Physical Understanding of Transient Generation of Tire Lateral Force and Aligning Torque

2019 ◽  
Vol 47 (4) ◽  
pp. 308-333 ◽  
Author(s):  
Pavel Sarkisov ◽  
Günther Prokop ◽  
Jan Kubenz ◽  
Sergey Popov
Keyword(s):  
Cross Sections ◽  
Physical Simulation ◽  
Optical Measurement ◽  
Structural Parameters ◽  
Lateral Force ◽  
Slip Angle ◽  
Contact Patch ◽  
Physical Description ◽  
Patch Shape ◽  
Tire Force

ABSTRACT Increasing vehicle performance requirements and virtualization of the development process require more understanding of the physical background of tire behavior, especially in transient rolling conditions with combined slip. The focus of this research is the physical description of the transient generation of tire lateral force and aligning torque. Apart from tire force and torque measurements, two further issues were investigated experimentally. Using acceleration measurement on the tire inner liner, it was observed that the contact patch shape of the rolling tire changes nonlinearly with slip angle and becomes asymmetric. Optical measurement outside and inside the tire has clarified that carcass lateral bending features both shear and rotation angle of its cross sections. A physical simulation model was developed that considers the observed effects. The model was qualitatively validated using not only tire force and torque responses but also deformation of the tire carcass. The model-based analysis explained which tire structural parameters are responsible for which criteria of tire performance. Change in the contact patch shape had a low impact on lateral force and aligning torque. Variation of carcass-bending behavior perceptibly influenced aligning torque generation.

Measurement of Uncoupled Lateral Carcass Deflections With a Wireless Piezoelectric Sensor and Estimation of Tire Road Friction Coefficient

2010 ◽  
Author(s):  
Gurkan Erdogan ◽  
Lee Alexander ◽  
Rajesh Rajamani
Keyword(s):  
Friction Coefficient ◽  
Leading Edge ◽  
Piezoelectric Sensor ◽  
Lateral Force ◽  
Slip Angle ◽  
Contact Patch ◽  
Tire Force ◽  
Coefficient Estimation ◽  
Road Friction ◽  
Road Friction Coefficient

A new tire-road friction coefficient estimation approach based on lateral carcass deflection measurements is proposed. The unique design of the developed wireless piezoelectric sensor decouples lateral carcass deformations from radial and tangential carcass deformations. The estimation of the tire-road friction coefficient depends on the estimation of the slip angle and the lateral tire force. The tire slip angle is estimated as the slope of the lateral deflection curve at the leading edge of the contact patch. The lateral tire force is obtained by using a parabolic relationship with the lateral deflections in the contact patch. The estimated slip angle and lateral force are then plugged into a tire brush model to estimate the tire-road friction coefficient. A specially constructed tire test-rig is used to experimentally evaluate the performance of the tire sensor and the developed approach. Experimental results show that the proposed tire-road friction coefficient estimation approach is quite promising.

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.

Simultaneous Optimal Distribution of Lateral and Longitudinal Tire Forces for the Model Following Control

2004 ◽  
Vol 126 (4) ◽  
pp. 753-763 ◽  
Author(s):  
Ossama Mokhiamar ◽  
Masato Abe
Keyword(s):  
Lateral Force ◽  
Longitudinal Force ◽  
Equality Constraints ◽  
Steering Wheel ◽  
Slip Angle ◽  
Force Distribution ◽  
Distribution Method ◽  
Tire Force ◽  
Model Following Control ◽  
Tire Forces

This paper presents a proposed optimum tire force distribution method in order to optimize tire usage and find out how the tires should share longitudinal and lateral forces to achieve a target vehicle response under the assumption that all four wheels can be independently steered, driven, and braked. The inputs to the optimization process are the driver’s commands (steering wheel angle, accelerator pedal pressure, and foot brake pressure), while the outputs are lateral and longitudinal forces on all four wheels. Lateral and longitudinal tire forces cannot be chosen arbitrarily, they have to satisfy certain specified equality constraints. The equality constraints are related to the required total longitudinal force, total lateral force, and total yaw moment. The total lateral force and total moment required are introduced using the model responses of side-slip angle and yaw rate while the total longitudinal force is computed according to driver’s command (traction or braking). A computer simulation of a closed-loop driver-vehicle system subjected to evasive lane change with braking is used to prove the significant effects of the proposed optimal tire force distribution method on improving the limit handling performance. The robustness of the vehicle motion with the proposed control against the coefficient of friction variation as well as the effect of steering wheel angle amplitude is discussed.

Physics of the Slipping Wheel. I. Force and Torque Calculations for Various Pressure Distributions

1969 ◽  
Vol 42 (4) ◽  
pp. 1014-1027 ◽  
Author(s):  
D. I. Livingston ◽  
J. E. Brown
Keyword(s):  
Pressure Distribution ◽  
Lateral Force ◽  
Slip Angle ◽  
Uniform Pressure ◽  
Elliptical Distribution ◽  
Side Force ◽  
Contact Patch ◽  
Pressure Distributions ◽  
Parabolic Distribution

Abstract Slipping wheel theory has been extended to predict the dependence of the lateral force and of the aligning torque on the nature of the pressure distribution over the contact patch between the wheel and the ground. Expressions have been derived for both side force and aligning torque as functions of the slip angle under: uniform pressure distribution, which applies to the behavior of an inflated membrane wheel; elliptical distribution, which describes the behavior of a solid wheel; and parabolic distribution. All appear appropriate in some respect to the actual tire.

Relationship Between Tire Tread Physical Properties and Tire Force and Moment Properties

1989 ◽  
Vol 17 (2) ◽  
pp. 109-125 ◽  
Author(s):  
M. G. Pottinger ◽  
A. M. Fairlie
Keyword(s):  
Physical Properties ◽  
Lateral Force ◽  
Hysteresis Effect ◽  
Design Parameters ◽  
Slip Angle ◽  
Tire Force ◽  
Torque Curve ◽  
Driving Range ◽  
Important Design

Abstract Tire lateral force and aligning torque are the most significant determinants of automotive handling. Tread compound physical properties are important design parameters for determination of tire lateral force and aligning torque behavior. This paper extends the published knowledge of the effects of tread compound physical properties on force and moment to cover the entire range of slip angles encountered in driving. Below 10 degrees slip angle lateral force increases with increasing compound stiffness and hysteresis. At and above 10 degrees slip angle there is a change in the general trend. In this range it appears that an optimal compound stiffness exists and that the hysteresis effect reverses. Aligning torque shows two distinctly different behaviors. One, like that governing lateral force in the general driving range, is valid below the peak of the aligning torque curve. The other, valid above the peak of the aligning torque curve, shows decreasing aligning torque with increasing tread stiffness and no hysteresis effect.

Investigation and Comparison of Tires Perfomance on Ice

2017 ◽  
Author(s):  
Andrius Ružinskas ◽  
Henrikas Sivilevicius
Keyword(s):  
Lateral Force ◽  
Operating Conditions ◽  
Slip Angle ◽  
Transmission Measurement ◽  
Force Transmission ◽  
Force Coefficient ◽  
Slip Ratio ◽  
The Road ◽  
Tire Force ◽  
Main Component

The risk of accident increases significantly when tire rolls on ice comparing to the dry surface. The vehicle tire becomes the main component of force transmission to the road and necessity of investigating the tire behavior becomes of high importance. This paper presents results of tire force transmission measurement with two different winter tires at the same operating conditions. Longitudinal and lateral force coefficient characteristics as the functions of slip ratio and slip angle are presented and discussed. The results showed a different lateral and longitudinal performance because of different tread pattern and rubber compound.

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.

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.

Structural Optimization of the Telescopic Boom of a Certain Type of Truck-Mounted Crane

2014 ◽  
Vol 548-549 ◽  
pp. 383-388
Author(s):  
Zhi Wei Chen ◽  
Zhe Cui ◽  
Yi Jin Fu ◽  
Wen Ping Cui ◽  
Li Juan Dong ◽  
...  
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Cross Sections ◽  
Optimization Design ◽  
Structural Parameters ◽  
Vertical Direction ◽  
Element Model ◽  
Shape Parameters ◽  
Conventional Design ◽  
Design Variables

Parametric finite element model for a commonly used telescopic boom structure of a certain type of truck-mounted crane has been established. Static analysis of the conventional design configuration was performed first. And then an optimization process has been carried out to minimize the total weight of the telescopic structures. The design variables include the geometric shape parameters of the cross-sections and the integrated structural parameters of the telescopic boom. The constraints include the maximum allowable equivalent stresses and the flexure displacements at the tip of the assembled boom structure in both the vertical direction and the circumferential direction of the rotating plane. Compared with the conventional design, the optimization design has achieved a significant weight reduction of up to 24.3%.

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.

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