Wheel Vibrations and Transient Tire Forces

SUMMARY

This paper presents a survey of the state-of-the-art in predicting the wheel vibrations in a complex dynamic vehicle suspension system and their influence on the forces transduced in a high frequency area from the tire to the vehicle's body. Secondly it presents also the transient evolution of tire models used for prediction and understanding high frequency movements in the tire's contact area, producing the guiding forces and torques during vehicle handling.     

Design and evaluation of sideslip angle observer for vehicle stability control

This paper presents a method for estimating the vehicle side slip angle, which is considered as a significant signal in determining the vehicle stability region in vehicle stability control systems. The proposed method combines the model-based method and kinematics-based method. Side forces of the front and rear axles are provided as a weighted sum of directly calculated values from a lateral acceleration sensor and a yaw rate sensor and from a tire model according to the nonlinear factor, which is defined to identify the degree of nonlinearity of the vehicle state. Then, the side forces are fed to the extended Kalman filter, which is designed based on the single-track vehicle model associated with a tire model. The cornering stiffness identifier is introduced to compensate for tire force nonlinearities. A fuzzy-logic procedure is implemented to determine the nonlinear factor from the input variables: yaw rate deviation from the reference value and lateral acceleration. The proposed observer is compared with a model-based method and kinematics-based method. An 8 DOF vehicle model and Dugoff tire model are employed to simulate the vehicle state in MATLAB/SIMULINK. The simulation results shows that the proposed method is more accurate than the model-based method and kinematics-based method when the vehicle is subjected to severe maneuvers under different road conditions.     

On the handling performance of a vehicle with different front-to-rear wheel torque distributions

ABSTRACT

The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.     

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.     

Design of a signal transducer for direct conversion of wheel linear accelerations into tire lateral forces

This paper describes a design of a real-time conversion system of wheel linear accelerations into tire lateral forces. Though the tire lateral forces are important elements for analyzing vehicle dynamic control performances, they cannot be easily measured in real-time owing to the non-linearities of tire dynamics, friction, and slippage on road. In this paper, we propose a practical direct method using wheel linear accelerations in order to estimate tire lateral forces transmitted into the vehicle in real-time. A simplified vehicle model based on force-acceleration analysis is proposed to assure the real-time performance. The acceleration values are obtained using three-axis accelerometers attached on each wheel location. For conditioning and rectifying the acceleration signals, a signal transducer is designed using a digital filter. And in order to investigate the feasibility and real-time performance, a prototype of signal transducer is fabricated using a digital signal processor. The experimental results and performance are validated with the road test results using six-component wheel force transducers.     

Direct tire force generation algorithm based on non-iterative nonlinear inverse tire model

The function of vehicle dynamics control system is adjusting the yaw moment, the longitudinal force and lateral force of a vehicle body through several chassis systems, such as brakes, steering and suspension. Individual systems such as ESC, AFS and 4WD can be used to achieve desired performance by controlling actuator variables. However, integrated chassis control systems that have multiple objectives may not simply achieve the desired performance by controlling the actuators directly. Usually those systems determine the required tire forces in an upper level controller and a lower level controller regulates the tire forces through the actuators. The tire force is controlled in a recursive way based on vehicle state measurement, which may not be sufficient for fast response. For immediate force tracking, we introduce a direct tire force generation method that uses a nonlinear inverse tire model, a pseudo-inverse model of vehicle dynamics and the relationship between longitudinal force and brake pressure.     

Selection of Actuator Combination in Integrated Chassis Control Using Taguchi Method

This paper presents a method to select the actuator combination in integrated chassis control using Taguchi method. Electronic stability control (ESC), active front and rear steering (AFS/ARS) are used as an actuator, which is needed to generate a control tire force. After computing the control yaw moment in the upper-level controller, it is distributed into the control tire forces, generated by ESC, AFS and ARS in the lower-level controller. In this paper, the weighted pseudo-inverse control allocation (WPCA) with variable weights is used to determine the control tire forces of each actuator. Taguchi method is adopted for sensitivity analysis on variable weights of WPCA in terms of the control performances such as the maneuverability and the lateral stability. For sensitivity analysis, simulation is performed on a vehicle simulation package, CarSim. From sensitivity analysis, the most effective actuator combination is selected.     

人工神经网络在车辆行驶称重技术中的应用

车辆行驶称重技术是通过测量分析车辆轮胎与路面作用力,从而计算车辆的静态载荷和静态轴载等相关参数的车辆载荷检测技术。基于人工神经网络综合分析了影响轮胎作用力的各个因素的影响关系,通过自行研制的油管传感器式车辆行驶称重仪进行了相关试验验证,达到了预定的精度和实用要求。     

Selfexcited Vibrations of the Tire

In this paper a mechanical work of external forces and torques, acting on the tire has been considered. A theory has been developed for the prediction of necessary conditions for selfexciting vibrations. The theory establishes, that the mechanical work of external forces and torques must be positive, or, what is equivalent, that the tire has to transmit energy from external environment to vehicle. The work of forces and torques has been considered as a convolution of functions, which next has been submitted to Laplace transformation. The condition of selfexcitation of vibrations, obtained from above in the frequency domain, establishes, that the imaginary part of all eigenvalues of frequency response matrix must be negative. As an example, the ranges of selfexcited vibrations of the tire have been calculated. The tire has been treated as a stretched circular string. Four different models have been considered. Three of them have been massles (kinematic), namely Pacejka's model, Von Schlippe's model and single-point model. As fourth model the dynamic Pacejka's model has been considered. The influences of longitudinal deflections on the shimmy tendency have been studied for all models

Frequency response characteristics have been numerically computed and compared for all models. A critical speed and a critical reduced frequency of first and second kind have been defined. Admissible, negative, imaginary parts of the eigenvalues of frequency response matrix have been established. These admissible values of imaginary parts of eigenvalues assure, that the energy absorbing does not excite shimmy vibrations.     

轮胎模型刚度对前部偏置碰撞结果的影响

建立了整车碰撞模型中的轮胎模型后,通过调整模型参数,使模拟的轮胎刚度特性曲线近似于试验的轮胎刚度特性曲线,并应用于整车前部偏置碰撞模拟中,分析轮胎刚度对偏置碰撞结果的影响.结果表明,轮胎刚度对碰撞过程整车加速度、截面力、防火墙侵入量等均有一定的影响.     

The Definition of the Tires Limit of Admissible Nonuniformity by Using the Vehicle Vibratory Model

Purpose of this article was to especially emphasize the contribution of tires nonuniformity radial and lateral force variation to vehicles vibrations, within developed nonlinear dynamic model of a vehicle. The tire nonuniformity force variations are introduced in simulations processes by radial and lateral dynamic forces in the area of wheels-road contact. The limits of admissible Peak - to - Peak radial and lateral force variation and Peak - to - Peak first harmonic radial and lateral force variation nonuniformity were defined by using a vehicle vibratory model. The tire nonuniformity parameters were defined from the aspect of vertical seat cushion and the steering wheel rim vibrations using the developed optimization program and the Pentium 90 MHz computer.     

Minimizing the Path Radius of Curvature for Collision Avoidance

Purpose of this article was to especially emphasize the contribution of tires nonuniformity radial and lateral force variation to vehicles vibrations, within developed nonlinear dynamic model of a vehicle. The tire nonuniformity force variations are introduced in simulations processes by radial and lateral dynamic forces in the area of wheels-road contact. The limits of admissible Peak - to - Peak radial and lateral force variation and Peak - to - Peak first harmonic radial and lateral force variation nonuniformity were defined by using a vehicle vibratory model. The tire nonuniformity parameters were defined from the aspect of vertical seat cushion and the steering wheel rim vibrations using the developed optimization program and the Pentium 90 MHz computer.     

Coordinated control of ESC and AFS with adaptive algorithms

This paper presents a coordinated control of electronic stability control (ESC) and active front steering (AFS) with adaptive algorithms for yaw moment distribution in integrated chassis control (ICC). In order to distribute a control yaw moment into control tire forcres of ESC and AFS, and to coordinate the relative usage of ESC to AFS, a LMS/Newton algorithm (LMSN) is adopted. To make the control tire forces zero in applying LMS and LMSN, the zero-attracting mechanism is adopted. Simulations on vehicle simulation software, CarSim®, show that the proposed algorithm is effective for yaw moment distribution in integrated chassis control.     

重型商用车汽车轮胎花纹对整车性能的影响

汽车轮胎是汽车的行驶系统的重要组成部分,对汽车保持正常的行驶起着重要的作用.除了承载着全车重量,传递驱动转矩外,车轮还还起着减震和缓冲,转向和制动的作用.轮胎对汽车的驾驶性、通过性、舒适性和安全性都有着直接的影响.文中从各轮胎花纹的性能,轮胎性能对整车性能的影响和分轮位配置花纹的优势,为整车提供更经济,安全,可靠的轮胎花纹的匹配方法.     

Effect of vehicle model on the estimation of lateral vehicle dynamics

A methodology is presented for estimating vehicle handling dynamics, which are important to control system design and safety measures. The methodology, which is based on an extended Kalman filter (EKF), makes it possible to estimate lateral vehicle states and tire forces on the basis of the results obtained from sinusoidal steering stroke tests that are widely used in the evaluation of vehicle and tire handling performances. This paper investigates the effect of vehicle-road system models on the estimation of lateral vehicle dynamics in the EKF. Various vehicle-road system models are considered in this study: vehicle models (2-DOF, 3-DOF, 4-DOF), tire models (linear, non-linear) and relaxation lengths. Handling tests are performed with a vehicle equipped with sensors that are widely used by vehicle and tire manufacturers for handling maneuvers. The test data are then used in the estimation of the EKF and identification of lateral tire model coefficients. The accuracy of the identified values is validated by comparing the RMS error between experimentally measured states and regenerated states simulated using the identified coefficients. The results show that the relaxation length of the tire model has a notable impact on the estimation of lateral vehicle dynamics.     

Method for measuring force transmitted from road surface to tires and its applications

The force transmission from road surface to a rolling tire has been successfully measured by force measurements on suspension parts and correction for interia forces of suspension parts. The results of the measurement have shown that the force from road to tire has a sharp directivity, which is inclined rearward in side view, within the frequency range between 5 and 15 Hz. And the inclination angle of the direction of action has been found to be dependent on the vehicle velocity. As the application of the finding, the optimal wheel center locus inclination in side view has been studied, to minimize the longitudinal force transmission. And the optimum angle has been confirmed to exist.     

A semi-empirical dynamic tire model for combined-slip forces

This article presents a semi-empirical combined-slip tire model including transient behavior. It is assumed that the transient behavior is a result from the dynamic deformation of the tire carcass and that the interaction between the lateral and longitudinal slip, and forces can be explained by the deformation of the rubber treads. The deformation of the tire carcass makes the tread slip deviate from the wheel-rim motion in a way that may be described by differential equations. A method based on brush-model tire mechanics is used to construct the combined-slip forces as nonlinear scalings of corresponding pure-slip forces.     

声全息方法识别汽车运动噪声

本文提出利用声全息原理，对运动状态下的汽车噪声源进行识别的方法，它能够用来分析汽车在高速运动过程中发动机的噪声，轮胎噪声和空气动力学噪声，通过低速和高速实验表明该方法是一种有效的方法，能够快速，准确识别运动车辆的噪声。     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.