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.

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.

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.

Steering and Stability of Single-track Vehicles

1951 ◽  
Vol 5 (1) ◽  
pp. 191-213 ◽  
Author(s):  
R. A. Wilson-Jones
Keyword(s):  
Lateral Force ◽  
Front Wheel ◽  
Slip Angle ◽  
Single Track ◽  
Motor Cycle ◽  
Low Mass ◽  
Low Speeds ◽  
The Stability ◽  
Straight Ahead

The author briefly states the elementary principles of equilibrium and claims that the stability of the conventional bicycle or motor cycle is automatic except at very low speeds. This is because the steering automatically turns in the direction in which the machine is leaning and returns to the straight ahead position when the machine is restored to the vertical. The achievement of these effects is largely due to the “trail” of the front wheel. The causes of “steering roll” and “steering wobble” and the purpose of the inclination of the steering head, are examined, as are the effects of high and low mass centres and of the rider leaning with and against the machine. It is shown how the elementary principles of steering apply to various types of vehicle, including single-track vehicles in which the necessary lateral force comes mainly from camber thrust rather than slip angle. The results are given of experiments on varying amounts of “trail”, and a method of measuring slip angles is described which is applicable to motor cycles. Finally, a method of indicating the direction of the torque applied to the handlebars when entering, holding, and leaving a bend is described.

scholarly journals Applying Two Simplified Ellipse-Based Tangential Models to Wheel-Rail Contact Using Three Alternative Nonelliptic Adaptation Approaches: A Comparative Study

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Boyang An ◽  
Ping Wang ◽  
Jiayi Zhou ◽  
Rong Chen ◽  
Jingmang Xu ◽  
...  
Keyword(s):  
Comparative Study ◽  
Computational Cost ◽  
Rolling Contact ◽  
Railway Vehicle ◽  
Normal Contact ◽  
Tangential Contact ◽  
Track Dynamics ◽  
Contact Models ◽  
Creep Force

In the modeling of railway vehicle-track dynamics and wheel-rail damage, simplified tangential contact models based on ellipse assumption are usually used due to strict limitation of computational cost. Since most wheel-rail contact cases appear to be nonelliptic shapes, a fast and accurate tangential model for nonelliptic contact case is in demand. In this paper, two ellipse-based simplified tangential models (i.e., FASTSIM and FaStrip) using three alternative nonelliptic adaptation approaches, together with Kalker’s NORM algorithm, are applied to wheel-rail rolling contact cases. It aims at finding the best approach for dealing with nonelliptic rolling contact. Compared to previous studies, the nonelliptic normal contact solution in the present work is accurately solved rather than simplification. Therefore, it can avoid tangential modeling evaluation affected by inaccurate normal contact solution. By comparing with Kalker’s CONTACT code, it shows both FASTSIM-based and FaStrip-based models can provide accurate global creep force. With regard to local rolling contact solution, only the accuracy of FaStrip-based models is satisfactory. Moreover, Ayasse-Chollet’s local ellipse approach appears to be the best choice for nonelliptic adaptation.

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.

Experimental Study on Tire Non-Steady State Slip Properties

2013 ◽  
Vol 753-755 ◽  
pp. 1736-1744
Author(s):  
Jie Liu ◽  
Xiao Ling Jia
Keyword(s):  
Linear System ◽  
Dynamic Performance ◽  
Lateral Force ◽  
Slip Angle ◽  
Test Results ◽  
Relaxation Length ◽  
Side Slip Angle ◽  
First Order ◽  
Depth Analysis ◽  
Yaw Angle

As for the two typical inputs of pure side slip angle and pure yaw angle, this paper presents the in-depth analysis of lateral force, aligning torque and relaxation length respectively within the domains of distance and spacial frequency, and also explains the test results by theoretical model. Within the small side slip angle, tire is a first-order linear system. Relaxation length is equivalent to the time constant of linear system, which decreases as slip angle increases. It indicates the dynamic performance of tire system.

Comparison of calculation methods for wheel–switch rail normal and tangential contact

2016 ◽  
Vol 231 (2) ◽  
pp. 148-161 ◽  
Author(s):  
Jingmang Xu ◽  
Ping Wang ◽  
Xiaochuan Ma ◽  
Jieling Xiao ◽  
Rong Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problems ◽  
Rolling Contact ◽  
The Finite Element Method ◽  
Normal Contact ◽  
Tangential Contact ◽  
Contact Models ◽  
Railway Turnout ◽  
Element Method

Wheel–rail contact is more complex in railway a turnout than in ordinary track and, thus, necessitates an advanced model to simulate dynamic interaction and predict rail wear. The main aim of the present work is to assess the application of several wheel–rail rolling contact models in railway turnout. For normal contact problems, wheel–rail contact models based on four different methods are compared: Hertz theory, the semi-Hertzian method, CONTACT, and the finite element method. The assessment is based on the results of contact patch shape and size and contact pressure for several wheelset lateral displacements. The load is set to a constant and equal to static wheel load. Calculations are performed at the section of switch rail head with width 35 mm in CN60-1100-1:18 turnout; both standard and worn rail profiles are accounted for. For tangential contact problems, four corresponding methods are assessed, based on the calculation of creep forces, distribution of the stick/slide region and computational efficiency: Shen–Hedrick–Elkins theory, FASTSIM, improved FASTSIM based on semi-Hertzian method, and CONTACT. It is found that the normal contact problems solved by the semi-Hertzian method and CONTACT correlate well with the finite element method, and the tangential contact problems solved by improved FASTSIM and CONTACT are quite favorable. The conclusions of this work can provide some guidance for contact model selection in the dynamic simulation and wear prediction of railway turnout.

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