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
计量
- 文章访问数: 449
- HTML全文浏览量: 287
- PDF下载量: 13
- 被引次数: 0
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

HTML全文

图 1 整车受力分析图

Figure 1. Force analysis of the whole vehicle

下载: 全尺寸图片幻灯片

图 2 轮胎侧向力

Figure 2. Lateral force of tires

下载: 全尺寸图片幻灯片

图 3 复平面图

Figure 3. Complex plan

下载: 全尺寸图片幻灯片

图 4 随半径变化的根轨迹图

Figure 4. Root locus with variable radius

下载: 全尺寸图片幻灯片

图 5 随超高变化的根轨迹图

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 7 (β~γ)相平面图 1

Figure 7. (β~γ)phase plan 1

下载: 全尺寸图片幻灯片

图 8 (β~γ)相平面图 2

Figure 8. (β~γ)Phase plan 2

下载: 全尺寸图片幻灯片

图 9 (β~γ)相平面图 3

Figure 9. (β~γ)Phase plan 3

下载: 全尺寸图片幻灯片

图 10 (β~γ)相平面图 4

Figure 10. (β~γ)Phase plan 4

下载: 全尺寸图片幻灯片

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

参考文献(20)

[1]	岳雷, 杜豫川, 姚红云. 基于行驶稳定性的山区公路弯道最小半径优化[J]. 交通运输系统工程与信息, 2018, 18(5): 204-210. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT201805030.htm YUE Lei, DU Yuchuan, YAO Hongyun. Optimization of the minimum radius index of mountain road curve based on driving stability[J]. Journal of Transportation Systems Engineering and Information Technology, 2018, 18(5): 204-210. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT201805030.htm
[2]	孙川, 吴超仲, 褚端峰, 等. 基于车辆侧向稳定性分析的弯道行驶安全评价[J]. 交通信息与安全, 2014, 32(6): 95-100. doi: 10.3963/j.issn.1674-4861.2014.06.016 SUN Chuan, WU Chaozhong, CHU Duanfeng, et al. Safety evaluation of driving on curves based on analysis of vehicle lateral stability[J]. Journal of Transport Information and Safety, 2014, 32(6): 95-100. (in Chinese) doi: 10.3963/j.issn.1674-4861.2014.06.016
[3]	BILGANA M, DRAZEN C. Evaluation of design consistency on horizontal curves for two-lane state roads in terms of vehicle path radius and speed[J]. The Baltic Journal of Road and Bridge Engineering, 2016, 11(2): 54-58. http://www.researchgate.net/publication/304170050_Evaluation_of_Design_Consistency_on_Horizontal_Curves_for_Two-Lane_State_Roads_in_Terms_of_Vehicle_Path_Radius_and_Speed
[4]	DONNELL E, WOOD J, HIMES S, et al. Use of side friction in horizontal curve design: A margin of safety assessment[J]. Transportation Research Record, 2016(1): 61-71. http://en.cnki.com.cn/Article_en/CJFDTotal-GCJS201615034.htm
[5]	陈一锴, 史婷, 石琴, 等. 侧向安全边界理论在圆曲线路段限速中的应用[J]. 哈尔滨工业大学学报, 2019, 51(3): 179-185. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX201903026.htm CHEN Yikai, SHI Ting, SHI Qin, et al. Setting speed limit for horizontal circular curve of mountain highway using lateral safety boundary theory[J]. Journal of Harbin Institute of Technology, 2019, 51(3): 179-185. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX201903026.htm
[6]	姜康, 张梦雅, 陈一锴. 山区圆曲线路段半挂汽车列车行驶安全性分析[J]. 交通运输工程学报, 2015, 15(3): 109-117. doi: 10.3969/j.issn.1671-1637.2015.03.015 JIANG Kang, ZHANG Mengya, CHEN Yikai. Driving safety analysis of semi-trailer train at circular curve section in mountain area[J]. Journal of Traffic and Transportation Engineering, 2015, 15(3): 109-117. (in Chinese) doi: 10.3969/j.issn.1671-1637.2015.03.015
[7]	刘飞, 熊璐, 邓律华, 等. 基于相平面法的车辆行驶稳定性判定方法[J]. 华南理工大学学报(自然科学版), 2014, 42 (11): 63-70. doi: 10.3969/j.issn.1000-565X.2014.11.010 LIU Fei, XIONG Lu, DENG Lühua, et al. Vehicle stability criterion based on phase plane method[J]. Journal of South China University of Technology: (Natural Science Edition), 2014, 42 (11): 63-70. (in Chinese) doi: 10.3969/j.issn.1000-565X.2014.11.010
[8]	韦超毅, 谢美芝, 盘朝奉, 等. 根轨迹法在汽车操纵稳定性研究中的应[J]. 农业机械学报, 2007(9): 19-22. doi: 10.3969/j.issn.1000-1298.2007.09.005 WEI Chaoyi, XIE Meizhi, PAN Chaofeng, et al. Integrated root locus method and stability factor to study handling stability of automobile[J]. Transactions of the Chinese Society for Agricultural Machinery, 2007(9): 19-22. (in Chinese) doi: 10.3969/j.issn.1000-1298.2007.09.005
[9]	钱宇彬, 肖凌云, 王婉秋. 双车道公路驾驶人-车辆-弯道(环境)系统模型[J]. 汽车技术, 2019(8): 32-38. https://www.cnki.com.cn/Article/CJFDTOTAL-QCJS201908008.htm QIAN Yubin, XIAO Lingyun, WANG Wanqiu. Driver-Vehicle-Curve(Environment)system model in two-lane highway[J]. Automobile Technology, 2019(8): 32-38. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-QCJS201908008.htm
[10]	金辉, 李世杰. 基于极限车速的车辆稳定性控制研究[J]. 汽车工程, 2018, 40(1): 48-56. doi: 10.3969/j.issn.1674-6546.2018.01.013 JIN Hui, LI Shijie. A research on vehicle stability control based on limited speed[J]. Automotive Engineering, 2018, 40 (1): 48-56. (in Chinese) doi: 10.3969/j.issn.1674-6546.2018.01.013
[11]	许建, 张政, 李翔, 等. 独立驱动电动汽车横摆力矩的模糊控制算法[J]. 西安交通大学学报, 2014, 48(7): 83-89. https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT201407015.htm XU Jian, ZHANG Zheng, LI Xiang, et al. A fuzzy control system for the direct yaw moment of 4WD electric vehicles[J]. Journal of Xi'an Jiaotong University, 2014, 48(7): 83-89. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT201407015.htm
[12]	PACEJKA H B. Tire and vehicle dynamics[M]. Oxford: Butterworth-Heinemann, 2002.
[13]	张先勇. 公路平曲线横向力系数的研究[D]. 武汉: 华中科技大学, 2005. ZHANG Xianyong. Research on the coefficient of lateral force of highway horizontal curve[D]. Wuhan: Huazhong University of Science and Technology, 2005. (in Chinese)
[14]	OMORODION I I, OBINABO C E, EVBOGBAI M J E. Modeling, design and simulation of active suspension system root locus controller using automated tuning technique[J]. Mathematical Theory and Modeling, 2016, 6(1): 52-56. http://www.iiste.org/Journals/index.php/MTM/article/download/28232/28978
[15]	张志达, 李韶华, 刘星, 等. 全轮转向多轴车辆性能分析及侧翻前馈预警研究[J]. 北京理工大学学报, 2018, 38(1): 142-146. ZHANG Zhida, LI Shaohua, LIU Xing, et al. Performance analysis and rollover feed-forward warning for multi-axle vehicle with all wheel steering[J]. Journal of Beijing Institute of Technology, 2018, 38(1): 142-146. (in Chinese)
[16]	李静, 王子涵, 王宣锋. 基于相平面法的制动方向稳定性分析[J]. 汽车工程, 2014, 36(8): 974-979. https://www.cnki.com.cn/Article/CJFDTOTAL-QCGC201408014.htm LI Jing, WANG Zihan, WANG Xuanfeng. An analysis on braking directional stability based on phase-plane technique[J]. Automotive Engineering, 2014, 36(8): 974-979. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-QCGC201408014.htm
[17]	VON V A, LU Haiyan, KIENCKE U. Detection of critical driving situations using phase plane method for vehicle lateral dynamics control by rear wheel steering[J]. IFAC Proceedings Volumes, 2008, 41(2): 5694-5699. doi: 10.3182/20080706-5-KR-1001.00960
[18]	ZHANG Lizeng, GUAN Hsin, JIA Xin, et al. A study on the effect of driver model parameters on the performance of driver-vehicle-road closed-loop system[J]. Applied Mechanics and Materials, 2014, 470(1): 604-608. http://www.scientific.net/AMM.470.604
[19]	LI Haiqing, ZHAO Youqun, WANG Haoyu, et al. Design of an improved predictive LTR for rollover warning systems[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017, 39(10): 3779-3791. doi: 10.1007/s40430-017-0796-7
[20]	MENESES H, ARRIETA O, PADULA F, et al. PI/PID control design based on a fractional-order model for the process[J]. IFAC PapersOnLine, 2019, 52(1): 976-981. doi: 10.1016/j.ifacol.2019.06.189