Wheel Vibrations and Transient Tire Forces

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.     

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.     

Literature review and fundamental approaches for vehicle and tire state estimation*

ABSTRACT

Most modern day automotive chassis control systems employ a feedback control structure. Therefore, real-time estimates of the vehicle dynamic states and tire-road contact parameters are invaluable for enhancing the performance of vehicle control systems, such as anti-lock brake system (ABS) and electronic stability program (ESP). Today's production vehicles are equipped with onboard sensors (e.g. a 3-axis accelerometer, 3-axis gyroscope, steering wheel angle sensor, and wheel speed sensors), which when used in conjunction with certain model-based or kinematics-based observers can be used to identify relevant tire and vehicle states for optimal control of comfort, stability and handling. Vehicle state estimation is becoming ever more relevant with the increased sophistication of chassis control systems. This paper presents a comprehensive overview of the state-of-the-art in the field of vehicle and tire state estimation. It is expected to serve as a resource for researchers interested in developing vehicle state estimation algorithms for usage in advanced vehicle control and safety systems.     

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.     

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

SUMMARY

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.     

Dynamics of Pneumatic Tire Vehicles with Connected Suspension Systems

SUMMARY

A vehicle model, with 10 degrees of freedom is used to investigate the skidding conditions of any wheel of the vehicle in motion. Equations for the load transfer and equations for the pneumatic tire spring and shock absorber are derived. Parameters such as gradual cornering, U-curve cornering, the wavy road surface of different wave lengths and cases of independent and connected suspension systems are inputs to the system. The tire calculated forces and their corresponding maximum resistance forces are the outputs of the systems. A connected suspension system is found to resist skidding better than the independent suspension system. The system is non-linear, and numerical solutions are obtained.     

Experimental Study of System Optimization for Suppression of Vehicle Vibration

SUMMARY

The improvements of ride comfort and vehicle maneuverability in the vehicle design can be achieved by using an active suspension. However, the problems in such a control are the complex control logic because of the control laws incompatible with the improvements of ride comfort and maneuverability, and the cost increase because of various sensors to be attached. Therefore, we examined the control abilities of ride comfort and maneuverability on a unique control law using frequency shaped LQ, and controlled the characteristic of the contact between tire and road without a road displacement sensor     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

Abstract

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Controller Development and Evaluation

SUMMARY

Due to increased traffic congestion and travel times, research in Advanced Vehicle Control Systems (AVCS) has focused on automated lateral and headway control. Automated vehicles are seen as a way to increase freeway capacity and vehicle speeds while reducing accidents due to human error. Recent research in automated lateral control has focused on vehicle control during low-g maneuvers. To increase safety, automated lateral controllers will need to recognize and react to emergency situations.

This paper investigates the effects of vehicle and tire model order on the response of automated vehicles to an emergency step lane change using a controller based on linear vehicle and tire models. From these studies it is concluded that control strategies based solely on linear vehicle and tire models are inadequate for emergency vehicle maneuvers.

A strategy is then proposed to automatically control vehicles through emergency maneuvers. Here the response of a nonlinear vehicle model is used with a linear state model to optimize controller gains for nonlinear maneuvers. An emergency step lane change is used as a preliminary test of the method.     

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.     

A Comparison between Four Computing Models of Different Complexity Describing the Steering Behavior of Two-axled Automobiles

SUMMARY

In this paper chassis controls for vehicle handling and active safety have been reviewed. In particular, we have observed the effectiveness and limit of 4WS and DYC. It is pointed out that DYC is more effective in vehicle motion with larger side-slip and/or higher lateral acceleration and taking the nonlinearity of tire and vehicle dynamics into consideration is essential for introducing the control law for the chassis controls and their integration/coordination. We wish to emphasize that there is a need to further propose control laws based on deeper observation and understanding on the tire and vehicle dynamics.     

Simulation of Vehicle and Power Steering Dynamics Using Tire Model Parameters Matched to Whole Vehicle Experimental Results

This paper uses simulation to investigate how vehicle loading conditions (driver only, passengers, cargo, and fuel) affect power steering system and overall vehicle dynamics. Our purpose of the study was to evaluate the power steering system model for possible use in the National Advanced Driving Simulator (NADS). The effects of changing loading conditions on inertial properties of passenger cars have been found experimentally using a Vehicle Inertia Measurement Facility (VIMF). This paper presents simulation results using a vehicle handling model combined with a power steering system model and a nonlinear tire model. A crucial part of this project was the adjustment of certain parameters of Pacejka's tire model in order to match simulation results with experimental measurements of vehicle and power steering variables in transient maneuvers.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development,Validation and Comparison

SUMMARY

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Semi-Active Suspension with Preview Using a Frequency-Shaped Performance Index

SUMMARY

The objective of this study is to develop a control law for a semi-active suspension for the purpose of ride quality improvement. The semi-active control law is determined by reproducing the control force of an optimally controlled active suspension while suppressing its damping coefficient variation. The performance index of the optimal control for the active suspension is modified to include frequency-shaping by use of Parseval's theorem, which allows us to de-emphasize the effects of particular variables over specific frequency bands.

Through the numerical simulations, it was found that the semi-active suspension may reduce the vertical acceleration of the driver's seat and the sprung mass motions significantly. The road-holding and tire deflections were not affected much.     

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.     

Road Surface Correction o f Tire Test Data

SUMMARY

Most tire data used for vehicle simulations is measured on laboratory test facilities. An investigation showed that the frictional properties of these laboratory machines can be quite different from actual road conditions. This paper describes a method to correct laboratory tire test data to be more like road data in order to achieve a higher degree of correlation between instrumented test- and simulation results.     

Vehicle Energy Dissipation Due to Road Roughness

SUMMARY

Road roughness and surface texture are known to affect tire rolling resistance; however, little emphasis has been placed on the consequent changes in total vehicle energy dissipation due to road roughness. Thus, tire rolling resistance, in isolation from vehicle contributed losses such as dissipation in the suspension, appears to be a weakness in present evaluation procedures as they relate to fuel economy and pollution level testing: Recent work by Funfsinn and Korst has shown that substantial and measurable increases in energy losses occur for vehicles traveling on rough roads. The present investigation uses vehicle axle accelerations as a means of examining various road surfaces. Correlation with computer simulations has allowed the development of a deterministic road roughness model which permits the prediction of energy dissipation in both the tire and suspension as functions of road roughness, tire pressure, and vehicle speed. Comparison to the experiments of Korst and Funfsinn results in good agreement and shows that total rolling loss increases of up to 20 percent compared to ideal smooth roads are possible. The aerodynamic drag coefficient is also found to increase while driving on rough roads.     

On the Stability of a Flexible Vehicle Controlled by a Human Pilot

SUMMARY

This paper presents a stability analysis of a vehicle flexible in the plane of yawing and being controlled by a human pilot. The vehicle is represented by a two degrees-of-freedom model and the pilot is assumed to respond to the lateral displacement and to the lateral velocity with a time delay. It is shown that in order for the pilot model to exhibit a realistic human operator behavior, driver's gain must be linearly proportional to vehicle velocity and also inversely related to frontal visibility. Moreover, application of the Hurwitz criterion indicated that flexibility of the vehicle frame has a destabilising effect on the lateral stability and reduces the stable domain of operation.     

How well a single-track linear model captures the lateral dynamics of long combination vehicles

ABSTRACT

The effect of centre-of-gravity heights on the high-speed performance measures of long combination vehicles including truck with double centre-axle trailers, Nordic, and A-double combination vehicles is investigated. The high fidelity three-dimensional models, used in this research, are validated against physical test data. These models are often accurate in terms of the actual dynamic behaviours of the vehicle. On the other hand, the simple yaw-plane single-track models with linear tires require less number of vehicle parameters. In this paper, it is investigated how accurate the estimations of performance measures are at high forward speeds by such single-track linear (STL) models. The influence of load height is especially studied. The high-speed performance-based standard or PBS measures considered are rearward amplifications of both lateral acceleration and yaw velocity; lateral load transfer; yaw damping and high-speed transient offtracking. The results show that tire relaxation has a large effect and it is rather easy to add to an STL model, so it is assumed to be modelled in STL. With realistically high payload and a required accuracy of PBS measures of approximately 10%, only the accuracy of rearward amplification of yaw velocity calculated by the frequency response is fulfilled by the STL. With low payload, the same statement is valid, but with around 5% in required accuracy. The roll dynamics effects are more important than the tire non-linearities.