基于侧向稳定性的圆曲线路段设计指标研究

张航; 储泽宇; 吕能超; 段和柱

doi:10.3963/j.jssn.1674-4861.2021.02.004

基于侧向稳定性的圆曲线路段设计指标研究

doi: 10.3963/j.jssn.1674-4861.2021.02.004

1.
武汉理工大学交通学院武汉 430063
2.
武汉理工大学智能交通系统研究中心武汉 430063

基金项目:

国家自然科学基金项目 52072290

详细信息

通讯作者:
张航(1967—)，博士，副教授.研究方向：道路规划与设计、路线设计理论与方法、道路交通安全设计与评价. E-mail：zhanghang1999@sina.com

中图分类号: U412.34
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出版历程
- 收稿日期: 2020-11-24

Design Indices of Circular Curve Section Based on Lateral Stability

1.
School of Transportation, Wuhan University of Technology, Wuhan 430063, China
2.
Intelligent Transportation Systems Reasarch Center, Wuhan University of Technology, Wuhan 430063, China

摘要

摘要: 车辆在附着系数较小的圆曲线路段转向时，轮胎会处于非线性区内工作，此时基于线性理论的侧向稳定性分析方法会产生较大误差。建立6自由度非线性车辆系统模型，分析其处于非线性域与线性域下不同的特性状态，得到不同车速、路面附着系数下使车辆系统处于临界状态的圆曲线路段半径、超高设计指标。对线性域与非线性域内的车辆系统分别采用基于线性理论的根轨迹法与基于非线性理论的相平面法分析侧向稳定性，得到综合考虑2种状态下车辆临界失稳状态的圆曲线路段指标。结果表明，车速为60 km/h，路面附着系数为0.24，超高小于6% 时，车辆发生侧向失稳时轮胎处于非线性域，此时使用相平面法分析得到侧向失稳临界指标；车速为60 km/h，路面附着系数为大于0.4，超高处于4%到10%之间时，车辆发生侧向失稳时轮胎处于线性域，此时使用根轨迹法分析得到侧向失稳临界指标。
- 交通安全 /
- 圆曲线路段 /
- 侧向稳定性 /
- 相平面法 /
- 根轨迹法 /
- 仿真
Abstract: When a vehicle turns in a circular curve section with a small adhesion coefficient, its tires work in a nonlinear zone, and the lateral stability analysis method based on the linear theory would generate large errors. This paper focuses on the different characteristics of the 6-DOF nonlinear vehicle system model in nonlinear and linear domains. Under different speed and road adhesion coefficients, the radius and superelevation design indices of the circular curve section with the critical state of the vehicle system are calculated. The root locus method based on the linear theory and the phase plane method based on the nonlinear theory are used to analyze the lateral stability of vehicle systems in linear and nonlinear domains, respectively. Then, a sectional index of the circular curve considering the critical instability state of vehicles in both states is obtained. The results show that when the vehicle speed is 60 km/h, with the road adhesion coefficient of 0.24, and the superelevation less than 6%. The tires are in the nonlinear domain when the vehicle lateral instability occurs. Besides, a critical index of lateral instability is obtained using the phase plane method. When the vehicle speed is 60 km/h, the road adhesion coefficient is greater than 0.4, and the superelevation is between 4 and 10%. The tires are in the linear domain when the vehicle lateral instability occurs, and the root system is used. Then a critical index of lateral instability is obtained by trajectory analysis.
- traffic safety /
- circular curve section /
- lateral stability /
- phase plane method /
- root locus method /
- simulation

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图 1 整车受力分析图

Figure 1. Force analysis of the whole vehicle

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图 2 轮胎侧向力

Figure 2. Lateral force of tires

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图 3 复平面图

Figure 3. Complex plan

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图 4 随半径变化的根轨迹图

Figure 4. Root locus with variable radius

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图 5 随超高变化的根轨迹图

Figure 5. Root locus varying with the cross slope of the road

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图 6 随路面附着系数变化的根轨迹图

Figure 6. Root locus with the variable adhesion coefficients of the road

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图 7 (β~γ)相平面图 1

Figure 7. (β~γ)phase plan 1

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图 8 (β~γ)相平面图 2

Figure 8. (β~γ)Phase plan 2

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图 9 (β~γ)相平面图 3

Figure 9. (β~γ)Phase plan 3

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图 10 (β~γ)相平面图 4

Figure 10. (β~γ)Phase plan 4

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表 1 整车参数

Table 1. Vehicle parameters

车辆参数	数值
整车质量/kg	1 416
转动惯量/(kg/m²)	1 523
质心-前轴距/m	1.016
质心-后轴距/m	1.562
轮距/m	1.534
轮胎半径/m	0.310

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表 2 部分半径值对应的前轮转角

Table 2. Front wheel turning angle corresponding to some radius values

编号	半径r/m	前轮转角δ/(°)
1	200	0.79
2	150	1.05
3	120	1.31
4	100	1.56
5	80	1.97
6	67	2.47
7	60	2.84
8	40	4.08

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表 3 车辆系统非线性域临界指标

Table 3. Critical index of the vehicle system in the nonlinear domain

车速/(km/h)	路面附着系数μ	超高θ/%	非线性域临界半径R₁/m
60	0.24	4	127
		6	109
		8	89
		10	76
	0.4	4	63
		6	54
		8	49
		10	42
	0.6	4	48
		6	45
		8	41
		10	37

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表 4 车辆系统侧向失稳状态临界指标

Table 4. Critical index of the laterally unstable state of a vehicle system

路面附着系数μ	超高θ/%	失稳状态临界半径R₁/m	非线性域临界半径R₂/m
0.24	4	86	127
	6	82	109
	8	77	89
	10	74	76
0.4	4	64	63
	6	62	54
	8	57	49
	10	55	42
0.6	4	52	48
	6	48	45
	8	45	41
	10	40	37

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表 5 非线性域侧向失稳状态临界指标

Table 5. Critical index of lateral instability in the nonlinear domain

路面附着系数μ	超高θ/%	失稳状态临界半径R₁/m	非线性域临界半径R₂/m
0.24	4	103	127
	6	107	109
	8	116	89
	10	124	76
0.4	4	74	61
	6	71	54
	8	84	49
	10	92	42
0.6	4	68	48
	6	71	45
	8	82	41
	10	87	37

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表 6 侧向稳定性分析准确性验证

Table 6. Verification of the accuracy of lateral stability analysis

路面附着系数μ	超高θ/%	仿真得到的极限失稳半径R₁/m	相平面法极限失稳半径R₂/m	根轨迹法极限失稳半径R₃/m	侧向失稳临界半径R₄/m
0.24	4	105	103	86	103
	6	97	107	82	107
	8	91	116	77	77
	10	85	124	74	74
0.4	4	67	74	64	64
	6	64	71	62	62
	8	61	84	57	57
	10	58	92	55	55
0.6	4	47	68	52	52
	6	45	71	48	48
	8	44	82	45	45
	10	42	87	40	40

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