scholarly journals A Brush-Type Tire Model with Nonsmooth Representation

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Ryo Kikuuwe
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Friction Force ◽  
Static Friction ◽  
Mathematical Representation ◽  
Generic Model ◽  
Tire Model ◽  
Integration Algorithm ◽  
Magic Formula ◽  
Proposed Model

This paper proposes a brush-type tire model with a new mathematical representation. The presented model can be seen as a generic model that describes the distributed viscoelastic force and Coulomb-like friction force, which are balancing each other at each point, in the contact patch. The model is described as a partial differential algebraic inclusion (PDAI), which involves the set-valuedness to represent the static friction. A numerical integration algorithm for this PDAI is derived through the implicit Euler discretization along both space and time. Some numerical comparisons with Magic Formula and a LuGre-based tire model are presented. The results show that, with appropriate choice of parameters, the proposed model is capable of producing steady-state characteristics similar to those of Magic Formula. It is also shown that the proposed model realizes a proper static friction state, which is not realized with a LuGre-based 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.

scholarly journals Tire Model with Temperature Effects for Formula SAE Vehicle

2019 ◽  
Vol 9 (24) ◽  
pp. 5328 ◽  
Author(s):  
Diwakar Harsh ◽  
Barys Shyrokau
Keyword(s):  
Steady State ◽  
Measurement Data ◽  
Transient Behavior ◽  
Lateral Acceleration ◽  
Tire Model ◽  
Magic Formula ◽  
Vehicle Simulation ◽  
Formula Sae ◽  
Full Vehicle ◽  
Design Competition

Formula Society of Automotive Engineers (SAE) (FSAE) is a student design competition organized by SAE International (previously known as the Society of Automotive Engineers, SAE). Commonly, the student team performs a lap simulation as a point mass, bicycle or planar model of vehicle dynamics allow for the design of a top-level concept of the FSAE vehicle. However, to design different FSAE components, a full vehicle simulation is required including a comprehensive tire model. In the proposed study, the different tires of a FSAE vehicle were tested at a track to parametrize the tire based on the empirical approach commonly known as the magic formula. A thermal tire model was proposed to describe the tread, carcass, and inflation gas temperatures. The magic formula was modified to incorporate the temperature effect on the force capability of a FSAE tire to achieve higher accuracy in the simulation environment. Considering the model validation, the several maneuvers, typical for FSAE competitions, were performed. A skidpad and full lap maneuvers were chosen to simulate steady-state and transient behavior of the FSAE vehicle. The full vehicle simulation results demonstrated a high correlation to the measurement data for steady-state maneuvers and limited accuracy in highly dynamic driving. In addition, the results show that neglecting temperature in the tire model results in higher root mean square error (RMSE) of lateral acceleration and yaw rate.

Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades

1984 ◽  
Vol 106 (1) ◽  
pp. 65-69 ◽  
Author(s):  
A. Sinha ◽  
J. H. Griffin
Keyword(s):  
Steady State ◽  
Turbine Blades ◽  
Time Integration ◽  
Ground Vibration ◽  
Static Friction ◽  
Steady State Solution ◽  
Forced Response ◽  
Steady State Response ◽  
Integration Algorithm ◽  
State Response

The effect of static friction on the design of flexible blade-to-ground vibration dampers used in gas turbine engines is investigated. It is found that for γ (ratio of dynamic and static friction coefficients) less than 1, the steady-state response is essentially harmonic when the damper slip load, S, is small. However, as S increases beyond a certain value, the steady-state response ceases to be simply harmonic and, while still periodic, is a more complex waveform. The transition slip load is found to be lower for smaller γ. The maximum possible reduction in vibratory stresses increases as γ decreases. These analytical results are compared with those from the conventional numerical time integration method. In addition, an efficient time integration algorithm is described which can be used to predict the peak displacements of the transition solution without tracing the whole waveform, a useful procedure when no harmonic steady-state solution exists. The conditions under which blade response can be adequately modeled by simulating only dynamic friction are established.

Drift Turning of Lateral Guided Vehicle With Sensor Steering Mechanism: Variable Kinetic Friction Model

2005 ◽  
Author(s):  
Yoshihiro Takita ◽  
Hisashi Date
Keyword(s):  
Friction Force ◽  
Coulomb Friction ◽  
High Speed ◽  
Static Friction ◽  
Friction Model ◽  
Tire Model ◽  
Kinetic Friction ◽  
Steering Mechanism ◽  
Three Stages ◽  
Coulomb Friction Model

In a previous paper, the simulated loci of high-speed cornering did not correspond with experimentally obtained results because the tire model used only the sticking in the Coulomb friction model. If the centrifugal force becomes larger than the cornering force of the tires, then the vehicle does not maintain the desired course. The cornering force is affected by the sticking or slipping condition of the tires. In order to simulate the high-speed cornering trajectory, the present paper assumes three stages of friction: low kinetic friction force at the beginning of slipping, the period of kinetic friction force, and the return to the static friction condition at small slip angles. In addition to the Rear motor Rear drive (RR) type vehicle, the Front motor Front drive (FF) type vehicle with a Sensor Steering Mechanism (SSM) and a 4-wheel steering mechanism is developed. In the experiments of present paper, both of these robots are run on an oval course at high speed. Numerical simulation and experimental results indicate effective prediction by the friction model.

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.

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.

scholarly journals Lane Departure Warning Estimation Using Yaw Acceleration

2020 ◽  
Vol 11 (1) ◽  
pp. 102-111
Author(s):  
Em Poh Ping ◽  
J. Hossen ◽  
Wong Eng Kiong
Keyword(s):  
Vehicle Dynamics ◽  
Dynamic Responses ◽  
Dynamics Simulation ◽  
Steering Wheel ◽  
Mathematical Representation ◽  
Vehicle Speed ◽  
Lane Departure Warning ◽  
Model Based ◽  
Lane Departure ◽  
Proposed Model

AbstractLane departure collisions have contributed to the traffic accidents that cause millions of injuries and tens of thousands of casualties per year worldwide. Due to vision-based lane departure warning limitation from environmental conditions that affecting system performance, a model-based vehicle dynamics framework is proposed for estimating the lane departure event by using vehicle dynamics responses. The model-based vehicle dynamics framework mainly consists of a mathematical representation of 9-degree of freedom system, which permitted to pitch, roll, and yaw as well as to move in lateral and longitudinal directions with each tire allowed to rotate on its axle axis. The proposed model-based vehicle dynamics framework is created with a ride model, Calspan tire model, handling model, slip angle, and longitudinal slip subsystems. The vehicle speed and steering wheel angle datasets are used as the input in vehicle dynamics simulation for predicting lane departure event. Among the simulated vehicle dynamic responses, the yaw acceleration response is observed to provide earlier insight in predicting the future lane departure event compared to other vehicle dynamics responses. The proposed model-based vehicle dynamics framework had shown the effectiveness in estimating lane departure using steering wheel angle and vehicle speed inputs.

scholarly journals Bubble wall velocity at strong coupling

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Francesco Bigazzi ◽  
Alessio Caddeo ◽  
Tommaso Canneti ◽  
Aldo L. Cotrone
Keyword(s):  
Phase Transitions ◽  
Steady State ◽  
Friction Force ◽  
Bubble Velocity ◽  
Strongly Coupled ◽  
First Order ◽  
Black Hole Background ◽  
Different Dimensions ◽  
Holographic Description ◽  
First Order Phase

Abstract Using the holographic correspondence as a tool, we determine the steady-state velocity of expanding vacuum bubbles nucleated within chiral finite temperature first-order phase transitions occurring in strongly coupled large N QCD-like models. We provide general formulae for the friction force exerted by the plasma on the bubbles and for the steady-state velocity. In the top-down holographic description, the phase transitions are related to changes in the embedding of $$ Dq\hbox{-} \overline{D}q $$ Dq ‐ D ¯ q flavor branes probing the black hole background sourced by a stack of N Dp-branes. We first consider the Witten-Sakai-Sugimoto $$ D4\hbox{-} D8\hbox{-} \overline{D}8 $$ D 4 ‐ D 8 ‐ D ¯ 8 setup, compute the friction force and deduce the equilibrium velocity. Then we extend our analysis to more general setups and to different dimensions. Finally, we briefly compare our results, obtained within a fully non-perturbative framework, to other estimates of the bubble velocity in the literature.

Experimental Study of Static Friction in a Spherical Elastic-Plastic Contact

2008 ◽  
Author(s):  
Andrey Ovcharenko ◽  
Gregory Halperin ◽  
Izhak Etsion
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Static Friction ◽  
Tangential Displacement ◽  
Accurate Identification ◽  
Elastic Plastic ◽  
Static Friction Coefficient ◽  
Wide Range ◽  
Material Good ◽  
Contact Diameter

The elastic-plastic contact between a deformable sphere and a rigid flat during pre-sliding is studied experimentally. Measurements of friction force and contact area are done in real time along with an accurate identification of the instant of sliding inception. The static friction force and relative tangential displacement are investigated over a wide range of normal preloads for several sphere materials and diameters. It is found that at low normal loads the static friction coefficient depends on the normal load in breach of the classical laws of friction. The pre-sliding displacement is found to be less than 5 percent of the contact diameter, and the interface mean shear stress at sliding inception is found to be slightly below the shear strength of the sphere material. Good correlation is found between the present experimental results and a recent theoretical model in the elastic-plastic regime of deformation.

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