耦合上装载荷的多轴车辆动力学建模与仿真

doi:10.12382/bgxb.2024.0647

摘要/Abstract

摘要：

多轴轮式车辆动力学模型是新型车辆快速开发及车辆设计参数优化、控制算法搭建的基础。目前普遍采用商用软件搭建,其动力学方程及模型梯度信息难以获取,无法将其应用于整车全局设计与控制参数的动态优化,且现有商业软件及理论建模研究对上装载荷动力学影响考虑较少。针对上述问题,基于拉格朗日动力学,考虑簧下质量纵横向运动及上装载荷反作用力对整车动力学的影响,应用矢量化建模方法搭建8×8轮式车辆24自由度动力学模型,分别基于C++和M语言进行软件开发。在变加速、阶跃转向、双移线、正弦扫频等多种工况下与商业软件TruckSim进行全面对比。研究结果表明,自主开发的仿真模型其轮胎力、悬架力及空气阻力、纵横垂向运动等与商业软件高度一致,最大误差小于5%,验证了新方法的准确性。

关键词: 多轴轮式车辆, 上装载荷, 矢量化建模, 动力学建模与仿真

Abstract:

Multi-axle wheeled vehicle dynamics model is the basis for the rapid development of new vehicle equipment,the optimization of vehicle design parameters and the construction of control algorithms.The commonly used commercial software is difficult to obtain the dynamic equations and model gradient information so that it cannot be used for the dynamic optimization of vehicle global design and control parameters.And the effects of top-loading dynamics have been given less consideration in existing commercial software and theoretical modelling studies.In order to address the aforementioned issues,a vectorized modeling method is employed to construct a 24-degrees-of-freedom dynamics model of an 8×8 wheeled vehicle based on Lagrangian dynamics,which considers the influences of the longitudinal and lateral motions of unsprung mass and the reaction force of top load on the vehicle dynamics.The modeling is based on Lagrangian dynamics,and the software is developed using C++ and M languages,respectively.The proposed model is comprehensively compared with the commercial software TruckSim under a variety of working conditions,including variable acceleration,step steering,double lane change,swept sine steering.The results demonstrate that the tire force,suspension force and air resistance,as well as the longitudinal,lateral and vertical motions of the proposed simulation model exhibit high consistency with those of the commercial software with an error of less than 5%.This verifies the accuracy of the methodology.

Key words: multi-axle wheeled vehicle, top load, vectorized modeling, dynamics modeling and simulation

李文浩, 于会龙, 卢玉传, 任延飞, 席军强. 耦合上装载荷的多轴车辆动力学建模与仿真[J]. 兵工学报, 2025, 46(8): 240647-.

LI Wenhao, YU Huilong, LU Yuchuan, REN Yanfei, XI Junqiang. Dynamics Modeling and Simulation of Multi-axle Wheeled Vehicle with Coupled Top Loads[J]. Acta Armamentarii, 2025, 46(8): 240647-.

图/表 15

图1 8×8轮式整车动力学模型框架

Fig.1 Framework of 8×8 wheeled vehicle model

图2 8×8轮式车辆模型示意图

Fig.2 Schematic diagram of 8×8 wheeled vehicle model

图3 8×8轮式车辆自由度示意图

Fig.3 Diagrammatic sketch of 8×8 wheeled vehicle's degree of freedoms

图4 8×8轮式车辆几何参数(左为车体几何参数, 右为炮塔几何参数)

Fig.4 Geometric parameters of 8×8 wheeled vehicle on X-Y plane(the left:the geometric parameters of vehicle body, and the right:the geometric parameters of turret)

图5 车辆受力

Fig.5 Forces and torques applied on the vehicle

图6 簧下质量所受力与力矩

Fig.6 Force and torque applied on the unsprung mass

图7 车辆模型解算流程图

Fig.7 Flowchart of vehicle model solving

表1 纵向变加速误差分析

Table 1 Longitudinal variable acceleration error

参数	最大绝对值误差	误差均方根
纵向速度/(m·s^-1)	9.68×10^-4	7.96×10^-4
垂向速度/(m·s^-1)	5.92×10^-4	7.42×10^-5
纵向位移/m	1.74×10^-2	1.33×10^-2
纵向加速度/(m·s^-2)	8.74×10^-2	4.80×10^-3
俯仰角速度/(rad·s^-1)	3.00×10^-3	2.19×10^-4

表2 转角阶跃输入工况误差分析

Table 2 Step steering maneuver error

参数	最大绝对值误差	误差均方根
纵向位移/m	7.95×10^-2	4.3×10^-2
纵向速度/(m·s^-1)	2.64×10^-2	9.3×10^-3
横向位移/m	9.70×10^-2	5.36×10^-2
横向速度/(m·s^-1)	1.46×10^-1	3.79×10^-2

表3 双移线工况误差分析

Table 3 Double lane change maneuver error

参数	最大绝对值误差	误差均方根
纵向位移/m	2.89×10^-1	1.21×10^-1
纵向速度/(m·s^-1)	6.35×10^-2	2.78×10^-2
横向位移/m	1.38×10^-1	6.41×10^-2
横向速度/(m·s^-1)	2.24×10^-1	7.58×10^-2

表4 sin转角工况误差分析

Table 4 Swept sine steering maneuver error

类别	最大绝对值误差	误差均方根
纵向位移/m	4.66×10^-1	2.18×10^-1
纵向速度/(m·s^-1)	4.17×10^-2	2.68×10^-2
横向位移/m	7.19×10^-2	4.17×10^-2
横向速度/(m·s^-1)	1.2×10^-1	6.2×10^-2

图8 车辆变加速运动对比结果

Fig.8 Comparison results of variable accelerations

图9 轮胎转角阶跃输入工况对比结果

Fig.9 Comparison results of step steer

图10 整车双移线工况对比结果

Fig.10 Compared results of double lane change

图11 轮胎sin转角工况对比结果

Fig.11 Compared results of sin steer

参考文献 31

[1]	李嘉麒, 魏曙光, 廖自力, 等. 陆战平台全电化关键技术发展综述[J]. 兵工学报, 2021, 42(10):2049-2059. doi: 10.3969/j.issn.1000-1093.2021.10.001
	LI J Q, WEI S G, LIAO Z L, et al. Review on the key technologies and development of all-electric land warfare platform[J]. Acta Armamentarii, 2021, 42(10):2049-2059. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.10.001
[2]	臧克茂. 陆战平台全电化技术研究综述[J]. 装甲兵工程学院学报, 2011, 25(1):1-7.
	ZANG K M. Study on the all-electric technology of land warfare platform[J]. Journal of Academy of Armored Force Engineering, 2011, 25(1):1-7. (in Chinese)
[3]	邹明虎, 刘长江, 彭顺堂, 等. 现代战斗车辆能量体系结构研究[J]. 兵工自动化, 2019, 38(4):15-19.
	ZOU M H, LIU C J, PENG S T, et al. Primary study on the technical status quo and key technology development of the electrical drive of the armored vehicles[J]. Ordnance Industry Automation, 2019, 38(4):15-19. (in Chinese)
[4]	DAL B N, BERTOLAZZI E, BIRAL F, et al. Comparison of direct and indirect methods for minimum lap time optimal control problems[J]. Vehicle System Dynamics, 2019, 57(5):665-696.
[5]	WISCHNEWSKI A, EULER M, GÜMÜS S, et al. Tube model predictive control for an autonomous race car[J]. Vehicle System Dynamics, 2022, 60(9):3151-3173.
[6]	YUAN D R, YU X Y, LI S Y, et al. Safe-by-construction autonomous vehicle overtaking using control barrier functions and model predictive control[J]. International Journal of Systems Science, 2024, 55(7):1283-1303.
[7]	HE S Y, ZENG J, ZHANG B K, et al. Rule-based safety-critical control design using control barrier functions with application to autonomous lane change[C]// Proceedings of 2021 American Control Conference. New Orleans,LA,US: IEEE, 2021:178-185.
[8]	GOH J Y M, THOMPSON M, DALLAS J, et al. Beyond the stable handling limits:nonlinear model predictive control for highly transient autonomous drifting[J]. Vehicle System Dynamics, 2024, 62(10):2590-2613.
[9]	REINA G, LEANZA A, MANTRIOTA G. Model-based observers for vehicle dynamics and tyre force prediction[J]. Vehicle System Dynamics, 2022, 60(8):2845-2870.
[10]	TIAN M J, ZHANG Q X, TIAN D Y, et al. Pre-stability control for in-wheel-motor-driven electric vehicles with dynamic state prediction[J]. IEEE Transactions on Intelligent Vehicles, 2024, 9(3):4541-4554.
[11]	MALLIKARJUNARAO C, SEGEL L. A study of the directional and roll dynamics of multiple-articulated vehicles[M]// FROHLING R,edited. The Dynamics of Vehicles on Roads and on Tracks. London,UK: Routledge, 2018:81-96.
[12]	JOHNSON P, MILLIKEN G A. A simple procedure for testing linear hypotheses about the parameters of a nonlinear model using weighted least squares[J]. Communications in Statistics-Simulation and Computation, 1983, 12(2):135-145.
[13]	CASTELLANOS M L M, MANCA R, HEGDE S, et al. Predictive handling limits monitoring and agility improvement with torque vectoring on a rear in-wheel drive electric vehicle[J]. Vehicle System Dynamics, 2023, 62(9):1-25.
[14]	REINA G, GENTILE A, MESSINA A. Tyre pressure monitoring using a dynamical model-based estimator[J]. Vehicle System Dynamics, 2015, 53(4):568-586.
[15]	KAROGAL I S. Independent torque distribution management systems for vehicle stability control[M]. Clemson,CA,US: Clemson University, 2008.
[16]	GHIKE C, SHIM T. 14 degree-of-freedom vehicle model for roll dynamics study[R]. Warrendale,PA,US: SAE Technical Paper, 2006.
[17]	YU H L, CHELI F, CASTELLI-DEZZA F. Optimal design and control of 4-IWD electric vehicles based on a 14-DOF vehicle model[J]. IEEE Transactions on Vehicular Technology, 2018, 67(11):10457-10469.
[18]	KIM W, YI K, LEE J. Drive control algorithm for an independent 8 in-wheel motor drive vehicle[J]. Journal of Mechanical Science and Technology, 2011, 25(6):1573-1581.
[19]	FAUROUX J C, VASLIN P. Modeling, experimenting,and improving skid steering on a 6×6 all-terrain mobile platform[J]. Journal of Field Robotics, 2010, 27(2):107-126.
[20]	ZHANG Y B, HUANG Y J, WANG H, et al. A comparative study of equivalent modelling for multi-axle vehicle[J]. Vehicle System Dynamics, 2018, 56(3):443-460.
[21]	DING J Q, GUO K H. Development of a generalised equivalent estimation approach for multi-axle vehicle handling dynamics[J]. Vehicle System Dynamics, 2016, 54(1):20-57.
[22]	AOKI A, MARUMO Y, KAGEYAMA I. Effects of multiple axles on the lateral dynamics of multi-articulated vehicles[J]. Vehicle System Dynamics, 2013, 51(3):338-359.
[23]	VANTSEVICH V V. Vehicle systems:coupled and interactive dynamics analysis[J]. Vehicle System Dynamics, 2014, 52(11):1489-1516.
[24]	ZHANG Y B, KHAJEPOUR A, HUANG Y J. Multi-axle/articulated bus dynamics modeling:a reconfigurable approach[J]. Vehicle System Dynamics, 2018, 56(9):1315-1343.
[25]	LI E H, YU H L, XI J Q, et al. Stability-guaranteed model predictive path tracking of autonomous tractor semi-Trailers under extreme conditions[J]. IEEE Transactions on Intelligent Vehicles, 2024, 99:1-14.
[26]	刘明春. 8×8轮毂电机驱动车辆操纵稳定性分析与控制研究[D]. 北京: 北京理工大学, 2015.
	LIU M C. Study on handling stability analysis and control for 8×8 in-wheel motor drive Vehicle[D]. Beijing: Beijing Institute of Technology, 2015. (in Chinese)
[27]	贾明琛. 8×8分布式轮毂电驱动车辆复合转向系统建模与仿真研究[D]. 北京: 北京理工大学, 2021.
	JIA M C. Modeling and simulation on composite steering system of 8×8 distributed inwheel motor drive vehicle[D]. Beijing: Beijing Institute of Technology, 2021. (in Chinese)
[28]	叶玉博. 8×8分布式电驱动车辆转向工况驱动力矩分配控制研究[D]. 北京: 北京理工大学, 2019.
	YE Y B. Research on drive torque distribution control of 8×8 distributed electric vehicles under steering conditions[D]. Beijing: Beijing Institute of Technology, 2019. (in Chinese)
[29]	张猛. 8×8轮毂电机驱动车辆转向稳定性控制策略研究[D]. 北京: 北京理工大学, 2018.
	ZHANG M. Research on steering stability control for 8×8 in-wheel motor drive vehicle[D]. Beijing: Beijing Institute of Technology, 2018. (in Chinese)
[30]	刘光远. 8×8分布式驱动车辆直驶稳定性控制策略研究[D]. 北京: 北京理工大学, 2020.
	LIU G Y. Research on straight driving stability control for 8×8 in-wheel motor drive vehicle[D]. Beijing: Beijing Institute of Technology, 2020. (in Chinese)
[31]	PACEJKA H B. Tire and vehicle dynamics[M]. Delft,Nederland: Delft University of Technology Consultant TNO Automotive Helmond the Netherlands, 2006.