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Structural and Multidisciplinary Optimization

, Volume 60, Issue 4, pp 1423–1436 | Cite as

Topology optimization of anisotropic magnetic composites in actuators using homogenization design method

  • Jaewook LeeEmail author
  • Jeonghoon Yoo
  • Seungjae Min
  • Minho Yoon
Research Paper
  • 237 Downloads

Abstract

This work presents topology optimization of anisotropic magnetic composites in actuators. The magnetic composite consists of two different ferromagnetic materials with high and low magnetic reluctivity, which correspond to matrix and fiber materials, respectively. The magnetic composite is expected to enhance the actuator performance when it is properly designed. The proposed design optimization scheme can find the composite layout, fiber volume fraction, and fiber orientations to achieve an actuator force maximization. In the proposed scheme, four microstructure design variables are assigned at each finite element, and the effective homogenized material property (i.e., magnetic reluctivity) is calculated using the asymptotic homogenization method. The microstructure design variables are then optimized to achieve the optimal distribution of the homogenized material property in a macroscopic scale. In the design result, discrete fiber orientations and volume fractions are achieved by applying the discrete penalization scheme. In addition, the obtained composite design result is visualized using the projection method proposed for a periodic composite design result. The effectiveness of the proposed topology optimization procedures is validated in magnetic actuator design examples. In addition, the design result of anisotropic composite is compared with the isotropic multi-material design result to validate the benefit of anisotropic composite in actuators.

Keywords

Topology optimization Homogenization design method Anisotropic magnetic composites Magnetic actuator 

Notes

Funding information

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016 R1D1A1B03931138), and Global University Project (GUP) grant funded by the GIST in 2018.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

References

  1. Asai Y, Ota T, Yamamoto T, Hirata K (2017) Proposed of novel linear oscillating actuator’s structure using topology optimization. IEEE Trans Magn 53(6):8203204CrossRefGoogle Scholar
  2. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Engrg 71(2):197–224CrossRefMathSciNetzbMATHGoogle Scholar
  3. Bendsøe MP, Sigmund O (2004) Topology Optimization - Theory, Methods and Applications. Springer, BerlinzbMATHGoogle Scholar
  4. Bensoussan A, Lions J-L, Papanicolaou G (2011) Asymptotic analysis for periodic structures. AMS Chelsea PublishingGoogle Scholar
  5. Bjørk R, Bahl CRH, Insinga AR (2017) Topology optimized permanent magnet systems. J Magn Magn Mater 437:78–85CrossRefGoogle Scholar
  6. Bjørk R, Insinga AR (2018) A topology optimized switchable permanent magnet system. J Magn Magn Mater 465:106–113CrossRefGoogle Scholar
  7. Bruyneel M (2011) SFP – A new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struc Multidisc Optim 43:17– 27CrossRefGoogle Scholar
  8. Bruyneel M, Fleury C (2002) Composite structures optimization using sequential convex programming. Adv Eng Softw 33:697– 711CrossRefzbMATHGoogle Scholar
  9. Choi JS, Izui K, Nishiwaki S, Kawamoto A, Nomura T (2011) Topology optimization of the stator for minimizing cogging torque of IPM motors. IEEE Trans Magn 47(10):3024–3027CrossRefGoogle Scholar
  10. Choi JS, Yamada T, Izui K, Nishiwaki S, Yoo J (2011) Topology optimization using a reaction–diffusion equation. Comput Methods Appl Mech Engrg 200:2407–2420CrossRefMathSciNetzbMATHGoogle Scholar
  11. Choi JS, Yoo J (2008) Structural optimization of ferromagnetic materials based on the magnetic reluctivity for magnetic field problems. Comput Methods Appl Mech Eng 197:4193– 4206CrossRefzbMATHGoogle Scholar
  12. Choi JS, Yoo J (2009a) Design of an eddy current brake system using microstructures. IEEE Trans Magn 45(6):2720–2723Google Scholar
  13. Choi JS, Yoo J (2009b) Simultaneous structural topology optimization of electromagnetic sources and ferromagnetic materials. Comput Methods Appl Mech Engrg 198:2111–2121Google Scholar
  14. Dede EM (2010) Simulation and optimization of heat flow via anisotropic material thermal conductivity. Comp Mater Sci 50:510–515CrossRefGoogle Scholar
  15. Dede EM, Lee J, Nomura T (2014) Multiphysics Simulation: Electromechanical System Applications and Optimization. Springer, BerlinCrossRefzbMATHGoogle Scholar
  16. Duan Z, Yan J, Zhao G (2015) Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struc Multidisc Optim 51:721–732CrossRefGoogle Scholar
  17. Fietz C (2013) Electro-magnetostatic homogenization of bianisotropic metamaterials. J Opt Soc Am B 30:1937–1944CrossRefGoogle Scholar
  18. Groen JP, Sigmund O (2017) Homogenization-based topology optimization for high-resolution manufacturable microstructures. Int J Numer Meth Eng 113:2009–2027MathSciNetGoogle Scholar
  19. Henrichsen SR, Lindgaard E (2015) Free material stiffness design of laminated composite structures using commercial finite element analysis codes. Struc Multidisc Optim 51:1097–1111CrossRefMathSciNetGoogle Scholar
  20. Huber C, Goertler M, Abert C, Bruckner F, Groenefeld M, Teliban I, Suess D (2018) Additive manufactured and topology optimized passive shimming elements for permanent magnetic systems. Sci Rep 8:14651CrossRefGoogle Scholar
  21. Ishikawa T, Mizuno S, Krita N (2017) Topology optimization method for asymmetrical rotor using cluster and cleaning procedure. IEEE Trans Magn 53(6):7001504Google Scholar
  22. Kawamoto A, Matsumori T, Yamasaki S, Nomura T, Kondoh T, Nishiwaki S (2011) Heavisde projection based topology optimization by a PDE-filtered scalar function. Struct Multidisc Optim 44:19–24CrossRefzbMATHGoogle Scholar
  23. Kuznetsov S, Guest JK (2017) Topology optimization of magnetic source distributions for diamagnetic and superconducting levitation. J Magn Magn Mater 438:60–69CrossRefGoogle Scholar
  24. Larsen SD, Sigmund O, Groen JP (2018) Optimal truss and frame design from projected homogenization-based topology optimization. Struc Multidisc Optim 57:1461–1474CrossRefMathSciNetGoogle Scholar
  25. Lee J (2010) Structural design optimization of electric motors to improve torque performance, Ph.D. dissertation, Dept. Mech. Eng., Univ. Michigan Ann Arbor, MI, USAGoogle Scholar
  26. Lee J, Kikuchi N (2010) Structural topology optimization of electrical machinery to maximize stiffness with body force distribution. IEEE Trans Magn 46(10):3790–3794CrossRefGoogle Scholar
  27. Lee J, Yoon SW (2015) Optimization of magnet and back-iron topologies in electromagnetic vibration energy harvesters. IEEE Trans Magn 51(6):7208807Google Scholar
  28. Lee J, Seo JH, Kikuchi N (2010) Topology optimization of switched reluctance motors for the desired torque profile. Struct Multidiscip Optim 42(5):783–796CrossRefGoogle Scholar
  29. Lee J, Dede EM, Nomura T (2011) Simultaneous design optimization of permanent magnet, coils, and ferromagnetic material in actuators. IEEE Trans Magn 47(12):4712–4716CrossRefGoogle Scholar
  30. Lee J, Nomura T, Dede EM (2017) Topology optimization of Halbach magnet arrays using isoparametric projection. J Magn Magn Mater 432:140–153CrossRefGoogle Scholar
  31. Lee J, Lee S-W, Kim K, Lee J (2018a) Multi-material topology optimization of magnetic actuator with segmented permanent magnets. IEEE Trans Magn 54(7):8202706Google Scholar
  32. Lee J, Kim D, Nomura T, Dede EM, Yoo J (2018b) Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite. structures. Compos Struct 201:217–233Google Scholar
  33. Lee J, Yoon M, Nomura T, Dede EM (2018) Topology optimization for design of segmented permanent magnet arrays with ferromagnetic materiasl. J Magn Magn Mater 449:571–581CrossRefGoogle Scholar
  34. Lee J, Nomura T, Dede EM (2019) Asymptotic homogenization of magnetic composite for controllable permanent magnet. Compos Part B 161:128–140CrossRefGoogle Scholar
  35. Lee SW, Lee J, Cho S (2016) Isogeometric shape optimization of ferromagnetic materials in magnetic actuators. IEEE Trans Magn 52(2):7200208CrossRefGoogle Scholar
  36. Lim S, Min S (2012) Design optimization of permanent magnet actuator using multi-phase level-set model. IEEE Trans Magn 48(4):1641–1644CrossRefGoogle Scholar
  37. Lim S, Min S Kazuhiro I, Nishiwaki S (2017) Design optimization of a magnetic actuator incorporating the concept of the hybrid analysis method. IEEE Trans Magn 53(6):7203404CrossRefGoogle Scholar
  38. Lindgaard E, Lund E (2011) Optimization formulations for the maximum nonlinear buckling load of composite structures. Struc Multidisc Optim 43:631–646CrossRefzbMATHGoogle Scholar
  39. Nomura T, Dede EM, Lee J, Yamasaki S, Matsumor T, Kawamoto A, Kikuchi N (2015) General topology optimization method with continuous and discrete orientation design using isoparametric projection. Int J Numer Meth Eng 101(8):571–605CrossRefMathSciNetzbMATHGoogle Scholar
  40. Park S, Min S (2010) Design of magnetic actuator with nonlinear ferromagnetic materials using level-set based topology optimization. IEEE Trans Magn 46(2):618–621CrossRefGoogle Scholar
  41. Park S, Min S, Yamasaki S, Nishiwaki S, Yoo J (2008) Magnetic actuator design using level set based topology optimization. IEEE Trans Magn 44(11):4037–4040CrossRefGoogle Scholar
  42. Petrovic M, Nomura T, Yamada T, Izui K, Nishiwaki S (2018) Orthotropic material orientation optimization method in composite laminates. Struc Multidisc Optim 57:815–828CrossRefMathSciNetGoogle Scholar
  43. Putek P, Gausling K, Bartel A, Gawrylczyk KM, Maten EJW, Pulch R, Günther M (2015) Robust Topology optimization of a permanent magnet synchronous machine using multi-level set and stochastic collocation methods. In: Scientific Computing in Electrical Engineering SCEE 2014 (Mathematics in Industry). New York, SpringerGoogle Scholar
  44. Putek P, Pulch R, Bartel A, Maten EJW, Günther M, Gawrylczyk KM (2016) Shape and topology optimization of a permanent -magnet machine under uncertainties. J Math Ind 6:11CrossRefMathSciNetzbMATHGoogle Scholar
  45. Ringertz UT (1993) On finding the optimal distribution of material properties. Struc Multidisc Optim 5:265–267CrossRefGoogle Scholar
  46. Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Meth Eng 62:2009– 2027CrossRefzbMATHGoogle Scholar
  47. Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12:555–73CrossRefMathSciNetzbMATHGoogle Scholar
  48. Teyber R, Trevizoli PV, Christiaanse TV, Govindappa P, Rowe A (2018) Topology optimization of reduced rare-earth permanent magnet arrays with finite coercivity. J Appl Phys 123 :193903CrossRefGoogle Scholar
  49. Wang S, Kang J (2002) Topology optimization of nonlinear magnetics. IEEE Trans Magn 38(2):1029–1032CrossRefGoogle Scholar
  50. Watanabe K, Suga T, Kitabatake S (2018) Topology optimization based on the on/off method for synchronous motor. IEEE Trans Magn 54(3):7201104CrossRefGoogle Scholar
  51. Wu C, Gao Y, Fand J, Lund E, Li Q (2017) Discrete topology optimization of ply orientation for a carbon fiber reinforced plastic (CFRP) laminated vehicle door. Mater Des 28:9– 19CrossRefGoogle Scholar
  52. Yoo J, Hong H (2004) A modified density approach for topology optimization in magnetic fields. Int J Solids Struct 41:2461– 2477CrossRefzbMATHGoogle Scholar
  53. Yoo J, Kikuchi N (2000) Topology optimization in magnetic fields using the homogenization method. Int J Numer Meth Eng 48:1463–1479CrossRefzbMATHGoogle Scholar
  54. Yoo J, Kikuchi N, Volakis JL (2001) Structural optimization in magnetic fields using the homogenization design method – part I. Arch Comput Meth in Engrg 8:387–406CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringGwangju Institute of Science and Technology (GIST)GwangjuSouth Korea
  2. 2.School of Mechanical EngineeringYonsei UniversitySeoulSouth Korea
  3. 3.Department of Automotive EngineeringHanyang UniversitySeoulSouth Korea
  4. 4.Department of Mechanical EngineeringKumoh National Institute of TechnologyGumiSouth Korea

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