Optimization design of the key parameters of McPherson suspension systems using generalized multi-dimension adaptive learning particle swarm optimization

Abstract

The performance parameters of suspension systems must be properly matched to ensure the handling and stability performance of a vehicle. Based on real vehicle measured data, a parameterized vehicle dynamic model is built, and the validity of the parameterized vehicle dynamic model is verified by comparing simulation results with real vehicle test results. Seven representative steady-state and transient single evaluation indicators of handling and stability of the vehicle are selected. The key parameters of McPherson suspension system, which significantly affects steady-state and transient handling and stability performance, are selected through a sensitivity analysis. Their contribution rates for each single evaluation indicator are calculated based on 81 simulation tests using the parameterized vehicle dynamic model. A comprehensive evaluation indicator system for the whole vehicle is established. This system contains the seven steady-state and transient single handling and stability evaluation indicators that are obtained using a quadratic response surface fitting for the selected key parameters. The comprehensive evaluation indicator system is used to show whether a vehicle has good steady-state and desirable transient responses. Moreover, a generalized multi-dimension adaptive learning particle swarm optimization is proposed to search for the global optimum of the comprehensive evaluation indicator system across the search space with rapid convergence. Optimization results show that a comprehensive handling and stability performance are improved, and simulation results of the parameterized vehicle dynamic model that is modified in accordance with the optimization results verify the improvement of the steady-state steering driving behavior and transient yaw response of the vehicle. In conclusion, the comprehensive evaluation indicator system is feasible, and the generalized multi-dimension adaptive learning particle swarm optimization is effective for the optimization design of the key parameters of the McPherson suspension system.

Keywords

Parameters optimization McPherson suspension steady-state and transient response surface fitting particle swarm optimization

Get full access to this article

View all access options for this article.

References

Bastow

Howard

Whitehead

JP.

Car suspension and handling. 4th ed. Warrendale, PA: Society of Automotive Engineers, 2004.

Lee

Kim

HJ.

Design optimization for kinematic characteristics of automotive suspension considering constraints. J Korea Acad Coop Soc 2017; 18: 306–311.

Kang

Rakheja

Zhang

Sensitivity analysis and optimisation of independent axle suspensions for a heavy-duty mining truck. Int J Heavy Veh Syst 2016; 23: 370–397.

Liu

Wang

, et al. Hardpoint correlation analysis and optimal design for front suspension of a formula SAE car. Aust J Mech Eng 2015; 13: 67–76.

Liao

Cao

Bin Wei

, et al. Robust optimization of multi-link suspension compliance characteristics based on Taguchi method. In: Proceedings of the 2nd international conference on computer engineering, information science & application technology, Wuhan, China, 8–9 July 2017, pp.726–732. Paris: Atlantis Press.

Wang

Beeh

Krüger

, et al. Topological optimization of a suspension concept considering the kinematics and compliance performance and the geometric non-linearity. Proc IMechE Part D: J Automobile Engineering 2018; 232: 318–329.

Tan

Ren

Optimal matching between the suspension and the rubber bushing of the in-wheel motor system. Proc IMechE Part D: J Automobile Engineering 2015; 229: 758–769.

Drehmer

LRC

Casas

WJP

Gomes

HM.

Parameters optimisation of a vehicle suspension system using a particle swarm optimisation algorithm. Vehicle Syst Dyn 2015; 53: 449–474.

Shirahatti

Prasad

PSS

Panzade

, et al. Optimal design of passenger car suspension for ride and road holding. J Brazil Soc Mech Sci Eng 2008; 30: 66–76.

10.

Nelder

Mead

A simplex method for function minimization. Comput J 1965; 7: 308–313.

11.

Klee

Minty

GJ.

How good is the simplex algorithm? New York: Academic Press, 1970, pp.159–175.

12.

Umeda

Ichikawa

A modified complex method for optimization. Ind Eng Chem Process Des Dev 1971; 10: 229–236.

13.

White

DJ.

Multiobjective programming and penalty functions. J Optim Theory Appl 1984; 43: 583–599.

14.

Rao

Annamdas

. Particle swarm methodologies for engineering design optimization. In: Proceedings of the ASME design engineering technical conference, San Diego, CA, 30 August–2 September 2009, pp.507–516. New York: American Society of Mechanical Engineers (ASME).

15.

Cheng

Lin

Multiobjective robust design of the double wishbone suspension system based on particle swarm optimization. Sci World J 2014; 3: 354857.

16.

Yildiz

AR.

A new hybrid particle swarm optimization approach for structural design optimization in the automotive industry. Proc IMechE Part D: J Automobile Engineering 2012; 226: 1340–1351.

17.

Alfi

Fateh

MM.

Parameter identification based on a modified PSO applied to suspension system. J Softw Eng Appl 2010; 3: 221–229.

18.

Jen

M-H

. Integration of kinematics and compliance measurement with vehicle dynamics validation for a shared platform. SAE Technical Paper 2007.

19.

Gillespie

TD.

The automotive chassis: engineering principles. 2nd ed. Oxford: Butterworth-Heinemann, 2001.

20.

Guo

. Simulation study of the handling and stability of a certain SUV. Dissertation, Changsha University of Science & Technology, Changsha, P.R. China, 2012.

21.

Chen

Analysis and suggestion for present evaluation index of automotive maneuvering stability. Automob Technol 2006; 9: 5–8.

22.

GB/T 6323-2014. Controllability and stability test procedure for automobile. Beijing, China: China Standards Press, 2014.

23.

Gillespie

TD.

Fundamentals of vehicle dynamics. Warrendale, PA: Society of Automotive Engineers, 1992.

24.

Heyes

Ray

Mitchell

, et al. Stimulus enhancement: controls for social facilitation and local enhancement. Learn Motiv 2000; 31: 83–98.

25.

Young

HP.

Innovation Diffusion in heterogeneous populations: contagion, social influence, and social learning. Am Econ Rev 2009; 99: 1899–1924.

26.

Heyes

CM.

Social learning in animals: categories and mechanisms. Biol Rev Camb Philos Soc 2010; 69: 207–231.

27.

Van Den Bergh

Engelbrecht

. A cooperative approach to particle swarm optimization. IEEE T Evol Comput 2004; 8: 225–239.

28.

Cheng

Jin

A social learning particle swarm optimization algorithm for scalable optimization. Inf Sci 2015; 291: 43–60.

29.

Tang

Luo

, et al. Multi-strategy adaptive particle swarm optimization for numerical optimization. Eng Appl Artif Intell 2015; 37: 9–19.