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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.

This paper proposes a dynamic obstacle avoidance system to help autonomous vehicles drive on high-speed structured roads. The system is mainly composed of trajectory planning and tracking controllers. The potential field (PF) model is introduced to establish a three-dimensional potential field for structured roads and obstacle vehicles. The trajectory planning problem that considers the vehicle’s and tires’ dynamics constraints is transformed into an optimization problem with muti-constraints by combining the model predictive control (MPC) algorithms. The trajectory tracking controller used in this paper is based on the 7 degrees of freedom (DOF) vehicle model and the UniTire tire model, which was discussed in detail in previous work [25, 26]. The controller maintains good trajectory tracking performance even under extreme driving conditions, such as roads with poor adhesion conditions, where the car’s tires enter the nonlinear region easily.

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.

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.

Four-wheel-drive electric vehicles (4WD Evs) utilize in-wheel electric motors and Electro-Hydraulic Braking system (EHB). Then, all wheels torque can be controlled independently, and the braking pressure can be controlled more accurately and more fast than conventional braking system. Because of these advantages, 4WD Evs have potential applications in control engineering. In this paper, the in-wheel electric motors and EHB are applied as actuators in the vehicle stability control system. Based on the Direct Yaw-moment Control (DYC), the optimized wheel force distribution is given, and the coordination control of the hydraulic braking and the motor braking torque is considered. Then the EHB hardware-in-the-loop test bench is established in order to verify the effectiveness of the vehicle stability control algorithm through experiments.

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 tire lateral force is essential to the vehicle handling and stability under cornering. However, it is difficult for engineers to get the tire lateral force under high loading condition due to the limitation of loading ability for most tire test machine in the world. The widely used semi-empirical tire lateral force models are obtained by curve-fitting experiments data and thus unable to predict the load dependent lateral force. The objective of this paper is to predict the tire lateral force under high-load condition based on the low-load tire data. The nonlinear characteristics of the tire cornering stiffness with the load are greatly affected by the tire carcass compliance. In this paper, a theoretical tire lateral model was built by considering carcass complex deformation. Combined with the relationship between the half-length of the tire contact patch and the load, the non-linear characteristics of the tire cornering stiffness with load were obtained.

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 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.

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.

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.

One of the most essential factors causing automobile and aircraft shimmy is energy import from road to tires due to tire hysteresis characteristic. The magnitudes and direction of the energy import are close to frequency responses of tire cornering properties (TCP), which can be calculated directly according to the presented non-steady state TCP theoretical model. Selfexcited shimmy is the main type of wheel shimmy and behaves as negative equivalent damping characteristic of the tire-road vibration subsystem. The values of energy import or equivalent damping determine the tendency of wheel shimmy. Tire structural parameters have certain effects on frequency response of TCP and thereby result in influences on wheel shimmy. Based on the tire model, some valid ways to decrease shimmy tendency are concluded through proper variations of carcass stiffness, tire-width, kingpin caster, tire pneumatic trail, tire cornering stiffness and so on.

Pressure following control is the basic function of Electro-Hydraulic Braking system (EHB), which is also the key technology of stability control system and regenerative braking system for hybrid and electric vehicles. Experimental research is an important method for the control and application of EHB. This paper describes a method to test and control the EHB system through experiment on the Hardware-in-the-loop (HIL) test bench and wheel motor electric vehicle. First, the HIL test bench was established, in which the EHB was tested, including the characteristics of solenoid valves and motor. Then the wheel cylinder pressure was controlled to follow the specific signal input and the master cylinder pressure. Based on this, EHB and the pressure following control method were applied to the wheel motor electric vehicle. The results show that the braking pressure can follow the driver's braking intention to realize the conventional braking function of electric vehicles.

This paper presents a general kinematical model for all variety of leaf springs, including traditional laminated, asymmetrical, and tapered leaf springs, to calculate the longitudinal and winding deformations of axles during bouncing, braking and traction, which may introduce additional steering effects or variations of roll-steer property of a vehicle. Some experiments were introduced to verify the model. Accordingly, braking performance of a light truck has been improved.

With the development of the advanced driver assistance system and autonomous vehicle techniques, a precise description of the driver’s steering behavior with mathematical models has attracted a great attention. However, the driver’s steering maneuver demonstrates the stochastic characteristic due to a series of complex and uncertain factors, such as the weather, road, and driver’s physiological and psychological limits, generating negative effects on the performance of the vehicle or the driver assistance system. Hence, this paper explores the stochastic characteristic of driver’s steering behavior and a novel steering controller considering this stochastic characteristic is proposed based on stochastic model predictive control (SMPC). Firstly, a search algorithm is derived to describe the driver’s road preview behavior.

Vehicle handling and stability performances are greatly determined by non-steady state (NSS) tire cornering properties. Analytical derivation of NSS tire cornering models are presented in this paper based on Pacejka's string-concept assumption, in which carcass is assumed to be a stretched string with lateral deformation and lateral relaxation. The lateral inputs of the models are either displacement-based (lateral displacement and yaw angle) or slip-based (slip angle and turn slip). The transient deformations in spatial domain in both longitudinal and lateral directions are obtained directly from geometric relationship of contact patch. The additional self-aligning moment due to longitudinal deformation of contact patch after effect of tire width is considered is also achieved according to geometric relationship of contact patch in longitudinal direction and two transient geometric conditions of contact point.

Non-steady state (NSS) tire cornering properties show obvious differences from steady state (SS) tire cornering properties. A two-DOF automobile model with steer angle as an input is established based on the known NSS tire model considering complex carcass deformation. The tire model can certainly be applied to modelling of a multi-DOF automobile system. The frequency responses of lateral acceleration and yaw rate are then derived. An evaluation index, amplitude-frequency characteristic of relative error (AFCRE), is used to analyze the influences of NSS front wheels (FW) and/or rear wheels (RW) on automotive handling. The influences of NSS FW are much greater than those of NSS RW only on automotive handling. The established automobile model can also be applied to other similar studies of vehicle dynamics.

In this paper, on the basis of the extant semi-empirical tire models of non-steady state with pure yaw angle input and pure side slip angle input, two empirical tire models of non-steady state side slip properties are established, one is pure yaw angle input, the other is pure side slip angle input, and both of them have been verified by test data. These two models can be used to approximately express tire force within low frequency. They have their own advantages, and make up for the disadvantages of existing tire models. They provide more choice for the simulation of vehicle dynamics.