Tire Lateral Force Modeling and the Bushing Analogy Tire Model

2005 ◽  
Vol 33 (1) ◽  
pp. 18-37 ◽  
Author(s):  
B. G. Kao ◽  
T. Warholic
Keyword(s):  
Lateral Force ◽  
Dynamic Responses ◽  
Slip Angle ◽  
Fe Model ◽  
Tire Model ◽  
Dynamic Features ◽  
Dynamics Modeling ◽  
Data Set ◽  
Vehicle Handling ◽  
Force Modeling

Abstract The Bushing Analogy Tire (BAT) model has been studied for tire dynamics modeling in vertical and lateral directions. It was shown that the vibration characteristics included in the BAT model in the vertical and lateral directions cover the tire modes in those directions up to about 100 Hz. This capability of the BAT model is suitable for vehicle ride simulations. However, in vehicle handling situations such as accident avoidance, the tire is subjected to sudden steering motions that are not included in the vertical and lateral dynamics. The steering generates tire slip angle and, hence, the lateral forces for vehicle direction change. The tire steering motion also generates the aligning torque, which modifies the slip angle of the tire with respect to the wheel input steering angle. The tire steering compliance is therefore important for the dynamic responses during the vehicle handling maneuvers. In this paper, tire compliance in the steering direction is studied by treating the steering motion as an independent motion of the 3-dimentional tires. In this paper, the steering stiffness (or compliance) of a tire is first derived from the analysis results of a tire Finite Element (FE) model. Comparing the steering direction vibration modes using the BAT model with the FE model extracted modes further validates the steering stiffness. The coupling of tire steering stiffness with the vertical forces is also studied. Then, the effects of the tire steering direction stiffness are used to study a data set of flat-track generated tire lateral force and moment. The procedure of generating required coefficients of a handling tire model coupled with tire dynamic features of the BAT model were also investigated.

scholarly journals A Novel Dynamic Data Driven Tire Model

2021 ◽  
Author(s):  
Junning Zhang ◽  
Shaopu YANG ◽  
Yongjie LU
Keyword(s):  
Experimental Data ◽  
Knowledge Base ◽  
Vehicle Dynamics ◽  
Mechanical Characteristics ◽  
Slip Rate ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Dynamics Simulation ◽  
Slip Angle ◽  
Tire Model

Abstract In the study of vehicle dynamics, the accurate description of tire mechanical characteristics is the basis and key of vehicle dynamics simulation. An innovative tire model is proposed based on fuzzy algorithm and a sinusoidal membership function is used to design fuzzy rules. In order to ensure the accuracy of tire behavior calculation, this model is driven by a small amount of experimental data of tire mechanical characteristics. This tire model consists of four layers of fuzzy systems, each of which has a knowledge base. The data in knowledge base I is obtained by experiments, and the data of knowledge base II is computed by the upper system, and so is the later system. Then, the input signal, the change rate of side slip angle and slip rate, is considered to improve the calculation accuracy of the model. The proposed fuzzy tire model can accurately predict the longitudinal force, lateral force and self-aligning torque of the tire under unknown conditions. Finally, by comparing the fuzzy tire model with the experimental data, it is found that the maximum RRMSE (Relative Root Mean Square Error) value is not more than 0.14. It is proved that the model can accurately describe the tire
mechanical characteristics under combined conditions.

Validation of a High-Fidelity Finite Element Tire Model on Pavement

2020 ◽  
Author(s):  
Tamer Wasfy ◽  
Hatem Wasfy ◽  
Paramsothy Jayakumar ◽  
Srinivas Sanikommu
Keyword(s):  
Finite Element ◽  
Normal Load ◽  
Rolling Resistance ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Friction Model ◽  
Rubber Matrix ◽  
Slip Angle ◽  
High Fidelity ◽  
Tire Model

Abstract The objective of this study is to validate a high-fidelity finite element tire model on hard pavement. In this model, the tire rubber matrix is modeled using locking-free brick elements with embedded thin beam elements along the tire’s circumference, meridian, and diagonals for modeling the tire’s reinforcements (belt, ply and bead). The internal air pressure is applied as a distributed force on the inner surface of the brick elements. Frictional contact between the outer surface of the brick elements and the pavement is modeled using the penalty method along with an asperity based Coulomb friction model. In order to validate the tire model, a medium duty truck tire is modeled and the following response quantities are compared to experimental results: (1) normal load versus deflection at different tire pressures; (2) rolling resistance versus speed; (3) longitudinal force versus slip; (4) lateral force versus slip angle for different normal loads; and (5) self-aligning torque versus slip angle for different normal loads.

Wheel Torque Controller Development Using a Simplified Tire Model for Vehicle Handling Enhancement

2009 ◽  
Author(s):  
Ganesh Adireddy ◽  
Taehyun Shim ◽  
Douglas Rhode
Keyword(s):  
Predictive Control ◽  
Essential Element ◽  
Control Algorithms ◽  
Slip Angle ◽  
Tire Model ◽  
Computationally Efficient ◽  
Vehicle Handling ◽  
Yaw Rate ◽  
Wheel Torque ◽  
Tire Models

A tire model is an essential element in the vehicle controller development and various complexities of tire models have been developed and used. It is highly desirable for the control systems to use a tire model that is computationally efficient and easy to implement in control algorithms while providing desired performance. In this paper, a wheel torque controller was developed using a non-linear predictive control theory, 8 degree of freedom vehicle model, and a simplified nonlinear tire model in order to control the vehicle yaw rate and side slip angle. The performance of this controller was compared to that based on well known Magic Formula tire model. The effectiveness and limitations of the proposed controller were discussed through simulation.

Experimental verification using a driving simulator of the effect of simultaneous optimal distribution of tyre forces for active vehicle handling control

2005 ◽  
Vol 219 (2) ◽  
pp. 135-149 ◽  
Author(s):  
O Mokhiamar ◽  
M Abe
Keyword(s):  
Computer Simulation ◽  
Driving Simulator ◽  
Experimental Studies ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Equality Constraints ◽  
Steering Wheel ◽  
Slip Angle ◽  
Force Distribution ◽  
Vehicle Handling

Both theoretical and experimental studies are carried out in order to prove the effect of the simultaneous optimum distribution of lateral and longitudinal tyre forces on enhancement of vehicle handling and stability assuming that all four wheels can be independently steered and driven/braked. A driving simulator is used as an experimental instrument to investigate the effect of the optimum tyre force distribution control. The inputs to the optimization process are the driver's commands (steering wheel angle and foot brake pressure/accelerator pedal pressure), while the outputs are lateral and longitudinal forces on all four wheels. Lateral and longitudinal tyre forces cannot be chosen arbitrarily, but must satisfy certain specified equality constraints. The equality constraints are related to the required total longitudinal force, total lateral force and total yaw moment to achieve a given vehicle motion. The total lateral force and total moment required are introduced using the model responses of side-slip angle and yaw rate to the driver's steering input, while the total longitudinal force is computed according to the driver's command (traction/braking). The results of either computer simulation or a driving simulator show that the influence of the proposed optimum tyre force distribution control on vehicle performance enhancement is significantly apparent. Furthermore, driving simulator results show very good agreement with the computer simulation results presented.

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

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.

Normalization of Tire Force and Moment Data

1993 ◽  
Vol 21 (2) ◽  
pp. 91-119 ◽  
Author(s):  
H. S. Radt ◽  
D. A. Glemming
Keyword(s):  
Surface Water ◽  
Lateral Force ◽  
Slip Angle ◽  
Inflation Pressure ◽  
Slip Ratio ◽  
Tire Force ◽  
Camber Angle ◽  
Potential Benefits ◽  
Overturning Moment ◽  
Semi Empirical

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.

A Double Interaction Brush Model for Snow Conditions

2019 ◽  
Vol 47 (2) ◽  
pp. 118-140
Author(s):  
Artem Kusachov ◽  
Fredrik Bruzelius ◽  
Mattias Hjort ◽  
Bengt J. H. Jacobson
Keyword(s):  
Low Complexity ◽  
Large Set ◽  
Tire Model ◽  
Vehicle Handling ◽  
Real Time Applications ◽  
Snow Conditions ◽  
Double Interaction ◽  
Tire Models ◽  
Force Characteristics ◽  
Model Approach

ABSTRACT Commonly used tire models for vehicle-handling simulations are derived from the assumption of a flat and solid surface. Snow surfaces are nonsolid and may move under the tire. This results in inaccurate tire models and simulation results that are too far from the true phenomena. This article describes a physically motivated tire model that takes the effect of snow shearing into account. The brush tire model approach is used to describe an additional interaction between the packed snow in tire tread pattern voids with the snow road surface. Fewer parameters and low complexity make it suitable for real-time applications. The presented model is compared with test track tire measurements from a large set of different tires. Results suggest higher accuracy compared with conventional tire models. Moreover, the model is also proven to be capable of correctly predicting the self-aligning torque given the force characteristics.

Simplified Prediction of Ply Steer in Radial Tires

1980 ◽  
Vol 8 (1) ◽  
pp. 3-9 ◽  
Author(s):  
C. W. Bert
Keyword(s):  
Composite Laminate ◽  
Ground Plane ◽  
Lateral Force ◽  
Rolling Contact ◽  
Slip Angle ◽  
Uniform Stress ◽  
Rubber Composite ◽  
Laminate Theory ◽  
Contact Models ◽  
Uniform Stress State

Abstract Ply steer is a rolling contact phenomenon which manifests itself as a lateral force acting at the ground plane of a tire constrained in yaw or a change in slip angle of a tire free to yaw. It has long been known that radial tires generally exhibit greater ply steer than do bias tires. However, the only previously published quantitative analysis of this phenomenon considered the multi-layer cord-rubber composite by means of netting analysis, which is not very accurate at cord angles typical of radial tire belts. A simple, explicit expression is developed herein by combining modern composite laminate theory with two very simple, uniform-stress-state tire-road contact models. The ply-steer results predicted by the resulting expressions are compared with some experimental results and the agreement is found to be reasonably satisfactory.

Lateral Tire Forces on Wet Roads

1977 ◽  
Vol 5 (2) ◽  
pp. 75-82 ◽  
Author(s):  
A. Schallamach
Keyword(s):  
Normal Load ◽  
The Self ◽  
Experimental Results ◽  
Slip Angle ◽  
Tire Model ◽  
Side Force ◽  
Tire Forces

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.

Theoretical Tire Model Considering Two-Dimensional Contact Patch for Force and Moment

2021 ◽  
Author(s):  
Y. Nakajima ◽  
S. Hidano
Keyword(s):  
Finite Element Method ◽  
Shear Force ◽  
The Self ◽  
Slip Angle ◽  
Force Distribution ◽  
Two Dimensional ◽  
Tire Model ◽  
Side Force ◽  
Contact Patch ◽  
Proposed Model

ABSTRACT The new theoretical tire model for force and moment has been developed by considering a two-dimensional contact patch of a tire with rib pattern. The force and moment are compared with the calculation by finite element method (FEM). The side force predicted by the theoretical tire model is somewhat undervalued as compared with the FEM calculation, while the self-aligning torque predicted by the theoretical tire model agrees well with the FEM calculation. The shear force distribution in a two-dimensional contact patch under slip angle predicted by the proposed model qualitatively agrees with the FEM calculation. Furthermore, the distribution of the adhesion region and sliding region in a two-dimensional contact patch predicted by the theoretical tire model qualitatively agrees with the FEM calculation.

Sign in / Sign up

Export Citation Format

Share Document