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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.

In this paper, a parasite system power empirical model of a PEM fuel cell engine suitable for the study of fuel cell vehicle simulation is developed by fitting the experimental data with quadratic polynomial. The assumption of the model is that the fuel cell stack is in steady-state condition. The properties of the parasite system power are analyzed. Based on the analysis of the properties of the parasite power, two parameters--- stack power factor RAS and FCE power factor RAF are introduced to evaluate the quality of the stack and the fuel cell engine. Moreover, the parasite system power model is verified by test data. The result indicates that the model is accurate to reflect the static performance of the parasite system. The advantage of the model is that its structure is simple, and its parameters are easy to be obtained. It is easy to apply to the study of fuel cell vehicle simulation.

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.

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.

In this paper, a hydrogen consumption rate model of a PEM fuel cell engine is developed based on experimental data. The assumption of the model is that fuel cell stack works in steady-state condition. The relationships between the hydrogen consumption rate and stack current, stack power and Fuel Cell Engine (FCE) power are analyzed. Based on the hydrogen consumption rate model, a hydrogen specific consumption model is developed. Moreover, the models presented in this paper are verified by test data. The results indicate that these models are accurate to reflect the static performance of fuel cell stack and fuel cell engine. The advantages of these models are that theirs structures are very simple, and theirs parameters are easy to be obtained. They are easy to be applied to the study of fuel cell vehicle simulation.

Fuel cell vehicle commercialization and mass production are challenged by the durability of fuel cells. In order to research the durability of fuel cell stack, it is necessary to carry out the related durability test. The performance prediction of fuel cell stack can be based on a short time durability test result to accurately predict the performance of the fuel cell stack, so it can ensure the timeliness of the test results and reduce the cost of test. In this paper, genetic algorithm-BP neural network (GA-BPNN) is proposed to modeling automotive fuel cell stack to predict the performance of it. Based on the strong global searching ability of genetic algorithm, the initial weights and threshold selection of neural networks are optimized to solve the shortcoming that the random selection of the initial weights and thresholds of BP neural network which can easily lead to the local optimal value.

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.

The vehicular fuel cell stack is unavoidably impacted by the vibration in the real-world usage due to the road unevenness. However, effects of vibration on stacks have yet to be completely understood. In this work, the mechanical integrity and gas-tightness of the stack were investigated through a strengthen road vibration test with a duration of 200 h. The excitation signals applied in the vibration test were simulated by the acceleration of the stack, which were previously measured in a vehicle vibration test. The load signals of the vehicle vibration test were iterated through a road simulator from vehicle acceleration signals which were originally sampled in the proving ground. Frequency sweep test was conducted before and after the vibration test. During the vibration test, mechanical structure inspection and pressure maintaining test of the stack were conducted at regular intervals.

Durability performance prediction is a critical issue in fuel cell research. During the demonstration operation of fuel cell commercial vehicles in China, this issue has attracted more attention. In this article, the long short-term memory neural network (LSTMNN), which is an improved recurrent neural network (RNN), and the demonstration operation data are used to establish the prediction model to predict the durability performance of the fuel cell stack. Then, a model based on a back-propagation neural network (BPNN) is established to be a control group. The demonstration operation data is divided into training group and validation group. The former is used to train the prediction model, and the latter is used to verify the validity and accuracy of the prediction model. The outputs of the prediction model, as the durability performance evaluation indexes of the fuel cell, are the polarization curve (current-voltage curve) and the voltage decay curve (time-voltage curve).

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.

Based on the tire cornering properties in steady state condition, a theoretical model of non-steady state tire cornering properties (NSSTCP) with small lateral inputs is presented. The outputs of the model are lateral force and aligning moment, while the inputs are yaw angle and lateral displacement (or turn slip and slip angle). The deformation characteristics of contact patch are analyzed in non-steady state condition. The flexibility of tread and that of carcass are both taken into account. The deformation of carcass is assumed to compose of translating part, bending part and twisting part. The tests of NSSTCP including pure yaw motion and pure lateral motion are realized with step inputs of yaw angle and slip angle respectively and test data is then transformed into frequency domain. The model is validated through comparing the computational results with test frequency response.

Tire lag property is a basic property of tire dynamics, and it has significant influence on the performance of vehicle dynamics. In distance domain, the side force and moments produced by a massless tire are basically displacement or path frequency dependent, rather than time dependent. In the paper, on the basis of the stretched-string model, the first-order filtering of deflection for the front point of the contact print and the first-order filtering of side force have been introduced. Tire system can be regarded as a first-order linear system under small slip angle. The force response of tire has the characteristics of the responses of first-order linear system under small angle. The relaxation length is an important parameter in studying tire lag property. It decreases with increasing slip angle. It plays an important role in the study of tire transient properties.

The objective of this study is to develop a non-steady & non-linear tire model for vehicle dynamic simulation and control for extreme lateral slip condition. This model is provided in a semi-analytical form based on the theoretical non-steady state model, presented at 2nd IAVSD Tyre Conference, Feb. 1997[6]. The tire model is based on a quasi-steady state concept, which generates the dynamic forces and moment according to the dynamic effective slip ratio cooperating with the Unified Semi-Empirical Tire Model for Steady State. Satisfying the theoretical boundary conditions at two sides (lowest & highest) in frequency domain, the tire model is capable of describing the transient force & moment characteristics of tires in higher frequency range, Comparing with the “Linear Approximation” model, presented at 4th AVEC Conference, Sept. 1998[4].

A generalized theoretical model of tire cornering properties is presented in steady state condition with lateral deflection of tread and complex deformation of carcass under consideration. The model is suitable for full range of vertical load and slip angle. Six parameters are defined to represent the characteristics of tire stiffness, contact pressure distribution and carcass deformation. The model is validated against test data. Some simplified models, e.g. brush model, HSRI model when longitudinal force is zero, Fiala model etc., can be derived as some specific cases of this model. The analytic model provides a sound foundation for semi-empirical expression and gains insight into study of vehicle system dynamics.