A Dynamic Tire Model for ABS Maneuver Simulations

2010 ◽  
Vol 38 (2) ◽  
pp. 137-154 ◽  
Author(s):  
Francesco Braghin ◽  
Edoardo Sabbioni
Keyword(s):  
Steady State ◽  
Order Differential Equation ◽  
Transient Behavior ◽  
Slip Angle ◽  
Tire Model ◽  
Relaxation Length ◽  
Steady State Condition ◽  
First Order ◽  
Significant Parameter ◽  
Tire Models

Abstract Due to the dimensions of the tire-road contact area, transients in a tire last approximately 0.1 s. Thus, in the case of abrupt maneuvers such as ABS braking, the use of a steady-state tire model to predict the vehicle’s behavior would lead to significant errors. Available dynamic tire models, such as Pacejka’s MF-Tire model, are based on steady-state formulations and the transient behavior of the tire is included by introducing a first order differential equation of relevant quantities such as the slip angle and the slippage. In these differential equations the most significant parameter used to describe the transient behavior is the so-called relaxation length, i.e., the distance traveled by the tire to settle to a new steady-state condition once perturbated. Usually this parameter is assumed to be constant.

A Fast and Reliable Dynamic Tyre-Road Contact Model for ABS Braking Manoeuvre Simulations

2006 ◽  
Author(s):  
Francesco Braghin ◽  
Federico Cheli ◽  
Emiliano Giangiulio ◽  
Federico Mancosu ◽  
Daniele Arosio
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Order Differential Equation ◽  
Transient Behavior ◽  
Slip Angle ◽  
Relaxation Length ◽  
Steady State Condition ◽  
Tyre Model ◽  
First Order ◽  
Significant Parameter

Due to the dimensions of the tyre-road contact area, transients in a tyre last approximately 0.1s. Thus, in the case of abrupt maneuvers such as ABS braking, the use of a steady-state tyre model to predict the vehicle’s behavior would lead to significant errors. Available dynamic tyre models, such as Pacejka’s MF-Tyre model, are based on steady-state formulations and the transient behavior of the tyre is included by introducing a first order differential equation of relevant quantities such as the slip angle and the slippage. In these differential equations the most significant parameter used to describe the transient behavior is the so-called relaxation length, i.e. the distance traveled by the tyre to settle to a new steady–state condition once perturbated. Usually this parameter is assumed to be constant.

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.

The Spectrum of Steady State Turbulent Convection

1971 ◽  
Vol 26 (7) ◽  
pp. 1140-1146
Author(s):  
F. Winterberg
Keyword(s):  
Integral Equation ◽  
Steady State ◽  
Energy Spectrum ◽  
Buoyancy Force ◽  
Radiative Heat ◽  
Order Differential Equation ◽  
Stellar Atmospheres ◽  
Turbulent Convection ◽  
First Order ◽  
Model Equations

Abstract Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

Virtual sensor for real-time estimation of the vehicle sideslip angle

Sensor Review ◽  
2019 ◽  
Vol 40 (2) ◽  
pp. 255-272
Author(s):  
Kanwar Bharat Singh
Keyword(s):  
Steady State ◽  
Unscented Kalman Filter ◽  
Time Estimation ◽  
Experimental Tests ◽  
Slip Angle ◽  
Successful Implementation ◽  
Tire Model ◽  
Sideslip Angle ◽  
Angle Estimation ◽  
Content Type

Purpose The vehicle sideslip angle is an important state of vehicle lateral dynamics and its knowledge is crucial for the successful implementation of advanced driver-assistance systems. Measuring the vehicle sideslip angle on a production vehicle is challenging because of the exorbitant price of a physical sensor. This paper aims to present a novel framework for virtually sensing/estimating the vehicle sideslip angle. The desired level of accuracy for the estimator is to be within +/− 0.2 degree of the actual sideslip angle of the vehicle. This will make the precision of the proposed estimator at par with expensive commercially available sensors used for physically measuring the vehicle sideslip angle. Design/methodology/approach The proposed estimator uses an adaptive tire model in conjunction with a model-based observer. The performance of the estimator is evaluated through experimental tests on a rear-wheel drive vehicle. Findings Detailed experimental results show that the developed system can reliably estimate the vehicle sideslip angle during both steady state and transient maneuvers, within the desired accuracy levels. Originality/value This paper presents a novel framework for vehicle sideslip angle estimation. The presented framework combines an adaptive tire model, an unscented Kalman filter-based axle force observer and data from tire mounted sensors. Tire model adaptation is achieved by making extensions to the magic formula, by accounting for variations in the tire inflation pressure, load, tread-depth and temperature. Predictions with the adapted tire model were validated by running experiments on the Flat-Trac® machine. The benefits of using an adaptive tire model for sideslip angle estimation are demonstrated through experimental tests. The performance of the observer is satisfactory, in both transient and steady state maneuvers. Future work will focus on measuring tire slip angle and road friction information using tire mounted sensors and using that information to further enhance the robustness of the vehicle sideslip angle observer.

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.

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.

The Transient Response of Orifices and Very Short Lines

1972 ◽  
Vol 94 (2) ◽  
pp. 483-489 ◽  
Author(s):  
J. E. Funk ◽  
D. J. Wood ◽  
S. P. Chao
Keyword(s):  
Steady State ◽  
Pressure Drop ◽  
System Analysis ◽  
Transient Flow ◽  
Transient Behavior ◽  
Short Term ◽  
State Equations ◽  
Steady State Condition ◽  
Orifice Flow ◽  
Flow Through

It is generally assumed that orifices and valves follow closely their steady-state characteristics during transient operation. However, this assumption of quasisteady behavior may lead to errors in predicting transient flow conditions under certain circumstances. In order to evaluate the transient behavior of an orifice, a differential equation relating the flow through and the pressure drop across an orifice was derived. An extension was made to include an axial dimension for the orifice. The solution of this equation for transient flow through an orifice subjected to a step change in pressure drop across the orifice is significantly different than that obtained using the steady state relationship. An experiment was designed to evaluate the theoretical results in which an orifice on the end of a line was subjected to a sudden pressure change and the resulting transient pressures were observed. It was found that a significant short term transient occurs before the orifice flow reaches the new steady state condition. The observed short term transient agrees well with that predicted by the theory. It is concluded that the behavior of an orifice can deviate considerably from that predicted by steady-state equations during periods of rapid pressure or flow changes. The dynamic description of orifice flow may be combined with a larger system analysis (e.g., using the method of characteristics) to more accurately predict the overall transient performance of flow systems.

Wheel Torque Controller Development Using a Simplified Tire Model for Vehicle Handling Enhancement

2009 ◽  
Author(s):  
Ganesh Adireddy ◽  
Taehyun Shim ◽  
Douglas Rhode
Keyword(s):  
Predictive Control ◽  
Essential Element ◽  
Control Algorithms ◽  
Slip Angle ◽  
Tire Model ◽  
Computationally Efficient ◽  
Vehicle Handling ◽  
Yaw Rate ◽  
Wheel Torque ◽  
Tire Models

A tire model is an essential element in the vehicle controller development and various complexities of tire models have been developed and used. It is highly desirable for the control systems to use a tire model that is computationally efficient and easy to implement in control algorithms while providing desired performance. In this paper, a wheel torque controller was developed using a non-linear predictive control theory, 8 degree of freedom vehicle model, and a simplified nonlinear tire model in order to control the vehicle yaw rate and side slip angle. The performance of this controller was compared to that based on well known Magic Formula tire model. The effectiveness and limitations of the proposed controller were discussed through simulation.

Wheel Speed Effect on Transient Lateral Force and Its Characterization by Ramp-Step Steer Test Method

2021 ◽  
Author(s):  
Yi Li
Keyword(s):  
Contact Point ◽  
Transient Behavior ◽  
Wheel Speed ◽  
Rolling Speed ◽  
Test Method ◽  
Slip Angle ◽  
Relaxation Length ◽  
Underlying Assumption ◽  
Lateral Response ◽  
Speed Effect

ABSTRACT The concept “relaxation length” serves as one of several ways to characterize the transient lateral response for a rolling tire. Most test methods developed to identify relaxation length tightly link to Pacejka's single-contact-point linear transient model. Its underlying assumption is that the traveled distance during the transition interval is always a constant regardless of the wheels' linear rolling speed. The current research provides physical data against this strong assumption. The data is acquired through a newly-developed test method named the “ramp-step steer method”. The ramp-step steer method features a nonstop, high rolling speed, and fast-changing slip angle procedure that cannot be fulfilled by the conventional “start-stop-resume” step steer method. Thanks to the high dynamic capability of the equipment in GCAPS Corp., the proposed test method becomes feasible. A novel data postprocessing scheme accompanies the test method as well. The ramp-step steer method is independent of any specific models and replicates the scenario of a rolling tire subjected to a sudden slip angle change from on-vehicle to an indoor environment. The wheel speed effect on the tires' transient lateral response is reflected through a proposed quantity, Ly, which is a more general descriptor and can downscale to relaxation length under specific circumstances. Ly itself does not associate with any model, so the remaining study explains the speed effect through an updated model. The present research aims to provide a better way of characterizing tires' lateral transient behavior and is not an alternative to identify the key parameter “relaxation length” in Pacejka's model. Another contribution of the research is categorizing and separating the hierarchy of various transient tire models.

A Empirical Tire Model of Non-Steady State Cornering Properties Considering Carcass Elasticity

2000 ◽  
Author(s):  
Yongping Hou ◽  
Yujin Hu ◽  
Chenggang Li ◽  
Konghui Guo
Keyword(s):  
Steady State ◽  
High Precision ◽  
Test Data ◽  
Vehicle Dynamics ◽  
Low Frequency ◽  
Frequency Region ◽  
Tire Model ◽  
Yaw Angle ◽  
Tire Models

Abstract The purpose of this paper is to present two empirical tire models of non-steady state cornering property with respect to yaw angle input in low frequency region on the basis of existing tire model and considering the elasticity of the carcass. Verified by test, theoretical values meet well with test data. Comparing with existing tire models, the models described in the paper have more advantages, and they also have high precision. They can be applied for vehicle dynamics studies.

Sign in / Sign up

Export Citation Format

Share Document