Tire Model Parameters Research Articles

Modeling and braking analyses of longitudinal-vertical coupling towbarless aircraft taxiing system

The variation of tire vertical load has effects on the vehicle braking performance, which may lead to the misjudgment of braking distance and increasement of the accident risks. In order to evaluate the braking distance of the towbarless aircraft taxiing system (TLATS) accurately, a longitudinal-vertical coupling model of the TLATS is established, in which the effects of the vertical vibration on braking dynamics is considered. An 11-degrees of freedom (DOF) dynamic model of the TLATS, which consists of the system longitudinal motion, vertical vibration, and an advanced Lugre tire model, is proposed. The tire vertical dynamic loads are obtained by calculating system vibration differential equations as the input for the Lugre tire model, in which an arbitrary pressure distribution function over the contact patch and load related parameters are used. The Lugre tire model parameters are identified based on the virtual experiment results in ADAMS/Car software through a multi-objective optimization (MOO) method. The proposed tire model is more accurate by comparing with the models using other pressure distribution functions. The advanced Lugre model is integrated into the longitudinal-vertical coupling dynamic model of the TLATS, and the fuzzy PID control method is used to achieve the optimal slip rate during the braking procedure. The tire friction and TLATS’s braking performances in terms of the slip rate, braking speed and braking distance are compared between the coupling and uncoupling models under different traction velocities and the road excitations when a same fuzzy control method is used for the system braking. The results show that the proposed longitudinal-vertical coupling TLATS dynamic model could assess the braking behaviors of the TLATS more accurately than the simplified uncoupling model, which could decrease the potential safety risk of the aircraft towing operation on the airport apron.

Novel high-fidelity tyre model for motorcycles to be characterised by quasi-static manoeuvres – rationale and numerical validation

Although diverse tyre model formulations exist in the literature, they are suited for characterisation using a dedicated test bench, preventing parameters' estimation in driving conditions. This study defined a novel motorcycle tyre model, characterisable through driving manoeuvres using simple instrumentation consisting in an inertial measurement unit, steering position sensor and wheel speed sensors. Acquired signals were used to estimate instantaneous tyre forces, moments, slip angle and other properties, which were employed to calculate tyre model's parameters. Tyre model development and validation were performed in a simulation environment: we used a Magic Formula tyre-equipped motorcycle model to perform a set of manoeuvres, which were employed to characterise the proposed tyre model. Lastly, a set of quasi-static manoeuvres was conducted using the same motorcycle model equipped with the two tyre models, and results were compared. Comparison results showed a close reproduction of real tyre forces, moments and slips by the proposed tyre model for quasi-static manoeuvres, accurately reproducing motorcycle dynamics. Therefore, steering torque was correctly predicted for different lateral acceleration values. These results show that the proposed tyre model can be characterised, for both longitudinal and lateral dynamics, using this limited set of manoeuvres and simple instrumentation; the correctly predicted steering torque could allow the use of this tyre model for handling description.

Indirect Damage Identification in Bridges Based on Dynamic Tyre Pressure Monitoring

This paper deals with an indirect health monitoring strategy for bridges using an instrumented vehicle. Thermodynamic principles are used to relate the change in Vehicle–Bridge-Interaction (VBI) forces to the change in dynamic tyre pressure. The damage identification process involves two stages. In the first stage, the unknown tyre model parameters are estimated using Bayesian inference based on the calibration data. The approach uses a Stein variational gradient descent implementation of the Bayes rule to quantify the uncertainty in the estimated tyre parameters. In the second stage, the calibrated tyre model is used to reconstruct the change in VBI force from measured tyre pressure data considering a damaged bridge. It is observed that damage present in the bridge produces notable changes in VBI force. Contour plots based on VBI force and natural frequency are developed for damage detection. The reconstructed VBI force change is used to quantify damage using the contour plots. Further, the least square estimation approach is adopted for damage identification by defining appropriate objective functions and imposing constraints on the damage indicators. The damage is estimated by minimizing the objective function using Cuckoo search algorithm. Numerical experiments reveal that the developed method could be used for accurate damage identification in the presence of measurement noise, uncertainty in estimated tyre parameters, and the uncertainty in bridge model parameters.

Identification of Tire Model Parameters with Artificial Neural Networks

Accurate modeling of tire characteristics is one of the most challenging tasks. Many mathematical models can be used to fit measured data. Identification of the parameters of these models usually relies on least squares optimization techniques. Different researchers have shown that the proper selection of an initial set of parameters is key to obtain a successful fitting. Besides, the mathematical process to identify the right parameters is, in some cases, quite time-consuming and not adequate for fast computing. This paper investigates the possibility of using Artificial Neural Networks (ANN) to reliably identify tire model parameters. In this case, the Pacejka’s “Magic Formula” has been chosen for the identification due to its complex mathematical form which, in principle, could result in a more difficult learning than other formulations. The proposed methodology is based on the creation of a sufficiently large training dataset, without errors, by randomly choosing the MF parameters within a range compatible with reality. The results obtained in this paper suggest that the use of ANN to directly identify parameters in tire models for real test data is possible without the need of complicated cost functions, iterative fitting or initial iteration point definition. The errors in the identification are normally very low for every parameter and the fitting problem time is reduced to a few milliseconds for any new given data set, which makes this methodology very appropriate to be used in applications where the computing time needs to be reduced to a minimum.

Research on tire model parameter identification strategy based on CDTire/3D

High accuracy tire modeling is essential to study the automotive fatigue-durability, handling-stability, and NVH performance in the virtual proving ground. Compared with other tire models, CDTire/3D can be directly used in multi-body dynamics simulation, and its linearized version can be adopted in road noise analysis. In consideration of its high generality for cost saving, CDTire/3D has an extensive engineering application prospective in the automotive industry. It is the critical technique to accomplish high-efficiency and high-precision CDTire/3D modeling by investigating the mechanical mechanism of tire and the influence of parameters on all test conditions, based on which a parameter identification strategy is conducted in this paper. The effectiveness of the strategy is verified by a tire modeling case.

Vehicle Sideslip Angle Estimation for a Heavy-Duty Vehicle via Extended Kalman Filter Using a Rational Tyre Model

Vehicle sideslip angle is a key state for lateral vehicle dynamics, but measuring it is expensive and unpractical. Still, knowledge of this state would be really valuable for vehicle control systems aimed at enhancing vehicle safety, to help to reduce worldwide fatal car accidents. This has motivated the research community to investigate techniques to estimate vehicle sideslip angle, which is still a challenging problem. One of the major issues is the need for accurate tyre model parameters, which are difficult to characterise and subject to change during vehicle operation. This paper proposes a new method for estimating vehicle sideslip angle using an Extended Kalman Filter. The main novelties are: i) the tyre behaviour is described using a Rational tyre model whose parameters are estimated and updated online to account for their variation due to e.g. tyre wear and environmental conditions affecting the tyre behaviour; ii) the proposed technique is compared with two other methods available in the literature by means of experimental tests on a heavy-duty vehicle. Results show that: i) the proposed method effectively estimates vehicle sideslip angle with an error limited to 0.5 deg in standard driving conditions, and less than 1 deg for a high-speed run; ii) the tyre parameters are successfully updated online, contributing to outclassing estimation methods based on tyre models that are either excessively simple or with non-varying parameters.

Non-linear tyre model–based non-singular terminal sliding mode observer for vehicle velocity and side-slip angle estimation

Vehicle velocity and side-slip angle are important vehicle states for the electronic stability programme and traction control system in vehicle safety control system and for the control allocation method of electric vehicles with in-wheel motors. This paper proposes an innovative side-slip angle estimator based on the non-linear Dugoff tyre model and non-singular terminal sliding mode observer. The proposed estimation method based on the non-linear tyre model can accurately present the tyre’s non-linear characteristics and can show advantages over estimation methods based on the linear tyre model. The utilised Dugoff tyre model has a relatively simple structure with few parameters, and the proposed non-linear observer can be applied in various vehicle tyres and various road conditions. Precise determination of the Dugoff tyre model parameters is not required and the proposed observer can still perform good estimation results even though tyre parameters and the tyre–road friction coefficient are not accurate. The proposed non-singular terminal sliding mode observer can achieve fast convergence rate and better estimation performance than the traditional sliding mode observer. At the end of this paper, simulations in various conditions are presented to validate the proposed non-linear estimator.

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

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.

In-Plane Flexible Ring Tire Model—Part 2: Parameterization

ABSTRACT The flexible ring tire model has recently gained significant attention in vehicle dynamics and analysis of road loads because it is able to capture the tire belt deflection under various driving conditions and compute more efficiently than the complex finite element tire model. This article presents the second part of the in-plane flexible ring tire model study with the recently developed flexible ring tire model to investigate several important aspects about tire model parameterization. First, we use the FTire® model in the MSC ADAMS/View® virtual test rig to generate five sets of spindle longitudinal and vertical loads on cleats with different heights, static loads, and speeds. These spindle loads are considered the “experimental data” in view of proving the accuracy of the commercial FTire® model that can accurately predict the spindle loads, especially in well-controlled test rigs. Next, one set of tire model parameters identified with a specific cleat test case is applied to other cleat test cases to predict the tire spindle forces, which are then compared with those corresponding experimental data. Similarly, this process is repeated for each cleat test case to yield different sets of parameters, respectively. Afterward, the predicted spindle loads are compared with the experimental data, respectively, based on SAE Standard J2812, and the predicted errors are assessed to determine which cleat test case is the best choice to identify parameters of the tire model. Finally, the effects of the belt point number and tread block number on the prediction accuracy and efficiency are discussed.

Optimal parameter estimation in semi-empirical tire models

Semi-empirical tire models are mathematical models, the parameters of which are identified after a process of error reduction to fit experimental data obtained in the laboratory. In this process, the algorithms used for estimating the model parameters are usually based on nonlinear least-squares fitting methods, in which only vertical residuals between the model and the test points are considered. Although extensively utilized, this type of fitting implicitly considers that errors in the slip data (horizontal residuals) are either nonexistent or negligible, which is not true. This paper introduces a new methodology to the identification of semi-empirical tire model parameters based on weighed orthogonal residuals, which takes into account possible errors inherent in the test measurements of dependent and independent variables. The results show that the methodology offers a reliable parameter identification providing an even fitting for all the zones of the mathematical semi-empirical tire model.

Design and Experimental Validation of a Stable Two-Stage Estimator for Automotive Sideslip Angle and Tire Parameters

This paper proposes and experimentally validates a two-stage approach for coupled lateral vehicle state and tire model estimation. In a first stage, an extended Kalman filter is employed which provides vehicle slip angles and lateral tire forces from commercial low-cost vehicle sensors. The obtained estimates are exploited in the second stage, where a (quasi-static) tire model is fitted to this data. A major issue in this estimation process is the typical instability of these estimators for situations with (prolonged) straight driving. This issue is traced back to a lack of local observability. The use of a variable model covariance is introduced as a practical method to obtain a stable estimator, irrespective of the unobservability. The developed methodology has a low computational load and the Kalman estimator is able to run in real time, whereas the tire model parameter fitting is cheap enough to run online. The proposed methodology is validated experimentally and provides reliable results in variable driving conditions.

Parameter identification of in-plane flexible ring tyre model based on static load-deflection data: some insights

Tyre model parameter identification is essential for its applications. Due to the costly and lengthy tyre model parameterisation tests, it is highly interesting to determine the necessary types of tests just enough to accurately identify all parameters. Among various types of laboratory tests, the standstill tyre load-deflection measurement may be the easiest and cheapest one for all kinds of tyres. This paper thus focuses on investigating how many tyre model parameters can be accurately identified only using the static load-deflection data, where the newly developed tyre model is based on in-plane flexible ring approach and the load-deflection target data are derived from the commercially available FTire model with ADAMS software. The paper further discusses whether the identification results can be improved by considering the length of the tyre/road contact patch. The tyre model parameter sensitivities to the static tyre-load deflection data are finally addressed.

A new efficient free-rolling tyre-testing procedure for the parameterisation of vehicle dynamics tyre models

This paper describes an efficient tyre test procedure that can be used to collect the data required to parameterise empirical tyre models used in the computer simulations of vehicle dynamics. The new GS2MF FreeRolling test procedure develops established methodologies, such as the time measurement procedure from the TIME project and the MICH2MF measurement protocol developed as alternatives to traditional square matrix testing. The new process is designed to reduce the number of expensive tyre tests without compromising the accuracy of the generated tyre model parameters. The process is demonstrated by a programme of tyre testing carried out using the Calspan TIRF tyre testing facility in the USA, and it is shown here how the GS2MF Flat-Trac® tyre test procedure can be used more efficiently to parameterise the pure lateral and self-aligning moment components for the well-known ‘magic formula’ tyre model. This is achieved using a ‘cruise’-type procedure which is more representative of conditions existing when driving a real vehicle. During the tests, a novel automated logic approach is also proposed to manage the temperature of the tyres. Finally, graph sweeps are introduced at the start and the end of the tests, allowing a judgement to be made as to the influence of the tyre wear on the data obtained throughout the tests. The development of accurate and representative tyre models remains a significant challenge as vehicle manufacturers target increased use of virtual prototypes and simulations. This work contributes to this challenge by improving the efficiency of the expensive testing process needed to parameterise the models.

A Particle Filter Approach for Identifying Tire Model Parameters From Full-Scale Experimental Tests

Mathematical models simulating the handling behavior of passenger cars are extensively used at a design stage for evaluating the effects of new structural solutions or control systems. The main source of uncertainty in these type of models lies in tire–road interaction, due to high nonlinearity. Proper estimation of tire model parameters is thus of utter importance to obtain reliable results. This paper presents a methodology aimed at identifying the magic formula-tire (MF-Tire) model coefficients of the tires of an axle only based on measurements carried out on board vehicle (vehicle sideslip angle, yaw rate, lateral acceleration, speed, and steer angle) during standard handling maneuvers (step-steers, double lane changes, etc.). The proposed methodology is based on particle filtering (PF) technique. PF may become a serious alternative to classic model-based techniques, such as Kalman filters. Results of the identification procedure were first checked through simulations. Then, PF was applied to experimental data collected using an instrumented passenger car.

剛体円環モデルを用いた農用タイヤのパラメータ同定

The objective of this study is to clarify the vibration generation mechanism of agricultural machinery caused by the interaction between the tire lugs and the road surface. It is important to investigate the lug excitation force occurring on a rolling agricultural tire in order to clarify the vibration generation mechanism. In our previous study, it is confirmed that the dynamic behavior of rolling tire is influenced by the vibration characteristics of the tire and only the rigid modes can affect the rolling tire behavior. Therefore, we modeled the tire as a circular rigid ring supported on an elastic foundation with a contact patch slip model in order to estimate the lug excitation force. An important aspect of tire modelling is the identification of the tire model parameters. In this research, the tire wheel system is modeled as a circular rigid ring connected to the wheel through the tire sidewalls with a contact patch slip model. As for an agricultural tire, the out-of-plane dynamics is also important because of cross-stich lugs. This model can describe not only the in-plane tire dynamics but also out-of-plane tire dynamics. The equations of motion of the dynamic tire model are derived and the equations of motion are rearranged to describe the in-plane and the out-of-plane dynamics. From the rearranged equations of motion, frequency equations are derived separately and calculation procedure for obtaining the natural frequencies of the rigid ring model is formulated. Furthermore, the model parameters are identified by minimizing the difference between measured and calculated natural frequencies using Downhill Simplex method. The natural frequencies and natural modes predicted by the calculation using the identified model parameters show good agreement with those obtained experimentally.

Tyre curve estimation in slip-controlled braking

Progress in reducing actuator delays in pneumatic brake systems creates an opportunity for advanced anti-lock braking algorithms to be used on heavy goods vehicles. However, these algorithms require knowledge of variables that are impractical to measure directly. This paper introduces a braking force observer and road surface identification algorithms to support a sliding-mode slip controller for air-braked heavy vehicles. Both the force observer and the slip controller are shown to operate robustly under a variety of conditions in quarter-car simulations. A non-linear least-squares algorithm was found to be capable of performing regressions on all the parameters of the tyre model from the University of Michigan Transportation Research Institute when used ‘in the loop’ with the controller and the observer. A recursive least-squares algorithm that is less computationally expensive than the non-linear algorithm was also investigated but gave only reasonable estimates of the tyre model parameters on high-friction smooth roads.

Efficient In-Plane Tire Mode Identification by Radial-Tangential Eigenvector Compounding

ABSTRACT Tire modal testing is frequently used for validation of numerical tire models and identification of structural tire model parameters. Most studies focus primarily on in-plane dynamic tire behavior and adopt the approach of the fixed boundary condition at the wheel center. Here, an identification method of in-plane tire dynamics was developed for the case of a free tire-rim combination. This particular case is important when the aim is to construct a full tire model, capable of predicting ride and noise, vibration, and harshness involving the whole vehicle, all from modal testing. Key attributes of the proposed approach include ease of implementation and efficient processing of measurements. For each type of excitation, i.e., radial and tangential, both radial and tangential responses were recorded. Compounding of the corresponding radial/tangential eigenvectors, which, in the context of the present work, refers to expressing the motion of the tire belt as a combination of the radial and tangential responses, results in smooth mode shapes that were found to agree with those published in other analytical and experimental studies.

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.

“Self-organizing maps” for identification of tire model longitudinal braking parameters of a vehicle on a roller brake tester and on flat ground

This paper discusses how to identify tire model coefficients that are used to compare longitudinal forces when braking. Those in the automotive world have worked extremely hard to obtain these parameters and different methods have been used to match the values of these parameters. This paper proposes the use of self-organizing maps to tackle this problem whereby interactively searches are carried out to find the optimum tire model parameters. The objective of this research is to prove the capability of self-organizing maps (SOMs) to classify a vehicle’s braking formula on a roller brake tester from the MOT (Ministry of Transport) and on flat ground. The neural network produced a good brake-slip ratio when presented with data that are not used in network training. This means that the methodology is feasible. This tool easily obtains the brake-slip equation of each experiment and the braking on two different experimental tests will be compared.