The electric assisted bicycle is the new transportation tool in the 21st century. The proposal of this article is to upgrade the fatigue safety factor for an electric assisted bicycle frame by integrating the uniform design, Kriging interpolation, entropy weighting method, grey relational analysis, and genetic algorithm. According to EN 15194 standard, the main objective function, the fatigue safety factor for an electric assisted bicycle frame is examined by ANSYS/Workbench software under three fatigue testing simulations. Five geometry parameters of an electric assisted bicycle frame are nominated to be the improved control factors. Since all control factors are continuous in the design space, the uniform design is certainly developed to construct a series of simulation experiments. For each model in the uniform design table, the fatigue finite element analysis is utilized to calculate the fatigue safety factor. Applying the multi-objective optimization procedure, the optimal design version of an electric bicycle frame has been obtained. For the fatigue safety factor, the revised design model has a maximum improvement of 19.59% when compared to the original design. Summery, the fatigue safety factor has been effectively elevated by executing the innovative multi-objective optimization procedure for an electric assisted bicycle frame system.
CovillDBeggSEltonE, et al. Parametric finite element analysis of bicycle frame geometries. Procedia Eng2014; 72: 441–446.
2.
GuptaRRaoGVRS. Analysis of mountain bike frame by FEM. IOSR J Mech Civil Eng2016; 13(2): 60–71.
3.
AkhyarAHusainiIskandarHAhmadF. Structural simulations of bicycle frame behaviour under various load conditions. Materials Science Forum2019; 961: 137–147.
4.
HullMLBolourchiF.Contributions of rider-induced loads to bicycle frame stress. J Strain Anal Eng Des1988; 23(3): 105–114.
5.
GautamRS. Sensitivity analysis of stress distribution in bicycle frame. Australian Journal of Mechanical Engineering2020; 1–12. 10.1080/14484846.2020.1763546.
6.
SandićUTomićRGrbovićA, et al. Failure analysis of bicycle frame composite structure based on stacking variant of laminate layers. Struct Integr Life2020; 20(1): 69–76.
7.
VargheseASSreejithNK.Structural analysis of bicycle frame using composite laminate. Int J Eng Trends Technol2015; 28(7): 321–327.
8.
HuňadyRBeliškoM.Structural design and impact test of a suspension mountain bicycle frame by using FEM analysis. Am J Mech Eng2015; 3(6): 211–214.
9.
GorenfloCRiosIGolabL, et al. Usage patterns of electric bicycles: an analysis of the webike project. J Adv Transport2017; 2017: 1-14.
10.
CahyonoSIAnwarMDiharjoK, et al. Finite element analysis of electric bicycle frame geometries. AIP Conf Proc2017; 1788: 030084-1–030084-5.
11.
UludamarEYıldızhanŞTosunE, et al. Finite element analysis of electric bike rims coupled with hub motor. Adv Automob Eng2016; 5(2): 1000142-1–1000142-4.
12.
MesicEMasicAMuratovićE, et al. Structural analysis and optimization of electric bike front drive with bottom bracket electric motor. Adv Sci Technol Res J2021; 15(1): 273–282.
13.
XiaoDLiuXDuW, et al. Application of topology optimization to design an electric bicycle main frame. Struct Multidiscipl Optim2012; 46(6): 913–929.
14.
LanTSZhangHWGaoJS, et al. Design and optimizated simulation of bicycle frame structure. In: 2020 IEEE Eurasia Conference on IOT, Communication and Engineering (ECICE), Yunlin, Taiwan, 23–25 October 2020, pp.301–304. New York: IEEE.
15.
LinCCHuangSJLiuCC.Structural analysis and optimization of bicycle frame designs. Adv Mech Eng2017; 9(12): 1–10.
16.
ChengYCLeeCKTsaiMT.Multi-objective optimization of an on-road bicycle frame by uniform design and compromise programming. Adv Mech Eng2016; 8(2): 1–15.
17.
SuppapitnarmASeffenKAParksGT, et al. Multiobjective optimisation of bicycle frames using simulated annealing. In: Proceedings of the first ASMO/ISSMO conference on engineering design optimization, vol. 1, Ilkley, West Yorkshire, MCB Press, 1999, pp.357–364.
18.
LeeSYLinSMSheuJJ, et al. Driving mechanism for the motorized bicycle. Patent US 2010/0051373A1, USA, 2010.
19.
EN 15194. Cycles - Electrically power assisted cycles - EPAC Bicycles. (2017), British Standards Institution.
20.
BaiSLiXXieZ, et al. A wireless fatigue monitoring system utilizing a bio-inspired tree ring data tracking technique. Sensors2014; 14: 4364–4383.
21.
Amine BouhlelMBartoliNRegisRG, et al. Efficient global optimization for high-dimensional constrained problems by using the kriging models combined with the partial least squares method. Eng Optim2018; 50(12): 2038–2053.
22.
AsaESaafiMMembahJ, et al. Comparison of linear and nonlinear kriging methods for characterization and interpolation of soil data. J Comput Civ Eng2012; 26(1): 11–18.
23.
OliverMAWebsterR.Kriging: a method of interpolation for geographical information systems. Int J Geogr Inf Syst1990; 4(3): 313–332.
24.
ChengYCWuPH.Optimisation for suspension system of a railway vehicle with a new non-linear creep model developed by uniform design. Int J Heavy Veh Syst2015; 22(2): 157–191.
25.
Ju-LongD.Control problems of grey systems. Syst Control Lett1982; 1: 288–294.
26.
HuangYLLinCT.Constructing grey relation analysis model evaluation of tourism competitiveness. J Inf Optim Sci2009; 30(6): 1129–1138.
27.
HasaniHTabatabaeiSAAmiriG.Grey relational analysis to determine the optimum process parameters for open-end spinning yarns. J Eng Fiber Fabr2012; 7(2): 81–86.
28.
JeganTMCAnandMDRavindranD.Determination of electro discharge machining parameters in aisi202 stainless steel using grey relational analysis. Procedia Eng2012; 38: 4005–4012.
29.
WangLYinKCaoY, et al. A new grey relational analysis model based on the characteristic of inscribed core (ic-gra) and its application on seven-pilot carbon trading markets of China. Int J Environ Res Public Health2018; 16(1): 99.
30.
ClausiusR.Ueber verschiedene für die anwendung bequeme formen der hauptgleichungen der mechanischen wärmetheorie. Ann Phys1865; 201(7): 353–400.
31.
IşıkATAdalıEA. The decision-making approach based on the combination of entropy and rov methods for the apple selection problem. Eur J Interdiscipl Stud2017; 3(3): 80–86.
32.
VatanseverKAkgűlY.Performance evaluation of websites using entropy and grey relational analysis methods: the case of airline companies. Decis Sci Lett2018; 7: 119–130.
33.
HeYGuoHJinM, et al. A linguistic entropy weight method and its application in linguistic multi-attribute group decision making. Nonlinear Dyn2016; 84: 399–404.
34.
YueC.Entropy-based weights on decision makers in group decision-making setting with hybrid preference representations. Appl Soft Comput2017; 60: 737–749.
35.
FangKTWangY.Number-theoretic methods in statistics. London: Chapman & Hall, 1994.
36.
LiBXWangWCZhangXP, et al. Integrating uniform design and response surface methodology to optimize thiacloprid suspension. Sci Rep2017; 7(1): 46018.
37.
LiTZYangXL.An efficient uniform design for kriging-based response surface method and its application. Comput Geotech2019; 109: 12–22.
38.
ChatterjeeKOuZPhoaFKH, et al. Uniform four-level designs from two-level designs: a new look. Stat Sin2017; 27: 171–186.
