Development and Validation of a Scaled Electric Combat Vehicle Tire Model

Pneumatic tire modeling and validation have been the topic of several research papers, however, most of these papers only deal with pneumatic passenger and truck tires. In recent years, wheeled-scaled vehicles have gained lots of attention as a feasible testing platform, nonetheless up to the authors’ knowledge there has been no research regarding the use of scaled tires and their effect on the overall vehicle performance characteristics. This paper presents a novel scaled electric combat vehicle tire model and validation technique. The pro-line lockdown tire size 3.00 × 7.35 is modeled using the Finite Element Analysis (FEA) technique and several materials including layered membrane, beam elements, and Mooney-Rivlin for rubber. The tire-rim assembly is then described, and the rigid body analysis is presented. The tire is then validated using an in-house custom-made static tire testing machine. The tire test rig is made specifically to test the pro-line tire model and is designed and manufactured in the laboratory. The tire is validated using vertical stiffness and footprint tests in the static domain at different operating conditions including several vertical loads. Then the tire is used to perform rolling resistance and steering analysis including the rolling resistance coefficient and the cornering stiffness. The analysis is performed at different operating conditions including longitudinal speeds of 5, 10, and 15 km/h. This tire model will be further used to determine the tractive and braking performance of the tire. Furthermore, the tire test rig will also be modified to perform cornering stiffness tests.

FEM tire model oriented to virtual experiment of off-road vehicle trafficability

In order to estimate the trafficability of off-road vehicles, the linear relationships between the pressure and the stiffness of the tire and the action of the vertical tire force with the viscoelasticity are analyzed. The method to improve the precision of the model by the coefficients is presented. The constitutive equation of the three-parameter linear model and the stiffness matrix of four-node isoparametric elements are derived to construct the FEM （finite element method） tire model in plan stress. A demarcation and verification system is designed based on the six-dimensional wheel force transducer and the vertical tire force is measured under different velocities. The results show that the model and the method proposed are reasonable.

An Adaptive Nonsingular Fast Terminal Sliding Mode Control for Yaw Stability Control of Bus Based on STI Tire Model

Due to the bus characteristics of large quality,high center of gravity and narrow wheelbase,the research of its yaw stability control(YSC)system has become the focus in the field of vehicle system dynamics.However,the tire nonlinear mechanical properties and the effectiveness of the YSC control system are not considered carefully in the current research.In this paper,a novel adaptive nonsingular fast terminal sliding mode(ANFTSM)control scheme for YSC is proposed to improve the bus curve driving stability and safety on slippery roads.Firstly,the STI(Systems Technologies Inc.)tire model,which can effectively reflect the nonlinear coupling relationship between the tire longitudinal force and lateral force,is established based on experimental data and firstly adopted in the bus YSC system design.On this basis,a more accurate bus lateral dynamics model is built and a novel YSC strategy based on ANFTSM,which has the merits of fast transient response,finite time convergence and high robustness against uncertainties and external disturbances,is designed.Thirdly,to solve the optimal allocation problem of the tire forces,whose objective is to achieve the desired direct yaw moment through the effective distribution of the brake force of each tire,the robust least-squares allocation method is adopted.To verify the feasibility,effectiveness and practicality of the proposed bus YSC approach,the TruckSim-Simulink co-simulation results are finally provided.The co-simulation results show that the lateral stability of bus under special driving conditions has been significantly improved.This research proposes a more effective design method for bus YSC system based on a more accurate tire model.

Effect of Tire Repeated Root Modal on Tire Modelling with Experimental Modal

The effect of tire repeated root modal（RRM）on tire modeling with an experimental modal is studied.Firstly,a radial tire with radial and tangential RRMs is tested and analyzed.By multi-point exciting of the radial tire,a multiple reference frequency domain method based on a least squares（LMS PolyMAX）algorithm is used to identify modal parameters.Then,modal stability diagram（MSD）,modal indication function（MIF）and modal assurance criteria（Auto-MAC）matrix are utilized to induce multiple inputs multiple outputs（MIMO）frequency response function（FRF）matrixes.The tests reveal that notable repeated roots exist in both radial and tangential response modes.Their modal frequencies and damping factors are approximately the same,the amplitudes of modal vectors are in the same order of magnitude,and the mode shapes are orthogonal.Based on the works mentioned,the method of trigonometric series modal shapes fitting is adopted,the effects of RRM model on tire modeling with a vertical experimental modal are discussed.The final results show that the effects of considering the RRM shapes are equivalent to the tire mode shapes depended on rotating the tire’s different exciting points during tire modeling,and since considering the RRM,the tire mode shapes can be unified and fixed during tire modeling.

A Discrete Tire Model for Cornering Properties Considering Rubber Friction

In this paper,a discrete tire model of comering properties for road vehicles relating to tire grip performance,which is important for driving stability and safety,is presented.The proposed tire model combines realistic rubber friction related to velocity and tire grip performance with deformation of the carcass.The model can describe the stress and strain of the carcass and tread,and the rubber friction coefficient at each point of the contact patch,which is affected by the di stribution of the slip velocity.Meanwhile,the model incorporates the effects of the viscoelastic rubber material and power spectrum of the road,which are explicitly reflected in the rubber friction model.First,an improved rubber friction model based on the Persson theory of rubber friction is introduced in this paper.A discrete analytical tire model,which considers carcass compliance and the discretization of the tread,is then proposed.In addition,important phenomena of tire properties arising from the carcass compl iance and rubber friction are analyzed and the effectiveness of the discrete analytical tire model is validated experimentally.The proposed model provides a new way to optimize the grip performance of a tire by adjusting the tire or rubber physical parameters even before the tire is made.

Mathematical Models of Tire-Longitudinal Road Adhesion and Their Use in the Study of Road Vehicle Dynamics

Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.

Parameter Identification of Magic Formula Tire Model Based on Fibonacci Tree Optimization Algorithm

The magic formula(MF)tire model is a semi-empirical tire model that can precisely simulate tire behavior.The heuristic optimization algorithm is typically used for parameter identification of the MF tire model.To avoid the defect of the traditional heuristic optimization algorithm that can easily fall into the local optimum,a parameter identification method based on the Fibonacci tree optimization(FTO)algorithm is proposed,which is used to identify the parameters of the MF tire model.The proposed method establishes the basic structure of the Fibonacci tree alternately through global and local searches and completes optimization accordingly.The global search rule in the original FTO was modified to improve its efficiency.The results of independent repeated experiments on two typical multimodal function optimizations and the parameter identification results showed that FTO was not sensitive to the initial values.In addition,it had a better global optimization performance than genetic algorithm(GA)and particle swarm optimization(PSO).The root mean square error values optimized with FTO were 5.09%,10.22%,and 3.98%less than the GA,and 6.04%,4.47%,and 16.42%less than the PSO in pure lateral and longitudinal forces,and pure aligning torque parameter identification.The parameter identification method based on FTO was found to be effective.

Dynamics of vehicle-pavement coupled system based on a revised flexible roller contact tire model

A revised flexible roller contact tire model (RFRC tire model) is proposed, which considers not only the geometric and flexible filtering effect, but also tire damping and pavement displacement. A vehi- cle-pavement coupled system is modeled as a two DOF oscillator moving along a simply supported beam on a linear viscoelastic foundation. By using the Galerkin’s and Direct Integral method, dynamical responses of the vehicle-pavement coupled system are obtained based on the RFRC tire model and the traditional single point contact tire model (SPC tire model). The simulation results are compared with test data and the validity of the proposed RFRC tire model is verified. Differences between the two models are also investigated. It is found that the dynamical behaviors for both models agree with each other quite well when road surface roughness is a long harmonic wave. On the other hand, they are different under short harmonic wave or impulse road excitation. Thus the RFRC tire model should be used to compute the tire force and investigate dynamical responses of vehicle and pavement.

Tire Dynamics Modeling Method Based on Rapid Test Method

Combined with the tire dynamics theoretical model,a rapid test method to obtain tire lateral and longitudinal both steady-state and transient characteristics only based on the tire quasi-steady-state test results is proposed.For steady state data extraction,the test time of the rapid test method is half that of the conventional test method.For transient tire characteristics the rapid test method omits the traditional tire test totally.At the mean time the accuracy of the two method is much closed.The rapid test method is explained theoretically and the test process is designed.The key parameters of tire are extracted and the comparison is made between rapid test and traditional test method.The result show that the identification accuracy based on the rapid test method is almost equal to the accuracy of the conventional one.Then,the heat generated during the rapid test method and that generated during the conventional test are calculated separately.The comparison shows that the heat generated during the rapid test is much smaller than the heat generated during the conventional test process.This benefits to the reduction of tire wear and the consistency of test results.Finally,it can be concluded that the fast test method can efficiently,accurately and energy-efficiently measure the steady-state and transient characteristics of the tire.

A dynamic tire model based on HPSO-SVM

In order to accurately describe the force mechanism of tires on agricultural roads and improve the life cycle of agricultural tires,a tire-deformable terrain model was established.The effects of tread pattern,wheel spine,tire sidewall elasticity,inflation pressure and soil deformation were considered in the model and fitted with a support vector machine(SVM)model.Hybrid particle swarm optimization(HPSO)was used to optimize the parameters of SVM prediction model,of which inertia weight and learning factor were improved.To verify the performance of the model,a tire force prediction model of agricultural vehicle with the improved SVM method was investigated,which was a complex nonlinear problem affected by many factors.Cross validation(CV)method was used to evaluate the training precision accuracy of the model,and then the improved HPSO was adopted to select parameters.Results showed that the choice randomness of specifying the parameters was avoided and the workload of the parameter selection was reduced.Compared with the dynamic tire model without considering the influence of tread pattern and wheel spine,the improved SVM model achieved a better prediction performance.The empirical results indicate that the HPSO based parameters optimization in SVM is feasible,which provides a practical guidance to tire force prediction of agricultural transport vehicles.

基于自主漂移的自动驾驶车辆极限工况轨迹规划与控制

为兼顾自动驾驶车辆在极限工况下的稳定性与轨迹跟踪性能,提出了一种基于自主漂移的自动驾驶车辆轨迹规划与控制方法。基于神经网络设计了神经网络轮胎动力学模型,提升了传统魔术轮胎公式的精度。为进一步拓展自动驾驶车辆极限工况下的稳定边界,基于漂移时轮胎饱和及最大侧滑特性结合质心侧偏角-横摆角速度相平面约束设计了漂移稳定边界,采用非线性模型预测控制(NMPC)在更大稳定范围内规划了安全漂移轨迹,并对规划轨迹进行了漂移跟踪控制。Simulink/CarSim联合仿真结果表明,该方法可充分利用漂移运动优势,在极限工况下确保车辆不发生失控,同时准确跟踪期望轨迹。

用于轮胎振动分析的壳模型优化研究

虽然现有壳模型在0~500 Hz频带内精度高,适合用于轮胎结构振动分析,但由于模型中耦合了胎侧二维壳模型,导致胎冠振动模态难以分离,且模型自由度和所需输入参数增加。本文对该壳模型进行改进:在保持胎冠壳模型不变的基础上,应用轮胎环模型和板模型中对胎侧的近似方法,采用弹性基底代替胎侧二维壳模型,简化了原模型的边界条件并缩减了输入参数个数;针对改进后的壳模型建立了求解方法,实现了胎冠模态频率和振型的求解。并通过与实验数据的对比,验证了改进后的壳模型及其求解方法的正确性。

Finite Element Analysis of Tire Traction Using a Rubber-Ice Friction Model

The friction of road surface covered by snow or ice is very low and that results in reducing vehicle traction forces and potential traffic accidents. In general, to establish a master curve on a rubber-ice friction model is difficult because the ice surface, being not far removed from its melting point, reacts itself very sen-sitively to pressure, speed, and temperature changes. In this paper, an accepta-ble frictional interaction model was implemented to finite element method to rationally examine the frictional interaction behavior on ice between the tire and the road surface. The formula of friction characteristic according to tem-perature and sliding velocity on the ice surface was applied for tire traction analysis. Numerical results were verified by comparing the outdoor test data and it was confirmed to indicate similar correlation. It is found that the rub-ber-ice friction model will be useful for the improvement of the ice traction performance of tire.

基于Uni-Tire轮胎模型的车辆质心侧偏角估计

针对车辆质心侧偏角估计的准确性和实时性能问题,提出了车辆质心侧偏角估计的非线性全维观测器设计方法.首先基于车辆动力学模型及纵滑-侧偏联合工况下的Uni-Tire轮胎模型,利用车载传感器测量车辆状态;观测器利用这些状态估计出车辆的纵向速度、侧向速度及横摆角速度,并由此得到车辆的质心侧偏角估计.其次利用输入-状态稳定(input-to-state stability,ISS)理论对观测器的稳定性进行了分析.最后采用红旗CA7180A3E型轿车的车辆参数使用车辆仿真软件veDYNA对极限工况下的估计结果进行了离线仿真研究,并利用xPC-Target仿真环境和dSPACE实时仿真系统搭建仿真平台,对非线性全维观测器的实时性进行验证.仿真结果表明,非线性估计方法估计精度较高,实时性较好,可以满足工程应用的要求.

UniTire与Magic Formula稳态模型的对比研究

荷兰学者Pacejka提出的魔术公式Magic Formula和我国郭孔辉教授提出的统一轮胎模型UniTire在汽车操纵动力学研究中得到了广泛的应用。通过对这两种模型建模机理的对比表明,UniTire轮胎模型比MagicFor-mula模型具有更强的理论基础;通过试验数据辨识模型参数对比两种模型的全局辨识精度以及预测精度的结果表明,UniTire轮胎模型的全局辨识精度略高于Magic Formula模型,而且明显具有更高的预测能力。

基于UniTire侧向力模型的汽车操纵稳定性的建模和仿真

为了进行汽车操纵稳定性建模和仿真,总结了非线性和线性Uni Ttire侧向力模型。基于平面假设,建立了考虑轮胎非线性和线性的汽车操纵稳定性二自由度模型,提出了基于线性和非线性Uni Ttire侧向力模型的操纵稳定性仿真算法。在常用车速60 km/h下,对某轿车操纵稳定性进行了仿真,获得了横摆角速度、质心侧偏角和侧向加速度的时间历程。研究结果表明,基于线性和非线性Uni Ttire侧向力模型仿真的横摆角速度、质心侧偏角和侧向加速度是不同的,研究汽车操纵稳定性应关注轮胎的非线性。

轮胎等效模型与快速计算研究

复杂的轮胎结构和橡胶等超弹材料是影响轮胎有限元模型精度和计算速度的重要因素。为实现模型的快速计算,通过探索线性材料构建轮胎有限元模型,对模型进行等效处理。构建了轮胎有限元精细模型,并通过台架试验对精细模型的有效性进行验证。对轮胎精细模型提出3种简化方式,分别为实体单元建模、实体单元和壳单元混合建模、实体单元和梁单元混合建模,并采用线性材料计算3种等效模型的充气侧向变形量、充气径向变形量以及径向加载下沉量,最终得到其最优等效模型。通过对等效模型接地印记和接地压力以及各阶模态与精细模型对比,验证了等效模型的准确性和计算效率,为整车有限元仿真提供一种轮胎建模方法。

UniTire统一轮胎模型

UniTire模型是用于车辆动力学仿真和控制的非线性非稳态轮胎模型,能够准确描述轮胎在复杂工况下的力学特性。UniTire模型以理论模型为基础,采用无量纲的表达形式,具有统一的滑移率定义;统一的无量纲印迹压力分布表达;统一的各向轮胎力无量纲建模;统一的各向摩擦系数表达;无量纲边界条件的统一满足;不同速度下轮胎模型的统一表达;稳态与非稳态特性的统一;侧倾、转偏作用与侧偏特性的统一。不仅能够对各种工况下的轮胎力学特性进行高精度的表达,还具有良好的外推能力和预测能力,能够对复合工况、不同路面和不同速度下的轮胎特性进行准确的预测。本研究围绕UniTire的建模思想,介绍UniTire建模的理论基础、稳态和非稳态模型以及模型的表达和预测能力并进行试验验证。

车辆在非光滑路面的接触动力学分析方法研究

车辆接触动力学研究有助于更加全面地了解整车力学性能,对整车稳定性和座舱舒适性设计具有指导性作用.文章基于非光滑多体系统理论,对车辆系统展开接触动力学研究.考虑到车辆在行驶过程中,轮胎是与地面接触的唯一部件,轮胎动力学模型对整车动力学分析发挥着重要的作用.首先,借助于张拉整体结构的思想,建立轮胎的等效模型.然后,采用拉格朗日乘子方法,将约束方程引入到拉格朗日函数中,并基于第二类拉格朗日方程,推导得到整车系统的一般动力学方程.由于接触碰撞的存在,会导致车辆的状态变量呈现出非连续性.利用牛顿碰撞定律,建立了碰撞响应的非光滑数学列式,并利用光滑化的Fischer-Burmeister函数将非光滑数学列式进行等效替换,以提高计算效率.其次,将摩擦响应的求解转化为优化问题进行描述,以避免求解摩擦方向时出现奇异.另外,将车辆系统的一般动力学模型分解为光滑部分与非光滑部分进行求解,并利用广义α离散策略给出了详细的求解流程.最后,对整车系统展开了多工况的接触碰撞数值仿真,分析了不同工况下的接触响应对整车动力学性能的影响,验证了所提方法的有效性.

UniTire轮胎稳态模型的速度预测能力

为了降低轮胎高速试验的条件限制与成本,通过利用TNO不同速度下的侧偏试验数据,研究了统一轮胎模型UniTire从低速试验数据预测高速轮胎力学特性的能力。其中包括速度对动摩擦系数的影响;速度对侧偏和纵滑刚度的影响;速度对气胎拖距的影响。试验结果证明了UniTire轮胎模型在从低速轮胎试验预测高速轮胎力学特性方面具有很高的预测精度。