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

摘要/Abstract

摘要：

针对车辆转向非线性平衡状态及其稳定性确定问题，提出了求解车辆转向非线性二自由度模型平衡状态的一种新方法及其稳定性判据。首先，建立了车辆转向非线性二自由度模型，采用简化魔术公式轮胎模型描述了轮胎非线性侧向力。然后，提出了求解相应模型转向非线性平衡状态的粒子群算法，通过理论分析得到平衡状态稳定性判据。最后，设计了前轮转角、路面附着系数和车速分别变化的3种行驶条件，应用粒子群算法和拟牛顿法对3种行驶条件下的转向非线性平衡状态进行了求解和稳定性判断。结果表明，本文方法可以准确求解车辆转向非线性二自由度模型平衡状态，求解效果优于拟牛顿法，稳定性判据适用于确定平衡状态的稳定性。

关键词: 车辆工程, 非线性, 转向稳定性, 平衡状态, 车辆转向二自由度模型, 粒子群算法

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）

中图分类号:

U461.6

李杰,贾长旺,赵旗. 车辆转向非线性平衡状态求解及其稳定性确定[J]. 吉林大学学报(工学版), 2023, 53(12): 3326-3334.

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.

图/表 7

图1

表1

车辆参数"

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

表1

表2

粒子群算法参数"

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］

表2

表3

u=70 km/h和μ=0.8时粒子群算法求解转向平衡状态"

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

表3

图2

图3

图4

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