This paper describes a method to minimize bearing forces as well as bearing and housing mass for a multistage gear reduction. This is done by finding the optimum dog-leg angles for the stages while leaving other aspects of the design unaltered. The optimization is demonstrated first for spur gears, and then for helical gears typically used in electric vehicles. A numerical example shows how bearing forces and mass of bearings and housing are reduced considerably by choosing the optimum dog-leg angle.
KimSCMoonSGSohnJH, et al. Macro geometry optimization of a helical gear pair for mass, efficiency, and transmission error. Mech Mach Theory2020; 144: 103634.
2.
HjelmRAhadiAWahlströmJ. Gear tolerancing for simultaneous optimization of transmission error and contact pressure. Results Eng2021; 9: 100195.
3.
WangCWangSWangG. Volume models for different structures of spur gear. Aust J Mech Eng2019; 17(2): 145–153.
4.
Laureano Moya-RodríguezJRoberto Marty-DelgadoIIJÉMarcelo Tacle-HumananteP. Optimización multiobjetivo en transmisiones por engranajes cilíndricos de dientes rectos asimétricos. Ing Mec2020; 23(2): e602.
5.
RaiPBarmanAG. Design optimization of spur gear using SA and RCGA. J Braz Soc Mech Sci Eng2018; 40: 257.
6.
PatilMRamkumarPKrishnapillaiS. Multi-objective optimization of two stage spur gearbox using NSGA-II. SAE paper 2017-28-1939, 2017.
7.
PatilMRamkumarPShankarK. Multi-objective optimization of the two-stage helical gearbox with tribological constraints. Mech Mach Theory2019; 138: 38–57.
8.
Farfan-CabreraLI. Tribology of electric vehicles: a review of critical components, current state and future improvement trends. Tribol Int2019; 138: 473–486.
9.
SanghviRCVashiASPatoliaHP, et al. Multi-objective optimization of two-stage helical Gear train using NSGA-II. J Optim2014; 2014: 1–8.
10.
PiVNThi HongTThi Phuong ThaoT, et al. Calculating optimum gear ratios of a two-stage helical reducer with first stage double gear sets. IOP Conf Ser Mater Sci Eng2019; 542: 012017.
11.
CamNTH NTHPiVN, et al. A study on calculation of optimum gear ratios of a two-stage helical gearbox with second stage double gear sets. Int J Mech Prod Eng Res Dev2019; 9(2): 613–620.
12.
Van CuongNLe HongKThi HongT, et al. Splitting total gear ratio of two-stage helical reducer with first-stage double gearsets for minimal reducer length. Int J Mech Prod Eng Res Dev2019; 9(6): 595–608.
13.
LiXJiangSZengQ. Optimization of two-stage cylindrical gear reducer with adaptive boundary constraints. J Softw2013; 8(8): 2052–2057. DOI: 10.4304/jsw.8.8.2052-2057
14.
MaJLiCCuiL. Transmission error analysis and disturbance optimization of two-stage spur Gear space driven mechanism with large inertia load. Shock Vib2018; 2018: 1–14.
15.
TudoseLBuigaOŞtefanacheC, et al. Automated optimal design of a two-stage helical gear reducer. Struct Multidiscipl Optim2010; 42: 429–435.
16.
GolabiSFesharakiJJYazdipoorM. Gear train optimization based on minimum volume/weight design. Mech Mach Theory2014; 73: 197–217.
17.
ThompsonDFGuptaSShuklaA. Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units. Mech Mach Theory2000; 35: 609–627.
18.
MaputiESAroraR. Design optimization of a gearbox: problem formulation procedure. In: 2018 international conference on automation and computational engineering (ICACE – 2018), Amity University Greater Noida Campus, Greater Noida, India, 3–4 October 2018. New York, NY: IEEE.
19.
MaputiESAroraR. Design optimization of a three-stage transmission using advanced optimization techniques. Int J Simul Multidiscip Des Optim2019; 10: A8.
20.
RenQCrollaDAMorrisA. 2009), Effect of transmission design on Electric Vehicle (EV) performance. In: 2009 IEEE vehicle power and propulsion conference, Dearborn, MI, 7–10 September 2009, pp.1260–1265. New York, NY: IEEE.
21.
MarjanovicNIsailovicBMarjanovicV, et al. A practical approach to the optimization of Gear trains with spur Gears. Mech Mach Theory2012; 53: 1–16.
22.
OthaganontPAssadianFAugerDJ. Multi-objective optimisation for battery electric vehicle powertrain topologies. Proc IMechE, Part D: J Automobile Engineering2017; 231(8): 1046–1065.
23.
CaiWWuXZhouM, et al. Review and development of electric motor systems and electric powertrains for new energy vehicles. Automot Innov2021; 4: 3–22.
24.
ISO 281:2007. Rolling bearings: dynamic load ratings and rating life, 2nd edition.
ISO 16281:2008. Rolling bearings: methods for calculating the modified reference rating life for universally loaded bearings, 1st edition.
27.
LangloisPBayduAHarrisO. Hybrid Hertzian and FE-based helical gear-loaded tooth contact analysis and comparison with FE. Gear Technol2016; 33: 54–63.
28.
de SantiagoJBernhoffHEkergårdB, et al. Electrical motor drivelines in commercial all-electric vehicles: a review. IEEE Trans Vehicular Technol2012; 61(2): 475–484.