Self-aligning Torque Research Articles

A semi-empirical tyre model for combined slips including the effects of cambering

This article presents the addition of camber to a previously published semi-empirical tyre model by the same authors. The model combines empirical models for pure braking, cornering and cambering with a model for simultaneous braking, cornering and cambering. It is based on brush-model tyre mechanics and aims to offer an easy-to-use accurate model for vehicle-handling simulations. The proposed model is a method to extract and rescale the adhesion and sliding forces from empirical pure-slip tyre models to account for the combined-slip condition. The combined-slip self-aligning torque is described likewise. Cambering affects the natural path of the tyre carcass on the road surface and deforms the threads to produce an additional force in the lateral direction. Thereby, the proportions of the sliding and adhesive forces changes. 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.

Study on Tire Dynamic Cornering Properties Using Experimental Modal Parameters

Based on the modeling of tire vertical characteristics and steady cornering properties, the model of tire nonsteady cornering is established in this paper using tire modal parameters extracted experimentally. In order to consider the influence of tire rolling effect on its cornering properties, the induced transfer function is introduced. The analytical formulae for calculation of transfer-function of lateral force and self-aligning torque with respect to lateral displacement and yaw angle are derived. The nonsteady cornering characteristics of tire under different loads can be calculated. The results of calculation are consistent with the experimental ones in the literature. The influence of rolling speed on tire cornering properties including the static case is analyzed. The nonsteady cornering properties in high frequency range are given by the model. The study demonstrates the consistency between steady and nonsteady tire modeling by using modal parameters.

A New Design Approach for Steer-By-Wire System by Dual-Port System

SUMMARYThe Dual-Port system, by which both the steering angle and the steering torque can be physically described as the functions of the steering wheel angle and the self-aligning torque, was proposed as a new design approach for a Steer-By-Wire system. This paper shows four examples of steering angle controller design. After that, to evaluate the controllers, the computer simulations and the experiments using fixed-base driving simulator were conducted. From the simulation and experiment results, the vehicle becomes more stable at high velocity if the yaw rate gain decreases. However, if the yaw rate gain is reduced too much, the vehicle becomes dull to turn and difficult to drive. Finally, we found that, by using the Dual-Port system, Steer-By-Wire controllers could be, systematically, designed and developed.

A Mathematical-physical 3D Tire Model for Handling/Comfort Optimization on a Vehicle: Comparison with Experimental Results

Abstract A new 3D mathematical-physical tire model is presented. This model considers not only the handling behavior of the tire but also its comfort characteristics, i.e., the dynamic properties in the lateral and the vertical planes. This model can be divided into two parts, the structural model and the contact area model. The structural parameters are identified by comparison with frequency responses of a 3D finite element model of the tire, whereas the contact parameters are directly calculated with a finite element model of the tread pattern. The 3D physical model allows predicting both steady state and transient behavior of the tire without the need of any experimental tests on the tire. The steady state analysis allows obtaining the friction circle diagram, i.e., the plot of the lateral force against the longitudinal force for different slip angles and for longitudinal slip, and the Gough plot, i.e., the diagram of the self-aligning torque versus the lateral force. The transient analysis allows obtaining the dynamic behavior of the tire for any maneuver given to the wheel. Among its outputs there are the relaxation length and the dynamic forces and torque transmitted to the suspension of the vehicle. Combining the tire model with the vehicle model it is possible to perform any kind of maneuver such as overtaking, changing of lane and steering pad at growing speed with or without braking, or accelerating. Therefore the 3D tire model can be seen as a powerful tool to optimize the tire characteristics through a sensitivity analysis performed with tire and vehicle models linked to each other without the need of building prototypes. Some preliminary comparisons with experimental data have been carried out.

Modeling of Tire Characteristics with Neural Netwoork System.

This study forms the first step in developing a new tire model to use in analyses of vehicle handling. The structure of a complete tire model describing static and dynamic tire behavior is proposed. In this paper, two parts of the complete tire model are described, one for steady-state behavior of side force and self-aligning torque, and the other for transient-state behavior of tires. The model is an empirical one and is constructed using neural networks. It is shown that the output of the model describes the actual tire characteristics not only qualitatively but also quantitatively.

Influence of Tire Characteristic Properties on the Vehicle Lateral Transient Response

Abstract This paper summarizes results from a recent program of tire-vehicle system research, using simulation techniques to identify the influence of tire characteristics on the vehicle response functions of yaw rate and lateral acceleration. Tire characteristics such as cornering stiffness, cornering stiffness-wheel load dependency, self-aligning torque, and dynamic tire behavior were varied with respect to a control tire. Computer simulations of vehicles undergoing a steering wheel pulse input were carried out using ADAMS full vehicle models and the Magic Formula tire model. Frequency responses were obtained from these vehicle handling simulations. The Four Parameter Evaluation Method of Lateral Transient Response was used to judge the vehicle handling performance. The influences of tire characteristic properties on the vehicle lateral transient response are explained by this method.

Shimmy Phenomenon on Steering System of Two-Wheeled Vehicles.

The shimmy that appears in two-wheeled vehicles has been regarded as a self-exited vibration, but this has yet to be clearly proven. Here, we provide experimental and theoretical analyses based on three experiments. It is found that the shimmy phenomenon can be clearly defined by the experimental analyses. It is impossible for previous theoretical models to describe the shimmy phenomenon. Therefore, we propose a new tire model which includes the dynamics of side force and self-aligning torque. From the results of the theoretical analyses, it is found that the model describes the shimmy phenomena not only qualitatively but also quantitatively. Furthermore we analyze the influence of the design parameters of the tire and their main influences on shimmy. Consequently, it is clarified that cornering stiffness, tire lateral and torsional rigidity, relaxation length of lateral displacement of contact patch, tire lateral damping and moment of inertia around the steering axis all have strong influences on shimmy.

Normalization of Tire Force and Moment Data

Abstract Semi-empirical theories of tire mechanics are employed to determine appropriate means to normalize forces, moments, angles, and slip ratios. Force and moment measurements on a P195/70R 14 tire were normalized to show that data at different loads could then be superimposed, yielding close to one normalized curve. Included are lateral force, self-aligning torque, and overturning moment as a function of slip angle, inclination angle, slip ratio, and combinations. It is shown that, by proper normalization of the data, one need only determine one normalized force function that applies to combinations of slip angle, camber angle, and load or slip angle, slip ratio, and load. Normalized curves are compared for the effects of inflation pressure and surface water thickness. Potential benefits as well as limitations and deficiencies of the approach are presented.

Study on Cornering Properties of Tire and Vehicle

Abstract This paper presents theoretical analysis on the cornering properties of tire and vehicle. First, the side force, braking driving forces and self-aligning torque on the tire are shown as functions of slip angle, slip ratio, camber angle and load. Next, the steady cornering properties of the vehicle using these tires are analyzed with the rolling conditions. Slip angle, slip ratio, camber angle and load, and forces and moments of the four tires are calculated. Effects of main factors on the above vehicle properties such as the load distribution, camber/roll ratio, front/rear drive ratio, tire size, tire wear, tire inflation pressure and tire friction are discussed.

Computer Modeling of a Tire under Cornering Loads

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

Cornerning radial tyres

An angular difference between direction of wheel motion and wheel plane produced a lateral force on a rolling tyre. A simple mechanism of shear stress generation in the contact area of tread is used. The coefficient of friction plays a limiting role. The resulting lateral force and self-aligning torque are computed by means of the belt model of a radial tyre. Finally, some numerical results are given to illustrate the theory.

Lateral Tire Forces on Wet Roads

Abstract Expressions are derived for side force and self-aligning torque of a simple tire model on wet roads with velocity-dependent friction. The results agree qualitatively with experimental results at moderate speeds. In particular, the theory correctly predicts that the self-aligning torque can become negative under easily realizable circumstances. The slip angle at which the torque reverses sign should increase with the normal load.

The Load Dependence of Side Force and Self-Aligning Torque of Pneumatic Tires

Abstract A conclusion to be drawn from this analysis of the load dependence of side force and self-aligning torque of pneumatic tires is that agreement between experimental and theoretical side force curves does not necessarily prove the soundness of the theory. On the other hand, even an inadequate theory is successful in suggesting a predictable and useful interrelation between load and slip dependence of the side force. Figure 4 demonstrates that quite a primitive transform of experimental data can lead to a unified presentation of its load and slip dependence although the resulting curve deviates quantitatively from theory in this particular case. This work forms part of a program of research undertaken by the Natural Rubber Producers' Research Association.

Distribution of Side Force and Side Slip in the Contact Area of the Pneumatic Tire

Abstract It is well known that, when a pneumatic tire is rolled over dry ground at a slip angle, a sideways force is developed. With the cornering force rig described here we are able to measure the front to rear distribution of the cornering force along the contact spot, the length of the contact area, the trail and the self-aligning torque. At the same time it is possible to derive the shape of the distorted tread and the front to rear distribution of side slip in the contact spot. By making certain assumptions concerning the distribution of the vertical force along the contact spot a relationship has been established between the forces of friction, rate of side slip and speed of rolling.

Tyre Characteristics as Applicable to Vehicle Stability Problems

The authors define the characteristics of a pneumatic tyre which affect the handling, or stability, of a car, and briefly describe a machine which was developed to measure these characteristics. The results are given of various experiments showing the effect of several factors on the characteristics; the applicability of these results to the behaviour of a tyre on the road is also discussed. Briefly defining oversteer and understeer, the authors outline a proposed method for directly determining the handling performance of a car while it is still in the drawing board stage. It is pointed out that this will only apply to steady conditions and some of the factors affecting transient behaviour are discussed. In particular, the importance of the self-aligning torque is stressed. The problem of breakaway is mentioned and doubts are cast on the applicability of the machine results to high-speed cornering, or racing; the technique of drifting a car round a corner is discussed. The MS. of this paper was received at the Institution on 17th November 1953, and in its revised form on 11th January 1954. For the report of the meeting in London, at which this paper was presented, see p. 134.