Cornering Force Research Articles

Sensitivity analysis of truck tire tread material properties for on-road applications

This research delves into the sensitivity analysis of a truck tire rubber compound concerning its impact on tire–road interaction characteristics. Initially, the study employs finite element analysis to model a 315/80R22.5 truck tire, which is subsequently validated through static and dynamic response assessments via various simulation tests. Following validation, the established tire model is utilized to conduct a sensitivity analysis of the tire rubber compound specifically applied on the tread. This analysis encompasses several material definitions, including Mooney–Rivlin, visco-Mooney–Rivlin, linear viscoelastic, and nonlinear viscoelastic materials. By exploring the effects of these material models, the research scrutinizes their influence on tire–road interaction characteristics across diverse operating conditions. The tire–road interaction characteristics include the rolling resistance coefficient, and the cornering force at operating conditions including the longitudinal speed, vertical load, and slip angle. This comprehensive investigation offers insights into the intricate relationship between tire composition and performance, thereby enhancing our understanding of tire behavior and informing potential advancements in tire technology.

Numerical analysis on tractor axle suspension for steering instability induced by bump disturbances

In Japan, small agricultural tractors without axle suspensions used on bumpy farm roads experience severe vibrations. Excessive vibrations often cause tyres to lose contact with the supporting ground or decrease the vertical tyre force such that the cornering force exceeds the static friction limit. The resulting bouncing and sliding motions induce steering instability, resulting in overturning accidents. This study investigated the effectiveness of axle suspension in alleviating bump disturbance-induced steering instability in small tractors. A step lane change test involving bump disturbances was newly proposed for the steering stability testing of small tractors. The numerical experiments compared four axle suspension structures: no-, front-, rear-, and full-suspensions. The results showed that bump disturbances induce steering instability in the no- and rear-suspension tractors. In contrast, the front- and full-suspension structures significantly improved the steering stability of the tractor by keeping the steering wheel in contact with the ground. The proposed testing method helped evaluate improvements in the steering stability brought about by increasing the ground contact of the steering wheel. Our results can aid in designing and testing suspension systems for small tractors.

Modeling and Validation of a Passenger Car Tire Using Finite Element Analysis

This paper focuses on the modeling and analysis of a four-groove passenger car tire, size 235/55R19, using finite element analysis. The Mooney–Rivlin material model is employed to define the hyperelastic behavior of the tire rubber compounds for all solid elements. The tire rim is modeled as a rigid body using aluminum alloy material, and the beads are modeled as beam elements using steel material. The tire model is validated in both static and dynamic domains through several simulations and is compared to published measured data. The tire is validated using footprint and vertical stiffness tests in the static domain. In the static footprint test, a steady-state vertical load is applied, and the tire–road contact area is computed. In the vertical stiffness test, a ramp vertical load is applied, and the tire’s vertical displacement is measured to calculate the tire’s vertical stiffness. In the dynamic domain, the tire is validated using drum-cleat and cornering tests. In the drum-cleat test, a drum with a 2.5 m diameter and a cleat with a 15 mm radius is used to excite the tire structure and obtain the frequency of the vertical and longitudinal first modes of vibration, that is, by applying the fast Fourier transformation (FFT) of the vertical and longitudinal reaction forces at the tire center. In addition to this test, the tire model is pre-steered on a flat surface with a two-degree slip angle and subjected to a steady state linear speed of 10 km/h to predict the cornering force and compute the cornering stiffness. In addition, the effect of tire longitudinal speed on the rolling resistance coefficient is then predicted at zero slip angle using the ISO 28580 rolling resistance test. The findings of this research work provide insights into passenger car tire–road interaction analysis and will be further used to perform tire rubber compound material model sensitivity analysis.

Notice of Violation of IEEE Publication Principles: Integrated Control of Braking and Steering Subsystems for Autonomous Vehicle based on an Efficient Yaw Moment Distribution

Notice of Violation of IEEE Publication Principles Control of Braking and Subsystems for Autonomous Vehicle based on an Efficient Yaw Moment by Shaobo Lu, Sheng Cen, Xiaosong Hu, Cheewah Lim and Jinlong Zhang, in the IEEE Transactions on Industrial Electronics, Early Access, May 2017 After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. This paper copies equations from the paper(s) cited below. The content was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. The lead and the second author of the paper were responsible for the violation. A correction letter for this misconduct was submitted and published at http://ieeexplore.ieee.org/document/8017449 Coordinated Control with Electronic Stability Control and Active Front Using the Optimum Yaw Moment Distribution Under a Lateral Force Constraint on the Active Front Steering by Seongjin Yim, Seungjun Kim and Heesung Yun, in the Proceedings of Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2016, Vol. 230(5) pp. 581-592 This paper presents an Integrated Chassis Control (ICC) strategy for Electronic Stability Control (ESC) and Active Four Wheel (AFWS) based on an efficient optimal yaw moment distribution. To further enhance the handling and lateral stability of vehicle equipped with ESC, a new Weighted Pseudo- inverse Control Allocation (WPCA) based ICC is proposed. The cornering forces of both front and rear wheels are used to cooperate with the ESC braking forces, so as to further extend the operational envelope of the vehicle. A bi-level hierarchical control structure is employed. In the upper level, the sliding mode control with a combined sliding surface is used to generate the desired virtual control. In the lower level, a revised optimal function is defined to tune the control authority of actuators, and an algebraic operation based WPCA method is adopted. To avoid tire forces saturation and enforce a certain stability margin, a boundary layer constraint is further considered in the proposed optimization problem. A severe lane change maneuver is used to investigate the performance via closed-loop driver-vehicle- controller simulations using CarSim and MATLAB/Simulink. Simulation results demonstrate that the proposed algorithm outperforms current control practice without violating the actuators physical limitation.

Multi-axis and cornering stiffness properties of non-pneumatic wheels with symmetric helical honeycomb spokes

Current non-pneumatic wheel (NPW) designs with non-helical honeycomb spokes generally show too high cornering stiffness and thereby rapid saturation of the cornering force, which may lead to inferior handling and directional control of the vehicle, particularly under high operating speeds. The design concept of NPWs with symmetric helical honeycomb spokes is thus proposed in this paper. Three-dimensional (3D) finite element (FE) models of a honeycomb NPW with symmetric helical spokes configurations of different cell and helix angles were developed in order to fundamentally study its multi-axis and cornering stiffness properties under a constant normal load. The validities of the developed NPW models with 0° helix angle and three different cell angles were demonstrated through comparisons of predicted wheel responses with results available in published studies. 3D simulations were conducted under two design constraints in terms of identical cell-wall thickness and identical load carrying capacity. The results suggest that increasing helix angle results in significantly greater in-plane shear stiffness of the honeycomb spokes and thus could effectively yield higher longitudinal and vertical stiffness of the NPW. An increase in helix angle also causes lower lateral stiffness for the wheel designs with 15.8° and 31.5° cell angles resulting from increases in the out-of-plane compliance of the spokes, apart from the notably lower cornering stiffness, particularly when it is increased to 30° and 45°. The cell-wall thickness, however, shows positive influences on multi-axis stiffness of the honeycomb wheel but negative effects on its cornering stiffness. The design concept of helical honeycomb spokes could offer better vehicle performances than the current designs in terms of braking/traction and handling characteristics. These are particularly important for promoting applications of the NPW in high-speed vehicles.

Cornering Force Maximization With Variable Slip Ratio Control for Independent-All-Wheel-Drive Electric Vehicle

The improvement of the maneuverability using fast and precise control of the electric motor is a crucial subject. A driving force controller (DFC) is considered to be a simple yet excellent method to secure the traction of the tire by directly limiting the slip ratio of the wheel. A conventional variable slip ratio limiter (VSRL) used for the DFC changed the limit value according the sideslip angle of the wheel, effectively maximizing either longitudinal or lateral forces of the tire. However, this did not necessarily maximize the cornering force, which is perpendicular to the vehicle body speed vector. This study presents a new variable slip ratio control method to maximize the cornering forces when the wheels have a large sideslip angle, with the aim of increasing maximum available lateral acceleration. An improved VSRL is proposed so that even when the sideslip angle of the tire is large, the tire force direction faces perpendicular to the vehicle body speed vector and the cornering force can be maximized. Simulations and experimental results using a real EV confirm that cornering maneuverability can be improved, increasing the yaw rate and lateral acceleration during cornering with a large sideslip angle of the tire on slippery roads.

Особливості руху еластичного колеса по криволінійній та прямолінійній траєкторії з відведенням

The results of the study of the motion of an elastic wheel as an integral mechanism along a curvilinear and a rectilinear trajectory with a slip on the ground plane having a high adhesion coefficient are presented. The previous researches analysis has shown that the most complete theory of wheel skidless rolling without slipping on elastic pneumatics was formulated by Keldysh V. M. who proposed the equation for calculating the curvature of the motion trajectory. Due to the difficulty of this equation coefficients determining, its use is currently limited. In this paper, the dependences for determining the components of the equation of the elastic wheel motion trajectory curvature have been proposed. According to the shimmy theory, during an elastic wheel rolling along a curvilinear trajectory, the rim turn and its lateral displacement relative to the tire-ground contact patch occur simultaneously. The rim turn causes tire body torsion, and the lateral displacement causes the elastic wheel moving with a slip angle. It is established that the absolute value of the tire body torsion angle is equal to the slip angle, and their values depend on the trajectory curvature, on the tire-ground contact patch longitudinal axis, and on the existence of traction there. The condition, under which the tire body energy distribution on the rim relative rotation and on its lateral displacement during the movement along a curved trajectory is uniform, has been determined. The experimental confirmation of the hypothesis of uniform distribution of the energy supplied to the elastic wheel during its movement along a curvilinear trajectory on the rim relative turning and its lateral displacement has been obtained. When the elastic wheel moves along a rectilinear trajectory with a slip, only the rim lateral displacement occurs, this displacement is accompanied by a cornering force applied in the center of the tire-ground contact patch and by the tire alining torque relative to the vertical axis passing through the contact patch geometric center. The energy consumption for the rim lateral displacement during the wheel rolling along a rectilinear trajectory with a slip has been also determined. The results of the research can be useful to professionals improving the wheeled vehicles performance characteristics, including maneuverability, handling, and road stability.

Finding optimum Ackermann geometry for a car undergoing steady state cornering using tire data

For a car to have minimum lap times across a track it should be able to produce the maximum cornering force or side force in order to complete the corner at the maximum velocity possible. The grip level of a particular tire limits the maximum side/lateral force it can produce. To find the best steering geometry for a car one should know the grip limit of the tire and at which slip angle it is being produced. This paper provides a simple methodology to find the appropriate Ackermann steering geometry, which can produce the maximum lateral tire grip going through different high speed constant radius corners. Hence, reducing the time spent on-track while testing to find out the suitable steering setup and improving the overall cornering ability of the car. The raw tire data from tire testing runs of the tire: Hoosier 18.0 X 6.0 – 10 R25b is used to fit curves to the raw data using two tire models based on the Magic Formula and Data Non-dimensionalization methods respectively. The results from both of the methods are compared. These tire models are then used to find the ideal steer angles of the front tires at various constant radius steady-state turns and thus the Ackermann geometry of a Formula Student car producing the maximum possible grip.

Application of interval state estimation in vehicle control

This paper mainly attempts to design an interval observer for vehicle dynamic system, and make interval observation of the state for moving vehicles. For this purpose, a novel robust estimation method was introduced to apply interval state estimation in vehicle control system. Considering the change of the turning angle, the cornering force of the tires, and the change of driving conditions, we designed a linear parameter varying interval observer, and proposed a estimation algorithm which proved effective through simulation. The employed state estimation technique could simultaneously compute the relevant signals, and make timely and effective detection of sensor faults, thereby improving the reliability and robustness of the active control system of the vehicle.

A comparative study of static and dynamic properties of honeycomb non-pneumatic wheels and a pneumatic wheel

Three-dimensional finite element (FE) models of the honeycomb NPWs with three different spokes’ configurations, realized by varying the cell angle, were formulated. The validity of the proposed NPW FE models was demonstrated by comparing the predicted wheel responses with the reported data. A FE model of the pneumatic wheel of identical size was also formulated and verified on the basis of the measured vertical force-deflection and cornering properties. The verified NPW models were subsequently employed to study their feasibility through comparisons of in-plane as well as out-of-plane properties with those of the pneumatic wheel. The influences of the cell angle and normal wheel load on the static and dynamic properties of the NPWs were also investigated. The results showed load-dependent longitudinal stiffness of the wheel due to strong coupling between radial and longitudinal deformations of the honeycomb spokes. The lateral stiffness, however, was observed to be load-independent due to negligible coupling between radial and lateral deformations of the spokes. The spokes of the honeycomb NPWs could thus be easily tuned to achieve vertical and longitudinal stiffness comparable to those of the reference pneumatic wheel. The lateral and cornering stiffness of the NPWs with the planar spokes, however, were substantially higher, irrespective of the spokes’ configuration considered. The significantly higher cornering stiffness resulted in rapid saturation of the cornering force of the NPWs at side-slip angles about 1.1°, which is likely to cause lateral sliding of the wheels and potential loss of directional control under higher side slip conditions.

Research on tire cornering force and self-aligning torque at low speeds and high speeds.

Research on tire cornering force and self-aligning torque at low speeds and high speeds.

A nonlinear dynamical approach to the path correction of multi-steering articulated vehicles

ABSTRACT When designing articulated tractor-trailer systems, engineers should take care to contrast some undesired phenomena associated with the lateral dynamics: the path off-tracking, namely the trajectory deviation of the points of the two units compared to the midpoint of the tractor fore; the rearward amplification of the transverse acceleration. The off-tracking may lead the vehicle tail to invade the opposite direction lane or the emergency lane, whereas the rearward amplification may involve the danger of the trailer rollover. Nonetheless, the arrangement of multi-steering axle systems with the proper correlation among the steering angles may substantially cancel the off-tracking, both along a path with constant curvature and while entering or leaving the road bend. Moreover, the proper control of the increase and decrease of the steering angle during the transient phases can restrain the lateral acceleration of the towed unit. The present analysis considers several nonlinear effects of the vehicle lateral dynamics, such as large steering angles, nonlinear cornering characteristics and changes of the cornering forces because of the centrifugal effect. The goal is a practical formulation of the correlation among the steering angles to correct the vehicle run and ensure lateral stability.

Numerical analysis of steering instability in an agricultural tractor induced by bouncing and sliding

Tractor overturning is a leading cause of fatalities for farmers. In Japan, small tractors are used for farming on harsh terrain, such as slippery fields and steep passage slopes. On such potentially dangerous terrain, steering instability induced by bouncing and sliding can cause tractor overturning accidents. Steering instability can also deteriorate the precision of trajectory tracking in autonomous driving tractors. The present study numerically investigated tractor steering instability due to bouncing and sliding. A bouncing model and bicycle model were coupled based on Coulomb's classical theory of friction, and numerical experiments were conducted using the developed model. In the simulations, the tractor's travel velocity, the static friction coefficient, the bump length, and the turning radius were considered as control parameters. A turning test was conducted to investigate the basic steering performance of the developed model. The numerical results revealed that the bouncing and sliding caused by the disturbance exciter reduced the cornering force to zero, which led to a deviation of the turning trajectory from the desired trajectory. The tractor was then operated on a steep passage slope similar to those reported in accidents in Japan. In the simulation, bouncing and sliding occurred because of the steep slope. The results obtained in this study strongly suggest that bouncing and sliding occurring on specific terrain result in steering instability and are a major cause of overturning accidents.

The potential capacity of tires to create cornering forces on the roads covered with chemical anti-icing materials

The paper presents the results of the study of the influence of chemical anti-icing materials on the capability of tires to create cornering forces that affect road holding and steerability of a vehicle. In this article bench and road methods of testing of tires rolling along the planes covered with chemical anti-icing materials have been applied. It demonstrates a research method used to determine the stationary and non-stationary characteristics of the elastic tires pull rolling along the planes covered with chemical anti-icing materials. The experiments are obtained in bench conditions on a special tire tester developed by scientists of the Department “Road transport” of Irkutsk National Research Technical University, as well as in road condition on a tire tester developed by scientists of the Department “Road transport” of Irkutsk National Research Technical University and the Department “Automobiles” of East Siberia State University of Technology and Management. The experimental results are presented in graphs. Obtained results allow concluding that on the roads covered with chemical anti-icing materials (CAIM) the capability of tires to create cornering forces is sharply reduced.

Model-based prediction of steering response

To predict steering response, this paper proposes a string tire model based on relaxation length and a vehicle model designed by using effective cornering force. The cornering force, lateral static, and distortion characteristics of a tire are significant factors that describe steering response. Nevertheless, it is difficult to define the contribution of each factor when a tire’s cornering motion is evaluated through subjective assessment. A new concept of tire model, which adopts distortion stiffness ([Formula: see text]), is defined. A modified vehicle dynamics model is adapted to represent tire force lag and converted cornering stiffness ([Formula: see text]) based on effective cornering force. This integration scheme is proposed to provide a more accurate modeling for steering response performance. The integration model is confirmed by dynamic response and validated through comparison with a steering response assessment by a subjective test engineer. The test results demonstrate the ability of this approach to predict steering response.

Prediction of influence of operating conditions and tyre design parameters on tyre cornering characteristics

Finite element (FE) tyre models are widely used for predicting tyre characteristics and dynamic properties used for vehicle dynamics simulation for CAE durability, ride comfort and handling assessment. Particularly, tyre FE simulation can be used to predict variation in tyre characteristics which would be too tedious to measure using laboratory tests, such as those due to changes in the tyre reinforcement material or structural layup. The cornering force characteristics of a tyre is one of the most influential factors in full vehicle dynamics simulation, having a significant effect on the directional control and handling stability of the vehicle. A validated FE tyre model developed using ABAQUS was used in parametric studies to determine factors affecting cornering force and aligning moment characteristics using design of experiments (DOE) method. Prediction of the cornering properties of the rolling tyre demonstrated the sensitivity of tyre cornering properties to tyre design parameters and operating conditions.

Prediction of influence of operating conditions and tyre design parameters on tyre cornering characteristics

Finite element (FE) tyre models are widely used for predicting tyre characteristics and dynamic properties used for vehicle dynamics simulation for CAE durability, ride comfort and handling assessment. Particularly, tyre FE simulation can be used to predict variation in tyre characteristics which would be too tedious to measure using laboratory tests, such as those due to changes in the tyre reinforcement material or structural layup. The cornering force characteristics of a tyre is one of the most influential factors in full vehicle dynamics simulation, having a significant effect on the directional control and handling stability of the vehicle. A validated FE tyre model developed using ABAQUS was used in parametric studies to determine factors affecting cornering force and aligning moment characteristics using design of experiments (DOE) method. Prediction of the cornering properties of the rolling tyre demonstrated the sensitivity of tyre cornering properties to tyre design parameters and operating conditions.

The Influence of Aggregate Lithological Nature on Pavement Texture Polishing: A Comparative Investigation on a Test Site in Southern Italy

Abstract Pavement surface performance plays a key role in tyre-road interaction phenomena and greatly affects road safety, vehicle's operational costs, and environmental sustainability. Surface texture and friction change over time with the action of the repeated passage of vehicle tires, especially those of heavy vehicles (long-term variations). Other factors related to asphalt mix composition, primarily the aggregates and their mineralogical composition, the binder and their combination, have a great effect on micro and macrotexture evolution. In particular, the extent to which a surface will polish depends on both the level of traffic and the ability of the aggregate to resist polishing. Moreover, an aggregate may provide different levels of skid resistance depending on where it is used because the polishing effect is also influenced by other stresses such as braking and cornering forces. In light of the above, this paper focused on a 4-year monitoring of a test site (both straight and curve sections) with four different dense graded friction courses designed and produced with aggregates of different petrographic nature: limestone, basalt, and expanded clay. Several devices and test methods (Skid Tester, Sand Patch Test, Laser Profilometer) were used in order to investigate skid resistance and macro-texture progression. Results showed that: (i) mixes have a different microtexture deterioration behavior in relation to aggregate type, especially during the pavement early life, confirming how limestone does not perform as well as basalt or expanded clay under traffic actions; (ii) macrotexture evolution trend is characterized by a consistent decrease after 4 years; the maximum value of macrotexture was registered 13 months after opening to traffic (when the migrated bitumen is completely removed by traffic). Results highlighted practical applications and perspectives for both practitioners and researchers.

Analysis of dynamic mechanism and global response of vehicle shimmy system with multi-clearance joints

Joints with clearance always exist in steering mechanism of vehicles due to the machining tolerances, deformations and wear, which should not be neglected in modeling and analysis of vehicle shimmy system. Based on Lagrange equation method, a six-DOF dynamic model of vehicle shimmy system with consideration of multi-clearance joints was established. The model of movement pairs with clearance was built based on Hertzian contact law. The nonlinear cornering force of pneumatic tire was described based on PAC2002 tire model, and its parameters were obtained by an identification method based on experimental data. Then numerical examples were employed to evaluate the dynamic response of the shimmy system. The influence of multi-clearance joints on the response of shimmy was analyzed, and it is compared with that of one clearance joint. The acting mechanism of contact force between movement pairs was investigated, and global dynamic analysis was carried out by using point mapping method. Moreover, the dynamic mechanism for vehicle shimmy was investigated based on energy input. The conclusions can provide theoretic evidence for attenuation of vehicle shimmy, especially for those in-service vehicles.

String tyre model for evaluating steering agility performance using tyre cornering force and lateral static characteristics

ABSTRACTThe cornering force and lateral static characteristics of a tyre are fundamental factors that describe the steering feel for handling performance. However, it is difficult to justify the contribution of each factor when the tyre’s cornering motion is evaluated through subjective assessment. Currently, the relaxation length of Pacejka’s tyre model is close to describing these tyre motions. Therefore, this paper proposes a string tyre model based on the relaxation length in order to represent the steering performance. The proposed method provides a more accurate modelling of the steering agility performance. Therefore, it is possible to use this model to predict the steering response performance, and this is validated through comparison with a real relaxation length.