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.

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.

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.

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.

Non-Uniform Pressure Distribution in Draw-Bend Friction Test and a New Methodology to Determine Non-Constant Friction Coefficient From the Test

2006 ◽  
Author(s):  
Young Suk Kim ◽  
Mukesh K. Jain ◽  
Don R. Metzger
Keyword(s):  
Friction Coefficient ◽  
Pressure Distribution ◽  
Uniform Pressure ◽  
Friction Coefficients ◽  
Average Value ◽  
Pressure Distributions ◽  
Element Simulation ◽  
Constant Friction ◽  
Pressure Dependency ◽  
Friction Models

Friction under lubricated conditions is known to depend on pressure, and experimental determination of this dependence has typically quantified pressure as an average value over the contact area. However, non-uniform pressure distributions at the contact interfaces of draw-bend tests have been reported from various experiments and simulations. A previous study by the authors has evaluated the current methodology, which assumes uniform pressure distribution to estimate friction coefficients from draw-bend friction tests, and has concluded that the current methodology is only valid for measuring an average friction coefficient over the pressure range, which exists in the specific draw-bend system. In this paper, a new methodology to extract non-constant friction coefficients from draw-bend friction tests is suggested. In the methodology, contact pressure maps obtained from simulations, instead of the uniform pressure assumption, are included in the analysis of test data to measure the pressure dependency of friction coefficient. The methodology is tested by applying the method to back predict the input friction data from finite element simulation results of draw-bend friction tests, in which non-constant friction models are used as friction input.

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.

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.

Measurement and Visualization of the Contact Pressure Distribution of Rubber Disks and Tires

1995 ◽  
Vol 23 (4) ◽  
pp. 238-255 ◽  
Author(s):  
E. H. Sakai
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Area ◽  
Light Absorption ◽  
Lateral Force ◽  
Contact Pressure Distribution ◽  
High Definition ◽  
The Road ◽  
Close Relationship ◽  
Processing Techniques

Abstract The contact conditions of a tire with the road surface have a close relationship to various properties of the tire and are among the most important characteristics in evaluating the performance of the tire. In this research, a new measurement device was developed that allows the contact stress distribution to be quantified and visualized. The measuring principle of this device is that the light absorption at the interface between an optical prism and an evenly ground or worn rubber surface is a function of contact pressure. The light absorption can be measured at a number of points on the surface to obtain the pressure distribution. Using this device, the contact pressure distribution of a rubber disk loaded against a plate was measured. It was found that the pressure distribution was not flat but varied greatly depending upon the height and diameter of the rubber disk. The variation can be explained by a “spring” effect, a “liquid” effect, and an “edge” effect of the rubber disk. Next, the measurement and image processing techniques were applied to a loaded tire. A very high definition image was obtained that displayed the true contact area, the shape of the area, and the pressure distribution from which irregular wear was easily detected. Finally, the deformation of the contact area and changes in the pressure distribution in the tread rubber block were measured when a lateral force was applied to the loaded tire.

scholarly journals Effect of Pressure Distribution on the Energy Dissipation of Lap Joints under Equal Pre-tension Force

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 320-328
Author(s):  
Delin Sun ◽  
Minggao Zhu
Keyword(s):  
Energy Dissipation ◽  
Pressure Distribution ◽  
Theoretical Basis ◽  
Lap Joints ◽  
Power Exponent ◽  
Lap Joint ◽  
Stick Slip ◽  
Pressure Distributions ◽  
Hysteretic Characteristics ◽  
Effective Use

Abstract In this paper, the energy dissipation in a bolted lap joint is studied using a continuum microslip model. Five contact pressure distributions compliant with the power law are considered, and all of them have equal pretension forces. The effects of different pressure distributions on the interface stick-slip transitions and hysteretic characteristics are presented. The calculation formulation of the energy dissipation is introduced. The energy dissipation results are plotted on linear and log-log coordinates to investigate the effect of the pressure distribution on the energy distribution. It is shown that the energy dissipations of the lap joints are related to the minimum pressure in the overlapped area, the size of the contact area and the value of the power exponent. The work provides a theoretical basis for further effective use of the joint energy dissipation.

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