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.

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.

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.

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。

大侧倾角下UniTire稳态侧倾侧偏工况侧向力模型

大侧倾角下,轮胎侧偏力学特性仅仅采用等效侧偏角的方法不能进行准确描述,还需要考虑侧倾对其他关键参数的影响。基于简单刷子模型,建立轮胎稳态侧倾侧偏工况侧向力物理模型,导出用于半经验建模的理论边界条件。采用定性分析及试验观察相结合的方法分析侧倾对侧偏刚度和摩擦因数的影响,并建立相应的半经验模型。根据理论边界条件,分析侧倾对UniTire稳态侧向力模型中曲率因子的影响,并提出新的曲率因子表达式。通过轮胎试验数据进行参数辨识,结果表明所建立的UniTire稳态侧向力模型具有很高的精度,并且能够表达大侧倾角下轮胎的力学特性。

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。

UniTire轮胎稳态模型的联合工况预测能力研究

通过少量的标准试验得到轮胎力学特性参数,可以预测联合工况下(纵滑、侧偏、侧倾)的力学特性,这样就能避免做大量的复合试验。通过对轮胎简化理论模型的简单介绍,提出满足高阶理论边界条件的统一轮胎模型Un iTire,并对动摩擦因数和总切力方向修正系数给予说明。通过轮胎试验数据,使用不同辨识方法验证其预测能力,证明Un iTire轮胎稳态模型具有很高的预测精度。

基于CKF的大型拖拉机状态参数估计研究

拖拉机运行状态的准确识别与估计是其安全行驶和平稳控制的重要依据。针对大型拖拉机状态参数的估计复杂、精确度不高等问题,建立大型拖拉机整车三自由度仿真模型,其中包含Dugoff轮胎模型,提出基于容积卡尔曼滤波理论的大型拖拉机状态参数估计算法,并对大型拖拉机的行驶参数进行估计,包含纵向速度、侧向速度、质心侧偏角、横摆角速度。利用Matlab软件仿真验证,在双移线路面附着系数为0.8和0.6的工况下,对比仿真的状态参数和算法估计的数值。结果表明,拖拉机横摆角速度、质心侧偏角和纵向速度仿真值与真实值的误差分别为0.1、0.2、0.4,验证基于容积卡尔曼滤波算法对大型拖拉机状态参数估计的可行性和准确性,为大型拖拉机的稳定性控制等提供借鉴和参考。

FTire模型的建立方法研究

在熟悉FTire模型结构及其特性基础上,提出一种基于虚拟样机软件ADAMS的建立方法,并通过适当的测试模型参数,建立了子午线轮胎的FTire模型。通过分析不同间距的三维等效容积路面仿真统计数据,可知FTire模型可以根据需求自动划分网格,但其最佳网格间距为20 mm。FTire模型的建立为进一步进行车辆动力学分析提供了有效的轮胎模型。

Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement.The adhesion between tire and road is the key to studying vehicle dynamics,and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses.However,in most models,only road roughness is considered,and the pavement vibration caused by vehicle-road interaction is ignored.In this paper,a vehicle is simplified as a spring-mass-damper oscillator,and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation.The road roughness is considered as a sine wave,and the shear stress is ignored on the pavement.According to the contact form between tire and road,the LuGre tire model is established to calculate the tire adhesion force.The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations.A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation,which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations.In addition,the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other.The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.