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.

Theoretical Tire Model for Wear Progress of Tires with Tread Pattern Considering Two-Dimensional Contact Patch

2021 ◽  
Author(s):  
Y. Nakajima ◽  
S. Hidano
Keyword(s):  
Shear Force ◽  
Rolling Resistance ◽  
Slip Condition ◽  
Slip Angle ◽  
Two Dimensional ◽  
Tire Model ◽  
Slip Ratio ◽  
Contact Patch ◽  
Crown Shape ◽  
External Forces

ABSTRACT A new theoretical tire model for the wear progress of tires with tread block pattern is developed considering a two-dimensional contact patch. In the model, the wear energy is calculated from the shear force and pressure distribution in a two-dimensional contact patch that are changed with not only shear forces in a contact patch but also with the wear and irregular wear of tires. The fore–aft shear force in a contact patch consists of six mechanisms related to slip ratio, camber, contact between a tire and a road, barrel deformation of a loaded block, rolling resistance, and a rolling tire with rounded crown shape, whereas the lateral shear force consists of three mechanisms related to slip angle/camber, contact of a tire with rounded crown shape, and barrel deformation of a loaded block. The heel and toe irregular wear and the progress of irregular wear under pure slip condition qualitatively agree with the conventional knowledge of tire engineers. The expected wear energy is introduced to predict the wear progress under combined slip condition in the wear course. Using the vehicle dynamics to predict the tire force history, a histogram of external forces is obtained by transforming from it. Calculating wear energies by changing slip angle and slip ratio, the relation between external forces and the wear energy is expressed as the response surface. Multiplying the wear energy by the histogram, the expected wear energy distribution in a block is calculated. Assuming that the worn depth is proportional to the expected wear energy, the wear progress is predicted.

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.

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.

Longitudinal Tire Dynamics Model for Transient Braking Analysis: ANCF-LuGre Tire Model

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Hiroki Yamashita ◽  
Yusuke Matsutani ◽  
Hiroyuki Sugiyama
Keyword(s):  
Structural Deformation ◽  
Model Parameters ◽  
Force Distribution ◽  
Force Model ◽  
Tire Model ◽  
Elastic Ring ◽  
Contact Patch ◽  
Tire Force ◽  
Tire Dynamics ◽  
Tire Friction

In this investigation, the flexible tire model based on the absolute nodal coordinate formulation (ANCF) is integrated with LuGre tire friction model for evaluation of the longitudinal tire dynamics under severe braking scenarios. The ANCF-LuGre tire model developed allows for considering the nonlinear coupling between the dynamic structural deformation of the tire and its transient tire force distribution in the contact patch using general multibody dynamics computer algorithms. To this end, the contact patch obtained by the ANCF elastic ring tire model is discretized into small strips and the state of friction at each strip is defined by the differential equation associated with the discretized LuGre friction parameters. The normal contact pressure distribution predicted by the ANCF elastic ring elements that are in contact with the road surface are mapped onto the LuGre strips in the contact patch to evaluate the tangential tire force distribution and then the tire forces evaluated at LuGre strips are fed back to the generalized tangential contact forces of the ANCF elastic ring tire model. By doing so, the structural deformation of the ANCF elastic ring tire model is dynamically coupled with the LuGre tire friction in the final form of the governing equations. Furthermore, the systematic and automated parameter identification procedure for the LuGre tire force model is developed. It is shown that use of the proposed procedure with the modified friction curve proposed for wet road conditions leads to accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Several numerical examples are presented in order to demonstrate the use of the in-plane ANCF-LuGre tire model for the longitudinal transient dynamics of tires under severe braking scenarios.

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.

Effect of Tread Design Changes on Tire Patch Dynamics at High Speeds Using a Dynamic Contact Force Measurement Rig

2020 ◽  
Author(s):  
Matthew D. Van Gennip ◽  
Kazuki Okamoto ◽  
Kohei Miyanishi ◽  
Hideaki Kashimata
Keyword(s):  
Contact Force ◽  
Force Measurement ◽  
Normal Load ◽  
Testing Machine ◽  
Dynamic Contact ◽  
Slip Angle ◽  
Force Distribution ◽  
Dynamic Force ◽  
Contact Patch ◽  
High Speeds

ABSTRACT The dynamic effects at the tire contact patch are one of the most difficult factors of a tire to measure. Generally, only the total forces at the tire axle are captured during the tests. There are a few methods for identifying the force distribution at the tire contact patch, but most of these methods are limited to static tests or dynamic tests at slow speeds under nonrepeatable conditions, such as with vehicle testing. Because of this limitation, A&D Company, Limited has developed a tire-testing machine called the dynamic contact force testing rig (DCFR) to measure the dynamic force distribution at the contact patch during high speeds and under reproducible conditions. Preliminary studies have shown that minute changes in shear stress and pressure distribution can be measured consistently. This study observes the dynamic force distribution in a high-performance tire under a variety of test conditions: varying normal load, speed, slip angle, and slip ratio. The tire tread was altered manually by siping additional longitudinal and lateral slits in the existing tread pattern. The tests were repeated for each tread pattern: stock tire tread, additional longitudinal slits, and additional lateral slits. The change in force distribution was compared along the longitudinal, lateral, and vertical axes. The results showed how small changes in tread design can influence tire performance. This article is a preliminary study, primarily investigating the capabilities of the DCFR while investigating basic observable trends in force distribution.

A simplified numerical and analytical study for assessing the seismic response of a gravity concrete lock

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Neander Berto Mendes ◽  
Lineu José Pedroso ◽  
Paulo Marcelo Vieira Ribeiro
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Study ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Fluid Structure ◽  
Analytical Formulation ◽  
Acoustic Cavity ◽  
Water Chamber ◽  
Structure Problem

ABSTRACT: This work presents the dynamic response of a lock subjected to the horizontal S0E component of the El Centro earthquake for empty and completely filled water chamber cases, by coupled fluid-structure analysis. Initially, the lock was studied by approximation, considering it similar to the case of a double piston coupled to a two-dimensional acoustic cavity (tank), representing a simplified analytical model of the fluid-structure problem. This analytical formulation can be compared with numerical results, in order to qualify the responses of the ultimate problem to be investigated. In all the analyses performed, modeling and numerical simulations were done using the finite element method (FEM), supported by the commercial software ANSYS.

An Analytical Transient Tire Model

2001 ◽  
Vol 29 (2) ◽  
pp. 108-132 ◽  
Author(s):  
A. Ghazi Zadeh ◽  
A. Fahim
Keyword(s):  
Transient Behavior ◽  
Stability Control ◽  
Vehicle Stability ◽  
Tire Model ◽  
Steering Angle ◽  
First Order ◽  
Vehicle Stability Control ◽  
Proposed Model ◽  
Depth Study ◽  
And Performance

Abstract The dynamics of a vehicle's tires is a major contributor to the vehicle stability, control, and performance. A better understanding of the handling performance and lateral stability of the vehicle can be achieved by an in-depth study of the transient behavior of the tire. In this article, the transient response of the tire to a steering angle input is examined and an analytical second order tire model is proposed. This model provides a means for a better understanding of the transient behavior of the tire. The proposed model is also applied to a vehicle model and its performance is compared with a first order tire model.

A Modified Dugoff Tire Model for Combined-slip Forces

2010 ◽  
Vol 38 (3) ◽  
pp. 228-244 ◽  
Author(s):  
Nenggen Ding ◽  
Saied Taheri
Keyword(s):  
Vehicle Dynamics ◽  
Tire Model ◽  
Magic Formula ◽  
Model Based ◽  
Proposed Model ◽  
Road Friction ◽  
On Line ◽  
Double Lane Change ◽  
Tire Forces ◽  
Tire Models

Abstract Easy-to-use tire models for vehicle dynamics have been persistently studied for such applications as control design and model-based on-line estimation. This paper proposes a modified combined-slip tire model based on Dugoff tire. The proposed model takes emphasis on less time consumption for calculation and uses a minimum set of parameters to express tire forces. Modification of Dugoff tire model is made on two aspects: one is taking different tire/road friction coefficients for different magnitudes of slip and the other is employing the concept of friction ellipse. The proposed model is evaluated by comparison with the LuGre tire model. Although there are some discrepancies between the two models, the proposed combined-slip model is generally acceptable due to its simplicity and easiness to use. Extracting parameters from the coefficients of a Magic Formula tire model based on measured tire data, the proposed model is further evaluated by conducting a double lane change maneuver, and simulation results show that the trajectory using the proposed tire model is closer to that using the Magic Formula tire model than Dugoff tire model.

In-Plane Flexible Ring Tire Model—Part 1: Modeling and Parameter Identification

2018 ◽  
Vol 46 (3) ◽  
pp. 174-219 ◽  
Author(s):  
Bin Li ◽  
Xiaobo Yang ◽  
James Yang ◽  
Yunqing Zhang ◽  
Zeyu Ma
Keyword(s):  
Static Load ◽  
Model Parameters ◽  
Tire Model ◽  
Test Results ◽  
Lumped Mass ◽  
Virtual Test ◽  
Proposed Model ◽  
Particle Swarm Method ◽  
Vehicle Dynamic Simulation ◽  
Flexible Ring

ABSTRACT The tire model is essential for accurate and efficient vehicle dynamic simulation. In this article, an in-plane flexible ring tire model is proposed, in which the tire is composed of a rigid rim, a number of discretized lumped mass belt points, and numerous massless tread blocks attached on the belt. One set of tire model parameters is identified by approaching the predicted results with ADAMS® FTire virtual test results for one particular cleat test through the particle swarm method using MATLAB®. Based on the identified parameters, the tire model is further validated by comparing the predicted results with FTire for the static load-deflection tests and other cleat tests. Finally, several important aspects regarding the proposed model are discussed.

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