Electronic stability control for electric vehicle with four in-wheel motors

The electric vehicle with four direct-driven in-wheel motors is an over actuated system. A three-level control strategy of electronic stability control (ESC) is proposed to achieve optimal torque distribution for four in-wheel motors. The first level is a gain-scheduled linear quadratic regulator which is designed to generate the desired yaw moment command for ESC. Control allocation is the second level which is used to distribute the desired longitudinal tire forces according to the yaw moment command while satisfying the driver’s intent for acceleration and deceleration. The associated weighting matrix is designed using the work load ratio at each wheel to prevent saturating the tire. The third level is slip ratio control (SRC) which is employed at each wheel to generate the desired longitudinal tire force based on a combined-slip tire model. Simulation results show that the proposed method can enhance the ESC performance for the test maneuvers. Since the tire model is often unknown for practical implementation, the effectiveness of the SRC is studied using the sine with dwell test. It is found that the SRC is not crucial for achieving performance similar to the proposed method with SRC, if the slip ratio can be maintained in the stable region using traction control system/anti-lock braking system.     

Longitudinal Tire Dynamics

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

Longitudinal Tire Dynamics

SUMMARY

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

A combined-slip predictive control of vehicle stability with experimental verification

In this paper, a model predictive vehicle stability controller is designed based on a combined-slip LuGre tyre model. Variations in the lateral tyre forces due to changes in tyre slip ratios are considered in the prediction model of the controller. It is observed that the proposed combined-slip controller takes advantage of the more accurate tyre model and can adjust tyre slip ratios based on lateral forces of the front axle. This results in an interesting closed-loop response that challenges the notion of braking only the wheels on one side of the vehicle in differential braking. The performance of the proposed controller is evaluated in software simulations and is compared to a similar pure-slip controller. Furthermore, experimental tests are conducted on a rear-wheel drive electric Chevrolet Equinox equipped with differential brakes to evaluate the closed-loop response of the model predictive control controller.     

Two-Dimensional Contact Area of a Pneumatic Tire Subjected to a Lateral Force

A mathematical model of a two-dimensional contact patch of pneumatic tires rolling over a rigid flat road surface at arbitrary slip and camber angles has been developed. The model is simple in concept, contains few parameters and is applicable to any tire simulation models. In addition to tire geometric parameters and vertical deflection, the carcass camber angle is introduced in the model. This angle is alone responsible for the asymmetric shape of the tire contact patch when the tire undergoes a lateral force. The computed contact patches agree well with the measured patches of an automotive tire at different slip and camber angles. Lastly, the influence of the contact patch geometry on the tire cornering and aligning properties has been discussed through a computational example. It has been shown that the effect of tire contact patch geometry on the steady state behavior is rather remarkable.     

车辆轮胎动力学仿真模型分析

分析了各种常用轮胎模型的特点和利用范围,介绍了ADAMS中轮胎试验台(tiretesting)这一轮胎参数可视化工具,利用这一工具分析比较一种物理轮胎模型与一种经验-半经验轮胎模型间关于侧向力与纵向力、纵向力与纵向滑移率、回正力矩与纵向滑移率的力学特性,针对一种魔术公式轮胎模型验证了侧向力和纵向滑移率、纵向力和纵向滑移率在不同载荷下的力学关系特性。     

大侧偏角下侧偏松弛长度特性的研究

本文在稳态指数统一模型和一阶线性微分方程的基础上，研究了大侧偏角下动态过程中侧偏松弛长度的特性。侧偏松弛长度是由轮胎的侧向弹性决定的。在大侧偏角下，侧偏松弛长度不再是一个常数，而是随着侧向有效滑移率的改变而改变，而且它们之间呈现非线性特性。深入了解侧偏松弛长度的特性对研究轮胎动态特性和建立轮胎动态模型具有重要的作用。     

轮胎非稳态侧偏特性的建模

分析了轮胎侧偏特性的建模机理，从胎面的印迹侧向变形和胎体的侧向平移变形出发，计算出运动状态下轮胎印迹瞬时变形的数学表达式，建立了考虑胎面弹性的轮胎非稳态侧偏特性模型。最后，将该理论模型与试验结果进行了对比。     

A novel semi-empirical tyre model for combined slips

A new tyre-force model for simultaneous braking and cornering is presented, which is based on combining existing empirical models for pure braking and cornering with brush-model tyre mechanics. The aim is to offer an easy-to-use, accurate model for vehicle-handling simulations. On a working tyre the contact patch between the tyre and the road is, in general, divided into an adhesion region where the rubber is gripping the road and a sliding region where the rubber slides on the road surface. The total force generated by the tyre is then composed of components from these two regions. The brush model describes this in a mechanical framework. The proposed model is based on a new method to extract adhesion and sliding forces from empirical pure-slip tyre models. These forces are then scaled to account for the combined-slip condition. The combined-slip self-aligning torque is also described. A particular feature of the model is the inclusion of velocity dependence, even if this is not explicitly present in the empirical pure-slip model. The approach is quite different from most previous combined-slip models, in that it is based on a rather detailed mechanical model in combination with empirical pure-slip models. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model and in this work the Magic Formula is used in examples. Results show good correspondence with experimental data.     

Study of the Pneumatic Tyre Behaviour on Dry and Rigid Road by Finite Element Method

The paper presents a physical tyre model capable of describing the complete pneumatic tyre behaviour during steady and transient states. Given the radial deflection, the longitudinal and lateral slip, the camber angle, the inner pressure and the mechanical parameters describing the tyre structure, the model returns the vertical load, the longitudinal and lateral forces, the self aligning torque. Particular attention has been devoted to the computation (by f.e.m.) of tyre carcass and tread deformations; it is explained how side force increases by moderate braking at constant slip angle. An experimental verification validates the model, although more studies could be needed to improve model effectiveness.     

Study of the Pneumatic Tyre Behaviour on Dry and Rigid Road by Finite Element Method

SUMMARY

The paper presents a physical tyre model capable of describing the complete pneumatic tyre behaviour during steady and transient states. Given the radial deflection, the longitudinal and lateral slip, the camber angle, the inner pressure and the mechanical parameters describing the tyre structure, the model returns the vertical load, the longitudinal and lateral forces, the self aligning torque. Particular attention has been devoted to the computation (by f.e.m.) of tyre carcass and tread deformations; it is explained how side force increases by moderate braking at constant slip angle. An experimental verification validates the model, although more studies could be needed to improve model effectiveness.     

工程车辆翻新轮胎承载变形特性

为了进一步明确工程车辆翻新轮胎的力学性能,提高其使用寿命,通过构建工程车辆翻新轮胎计算机几何模型、有限元分析模型、承载变形特性试验系统,对工程车辆翻新轮胎承载变形特性进行有限元分析及试验研究,并与同型号新轮胎进行对比分析,获得静态接地工况下工程车辆翻新轮胎的载荷-变形、载荷-刚度、载荷-压缩率等特性规律,构建26.5R25工程车辆翻新轮胎径向承载变形数学模型。研究结果表明：工程车辆翻新轮胎的径向变形、侧向变形变化规律与新轮胎接近,径向与侧向变形均比同型号新轮胎稍小;当胎压一定时,随着载荷的增加,工程车辆翻新轮胎径向变形呈线性增大,当胎压较低时侧向变形呈线性增大,当胎压较高时侧向变形呈非线性增大;工程车辆翻新轮胎的径向刚度及压缩率受径向载荷和胎压的影响较大,载荷一定时,径向刚度随胎压的增大而增大;胎压一定时,工程车辆翻新轮胎的压缩率随径向载荷的增大而增大,且稍小于同品牌、同型号新轮胎的压缩率;旧胎体的不同老化程度对工程车辆轮胎翻新后的承载-变形特性会产生较大的影响;在低载工况下,工程车辆翻新轮胎和新轮胎径向刚度差异不大,在接近标准载荷及高载工况下,工程车辆翻新轮胎径向刚度较新轮胎大,且随着载荷的增大,工程车辆翻新轮胎和新轮胎径向变形差异不断加大。     

Independent Suspension, Self Steered Axle, and 4WS for Busses

The dynamic behavior of commercial vehicles fitted with differentr types of suspension mechanisms and steering devices is investigated in this paper. Six vehicle models have been constructed: 2WS-SA is a standard two wheel steering bus with solid axles; 2WS-DW is a 2WSA vehicle with independent double wishbone suspension in front and rear axles; SSA-SA is a 2WS system with solid axles, the rear one being mounted on a self steered mechanism; SSA-DW is a vehicle with independent double wishbone suspension in the front axle, and a solid self steered rear axle; 4WS-SA has four wheel steering with solid axles; and 4WS-DW is a 4WS vehicle with independent double wishbone suspension in front and rear axles. The dynamic response of these models has been assessed in terms of lateral acceleration, yaw velocity, tire forces, tire force reserves, and slip angles. The expected advantages of a 4WS system (higher acceleration rates and lower slip angles) will be corroborated but, at the same time, it will be shown that they are obtained at the cost of lower force reserves. Self steered mechanisms produce smaller body slip angles, but it will be shown that they give rise to larger yaw velocity overshootings. The particular independent suspension analyzed does not show significant improvements with respect to the solid axle counterpart.     

A Versatile Flat Track Tire Testing Machine

Summary A flat track tire testing machine developed by the IMMa group is described. It permits the simulation and study of the dynamic behavior of a great variety of tires under controllable and repetitive highly dynamic realistic working conditions in the laboratory for a diversity of vehicles, from motorcycles to light trucks. The machine incorporates: – a hydraulically operated tire support and loading system with wide operating ranges; – a computer controlled brake system to simulate braking maneuvers with ABS systems; – a complete sensorial system; – a data acquisition and control system continually monitoring and acting on the experimental variables, i.e., tire and belt speed, longitudinal slip, slip and camber angles, tire pressure, tire normal force, etc. As an application example, results are presented that adjust the parameter of the magic formula for a standard 175/70 R14 passenger vehicle tire. Accurate mathematical tire models are recognized as essential for the prediction of vehicle dynamic performances using simulation tools.     

轮胎原地转向离散仿真模型

建立了轮胎印记范围内的原地转向物理模型,对印记内的胎面进行了离散处理,分析了胎面单元的变形和滑移情况,通过胎体上下表面的力矩平衡,得到轮胎所受回正力矩,并对计算过程进行了详细说明。给出不同工况下原地转向时轮胎所受回正力矩,并进行了试验验证。结果表明,该离散仿真模型能较好的反应轮胎的原地转向特性,能方便地分析轮胎结构参数及印迹内压力分布对原地转向特性的影响。     

A Versatile Flat Track Tire Testing Machine

Summary A flat track tire testing machine developed by the IMMa group is described. It permits the simulation and study of the dynamic behavior of a great variety of tires under controllable and repetitive highly dynamic realistic working conditions in the laboratory for a diversity of vehicles, from motorcycles to light trucks. The machine incorporates: - a hydraulically operated tire support and loading system with wide operating ranges; - a computer controlled brake system to simulate braking maneuvers with ABS systems; - a complete sensorial system; - a data acquisition and control system continually monitoring and acting on the experimental variables, i.e., tire and belt speed, longitudinal slip, slip and camber angles, tire pressure, tire normal force, etc. As an application example, results are presented that adjust the parameter of the magic formula for a standard 175/70 R14 passenger vehicle tire. Accurate mathematical tire models are recognized as essential for the prediction of vehicle dynamic performances using simulation tools.     

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

Four-wheel vehicle kinematic and geometric constraints for definition of tire slip angle

When considering vehicle safety, tires and all that they represent are a fundamental topic. Tire studies have received a considerable amount of attention from the research community because their improvement has a direct and strong impact on vehicle handling and braking. Within this eld of analysis lies an important behavioral feature: the tire slip angle, which is a consequence of lateral forces acting on the tire. This characteristic is predicted in some cases and evaluated experimentally in others. This paper addresses another way to assess the slip angle. We propose a mathematical model that describes a constraint linking the slip angle and steering angle that make a vehicle turn. We present a simplied kinematic model (based on the classic bicycle model) and a four-wheel model, which makes all of the angles involved compatible with each other. In our case, the match will be given by the determination of the turning radius. Two different scenarios, understeering and oversteering vehicles, were simulated, and the results and conclusions reached are presented herein.     

轮胎制动力—滑移率特性的动态模型研究

轮胎制动力及滑移率对制动力矩的响应存在着显著的低频衰减振荡现象，这从制动力－滑移率特性曲线上看，表现为一系列的以稳态点为中心的旋涡状过渡曲线。这是稳态的轮胎模型所不能描述的。本文在稳态ｂｒｕｓｈ轮胎模型基础上，通过印迹前端蹼处胎冠一阶变形模型，建立了轮胎制动力－滑移率的动态模型，并根据转鼓试验台上的轮胎制动试验，验证了该模型的仿真效果。