Dynamic analysis is an essential task in the geometry design of suspension systems. Whereas the dynamic simulation based on numerical software like Adams is quite slowly and the existing analytical models of the nonlinear suspension geometry are mostly based on small displacement hypothesis, this paper aims to propose a whole-range dynamic model with high computational efficiency for planar double wishbone suspensions and further achieve the fast optimal design of suspension geometry. Selection of the new generalized coordinate and explicit solutions of the basic four-bar mechanism dramatically reduce the complexity of suspension geometry representation and provide analytical solutions for all of the time varying dimensions. By this means, the running speed and computational accuracy of the new model are guaranteed simultaneously. Furthermore, an original Matlab/Simulink implementation is given to maintain the geometric nonlinearity in the solving process of dynamic differential equations. After verifying its accuracy with an ADAMS prototype, the presented whole-range model is used in the vast-parameter optimization of suspension geometry. Since both kinematic and dynamic performances are evaluated in the objective function, the optimization is qualified to give a comprehensive suggestion to the design of suspension geometry.
HongKJeonDYooW, et al. A new model and an optimal pole-placement control of the Macpherson suspension system. SAE Trans1999; 108: 2452–2461.
2.
FernandesJCMGonçalvesPJPSilveiraM. Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort. Nonlinear Dyn2020; 99: 1561–1576.
3.
AllisonJTGuoTHanZ. Co-design of an active suspension using simultaneous dynamic optimization. J Mech Des2014; 136: 081003.
4.
GadhviBSavsaniVPatelV. Multi-objective optimization of vehicle passive suspension system using NSGA-II, SPEA2 and PESA-II. Procedia Technol2016; 23: 361–368.
5.
NagarkarMPPatilGJVPatilRNZ. Optimization of nonlinear quarter car suspension-seat-driver model. J Adv Res2016; 7: 991–1007.
6.
WangRJingHYanF, et al. Optimization and finite-frequency H∞ control of active suspensions in in-wheel motor driven electric ground vehicles. J Franklin Inst2015; 352: 468–484.
7.
ThompsonAG. An active suspension with optimal linear state feedback. Veh Syst Dyn1976; 5: 187–203.
8.
SunWGaoHKaynakO. Finite frequency H∞ control for vehicle active suspension systems. IEEE Trans Control Syst Technol2011; 19: 416–422.
9.
DuHYim SzeKLamJ. Semi-active H∞ control of vehicle suspension with magneto-rheological dampers. J Sound Vib2005; 283: 981–996.
10.
SavaresiSMPoussot-VassalCSpeltaC, et al. Semi-active suspension control design for vehicles. Oxford: Butterworth-Heinemann Elsevier, 2010.
11.
NguyenATRathJGuerraTM, et al. Robust set-invariance based fuzzy output tracking control for vehicle autonomous driving under uncertain lateral forces and steering constraints. IEEE Trans Intell Transp Syst. Epub ahead of print 23September2020. DOI: 10.1109/tits.2020.3021292.
12.
LiuMGuFHuangJ, et al. Integration design and optimization control of a dynamic vibration absorber for electric wheels with in-wheel motor. Energies2017; 10: 2069.
13.
AfkarAMahmoodi-KaleibarMPaykaniA. Geometry optimization of double wishbone suspension system via genetic algorithm for handling improvement. J Vibroengineering2012; 14: 827–837.
14.
ZhangJPeiJZhangJ. The optimization study of the front suspension structure parameters for the mine truck based on adams/car. In: International conference on vehicle, mechanical and electrical engineering, Lancaster, Pennsylvania, U.S.A., July 2016, pp.1–9.
15.
ThomasSSPalandriJLakehal-ayatM, et al. Designing MacPherson suspension architectures using Bayesian optimization. In: Proceedings of the 31st Benelux Conference on Artificial Intelligence and the 28th Belgian Dutch Conference on Machine Learning, Brussels, Belgium, 6–8 November 2019.
16.
SancibrianRGarciaPViaderoF, et al. Kinematic design of double-wishbone suspension systems using a multiobjective optimisation approach. Veh Syst Dyn2010; 48: 793–813.
17.
ZhangJJiaXZhaoZ, et al. Optimization of positioning parameters for McPherson front suspension based on ADAMS/car. In: International conference on computer science and mechanical automation (CSMA), Hangzhou, China, 23–25 October 2015, pp.297–301. IEEE.
18.
ShiQZhangH. Fault diagnosis of an autonomous vehicle with an improved SVM algorithm subject to unbalanced datasets. IEEE Trans Ind Electron2021; 68: 6248–6256.
19.
NiuZLiZJinS, et al. Assembly variation analysis of compliant mechanisms by combining direct linearization method and Lagrange’s equations. Assemb Autom2019; 39: 740–751.
20.
NiuZJinSLiZ. Assembly variation analysis of incompletely positioned MacPherson suspension systems considering vehicle load change. J Mech Des2020; 143: 052001.
EskandariAMirzadehOAzadiS, Optimization of a McPherson suspension system using the design of experiments method. SAE technical paper 2006-01-1953, 2006.
23.
Mahmoodi-KaleibarMJavanshirIAsadiK, et al. Optimization of suspension system of off-road vehicle for vehicle performance improvement. J Cent South Univ2013; 20: 902–910.
24.
ZhangLMulukenTWDongE. Robust optimization design of suspension system based on spatial structure. In: International conference on computer network, electronic and automation, Xi'an, China, 27–29 September 2019, pp.474–479. IEEE.
25.
KimHMMichelenaNFPapalambrosPY, et al. Target cascading in optimal system design. J Mech Des2003; 125: 474–480.
26.
KangDOHeoSKimMS, et al. Robust design optimization of suspension system by using target cascading method. Int J Automot Technol2012; 13: 109.
27.
BlancoJCMunozLE. Multi-objective optimization of the geometry of a double wishbone suspension system. Vibroengineering Procedia2014; 3: 70–75.
28.
TaoSShintaniKBostanabadR, et al. Enhanced Gaussian process metamodeling and collaborative optimization for vehicle suspension design optimization. In: International design engineering technical conferences and computers and information in engineering conference, Cleveland, OH, 6–9 August 2017.
29.
BalikeKPRakhejaSStiharuI. Development of kineto-dynamic quarter-car model for synthesis of a double wishbone suspension. Veh Syst Dyn2011; 49: 107–128.
30.
HurelJPeraltaJAmayaJ, et al. Determination of the equivalent parameters for modelling a McPherson suspension with a quarter-car model. In: IEEE 26th international symposium on industrial electronics (ISIE), Edinburgh, 19–21 June 2017, pp.454–459. IEEE.
31.
ZhouGKimHSChoiYJ. A new method of identification of equivalent suspension and damping rates of full-vehicle model. Veh Syst Dyn2018; 57: 1573–1600.
32.
ZhouGWangYDuH. A generalized method for three-dimensional dynamic analysis of a full-vehicle model. Proc IMechE, Part D: J Automobile Engineering2020; 234: 2485–2499.
33.
SuhCH. Synthesis and analysis of suspension mechanisms with use of displacement matrices. SAE Trans1989; 98: 171–182.
34.
BalikeKPRakhejaSStiharuI. Kineto-dynamic performance analysis of vehicle with an asymmetric suspension damper using a roll-plane model. Int J Veh Perform2013; 1: 69–91.
35.
HurelJMandowAGarcía-CerezoA. Kinematic and dynamic analysis of the McPherson suspension with a planar quarter-car model. Veh Syst Dyn2013; 51: 1422–1437.
36.
HurelJMandowAGarcia-CerezoA. Nonlinear two-dimensional modeling of a McPherson suspension for kinematics and dynamics simulation. In: 12th IEEE international workshop on advanced motion control (AMC), Sarajevo, Bosnia and Herzegovina, 25–27 March 2012, pp.1–6. IEEE.
37.
FallahMSBhatRXieWF. New model and simulation of Macpherson suspension system for ride control applications. Veh Syst Dyn2009; 47: 195–220.
38.
StenssonAAsplundCKarlssonL. The nonlinear behaviour of a MacPherson strut wheel suspension. Veh Syst Dyn1994; 23: 85–106.
39.
GreenwoodDT. Advanced dynamics. Cambridge: Cambridge University Press, 2006.
40.
HaugEJ. Computer aided kinematics and dynamics of mechanical systems. Berlin: Spring-Verlag, 1984.
41.
QiZShiQZhangH. Tuning of digital PID controllers using particle swarm optimization algorithm for a CAN-based DC motor subject to stochastic delays. IEEE Trans Ind Electron2020; 67: 5637–5646.
42.
AudetCDennisJEJr.Analysis of generalized pattern searches. SIAM J Optim2002; 13: 889–903.
43.
RajendranIVijayaranganS. Simulated annealing approach to the optimal design of automotive suspension systems. Int J Veh Des2007; 43: 11–30.
