车辆转向非线性平衡状态求解及其稳定性确定

doi:10.13229/j.cnki.jdxbgxb.20220061

Abstract

Abstract:

Aiming at the problem of vehicle steering nonlinear equilibrium state and its stability determination， a new method for solving the equilibrium state of vehicle steering nonlinear two degree of freedom model and its stability criterion was proposed. Firstly， the nonlinear two degree of freedom model of vehicle steering was established， and the simplified magic formula tire model was used to describe the nonlinear tire lateral force. Then， the particle swarm optimization algorithm for solving the nonlinear equilibrium state of the corresponding model was established， and the stability criterion of the equilibrium state was deduced through theoretical analysis. Finally， three driving conditions with different front wheel steer angle， road adhesion coefficient and vehicle speed were designed， and the particle swarm optimization algorithm and the quasi Newton method were used to solve the steering nonlinear equilibrium state under the three driving conditions and to judge the stability of three kinds of driving conditions respectively. The results show that the proposed method can accurately solve the equilibrium state of the vehicle steering nonlinear two degree of freedom model， the solution effect is better than the quasi Newton method， and the stability criterion is suitable for determining the stability of the equilibrium state.

Key words: vehicle engineering, nonlinearity, steering stability, equilibrium state, two degree of freedom vehicle steering model, particle swarm optimization （PSO）

CLC Number:

U461.6

Jie LI,Chang-wang JIA,Qi ZHAO. Solution of nonlinear equilibrium state of vehicle steering and its stability determination[J].Journal of Jilin University(Engineering and Technology Edition), 2023, 53(12): 3326-3334.

Figures/Tables 7

Fig.1

Table 1

Vehicle parameters"

参数	数值
车辆总质量 $m$ /kg	1022
横摆转动惯量 $I z$ /（kg·m²）	1471.7
质心到前轴距离 $a$ /m	1.197
质心到后轴距离 $b$ /m	1.123
前轴轮胎参数 $C f$	1.162
前轴轮胎参数 $B f$	0.2
后轴轮胎参数 $C r$	1.313
后轴轮胎参数 $B r$	0.25

Table 1

Table 2

PSO parameters"

参数	数值
维数 $n$	2
粒子数目 $N$	50
最大迭代数 $M$	200
精度 $ε$	$10 - 4$
学习因子 $c 1$	1.5
学习因子 $c 2$	2.5
惯性权重 $w$	0.5
侧偏角位置范围 $[β m i n, β m a x]$	［-1，1］
横摆角速度位置范围 $[γ m i n, γ m a x]$	［-2，2］
侧偏角速度范围 $[- v β m, v β m]$	［-0.2，0.2］
横摆角速度范围 $[- v γ m, v γ m]$	［-0.5，0.5］

Table 2

Table 3

Steering equilibrium states at u=70 km/h andμ=0.8 solved by PSO"

平衡状态	前轮转角 $δ$ /rad	质心侧偏角 $β$ /rad	横摆角速度 $γ$ /（rad·s^-1）	适应值/10^-4
1	0	-0.2541	0.3975	0.5443
	0.02	-0.2425	0.3984	0.6840
	0.04	-0.2315	0.3993	0.9469
	0.06	-0.2213	0.3999	0.9681
	0.08	-0.2118	0.4006	0.8373
	0.10	-0.2030	0.4012	0.4632
	0.12	-0.1949	0.4017	0.0342
	0.14	-0.1875	0.4022	0.2721
	0.16	-0.1807	0.4025	0.6581
	0.18	-0.1745	0.4028	0.3866
	0.20	-0.1690	0.4030	0.9367
2	0	0	0	0.4808
	0.02	-0.0089	0.1135	0.6065
	0.04	-0.0197	0.2167	0.6575
	0.06	-0.0339	0.2974	0.4478
	0.08	-0.0510	0.3485	0.6475
	0.1	-0.0684	0.3753	0.2146
	0.12	-0.0842	0.3887	0.2247
	0.14	-0.0981	0.3955	0.0242
	0.16	-0.1101	0.3991	0.8736
	0.18	-0.1208	0.4010	0.9344
	0.20	-0.1304	0.4023	0.6673
3	0	0.2540	-0.3976	0.5801
	0.02	0.2664	-0.3966	0.5494
	0.04	0.2793	-0.3956	0.4685
	0.06	0.2929	-0.3948	0.8474
	0.08	0.3070	-0.3938	0.8171
	0.1	0.3217	-0.3927	0.9006
	0.12	0.3368	-0.3917	0.7133
	0.14	0.3523	-0.3906	0.4010
	0.16	0.3682	-0.3897	0.3474
	0.18	0.3845	-0.3888	0.3639
	0.20	0.4011	-0.3878	0.7732

Table 3

Fig.2

Fig.3

Fig.4

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Solution of nonlinear equilibrium state of vehicle steering and its stability determination

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