Abstract
To increase the energy storage density, one of the critical evaluations of flywheel performance, topology optimization is used to obtain the optimized topology layout of the flywheel rotor geometry. Based on the variable density method, a two-dimensional flywheel rotor topology optimization model is first established and divided into three regions: design domain, inner ring, and outer ring. Then the optimized flywheel topology layout can be obtained through the post-processing combined with the finite element analysis. In addition, several influence factors significantly affecting the topology optimization result are further investigated. Finally, a series of optimized flywheel layouts are obtained under different manufacturing constraints, stress constraints, and volume fraction constraints. These optimized flywheels obtained by topology optimization can provide a valuable guidance for the energy storage flywheel design in practical engineering.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arslan MA (2008) Flywheel geometry design for improved energy storage using finite element analysis [J]. Mater Des 29(2):514–518. doi:10.1016/j.matdes.2007.01.020
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method [J]. Comput Methods Appl Mech Eng 71(2):197–224. doi:10.1016/0045-7825(88)90086-2
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization [J]. Arch Appl Mech 69(9–10):635–654. doi:10.1007/s004190050248
Bendsøe MP, Díaz A, Kikuchi N (1993) Topology and generalized layout optimization of elastic structures [M]//Topology Design of Structures. Springer Netherlands: 159–205. doi:10.1007/978-94-011-1804-0_13
Bitterly JG (1998) Flywheel technology: past, present, and 21st century projections. IEEE Aerosp Electron Syst Mag 13(8):13–16. doi:10.1109/62.707557
Bolund B, Bernhoff H, Leijon M (2007) Flywheel energy and power storage systems [J]. Renew Sustain Energy Rev 11(2):235–258. doi:10.1016/j.rser.2005.01.004
Christopher DA, Beach R (1998) Flywheel technology development program for aerospace applications [J]. IEEE Aerosp Electron Syst Mag 13(6):9–14. doi:10.1109/62.683723
Diaz A, Sigmund O (1995) Checkerboard patterns in layout optimization [J]. Struct Optim 10(1):40–45. doi:10.1007/BF01743693
Eby D, Averill RC, Gelfand B, Punch W, Mathews O, Goodman E (1997) An injection island GA for flywheel design optimization [C]//5th European Congress on Intelligent Techniques and Soft Computing EUFIT’97. Morgan Kaufmann, Aachen, Germany, 1: 687–691
Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: A review*[J]. Appl Mech Rev 54(4):331–390. doi:10.1115/1.1388075
Genta G (1989) Some considerations on the constant stress disc profile [J]. Meccanica 24(4):235–248. doi:10.1007/BF01556455
Guest JK, Prévost JH, Belytschko T (2014) Achieving minimum length scale in topology optimization using nodal design variables and projection functions [J]. Int J Numer Methods Eng 61(2):238–254. doi:10.1002/nme.1064
Huang X, Xie YM (2008) Optimal design of periodic structures using evolutionary topology optimization [J]. Struct Multidiscip Optim 36(6):597–606. doi:10.1007/s00158-007-0196-1
Jiang L, Zhang W, Ma GJ, Wu CW (2016) Shape optimization of energy storage flywheel rotor [J]. Struct Multidiscip Optim 2016:1–12. doi:10.1007/s00158-016-1516-0
Kress GR (2000) Shape optimization of a flywheel [J]. Struct Multidiscip Optim 19(1):74–81. doi:10.1007/s001580050087
Liu H, Jiang J (2007) Flywheel energy storage—An upswing technology for energy sustainability [J]. Energy Build 39(5):599–604. doi:10.1016/j.enbuild.2006.10.001
Mei YL, Wang XM (2004) A level set method for structural topology optimization and its applications [J]. Adv Eng Softw 35(7):415–441. doi:10.1016/j.advengsoft.2004.06.004
Moses E, Fuchs MB, Ryvkin M (2002) Topological design of modular structures under arbitrary loading [J]. Struct Multidiscip Optim 24(6):407–417. doi:10.1007/s00158-002-0254-7
Park JS, Song HC, Yoon KS, Choi TS, Park JH (2005) Structural integrity evaluation for interference-fit flywheels in reactor coolant pumps of nuclear power plants [J]. J Mech Sci Technol 19(11):1988–1997. doi:10.1007/BF02916491
Sigmund O (2007) Morphology-based black and white filters for topology optimization [J]. Struct Multidiscip Optim 33(4-5):401–424. doi:10.1007/s00158-006-0087-x
Tso PL, Li CH (2008) Study of servo press with a flywheel [J]. J Adv Mech Des Syst Manuf 2(1):1–11
Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization [J]. Comput Methods Appl Mech Eng 192(1):227–246. doi:10.1016/S0045-7825(02)00559-5
Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization [J]. Comput Struct 49(5):885–896. doi:10.1016/0045-7949(93)90035-C
Zhou M, Shyy YK, Thomas HL (2001) Checkerboard and minimum member size control in topology optimization [J]. Struct Multidiscip Optim 21(2):152–158. doi:10.1007/s001580050179
Acknowledgments
This work was supported by the National Basic Research Program of China (Grant No.2015CB057306), the National Natural Science Foundation of China (Grant No.11272080, Grant No.11572080), and Fundamental Research Funds for the Central Universities of China (Grant No. DUT15JJG06)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Jiang, L., Wu, C.W. Topology optimization of energy storage flywheel. Struct Multidisc Optim 55, 1917–1925 (2017). https://doi.org/10.1007/s00158-016-1576-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-016-1576-1