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A tire may be one of the most critical and complex components in vehicle dynamics and road loads analyses because it serves as the only interface between the road surface and the vehicle. Extensive research and development activities about vehicle dynamics and tire models have been published in the past decades, but it is still not clear about the applications and parameter identification associated with all of these tire models. In this literature review study, various published tire models used for vehicle dynamics and road loads analyses are compared in terms of their modeling approaches, applications and parameters identification process and methodologies. It is hoped that the summary of this literature review work can help clarify and guide the future research and development direction about tire modeling.

In this study, a three-axle vehicle model established with ADAMS/Car is first correlated with field test data from quasi-static tilt table and highly dynamic NATO double lane change maneuver tests, respectively. It is then applied to predict the vehicle static rollover threshold (SRT) and dynamic rollover threshold (DRT). With the optimization approach proposed in this study it is possible to efficiently tune the anti-roll bar stiffness at each axle, to either maximize SRT or DRT, or balance both. The sensitivity results derived from the optimization iteration process can be applied to effectively size the three anti-roll bars that balance the static and dynamic roll stability performances. The proposed method can be potentially applied to include other parameters to address the roll stability issues and beyond.

In this study, a closed-loop driver-vehicle system model is established with ADAMS/CAR. A double lane change maneuver path boundary is setup based on NATO AVTP 03-160W requirement. Multiple choices of driver preview path are derived from optimization of the closed-loop driver-vehicle-road system, where the objective is to successfully pass the double lane change maneuver at a given forward speed without violating the boundary. With the multiple choices of preview path, the vehicle dynamic responses, such as tire patch load, vehicle lateral acceleration, yaw velocity, steering wheel angle and roll angle, will vary associated with each driver's preview path. The relationship between the path clearance and vehicle dynamic responses as well as the forward speeds is further investigated. Finally a methodology to predict the maximum forward speed to successfully pass double lane change is proposed.

Tyre behavior plays an important role in vehicle dynamics simulation. The Magic Formula Tyre Model is a semi-empirical tyre model which describes tyre behavior quite accurately in the handling simulation. The Magic Formula Tyre Model needs a set of parameters to describe the tyre properties; the determination of these parameters is nontrivial task due to its nonlinear nature and the presence of a large number of coefficients. In this paper, the homotopy algorithm is applied to the parameter identification of Magic Formula tyre model. A morphing parameter is introduced to correct the optimization process; as a result, the solution is directed converging to the global optimal solution, avoiding the local convergence. The method uses different continuation methods to globally optimize the parameters, which ensures that the prediction of the Magic Formula model can be very close to the test data at all stages of the optimization process.

In this paper, a detailed three dimensional (3D) flexible ring tire model is first proposed which includes a rigid rim with thickness, different layers of discretized belt points and a number of massless tread blocks attached on the belt. The parameters of the proposed 3D tire model can be divided into in-plane parameters and out-of-plane parameters. In this paper, the relationship of the in-plane parameters between the 3D tire model and the 2D tire model is determined according to the connections among the tire components. Based on the determined relationship, it is shown that the 3D tire model can produce almost the same prediction results as the 2D tire model for the in-plane tire behaviors.

The statistical trends of the spindle loads extracted from road load test data of vehicles with different variants are presented in this paper. The road load data of a vehicle moving on the same track with single speed are considered with different variants of the vehicle. The variants considered are repeat runs, spindle loads in vehicles with different ballast conditions, difference in type of leaf spring shackles and changed number of frame to body mounts. The parameters considered for the statistical trend comparison are the spindle forces, spindle moments and spindle accelerations monitored in different directions. The data analysis was performed using the software functions in N-soft and MATLAB. The analyzed results were grouped and bar charts are prepared to bring out the statistical variations of different parameters.

In this paper, cradle design functional objectives are briefly reviewed and a durability development process is proposed focusing on the cradle loads, stress, strain, and fatigue life analysis. Based upon the proposed design process, sample isolated and non-isolated cradle finite element (FE) models for a uni-body sport utility vehicle (SUV) under different design phases are solved and correlated with laboratory bench and proving ground tests. The correlation results show that the applied cradle models can be used to accurately predict the critical stress spots and fatigue life under various loading conditions.

Dynamic interactions of urban buses with urban roads are investigated in view of the vibration environment for the driver and dynamic tire forces transmitted to the roads. The static and dynamic properties of suspension component and tires are characterized in the laboratory over a wide range of operating conditions. The measured data is used to derive nonlinear models of the suspension component, and a tire model as a function of the normal load and inflation pressure. The component models are integrated to study the vertical and roll dynamics of front and rear axles of the conventional and modern low floor designs of urban buses. The resulting nonlinear vehicle models are thoroughly validated using the fieldmeasured data on the ride vibration and tire force response of the buses.

In this paper, based on our previously preliminary out-of-plane tire model, a complete out-of-plane flexible tire model is further developed by considering the variation of dimension and parameter values among different slices of the tire model. This tire model is validated via various MSC ADAMS® FTire virtual cleat tests. Especially, the cleat tests with non-zero tire camber angles and non-symmetric cleat shapes, which can better capture the out-of-plane tire properties, are included. By comparing the predicted results of the proposed tire model with FTire for various cleat tests, it shows that the complete out-of-plane flexible ring tire model is better at fully representing the actual tire properties for some complicated cleat testing scenarios.

Vehicle tire performance is an important consideration for vehicle handling, stability, mobility, and ride comfort as well as durability. Significant efforts have been dedicated to tire modeling in the past, but there is still room to improve its accuracy. In this study, a detailed in-plane flexible ring tire model is proposed, where the tire belt is discretized, and each discrete belt segment is considered as a rigid body attached to a number of parallel tread blocks. The mass of each belt segment is accumulated at its geometric center. To test the proposed in-plane tire model, a full-vehicle model is integrated with the tire model for simulation under a special driving scenario: acceleration from rest for a few seconds, then deceleration for a few seconds on a flat-level road, and finally constant velocity on a rough road. The simulation results indicate that the tire model is able to generate tire/road contact patch forces that yield reasonable vehicle dynamic responses.