal Des 44:696–704

    Article  MathSciNet  Google Scholar 

  • Guest JK (2009a) Topology optimization with multiple phase projection. Comput Methods Appl Mech Eng 199:123–135

    Article  MathSciNet  MATH  Google Scholar 

  • Guest JK (2009b) Imposing maximum length scale in topology optimization. Struct Multidisc Optim 37:463–473

    Article  MathSciNet  MATH  Google Scholar 

  • Guest JK (2015) Optimizing the layout of discrete objects in structures and materials: a projection-based topology optimization approach. Comput Methods Appl Mech Eng 283:330–351

    Article  Google Scholar 

  • Guest JK, Zhu M (2012) Casting and milling restrictions in topology optimization via projection-based algorithms. Proc ASME 2012 Int Design Eng Tech Conf Comput Inform Eng Conf, Chicago, IL, USA

  • Guest JK, Prevost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61:238–254

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Guo X, Zhang WS, Zhong WL (2014b) Doing topology optimization explicitly and geometrically – a new moving morphable components based framework. J Appl Mech 81:081009-1:12

  • Ha SH, Guest JK (2014) Optimizing inclusion shapes and patterns in periodic materials using discrete object projection. Struct Multidiscip Optim 50:65–80

    Article  Google Scholar 

  • Hoque ASM, Halder PK, Parvez MS, Szecsi T (2013) Integrated manufacturing features and design-for-manufacture guidelines for reducing product cost under CAD/CAM environment. Comput Ind Eng 66:988–1003

    Article  Google Scholar 

  • Kang Z, Wang YQ (2013) Integrated topology optimization with embedded movable holes based on combined description by material density and level sets. Comput Methods Appl Mech Eng 255:1–13

    Article  MathSciNet  MATH  Google Scholar 

  • Kang M, Kim G, Eum K, Park MW, Kim JK (2014) A classification of multi-axis features based on manufacturing process. Int J Precis Eng Manuf 15:1255–1263

    Article  Google Scholar 

  • Kang Z, Wang YG, Wang YQ (2016) Structural topology optimization with minimum distance control of multiphase embedded components by level set method. Comput Methods Appl Mech Eng 306:299–318

    Article  MathSciNet  Google Scholar 

  • Khanoki SA, Pasini D (2012) Multiscale design and multiobjective optimization of orthopedic hip implants with functionally graded cellular material. J Biomech Eng 134:031004

    Article  Google Scholar 

  • Lauwers B, Klocke F, Klink A, Tekkaya AE, Neugebauer R, Mcintosh D (2014) Hybrid processes in manufacturing. CIRP Ann Manuf Technol 63:561–583

    Article  Google Scholar 

  • Lazarov BS, Wang FW, Sigmund O (2016) Length scale and manufacturability in density-based topology optimization. Arch Appl Mech 86:189–218

    Article  Google Scholar 

  • 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 

  • Liu JK (2016) Guidelines for AM part consolidation. Virtual Phys Prototyp 11:133–141

    Article  Google Scholar 

  • Liu JK, Ma YS (2015) 3D level-set topology optimization: a machining feature-based approach. Struct Multidisc Optim 52:563–582

    Article  MathSciNet  Google Scholar 

  • Liu JK, Ma YS, Fu JY, Duke K (2015a) A novel CACD/CAD/CAE integrated design framework for fiber-reinforced plastic parts. Adv Eng Softw 87:13–29

    Article  Google Scholar 

  • Liu ST, Li Q, Chen WJ, Hu R, Tong LY (2015b) H-DGTP – a Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures. Struct Multidisc Optim 52:903–913

    Article  MathSciNet  Google Scholar 

  • Lu JN, Chen YH (2012) Manufacturable mechanical part design with constrained topology optimization. J Eng Manuf 226:1727–1735

    Article  Google Scholar 

  • Luo JZ, Luo Z, Chen SK, Tong LY, Wang MY (2008) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198:318–331

    Article  MATH  Google Scholar 

  • Masmiati N, Sarhan AAD, Hamdi M (2012) Optimizing the cutting parameters for better surface quality in 2.5D cutting utilizing titanium coated carbide ball end mill. Int J Precis Eng Manuf 13:2097–2102

    Article  Google Scholar 

  • Mei YL, Wang XM, Cheng GD (2008) A feature-based topological optimization for structure design. Adv Eng Softw 39:71–87

    Article  Google Scholar 

  • Meisel N, Williams C (2015) An investigation of key design for additive manufacturing constraints in multimaterial three-dimensional printing. J Mech Des 137:111406

    Article  Google Scholar 

  • Munk DJ, Vio GA, Steven GP (2015) Topology optimization methods using evolutionary algorithms: a review. Struct Multidisc Optim. doi:10.1007/s00158-015-1261-9

    MathSciNet  Google Scholar 

  • Norato JA, Bell BK, Tortorelli DA (2015) A geometry projection method for continuum-based topology optimization with discrete elements. Comput Methods Appl Mech Eng 293:306–327

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Rozvany GIN (2001) Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct Multidisc Optim 21:90–108

    Article  Google Scholar 

  • Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37:217–237

    Article  MathSciNet  MATH  Google Scholar 

  • Schevenels M, Lazarov BS, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Methods Appl Mech Eng 200:3613–3627

    Article  MATH  Google Scholar 

  • Schramm U, Zhou M (2006) Recent developments in the commercial implementation of topology optimization. In: IUTAM symposium on topological design optimization of structures, machines and materials, Springer 137:239–248

  • Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424

    Article  Google Scholar 

  • Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sin 25:277–239

    Article  MATH  Google Scholar 

  • Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidisc Optim 48:1031–1055

    Article  MathSciNet  Google Scholar 

  • Stromberg N (2010) Topology optimization of structures with manufacturing and unilateral contact constraints by minimizing an adjustable compliance-volume product. Struct Multidisc Optim 42:341–350

    Article  MathSciNet  MATH  Google Scholar 

  • Tang YL, Kurtz A, Zhao YF (2015) Bidirectional evolutionary structural optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing. Comput Aided Des 69:91–101

    Article  Google Scholar 

  • Ulu E, Korkmaz E, Yay K, Ozdoganlar OB, Kara LB (2015) Enhancing the structural performance of additively manufactured objects through build orientation optimization. J Mech Des 137:111410

    Article  Google Scholar 

  • van Dijk NP, Maute K, Langelaar M, van Keulen F (2013) Level-set methods for structural topology optimization: a review. Struct Multidisc Optim 48:437–472

    Article  MathSciNet  Google Scholar 

  • Verma AK, Rajotia S (2008) A hint-based machining feature recognition system for 2.5D parts. Int J Prod Res 46:1515–1537

    Article  MATH  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  MathSciNet  MATH  Google Scholar 

  • Wang FW, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidisc Optim 43:767–784

    Article  MATH  Google Scholar 

  • Wang YQ, Zhang L, Wang MY (2016) Length scale control for structural optimization by level sets. Comput Methods Appl Mech Eng 305:891–909

    Article  MathSciNet  Google Scholar 

  • Xia Q, Shi TL (2015) Constraints of distance from boundary to skeleton: for the control of length scale in level set based structural topology optimization. Comput Methods Appl Mech Eng 295:525–542

    Article  MathSciNet  Google Scholar 

  • Xia Q, Shi TL, Wang MY, Liu SY (2010) A level set based method for the optimization of cast part. Struct Multidisc Optim 41:735–747

    Article  Google Scholar 

  • Xia L, Zhu JH, Zhang WH, Breitkopf P (2013) An implicit model for the integrated optimization of component layout and structure topology. Comput Methods Appl Mech Eng 257:87–102

    Article  MathSciNet  MATH  Google Scholar 

  • Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896

    Article  Google Scholar 

  • Xu JT, Sun YW, Zhang XK (2013) A mapping-based spiral cutting strategy for pocket machining. Int J Adv Manuf Technol 67:2489–2500

    Article  Google Scholar 

  • Zegard, T., & Paulino, G.H. (2016). Bridging topology optimization and additive manufacturing. Structural and Multidisciplinary Optimization, 53(1), 175-192.

  • Zhang WH, Xia L, Zhu JH, Zhang Q (2011) Some recent advances in the integrated layout design of multicomponent systems. J Mech Des 133:104503-1-15

  • Zhang J, Zhang WH, Zhu JH, Xia L (2012) Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis. Comput Methods Appl Mech Eng 245–246:75–89

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang WS, Zhong WL, Guo X (2014) An explicit length scale control in SIMP-based topology optimization. Comput Methods Appl Mech Eng 282:71–86

    Article  MathSciNet  Google Scholar 

  • Zhang WS, Zhong WL, Guo X (2015a) Explicit layout control in optimal design of structural systems with multiple embedding components. Comput Methods Appl Mech Eng 290:290–313

    Article  MathSciNet  Google Scholar 

  • Zhang P, Toman J, Yu YQ, Biyikli E, Kirca M, Chmielus M, To AC (2015b) Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing: theory and validation. J Manuf Sci Eng 137:021004

    Article  Google Scholar 

  • Zhang WS, Yuan J, Zhang J, Guo X (2016) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidisc Optim 53:1243–1260

    Article  MathSciNet  Google Scholar 

  • Zhou MD, Wang MY (2013) Engineering feature design for level set based structural optimization. Comput Aided Des 45:1524–1537

    Article  MathSciNet  Google Scholar 

  • Zhou M, Fleury R, Shyy YK, Thomas HL (2002) Progress in topology optimization with manufacturing constratins. Proce 9th AIAA/ISSMO Symp Multidisciplinary Anal Optimization, Atlanta, GA, USA

  • Zhou MD, Lazarov BS, Wang FW, Sigmund O (2015) Minimum length scale in topology optimization by geometric constraints. Comput Methods Appl Mech Eng 293:266–282

    Article  MathSciNet  Google Scholar 

  • Zhu Z, Dhokia V, Nassehi A, Newman ST (2013) A review of hybrid manufacturing processes – state of the art and future perspectives. Int J Comput Integr Manuf 26:596–615

    Article  Google Scholar 

  • Zhu JH, Gao HH, Zhang WH, Zhou Y (2015) A multi-point constraints based integrated layout and topology optimization design for multi-component systems. Struct Multidisc Optim 51:397–407

    Article  Google Scholar 

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Acknowledgments

The authors would like to acknowledge the support from China Scholarship Council (CSC) and US National Science Foundation (CMMI-1634261).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alberta, Edmonton, Canada

    Jikai Liu

  2. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    Albert C. To

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Correspondence to Albert C. To.

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Liu, J., To, A.C. Topology optimization for hybrid additive-subtractive manufacturing. Struct Multidisc Optim 55, 1281–1299 (2017). https://doi.org/10.1007/s00158-016-1565-4

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