Distribution of Side Force and Side Slip in the Contact Area of the Pneumatic Tire

1959 ◽  
Vol 32 (2) ◽  
pp. 490-502
Author(s):  
D. H. Cooper
Keyword(s):  
Contact Area ◽  
Contact Spot ◽  
The Self ◽  
Slip Angle ◽  
Vertical Force ◽  
Pneumatic Tire ◽  
Side Force

Abstract It is well known that, when a pneumatic tire is rolled over dry ground at a slip angle, a sideways force is developed. With the cornering force rig described here we are able to measure the front to rear distribution of the cornering force along the contact spot, the length of the contact area, the trail and the self-aligning torque. At the same time it is possible to derive the shape of the distorted tread and the front to rear distribution of side slip in the contact spot. By making certain assumptions concerning the distribution of the vertical force along the contact spot a relationship has been established between the forces of friction, rate of side slip and speed of rolling.

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.

A Laboratory Method to Comprehensively Evaluate Abrasion, Traction and Rolling Resistance of Tire Tread Compounds

2007 ◽  
Vol 80 (4) ◽  
pp. 580-607 ◽  
Author(s):  
M. Heinz ◽  
K. A. Grosch
Keyword(s):  
Friction Coefficient ◽  
Laboratory Test ◽  
Rolling Resistance ◽  
Limited Range ◽  
Slip Angle ◽  
Testing Conditions ◽  
Side Force ◽  
The Road ◽  
Wide Range ◽  
On The Road

Abstract A laboratory test method has been developed which allows the evaluation of diverse properties of tire tread compounds on the same sample. The laboratory test instrument consists of a rotating abrasive disk against which a rubber sample wheel runs under a given load, slip angle and speed. All three force components acting on the wheel during the tests are recorded. By changing the variable values over a wide range practically all severities encountered in tire wear are covered. The well-known fact that compound ratings depend on the road testing conditions is verified. Most compounds are only significantly distinguishable against a control over a limited range of testing conditions. Using a road test simulation computer program based on the laboratory data shows that not only ratings correspond to practical experience but also calculated absolute tire life times do. Tests on surfaces of different coarseness and sharpness indicate that sharp coarse surfaces give the best results with road tests, which of necessity are mostly carried out on public roads of differing constitution. The abrasive surface can be wetted with water at different temperatures and hence either the friction force at a locked wheel or the side force at a slipping wheel can be measured over a wide range of temperatures and speeds. At small slip angles the side force is dominated by dynamic cornering stiffness of the compound, at large slip angles by the friction coefficient. In this case, too, good correlations to road experience exist over a limited range of testing conditions. Low water temperatures and low slip speed settings in the laboratory produce side force ratings, which correlate closely with ABS braking on the road High and higher slip speeds give ratings in close agreement with locked wheel braking on the road. A heatable/coolable disk enables traction measurements on ice and newly abrasion measurements on surfaces at elevated surface temperature. Ice surface temperatures between −5 °C and −25 °C are possible. Friction measurements show that the difference in compound rating between summer and winter compounds is maintained over the whole temperature range. New investigations show not only a differentiation between different winter tire treads qualities but also an excellent correlation between tire and laboratory results. As a new topic side force measurements on dry surfaces highlight the correlation to dry handling of tires. The tire tread compound contributes to this performance through its shear stiffness and its friction coefficient. The shear stiffness contributes to the response of the tire in directional changes. The friction coefficient determines the maximum force, which can be transmitted. A simple operation possibility for evaluation of determined side forces is demonstrated. In addition to antecedent investigations the rolling resistance of the rubber wheel can be measured over a range of loads and speeds with the slip angle set at zero. Again for these new results good correlations are achieved with practical experience. In particular, the dependence of the rolling resistance on the velocity and loads are pointed out. Ultimately a good correlation between tire test and laboratory test results was demonstrated.

Investigation of the tyre characteristics under non-steady-state conditions on the basis of road tests

2016 ◽  
Vol 231 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Hubert Sar ◽  
Andrzej Reński ◽  
Janusz Pokorski
Keyword(s):  
Steady State ◽  
Computer Simulations ◽  
Dynamic Characteristics ◽  
Slip Angle ◽  
Real Motion ◽  
Side Force ◽  
The Real ◽  
Different Types ◽  
Non Linear ◽  
The Difference

This paper presents a method of identifying the dynamic characteristics of tyres for non-steady-state conditions on the basis of road measurements on a vehicle. The side force acting on the tyre is presented as a function of not only the slip angle but also the slip angle derivative (i.e. the velocity of the change in the slip angle). Hence, the influence of the manoeuvre dynamics on the tyre characteristics and the difference between the characteristics obtained for steady-state conditions and the characteristics for non-steady-state conditions are shown. Also the results of computer simulations prepared for different types of tyre characteristics are presented in this paper. It is evident from the presented graphs that applying dynamic non-linear tyre characteristics for computer simulations instead of steady-state characteristics enables us to describe the real motion of a vehicle better.

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.

Jackknifing of Tractor-Semitrailer Trucks—Detection and Corrective Action

1974 ◽  
Vol 96 (2) ◽  
pp. 244-252 ◽  
Author(s):  
E. A. Susemihl ◽  
A. I. Krauter
Keyword(s):  
Corrective Action ◽  
Slip Angle ◽  
Side Force ◽  
Local Linearization ◽  
Adequate Definition ◽  
Quantitative Manner ◽  
Definition Of ◽  
Real Vehicle

This paper is concerned with the detection of an incipient tractor jackknife of a tractor-semitrailer truck and with corrective action which can be taken after the onset of jackknifing has been sensed. An approach termed local linearization is used to define tractor jackknifing in a quantitative manner. Local linearization is then used to evaluate a second approach, termed side force-slip angle combination. This side force-slip angle combination is employed to study three forms of automatic corrective action that involve braking of the vehicle. The results obtained indicate that local linearization provides an adequate definition of the onset of jackknifing. The results also indicate that the side force-slip angle combination is useful in sensing the onset of a tractor kackknife. Through the use of approximations, the side force-slip angle combination can be implemented in a real vehicle—this implementation is found to require only simple measurements. The results of the corrective action study indicate that a certain anti-skid braking procedure may be effective in the prevention of an incipient jackknife.

Theoretical analysis of the yarn fracture mechanism of self-twist jet vortex spinning

2016 ◽  
Vol 87 (11) ◽  
pp. 1394-1402 ◽  
Author(s):  
Chenchen Han ◽  
Wenliang Xue ◽  
Longdi Cheng ◽  
Zhuanyong Zou
Keyword(s):  
Theoretical Analysis ◽  
Tensile Properties ◽  
Contact Area ◽  
Fracture Mechanism ◽  
The Self ◽  
Mutual Contact ◽  
Spun Yarn ◽  
Spinning Speed

According to the yarn mechanism of self-twist jet vortex spinning, this article analyzes the structure and the fracture mechanism of self-twist jet vortex spinning yarn. Combined with experiments, this article established that the fiber in self-twist jet vortex spun yarn has self-twist, which increases the mutual contact area and the cohesion between the fibers in the yarn. This is helpful to improve the evenness and tensile properties of jet vortex spun yarn. The self-twist jet vortex spinning can keep the high spinning speed of the jet vortex spinning at the same time. The research on self-twist jet vortex spinning lays the foundation for the research and the development of jet vortex spinning.

Study on Cornering Properties of Tire and Vehicle

1990 ◽  
Vol 18 (3) ◽  
pp. 136-169 ◽  
Author(s):  
H. Sakai
Keyword(s):  
Load Distribution ◽  
Driving Forces ◽  
Slip Angle ◽  
Inflation Pressure ◽  
Slip Ratio ◽  
Side Force ◽  
Camber Angle ◽  
Tire Wear ◽  
Main Factors ◽  
Tire Friction

Abstract This paper presents theoretical analysis on the cornering properties of tire and vehicle. First, the side force, braking driving forces and self-aligning torque on the tire are shown as functions of slip angle, slip ratio, camber angle and load. Next, the steady cornering properties of the vehicle using these tires are analyzed with the rolling conditions. Slip angle, slip ratio, camber angle and load, and forces and moments of the four tires are calculated. Effects of main factors on the above vehicle properties such as the load distribution, camber/roll ratio, front/rear drive ratio, tire size, tire wear, tire inflation pressure and tire friction are discussed.

Theoretical and Experimental Evaluation of Impact on Soil by Wheel Drives of the Self-Propelled Seeder

2020 ◽  
pp. 139-163
Author(s):  
Alexandr Vladimirovich Lavrov ◽  
Maksim Nikolaevich Moskovskiy ◽  
Natalia Sergeevna Kryukovskaya
Keyword(s):  
Contact Pressure ◽  
Contact Area ◽  
Experimental Methods ◽  
The Self ◽  
Soil Density ◽  
Axial Loads ◽  
Soil Hardness ◽  
Different Depths ◽  
Maximum Contact ◽  
Maximum Discrepancy

Dedicated vertical axial loads on the soil from the wheels of a self-propelled seed drill, the area of the contact patch, the maximum contact pressure for the front and rear wheels and the density of the soil are determined by evaluations and experimental methods. The discrepancy between the theoretical and experimental indicators was: 1.4% and 2.0% for the rear and front wheels in vertical axial loads; 2.8% and 2.2% for the rear and front wheels by the contact area of the tires of the seeder with the soil and the maximum contact pressure; 6.2% – the maximum discrepancy on the values of soil density at a depth of 7.6 cm. Soil hardness was measured in three zones: before the seeder's passage and after each of its passage in a rut behind the front and rear wheels at six different depths, determined by the marks on the soil densimeter tester density. Graphics of dependencies of soil hardness on the depth of measurement were constructed.

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