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In this paper a yaw stability control algorithm along with an emergency roll control strategy have been developed. The yaw stability controller and emergency roll controller were both developed using linear two degree-of-freedom vehicle models. The yaw stability controller is based on Lyapunov stability criteria and uses vehicle lateral acceleration and yaw rate measurements to calculate the corrective yaw moment required to stabilize the vehicle yaw motion. The corrective yaw moment is then applied by means of a differential braking strategy in which one wheel is selected to be braked with appropriate brake torque applied. The emergency roll control strategy is based on a rollover coefficient related to vehicle static stability factor. The emergency roll control strategy utilizes vehicle lateral acceleration measurements to calculate the roll coefficient. If the roll coefficient exceeds some predetermined threshold value the emergency roll control strategy will deploy.

A graphical user interface (GUI) toolbox called Vehicle System Simulator (VSS) is developed in MATLAB to ease the use of this vehicle model and hopefully encourage its widespread application in the future. This toolbox uses the inherent MATLAB discrete-time solvers and is mainly based on Level-2 s-function design. This paper describes its built-in vehicle dynamics model based on multibody dynamics approach and nonlinear tire models, and traction/braking control systems including Cruise Control and Differential Braking systems. The built-in dynamics model is validated against CarSim 8 and the simulation results prove its accuracy. This paper illustrates the application of this new MATLAB toolbox called Vehicle System Simulator and discusses its development process, limitations, and future improvements.

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.

This study addresses the critical need for computational tools to model complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. Polynomial chaos has been used extensively to model uncertainties in structural mechanics and in fluids, but to our knowledge they have yet to be applied to multibody dynamic simulations. We show that the method can be successfully applied to quantify uncertainties in time domain and frequency domain for constrained multibody dynamic systems.

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.

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.

This paper presents a parametric study of two semiactive adaptive control algorithms through simulation: the non-model based skyhook control, and the newly developed model-based nonlinear adaptive vibration control. This study includes discussion of suspension model setup, dynamic analysis approach, and controller tuning. The simulation setup is from a heavy-duty truck seat suspension with a magneto-rheological (MR) damper. The dynamic analysis is performed in the time domain using sine sweep excitations without the need to linearize such a nonlinear semiactive system that is studied here. Through simulation, the effectiveness of both control algorithms is demonstrated for vibration isolation. The computation flops of the simulation in the SIMULINK environment are compared, and the adaptability is studied with respect to plant variations and different excitation profiles, both of which come across typically for vehicle suspension systems.

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 main intent of this study is to provide a simulation analysis of rollover dynamics of multi-trailer commercial vehicles in roundabouts. The results are compared with conventional tractor-semitrailer with a single 53-ft trailer for roundabouts that are of typical configuration to those in the U.S. cities. The multi-trailer commercial vehicles that are considered in this study are the A-double trucks commonly operated in the U.S. roads with the trailer length of 28 ft, 33 ft, and 40 ft. The multi-body dynamic models for analyzing the rollover characteristics of the trucks in roundabouts are established in TruckSim®. The models are intended to be used to assess the maximum rollover indexes of each trailer combination subjected to various circulating speeds for two types of roundabouts, 140-ft single-lane and 180-ft double-lane.

Dynamic “Game Theory” brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In previous studies, it was shown that vehicle stability can be represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the vehicle stability controller (VSC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the VSC command is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion. This study focus on the uncertainty in the inputs, and more specifically, the driver's steering input.

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.

This study provides a simulation evaluation of the effect of maintaining balanced airflow, both statically and dynamically, in heavy truck air suspensions on vehicle roll stability. The model includes a multi-domain evaluation of the truck multi-body dynamics combined with detailed pneumatic dynamics of drive-axle air suspensions. The analysis is performed based on a detailed model of the suspension's pneumatics, from the main reservoir to the airsprings, of a new generation of air suspensions with two leveling valves and air hoses and fittings that are intended to increase the dynamic bandwidth of the pneumatic suspensions. The suspension pneumatics are designed such that they are able to better respond to body motion in real time. Specifically, this study aims to better understand the airflow dynamics and how they couple with the vehicle dynamics.

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.

A detailed study of the effects of shim stack assemblies on performance of hydraulic mono-tube vehicle shock absorbers is presented. Currently, shim stacks are modeled as blow-off valves in hydraulic models of shock absorbers. Using this simplification, important material and geometrical properties of shim stacks cannot be studied and their effects cannot be understood on overall damper performance. In this paper, shim stack deflection is investigated and a mathematical model is presented for shim stack deflection. This model is then incorporated into the mathematical model of a hydraulic damper and various properties of shim stack and their effects on damper characteristics are studied. Energy and variational methods were used to develop the mathematical model of the shim stack. The mathematical model also takes into account the sliding effects of the shims on each other when the shim stack is deflected.

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.

Dynamic game theory brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion.