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The tire mechanics characteristics are essential for analysis, simulation and control of vehicle dynamics. This paper develops the UniTire model for tire forces and moments under combined slip conditions with anisotropic tire slip stiffness. The anisotropy of tire slip stiffness, which means the difference of tire longitudinal slip stiffness and cornering stiffness, will cause that the direction of tire resultant shear stress in adhesion region is different from that in sliding region. Eventually the tire forces and moments under combined slip conditions will be influenced obviously. The author has proposed a “direction factor” before to modify the direction of resultant force in the tire-road contact patch, which can describe tire forces at cornering/braking combination accurately. However, the aligning moments which are very complicated under combined slip conditions are not considered in previous analysis.

The tire mechanics characteristics are essential for analysis and control of vehicle dynamics. Basically, the effects of sideslip, longitudinal slip, camber angle and vertical load are able to be represented accurately by current existing tire models. However, the research of velocity effects for tire forces and moments are still insufficient. Some experiments have demonstrated that the tire properties actually vary with the traveling velocity especially when the force and moment are nearly saturated. This paper develops an enhanced brush tire model and the UniTire semi-physical model for tire forces and moments under different traveling velocities for raising need of advanced tire model. The primary effects of velocity on tire performances are the rubber friction distribution characteristics at the tire-road interface.

To improve the quantitative accuracy of vehicle vibration studies, a roller contact tire model with the geometric filtering concept and a method to determine the effective road input are proposed. Computer simulation with the 13 DOF vehicle model for a light truck, based on two different tire models, and relevant outdoor tests for measuring the vehicle accelerations of both sprung and unsprung masses are presented. Comparisons of test data and simulation results show that the roller contact tire model renders much better simulation accuracy than the single point contact tire model. It is concluded that the roller contact tire model is a powerful concept which acts as a geometric filter, giving a simple method to calculate the enveloping effects of tires and the effective road elevation input.

The properties of contact patch are key factors for tire modeling. Researchers have paid more attention to the contact patch shape and vertical pressure distribution. Some innovative concepts, such as Local Carcass Camber, have been presented to explain special tire modeling phenomena. For a pragmatic tire model, a concise model structure and fewer parameters are considered as the primary tasks for the modeling. Many empirical tire models, such as the well-known Magic Formula model, would become more complex to achieve satisfactory modeling accuracy, due to increasing number of input variables, so the semi-empirical or semi-physical modeling method becomes more attractive. In this paper, the concept of Tire Carcass Camber is introduced first. Different from Local Carcass Camber, Tire Carcass Camber is an imaginary camber angle caused only by lateral force on the unloaded tire.

Snow-covered ground severely affects vehicle mobility in cold regions due to low friction coefficients and snow sinkage. Simulation and evaluation of vehicle mobility in cold regions require real-time friendly tire-snow interaction models that are applicable for quasi-real driving conditions. Recently, we have developed tire-snow dynamics models that are snow depth dependent, sinkage dependent and normal load dependent. The number of model parameters is reduced through theoretical analysis of normal indentation, contact pressure and shear stress within the tire-snow interface. In-plane and out-of-plan motion resistances and traction forces (gross traction and net traction) are analytically calculated for combined slip conditions.

With the development of computer and vehicle research to high frequency, the driving simulator plays an important role on vehicle research and pre-development. The driving simulator have already been used for research about human factors, advanced active system (ABS, ESP et al), the vehicle dynamics and intelligent transportation systems (ITS) et al. The crucial requirement for a driving simulator is that it should have realistic behavior. The realistic behavior base on high-fidelity dynamics models especially tire model. “Tire/road” model is of special importance model for its influence on vehicle performances. The forces for accelerating, braking and steering are all came from tire road contact. The simulator simulation faces all possible driving scenes as driving in the real word, like parking on the hill, stop and start again, sharp steering and sharp braking et al.

High-quality dynamics model is one of the trends of vehicle dynamics model research and development. The engine generates high frequency excitation during operation, which may cause dynamic response in full vehicle. However, the widely-used internal-combustion engine model in vehicle dynamics simulation is steady-state model, which can't describe the fluctuation of engine drive torque along with the crankshaft angle. Consequently, this article concentrates on the modeling of instantaneous engine drive torque in order to improve the dynamic performance of the vehicle model. The paper has built the quasi-instantaneous engine model based on indicator diagram. To satisfy the requirement of real-time simulation, dynamically equivalent piston-connecting rod model is built and fast interpolation algorithm is researched. The linkage was simplified to spring and damper, and decoupled the piston translation and the crank rotation movements.

Magneto-rheological fluid squeeze mode investigations at CVeSS have shown that MR fluids show large force capabilities in squeeze mode. A novel MR squeeze mount was designed and built at CVeSS, and a dynamic mathematical model was developed, which considered the inertial effect and was validated by the test data. A variant engine mount that will be used for isolating vibration, based on the MR squeeze mode is proposed in the paper. The mathematical governing equations of the mount are derived to account for its operation with MR squeeze mode. The design method of a robust H✓ controller is addressed for the squeeze mount subject to parameter uncertainties in the damping and stiffness. The controller parameter can be derived from the solution of bilinear matrix inequalities (BMIs). The displacement transmissibility is constrained to be no more than 1.05 with this robust H✓ controller. The MR squeeze mount has a very large range of force used to isolate the vibration.

Simulations of tire cornering properties with small-amplitude lateral inputs are carried out in non-steady state conditions. The simulation algorithm is derived and the discrete expressions are presented in detail. Based on the simulations, lateral force and aligning moment can be calculated numerically with time-varying yaw angle and lateral displacement as inputs in spatial domain. The flexibility of both tread and carcass along with tire width is taken into account effectively in the simulations, in which the flexibility of carcass includes translating, bending and twisting flexibility. The simulations in non-dimensional form are associated with four tire structure parameters only, which are non-dimensional parameters reflecting the characteristics of tire stiffness, tire width and contact length. Simulation results are validated by test data from step lateral inputs tests. Several typical simulation results are provided.

The objective of this paper is to assess the effect of snow density on tire-snow interaction in the presence of uncertainty. The snow-depth dependent finite element analysis (FEA) and semi-analytical models we have developed recently can predict tire-snow interfacial forces at a given density under combined slip conditions. One drawback of the models is that they are only applicable for fresh, low-density snow due to the unavailability of a density-dependent snow model. In reality, the snow density on the ground can vary between that of fresh snow to heavily compacted snow that is similar to ice. Even for fresh snow on the ground, as a vehicle moves forward, the rear wheels experience higher snow densities than the front wheels. In addition, being a natural material, snow's physical properties vary significantly even for the same density.

A closed-loop comprehensive evaluation and a test method for vehicle handling and stability have been studied by using development driving simulator. Simulator test scheme has been designed and carried out with 14 vehicle configurations, and subjective evaluation has been made for easy handling of vehicle by drivers. A closed-loop comprehensive evaluation index has been put forward considering the factors affecting vehicle handling and stability. The reliability of the index has been validated by driver's subjective evaluation. A driver/vehicle/ road closed-loop system model has been established, and the theoretical predictive evaluation has been carried out with 14 vehicle configurations. Simulation showed that similar result for both theoretical predictive evaluation and subjective evaluation.

There is a scarcity of comprehensive tire-snow interaction models for combined (longitudinal and lateral) slips. Current tire-snow interaction empirical and finite element models mostly focus on force-slip relationships in the longitudinal direction only, following the approach used for tire-soil interaction models. One of the major differences between tire-snow and tire-soil interactions is that the former is typically depth-dependent, especially for shallow snow. Our approach in the modeling of tire-snow interaction is to rely on the underlying physics of the phenomena, wherever we could, and use test data (or finite element simulation results in the absence of test data) to calibrate the required model parameters. We also make contact with on-road models and extend them for off-road applications.

High-fidelity finite element (FE) tire-snow interaction models have the advantage of better understanding the physics of the tire-snow system. They can be used to develop semi-analytical models for vehicle design as well as to design and interpret field test results. For off-terrain conditions, there is a high level of uncertainties inherent in the system. The FE models are computationally intensive even when uncertainties of the system are not taken into account. On the other hand, field tests of tire-snow interaction are very costly. In this paper, dynamic metamodels are established to interpret interaction forces from FE simulation and to predict those forces by using part of the FE data as training data and part as validation data. Two metamodels are built based upon the Krieging principle: one has principal component analysis (PCA) taken into account and the other does not.

In this paper, a shock absorber physical model is developed. Firstly, a rebound valve model which is based on its structure parameters is built through using the large deflection theory. The von Karman equations are introduced to discover the physical relationships between the load and the deflection of valve discs. An analytical solution of the von Karman equations is then deducted via perturbation method. Secondly, the flow equations and the pressure equations of the shock absorber operating are investigated. The relationship between fluid flow rate and pressure drop of rebound valve is analyzed based on the analytical solution of valve discs deflection. Thirdly, an inter-iterative process of flow rate and pressure drop is employed in order to adequately consider the influence of fluid flow on damping force. Finally, the physical model is validated by comparing the experimental data with the simulation output.

This paper presents a torque distribution algorithm to improve the energy efficiency of four-wheel-drive (4WD) electric vehicles with PMSM hub motors. In order to optimize the torque distribution method, at first the motor model considering the affect of iron loss and the loss model of multi-motors drive system of 4WD electric vehicle with PMSM hub motors, which operate at straight-line condition, are established. Besides, realize the online identification of motor parameters based on the MARS, which is important for updating the loss model parameters of the motor drive system. By doing this, the ideal torque distribution ratio can be obtained from the loss model in real-time. The simulation result using different distribution algorithms shows that the optimized torque distribution algorithm based on the loss model can be useful for improving the energy efficiency.

In this research, off-road vehicle simulation is performed with tire-soil interaction model. The predictive semi-analytical model, which is originally developed for tire-snow interaction model by Lee [4], is applied as a tire-soil interaction model and is implemented to MSC/ADAMS, commercial multi-body dynamic software. It is applied to simulate the handling maneuver of military vehicle HMMWV. Two cases are simulated with Michigan sandy loam soil property. Each case has two maneuvers, straight-line brake and step steer (J-turn). First, tire-soil interaction model and conventional on-road tire model are simulated on the flat road of the same frictional coefficient. The proposed tire-soil interaction model provided larger force under the same slip. Second, the same maneuvers are performed with real off-road frictional coefficient. The proposed tire-soil model can be validated and the behavior of the off-road vehicle can be identified through two simulation cases.

A novel predictable tire model has been proposed for combined braking and cornering forces, which is based on only a few pure baking and pure cornering tests. It avoids elaborate testing of all kinds of combinations of braking and side forces, which are always expensive and time consuming. It is especially important for truck or other large size tires due to the capability constraints of tire testing facilities for combined shear forces tests. In this paper, the predictive model is based on the concept of slip circle and state stiffness method. The slip circle concept has been used in the COMBINATOR model to obtain the magnitude of the resultant force under combined slip conditions; however the direction assumption used in the COMBINATOR is not suitable for anisotropic tire slip stiffness.

Vehicle model plays an important role during the development process of a new car chassis. There are 2 different ways to set up the vehicle mathematics model, one is set up based on understanding the system mechanism and the other is based on system identification technique. In this paper, the transfer functions of the vehicle at 100 km/h, including yaw rate to the steering angle and lateral acceleration to the steering angle, were identified. And then the transfer functions under other forward speed were derived through studying two degrees of freedom vehicle model equation. At last the identified model at different speed was used to analysis the stability of closed loop system from the classical control theory viewpoint.

In the paper, the Flat Plank Tire Tester of Changchun Automobile Institute is introduced. This paper, according to practical experiences, generalizes some issues in the tire's non-steady state test. In the non-steady state test, it must be assured that the footprint centerline of tire coincides with that of slid platform, which guarantees no sliding motion between tire and slid platform during the movement. Due to tire taper effect and inhomogeneous tire material, when its side slip angle is zero, side force and aligning torque are not zeros, but have initial values. Here two approaches are discussed to eliminate the side force and aligning torque. Besides, other factors in the test are put forward for discussion. Eliminating the interference can obviously improve the test accuracy. This paper also provides test curves of both pure side slip angle input and pure yaw angle input.

All the frictional forces developed from tire-snow interfaces are closely associated with snow depth and snow sinkage. One of the important differences between tire-soil interaction and tire-snow interaction is that the latter is explicitly snow depth dependent. Based on our established depth-dependent upper bound indentation model, the effects of snow depth on tire-snow interaction are presented in this paper. Snow is considered as a pressure-sensitive Drucker-Prager material. The required snow material parameters of the model are Drucker-Prager material constants only. Snow sinkages, for longitudinal slip close to zero, under different snow depths are numerically solved through the sinkage solver. The comparison between sinkage obtained analytically and the sinkage computed from finite element simulation is very good.