Abstract
One of the bottlenecks encountered in the development of automobile wheels made of lightweight materials is the 13-degree bench impact test. To improve the impact resistance of lightweight material wheels, the topology optimization (TO) model of multi-design spaces and multi-load cases and the combination of gray relational analysis (GRA) and principal component analysis (PCA) are simultaneously integrated into a multi-objective topology optimization (MOTO) approach to obtain the optimized topology layout of the wheel. Firstly, a three-dimensional wheel TO model is established based on the variable density method and divided into three design spaces and two non-design spaces. Secondly, the load parameters of the wheel under cornering, radial, and 13-degree impact load cases are determined, and the corresponding finite element models are established. For the 13-degree impact load case, the real-time energy reduction coefficient is introduced to compensate for the tire absence, thereby determining the dynamic load of the striker acting on the wheel alone. And then, a series of extracted forces data during the whole impact simulation are equivalent to a concentrated load suitable for the wheel static TO through the weighted sum compliance method. Thirdly, the combination of GRA and PCA is introduced to determine the weight coefficient (WC) of each sub-objective. Next, the MOTO of the wheel is implemented, and the influence of different constraints on the wheel topology layout is analyzed. Finally, the modal analysis and 13-degree impact simulation are performed on the reconstructed wheels with different topology layouts to verify their performance. The results show that the natural frequencies of the optimized wheels meet the requirements and a variety of wheel topology layouts with improved impact resistance are obtained, which provides a valuable guidance for the development of wheel in practical engineering.
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References
Altair OptiStruct (2014) OptiStruct 14.0 user manual. Altair Engineering Inc., Troy, MI, U.S.A.
Bae JH, Jung KC, Yoo SH, Chang SH, Kim M, Lim T (2015) Design and fabrication of a metal-composite hybrid wheel with a friction damping layer for enhancement of ride comfort. Compos Struct 133:576–584. https://doi.org/10.1016/j.compstruct.2015.07.113
Bai YC, Zhou HS, Lei F, Lei HS (2018) An improved numerically-stable equivalent static loads (ESLs) algorithm based on energy-scaling ratio for stiffness topology optimization under crash loads. Struct Multidiscip Optim 59:117–130. https://doi.org/10.1007/s00158-018-2054-8
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224. https://doi.org/10.1016/0045-7825(88)90086-2
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654. https://doi.org/10.1007/s004190050248
Chai WH, Liu XD, Shan YC, Wan XF, Jiang E (2018) Research on simulation of the bending fatigue test of automotive wheel made of long glass fiber reinforced thermoplastic considering anisotropic property. Adv Eng Softw 116:1–8. https://doi.org/10.1016/j.advengsoft.2017.11.004
Chen TY, Wu SC (1998) Multiobjective optimal topology design of structures. Comput Mech 21:483–492. https://doi.org/10.1007/s004660050327
Gao Q, Shan YC, Wan XF, Feng QZ, Liu XD (2019) 90-degree impact bench test and simulation analysis of automotive steel wheel. Eng Fail Anal 105:143–155. https://doi.org/10.1016/j.engfailanal.2019.06.097
Guo X, Zhang WS, Zhang L (2013) Robust structural topology optimization considering boundary uncertainties. Comput Methods Appl Mech Eng 253:356–368. https://doi.org/10.1016/j.cma.2012.09.005
Guo X, Zhang WS, Zhang J, Yuan J (2016) Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comput Methods Appl Mech Eng 310:711–748. https://doi.org/10.1016/j.cma.2016.07.018
Hu DJ, Shan YC, He T, Liu XD, Wan XF (2019) Research on simulation method of impact resistance of composite wheels made of long glass fiber reinforced thermoplastic introducing anisotropic property. Compos Struct 223:110965. https://doi.org/10.1016/j.compstruct.2019.110965
Huang XD, Xie YM (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683. https://doi.org/10.1007/s00158-010-0487-9
Jang GW, Yoon MS, Park JH (2010) Lightweight flatbed trailer design by using topology and thickness optimization. Struct Multidiscip Optim 41:295–307. https://doi.org/10.1007/s00158-009-0409-x
Jiang L, Wu CW (2017) Topology optimization of energy storage flywheel. Struct Multidiscip Optim 55:1917–1925. https://doi.org/10.1007/s00158-016-1576-1
Khan ZA, Kamaruddin S, Siddiquee AN (2010) Feasibility study of use of recycled high density polyethylene and multi response optimization of injection moulding parameters using combined grey relational and principal component analyses. Mater Des 31:2925–2931. https://doi.org/10.1016/j.matdes.2009.12.028
Lei F, Qiu RB, Bai YC, Yuan CF (2018) An integrated optimization for laminate design and manufacturing of a CFRP wheel hub based on structural performance. Struct Multidiscip Optim 57:2309–2321. https://doi.org/10.1007/s00158-017-1861-7
Li C, Kim IY, Jeswiet J (2014) Conceptual and detailed design of an automotive engine cradle by using topology, shape, and size optimization. Struct Multidiscip Optim 51:547–564. https://doi.org/10.1007/s00158-014-1151-6
Ma HF, Wang JX, Lu YN, Guo YW (2018) Lightweight design of turnover frame of bridge detection vehicle using topology and thickness optimization. Struct Multidiscip Optim 59:1007–1019. https://doi.org/10.1007/s00158-018-2113-1
Miller WS, Zhuang L, Bottema J, Wittebrood AJ, Vieregge A (2000) Recent development in aluminum alloys for the automotive industry. Mat Sci Eng A 280:37–49. https://doi.org/10.1016/S0921-5093(99)00653-X
Min S, Nishiwaki S, Kikuchi N (2000) Unified topology design of static and vibrating structures using multiobjective optimization. Comput Struct 75:93–116. https://doi.org/10.1016/S0045-7949(99)00055-3
Previati G, Ballo F, Gobbi M, Mastinu G (2019) Radial impact test of aluminum wheels-numerical simulation and experimental validation. Int J Impact Eng 126:117–134. https://doi.org/10.1016/j.ijimpeng.2018.12.002
Stearns J, Srivatsan TS, Prakash A, Lam PC (2004) Modeling the mechanical response of an aluminum alloy automotive rim. Mat Sci Eng A 366:262–268. https://doi.org/10.1016/j.msea.2003.08.017
Teixeira D, Giovanela M, Gonella LB, Crespo JS (2015) Influence of injection molding on the flexural strength and surface quality of long glass fiber-reinforced polyamide 6.6 composites. Mater Des 85:695–706. https://doi.org/10.1016/j.matdes.2015.07.097
Wan XF (2017) Research on tire-wheel load transfer characteristic and its application in the simulation of wheel strength test. Ph.D. dissertation, Beihang University, Beijing
Wang XY, Liu XD, Shan YC, Wan XF, Liu WH, Pan Y (2016) Lightweight design of automotive wheel made of long glass fiber reinforced thermoplastic. J Mech Eng Sci 230:1634–1643. https://doi.org/10.1177/0954406215583081
Wang DF, Zhang S, Xu WC (2019) Multi-objective optimization design of wheel based on the performance of 13° and 90° impact tests. Int J Crashworthines 24:1–26. https://doi.org/10.1080/13588265.2018.1451229
Xiao DH, Liu XD, Du WH, Wang JY, He T (2012) Application of topology optimization to design an electric bicycle main frame. Struct Multidiscip Optim 46:913–929. https://doi.org/10.1007/s00158-012-0803-7
Xiao DH, Zhang H, Liu XD, He T, Shan YC (2014) Novel steel wheel design based on multi-objective topology optimization. J Mech Sci Technol 28:1007–1016. https://doi.org/10.1007/s12206-013-1174-8
Yi JJ, Liu XD, Shan YC, Dong H (2019) Characteristics of sound pressure in the tire cavity arising from acoustic cavity resonance excited by road roughness. Appl Acoust 146:218–226. https://doi.org/10.1016/j.apacoust.2018.11.025
Zhang S (2018) Research on multi-disciplinary lightweight optimization design method for fatigue-impact-aerodynamic performance of the wheel. Ph.D. dissertation, Jilin University, Jilin
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 Multidiscip Optim 53:1243–1260. https://doi.org/10.1007/s00158-015-1372-3
Zhou M, Shyy YK, Thomas HL (2001) Checkerboard and minimum member size control in topology optimization [J]. Struct Multidiscip Optim 21:152–158. https://doi.org/10.1007/s001580050179
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This work was supported by the National Natural Science Foundation of China (Grant No. 51875025).
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Zhang, Y., Shan, Y., Liu, X. et al. An integrated multi-objective topology optimization method for automobile wheels made of lightweight materials. Struct Multidisc Optim 64, 1585–1605 (2021). https://doi.org/10.1007/s00158-021-02913-3
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DOI: https://doi.org/10.1007/s00158-021-02913-3