Pneumatic Trail Research Articles

A Soft Sensor for Estimating Tire Cornering Properties for Intelligent Tires

Intelligent tire systems are promising solutions for achieving precise vehicle state estimations, localization, and motion control in the context of autonomous driving. Tire cornering properties, namely, lateral force, aligning moment, and pneumatic trail, are crucial factors that should be accurately estimated for vehicle dynamics control purposes. In this work, a soft sensor for estimating tire cornering properties based on intelligent tire and machine learning is developed. The intelligent tire system is based on a triaxial accelerometer mounted on the inner liner of the tire tread, which provides acceleration measurements from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$</tex-math> </inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$</tex-math> </inline-formula> directions. Partial least squares and variable importance in the projection scores (PLS-VIP) are used in the feature extraction of the acceleration signals over the contact patch. A Gaussian process regression (GPR) model is trained to predict the cornering properties with confidence intervals under different input conditions. Based on the variances in the GPR predictions and minimum mean-square error criterion, a data fusion method for pneumatic trail estimation is proposed. It is demonstrated that the developed GPR models for cornering properties and the data fusion method for pneumatic trail estimation have satisfactory accuracy and reliability. The experimental results show that the soft sensor proposed in this work is a strong candidate for further applications in the development of vehicle state estimation and control algorithms.

Estimation of Tire-road Friction Limit with Low Lateral Excitation Requirement Using Intelligent Tire

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Tire-road friction condition is crucial to the safety of vehicle driving. The emergence of autonomous driving makes it more important to estimate the friction limit accurately and at the lowest possible excitation. In this paper, an early detection method of tire-road friction coefficient based on pneumatic trail under cornering conditions is proposed using an intelligent tire system. The previously developed intelligent tire system is based on a triaxial accelerometer mounted on the inner liner of the tire tread. The friction estimation scheme utilizes the highly sensitive nature of the pneumatic trail to the friction coefficient even in the linear region and its approximately linear relationship with the excitation level. An indicator referred as slip degree indicating the utilization of the road friction is proposed using the information of pneumatic trail, and it is used to decide whether the excitation is sufficient to adopt the friction coefficient estimate. The friction coefficient is estimated by the ratio of the normalized lateral force and the nonlinear adaptation of the slip degree. The tire forces and pneumatic trail are estimated by neural networks. The experimental validation demonstrates that the pneumatic trail has a good potential to precisely predict the friction coefficient at a low excitation under cornering conditions.&lt;/div&gt;&lt;/div&gt;

Selection of Optimal Tire and Design Optimisation of Steering System for a Formula Student Race Car through Tire Data Treatment

Selection of tires plays a crucial role in Vehicle Dynamics, which is important to design the steering and suspension system. An attempt is made to select the most optimum tire for lateral performance by using the tire data acquired from Tire Testing Consortium. Parameters including the tire’s lateral grip, cornering stiffness, cornering stiffness coefficient, camber stiffness, and lateral frictional coefficient have aided this selection. The tire is modelled using the Pacejka Magic Formula where the lateral and aligning coefficients are found, and used to get pneumatic trail, a parameter not provided in the raw data. The novelty of the work is seen when the selected tire is analysed to set the camber, pressure, and caster using the Design of Experiments method, without the need for building and testing a car. Making the best use of the tires’ forces and moments, the steering geometry is designed for a target range of radii by operating the tire slip angles at its optimum value. Further the influence of the change in toe angle on the Ackermann percentage is examined. Steering moment, calculated using the aligning moment curves of the tire, is applied to the steering column to conduct finite element analysis.

타이어 뉴메틱 트레일 정보를 활용한 횡방향 타이어 노면 마찰 계수에 관한 연구

The demands for vehicle safety systems such as ABS and ESC have been increased. Accurate vehicle state estimation is required to realized the abovementioned systems and tire-friction coefficient is crucial information. Estimation of lateral tire-road friction coefficient using pneumatic trail information is mainly dealt in this paper. Pneumatic trail shows unique characteristics according to the wheel side slip angle and these property is highly sensitive to vehicle lateral motion. The proposed algorithm minimizes the use of conventional tire models such as magic formula, brushed tire model and Dugoff tire model. The pure side slip maneuver, which means no longitudinal dynamics, is assumed to achieve the ultimate goal of this paper. A simulation verification using Carsim and Simulink is performed and the results show the feasibility of the proposed algorithms.

FTire and puzzling tyre physics: teacher, not student

ABSTRACTBy means of some instructive examples, the contribution shows how even complex phenomena and relations in tyre physics are better understood by using a physics-based tyre simulation model like FTire. In contrast to approximation-based phenomenological models, such an approach will give insight into, rather than requiring description of, the tyre's behaviour.Examples studied here comprisepredicted influence of wheel load, inflation pressure, camber angle, and slow rolling speed on parking torque,predicted influence of inflation pressure on cornering stiffness and pneumatic trail,relaxation length: ramping up and down slip angle and wheel load,handling characteristic on very rough roads,a strange phenomenon: cleats that ‘attract’ a tyre.Related to these studies, user-friendly simulation tools on the basis of FTire are introduced, which help in understanding the above-mentioned complex tyre properties. One of these tools, being valuable both in teaching and for vehicle/tyre dynamics experts in industry and research, allows the user to interactively modify, during a running simulation, tyre geometry, material data, and operating conditions. The impact of these variations both on tyre forces and moments as well as on internal tyre states can be directly seen in a running animation, and later analysed with a large variety of post-processing tools. Animations for all case studies are available for download on www.cosin.eu/animationswww.cosin.eu/animations. All registered trademarks used here are properties of their respective owners.

Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction

Multiaxle steering is widely used in commercial vehicles. However, the mechanism of the self-excited shimmy produced by the multiaxle steering system is not clear until now. This study takes a dual-front axle heavy truck as sample vehicle and considers the influences of mid-shift transmission and dry friction to develop a 9 DOF dynamics model based on Lagrange’s equation. Based on the Hopf bifurcation theorem and center manifold theory, the study shows that dual-front axle shimmy is a self-excited vibration produced from Hopf bifurcation. The numerical method is adopted to determine how the size of dry friction torque influences the Hopf bifurcation characteristics of the system and to analyze the speed range of limit cycles and numerical characteristics of the shimmy system. The consistency of results of the qualitative and numerical methods shows that qualitative methods can predict the bifurcation characteristics of shimmy systems. The influences of the main system parameters on the shimmy system are also discussed. Improving the steering transition rod stiffness and dry friction torque and selecting a smaller pneumatic trail and caster angle can reduce the self-excited shimmy, reduce tire wear, and improve the driving stability of vehicles.

Research on the Influence Factors for Bus Based on Nonlinear Model

Improved 5-DOF vehicle which contains nonlinear steering and tire models was established to solve the deficiency of conventional dynamic linear models to analyze coupling characteristics. Based on GPS technology, a developed vehicle handing and steering stability detecting system comprised by Steering Force and Angle Tester, GPS, Gyroscope and high precision Data Collector was introduced. According to Matlab/Simulink platform and vehicle test, the dynamic model was verified. Then some influence factors on bus handing and steering stability such as structure parameters, suspension parameters and tire parameters were analyzed. The results show that the longitudinal position of gravity and the vertical distance of gravity and roll axis have a good effect on vehicle yaw and roll responses. Spring roll stiffness is important parameter for vehicle roll. The pneumatic trail is closely related on steering reversibility and comfort. These researches have direct reference value for bus design.

Estimation of Tire Slip Angle and Friction Limits Using Steering Torque

Knowledge of the vehicle's lateral handling limits is important for vehicle control systems which aim to enhance vehicle handling and passenger safety. This paper presents a model-based estimation method that utilizes pneumatic trail information in steering torque to identify a vehicle's lateral handling limits, which are defined by the tire slip angle and peak lateral force limits. This method uses measurements available on many current production vehicles. Most importantly, it takes advantage of the early friction information encoded in the tire pneumatic trail. Pneumatic trail decreases as a function of the tire parameters even in the linear handling region, enabling early detection of the limits before they are reached. Experimental results on an independent front steering steer-by-wire research vehicle demonstrate the observer's ability to provide accurate real-time estimates of tire slip angle up to the limits of handling. Testing conditions include maneuvers performed on dry, flat paved road, as well as on lower-friction, dry gravel.

Analytical Tire Forces and Moments with Physical Parameters

Abstract The pneumatic tire behaves as a highly nonlinear system. Its complexity has limited the development of a complete and reasonable theory governing its mechanics. Practical tire models used in vehicle dynamics simulation and tire-related research rely basically on curve-fitted experimental data and empirical adjustments of theoretical models. This paper introduces a validated analytical model based on the physical properties of the tire by formulating the shear contact phenomena with elliptical normal pressure distribution and planar stress-strain laws. Adjustments are introduced to current methods for estimating distributed stiffness, the use of friction, and the forces saturation phenomena. The analytical model is formulated and normalized to accept tire physical parameters that are easily estimated from force and moments measurements. These parameters are universal to all tires: lateral and longitudinal stiffnesses, aligning pneumatic trail, overturning effective moment arm, and frictional properties. The method of using fundamental mechanics for modeling contact patch forces and moments with tire physical parameters constitutes a significant advancement. The tire model is validated with experimental data.

A MEASUREMENT BASED TYRE CHARACTERISTICS APPROXIMATION

Abstract To derive an approximation from the steady state measurements of tyre characteristics an approach in two steps is chosen. First the measurements of the tyre forces in a preprocessed form are normalized with the maximum contact coefficients and the corresponding slip values. Then, with the measurements now forming a very narrow band, a single curve can be used to approximate the whole tyre characteristics. The mutual influences of lateral and longitudinal forces are taken into account with combined slip values, which cover the whole range from locked wheels to heavy spinning wheels including small camber angles. Different surface conditions are considered with three parameters and the sliding coefficient so that the change of original characteristics can be handled easily. The self aligning torque is described by three components: the lateral force times pneumatic trail, the spin-slip torque and the reaction of lateral deflection and longitudinal force. Once again for the approximation of the pneumatic trail a normalization is used leading to a single curve for the whole characteristic. A similar method was applied to get a feasible approximation for the spin-slip torque. For the validation of the approximation comparisons of calculated and measured characteristics are presented. Whole characteristics for a tyre moving with lateral and longitudinal slip demonstrate the possible range of application.

Pragmatic Tyre Model for Short Wavelength Side Slip Variations

The first-order relaxation length concept is often used to model transient tyre behaviour. It gives a rather good representation of the lateral force response, also at shorter wavelengths. The self aligning moment appears to behave rather differently and its responses cannot be represented by a relaxation length system only. Based on the analytical frequency response functions of the pneumatic trail of the brush type tyre model, a new pragmatic approach is developed. The model consists of a phase leading system in series with the first-order model for the lateral force. The results are compared to the responses of a discrete brush type simulation model. It appears that the aligning moment can be represented by this new pragmatic model very well.

Magic Formula Tyre Model with Transient Properties

ABSTRACT The tyre force and moment generating properties connected with the vehicle's horizontal motions are considered. Knowledge of tyre properties is necessary to properly design vehicle components and advanced control systems. For this purpose, mathematical models of the tyre are being used in vehicle simulation models. The steady-state empirical ‘Magic Formula tyre model’ is discussed. The aligning torque description is based on the concepts of pneumatic trail and residual torque. This facilitates its combined slip description. Following Michelin, weighting functions have been introduced to model the combined slip force generation. A full set of equations of the steady-state part of the model of the new version ‘Delft Tyre 97’ is presented. The non-steady state behaviour of the tyre is of importance in rapid transient maneuvres, when cornering on uneven roads and for the analysis of oscillatory braking and steering properties. A relatively simple model for longitudinal and lateral transient responses restricted to relatively low time and path frequencies is introduced.

Friction Recognition Using the Tyre as Sensor

Continuously updated knowledge of the friction potential and the friction demand can help to improve manoeuvrability and thereby safety of vehicles under slippery road conditions. An on line estimation method, based on recognition of the pneumatic trail, is presented using a simple brush type tyre model. The method is verified by outdoor experiments using a tyre test trailer. Disturbances such as camber, residual forces and moments, combined slip of the tyre and dynamic behaviour of the tyre are considered. Neural networks have been used both for modelling and identification. Finally, a low-cost implementation of the system in the front wheel suspension of a passenger car is discussed.

A MEASUREMENT BASED TYRE CHARACTERISTICS APPROXIMATION

Abstract To derive an approximation from the steady state measurements of tyre characteristics an approach in two steps is chosen. First the measurements of the tyre forces in a preprocessed form are normalized with the maximum contact coefficients and the corresponding slip values. Then, with the measurements now forming a very narrow band, a single curve can be used to approximate the whole tyre characteristics. The mutual influences of lateral and longitudinal forces are taken into account with combined slip values, which cover the whole range from locked wheels to heavy spinning wheels including small camber angles. Different surface conditions are considered with three parameters and the sliding coefficient so that the change of original characteristics can be handled easily. The self aligning torque is described by three components: the lateral force times pneumatic trail, the spin-slip torque and the reaction of lateral deflection and longitudinal force. Once again for the approximation of the pneu...

Tyre Tests and Interpretation of Experimental Data

The test techniques and associated equipment developed for use of the Air Force-Cornell Tire Tester have permitted road tests yielding unique data on the cornering characteristics of pneumatic tyres. Account is given of tests performed for the Dunlop Tire and Rubber Corporation, involving variations of inflation pressure (18 to 45 lb. per sq. in.), camber (±30 deg.), and steer (±30 deg.); these angular ranges are unprecedented. The tyres were nominally 5.00, 6.00, and 7.00 by 16 section, of normal construction but smooth and round to eliminate effects deriving from tread pattern. The ensuing data analysis was based upon familiarity with aircraft derivative notation, the advantages of which are described, and upon simple tyre theory, which is outlined in an appendix. The outstanding conclusions, from a practical standpoint, are (1) that camber thrust strongly affects the static stability of the typical automobile; (2) that the motor cycle operates with negligible slip angle below 35-deg. tilt, whereas above 35-deg. tilt appreciable slip angle must be developed; (3) that a plot of pneumatic trail against side force has great value because of its linearity and ready significance; and (4) that tyre theory should be utilized to permit rational, concise interpretations of empirical data.