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Vehicle systems often operate with some degree of uncertainty. This study applies the Chebyshev interval method to model vehicle dynamic systems operating in the presence of interval parameters. A full vehicle model is used as the numerical model and the methodology is illustrated on the steering wheel angle pulse input test. In the numerical simulation, suspension stiffness coefficients and suspension damping coefficients are chosen as interval parameters and lateral acceleration and yaw rate are chosen to capture vehicle dynamic characteristics. System responses in time domain are validated against Monte Carlo simulations and against the scanning approach. Results indicate that the Chebyshev interval method is more efficient than Monte Carlo simulations. The results of scanning method are similar to the ones obtained with the Chebyshev interval method.

In contemporary trajectory planning research, it is common to rely on point-mass model for trajectory planning. However, this often leads to the generation of trajectories that do not adhere to the vehicle dynamics, thereby increasing the complexity of trajectory tracking control. This paper proposes a local trajectory planning algorithm that combines sampling and sequential quadratic optimization, considering the vehicle dynamics model. Initially, the vehicle trajectory is characterized by utilizing vehicle dynamic control variables, including the front wheel angle and the longitudinal speed. Next, a cluster of sampling points for the anticipated point corresponding to the current vehicle position is obtained through a sampling algorithm based on the vehicle's current state. Then, the trajectory planning problem between these two points is modeled as a sequential quadratic optimization problem.

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.

The design of suspension affects the vehicle dynamics such as ride comfort and handling stability. Nonlinear characteristics and friction are important characteristics of suspension system, and the influence on vehicle dynamic performance cannot be ignored. Based on the seven-degree-of-freedom vehicle vibration nonlinear model with friction, the vibration response process of the vehicle and the influence of suspension friction on vehicle ride comfort and suspension action process were studied. The results show that friction will significantly affects the simulation of ride comfort and coincide with the function of the shock absorber. The suspension shock absorbers of vehicles were optimized with and without suspension friction. The results showed that the suspension tended to choose softer shock absorbers when there was friction. However, both of the two optimizations are able to improve the ride comfort of vehicles, and the simulation results were similar.

This paper investigates a hierarchical optimization procedure for the optimum synthesis of a double-axle steering mechanism by considering the dynamic load of a vehicle which is seldom discussed in the previous literature. Firstly, a multi-body model of double-axle steering is presented by characterizing the detailed leaf spring effect. Accordingly, the influences of dynamic load including the motion interference of steering linkage resulted from the elastic deformation of leaf spring, and the effects of wheel slip angle and the position discrepancy of wheel speed rotation centers are explored systematically. And then, a hierarchical optimization method based on target cascading methodology is proposed to classify the design variables of double-axle steering mechanism into four levels. At last, a double-axle steering mechanism of a heavy-duty truck is utilized to demonstrate the validity of this method.

To study the torque distribution of track and tire in the wheel-track hybrid drive vehicle driving along the shoreline, an analysis model of wheel-track hybrid drive vehicle was established by using multi-body dynamics (MBD), discrete element (DEM), and shoreline pavement construction methods. The vehicle speed, acceleration, torque, vertical load, sinkage, slip, and other indicators when the vehicle passes the shoal at different wheel speed of rotation are analyzed. The relationships between wheel speed of rotation and slip, sinkage and slip, and vertical load and driving moment were studied, and the laws that the sinkage of tires and tracks is positively related to their slippage and the driving moment of wheels and tracks is positively related to their vertical load were obtained.

In the petroleum and gas industry, cargo truck is one of the most important ways to transfer the skid-mounting from the manufacturer to the job location. Under the condition of bumpy road surface, the random vibration from the ground can easily cause the resonance of the internal equipment components of the skid-mounting, produce large deformation in the pipeline and equipment connection, and even the equipment will be damaged. In this paper, the finite element analysis model and dynamic rigid flexible coupling model of a TEG (Triethyleneglycol) dehydration unit regeneration skid-mounting are established by using the finite element analysis and multi-body dynamics software. The modal analysis of the skid and the vibration of the whole vehicle under different road excitation and driving conditions are carried out. Two solutions are proposed to improve the anti-vibration ability of the skid, and comparative analysis is made.

A Special Analytical Target Cascading (SATC) process is developed for design problem which is difficult to ascertain the targets cascaded from upper level to lower level. The methodology is applied to achieve improving Handling Performance and Ride Quality (HPRQ) of a passenger car. A bi-level hierarchical structure with target-transforming process is established based on conceptual suspension model and multi-body models. DOE, RSM and a combined optimization method of simulated annealing and Programming Quadratic Line search is applied to execute the optimization process. The result shows that HPRQ is improved through special ATC based on CSM and multi-body modeling technique.

As is known to all, there are some contradictions between the handling and ride performance during the design process of vehicles. Sometimes owing to serious collisions of each criterion in the high-dimensional solution space, the common method to deal with the contradiction is to transform into a single target according to weights of each objective, which may not obtain a desired result. A multi-criteria approach is therefore adopted to optimize both properties and the result of a multi-criteria design is not a unique one but a series of balanced solutions. This paper is focused on the robust design of a simplified vehicle model in terms of not only ride comfort but also handling and stability using a multi-objective evolutionary algorithm (MOEA) method. Using the proposed method, the conflicting performance requirements can be better traded off. One of the most important indexes to characterize the vertical ride comfort is the acceleration of the sprung mass.

There are many uncertain parameters in shock absorbers, which are induced by the manufacturing error, the wear of components and the aging of materials in real vehicle environment. These uncertainties often cause some deterioration of vehicle performance. To optimize the ride characteristic of a vehicle when the shock absorber includes uncertain parameters, the robust design method is used. In this paper, a Twin Tube shock absorber fluid system model has established on the multi-domain modeling environment. This model not only includes the commonly used parameters of the shock absorber but also takes into account the structure parameters of various valves in the shock absorber, which is more detailed and accurate than those models in the past literature. The robust design of the shock absorber parameters is successfully approached using the co-simulation technique, and the ride comfort performance of the vehicle is also improved.

A new recursive method is presented for real-time estimating the inertia parameters of a vehicle using the well-known Two-Degree-of- Freedom (2DOF) bicycle car model. The parameter estimation is built on the framework of polynomial chaos theory and maximum likelihood estimation. Then the most likely value of both the mass and yaw mass moment of inertia can be obtained based on the numerical simulations of yaw velocity by Newton method. To improve the estimation accuracy, the Newton method is modified by employing the acceptance probability to escape from the local minima during the estimation process. The results of the simulation study suggest that the proposed method can provide quick convergence speed and accurate outputs together with less sensitivity to tuning the initial values of the unidentified parameters.

Steering returnability is an important index for evaluating vehicle handling performance. A systematic method is presented in this paper to reduce the high yaw rate residue and the steering response time for a light duty truck in the steering return test. The vehicle multibody model is established in ADAMS, which takes into consideration of the frictional loss torque and hydraulically assisted steering property in the steering mechanism, since the friction, which exists in steering column, spherical joint, steering universal joint, and steering gear, plays an important role in vehicle returnability performance. The accuracy of the vehicle model is validated by road test and the key parameters are determined by executing the sensitivity analysis, which shows the effect of each design parameter upon returnability performance.

In vehicle driving environment, the driver is subjected to the vibrations in horizontal, vertical, and fore-aft directions. The human body is very much sensitive to whole body vibration and this vibration transmission to the body depends upon various factors including road irregularities, vehicle suspension, vehicle dynamics, tires, seat design and the human body's properties. The seat design plays a vital role in the vibration isolation as it is directly in contact with human body. Vibration isolation properties of a seat depend upon its dynamic parameters which include spring stiffness and damping of seat suspension and cushion. In this paper, an optimization-based method is used to determine the optimal seat dynamic parameters for seat suspension, and cushion based on minimizing occupant's body fatigue (occupant body absorbed power). A 14-degree of freedom (DOF) multibody biodynamic human model in 2D is selected from literature to assess three types of seat arrangements.

To solve the dynamic response problem that contains uncertain parameters needs, the stochastic differential equations needs to be calculated. Interval analysis has been widely used to solve engineering problems which contain many uncertain parameters usually. But the numerical solution method for stochastic differential equations based on the interval analysis method was seldom investigated. In this study a new numerical interval method for the stochastic differential equations based on the Euler's method is presented, which can be used to solve the linear system effectively and efficiently. The probabilistic and interval dynamics analysis of a two-degree-of-freedom bike car model with uncertain parameters are presented.

Suspension kinematics and compliance strongly influence the handling performance of the vehicle. The kinematics and compliance characteristics are determined by the suspension geometry and stiffness of suspension bodies and elastic components. However, it is usually inefficient to model all the joints, bushings, and linkage deformation in a full vehicle model. By transforming the complex modeling problem into a data-driven problem tends to be a good solution. In this research, the neural-network-based suspension kinematics and compliance model is built and implemented into a 17 DOF full vehicle model, which is a hybrid model with state variables expressed in the global coordinate system and vehicle coordinate system. The original kinematics and compliance characteristics are derived from multibody dynamics simulation of the suspension system level.

In order to reasonably match the variable stiffness and location of the Powertrain Mounting System (PMS) and optimize the ride comfort of commercial vehicle, a thirteen degrees of freedom (DOF) model of a commercial vehicle was established in Adams/view. Specially, the support rod installed on the upside of the transmission case was modeled as a flexible body. The vibration isolation provided by the PMS was evaluated in three aspects: the energy decoupling of the powertrain, the response force of the mount and the displacement of the powertrain. The energy decoupling ratio, the force RMS of the mount when force excitation was applied on the powertrain and the displacement of the powertrain Center of Gravity (C.G) when displacement excitation was applied on the vehicle chassis were selected as the optimal target. Adams and MATLAB were integrated into the optimization software iSIGHT to optimize the PMS. NSGA-II is used to obtain some Pareto-optimal solutions of PMS.

With the development of hardware and control theory, the application of quadcopters is constantly expanding. Quadcopters have emerged in many fields, including transportation, exploration, and object grabbing and placement. These application scenarios require accurate, stable, and rapid control, and a suitable dynamic model is one of the prerequisites. At present, many works are related to it, most of which are modeled using the Newton-Euler method. Some works have also adopted other methods, including the Lagrangian and Hamiltonian methods. This article proposes a new method that solves the Hamiltonian equation of a quadcopter expressed in quasi-coordinate. The external forces and motion of the body are expressed in the quasi-coordinate system of the body, and solved through the Hamiltonian equation. This method simplifies operations and improves computational efficiency. Additionally, a single pendulum is attached to the quadcopter to simulate application scenarios.

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.

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 new computational method is provided to identify the uncertain parameters of Load Sensing Proportional Valve (LSPV) in a heavy truck brake system by using the polynomial chaos theory. The simulation model of LSPV is built in the software AMESim depending on structure of the valve, and the estimation process is implemented relying on the experimental measurements by pneumatic bench test. With the polynomial chaos expansion carried out by collocation method, the output observation function of the nonlinear pneumatic model can be transformed into a linear and time-invariant form, and the general recursive functions based on Newton method can therefore be reformulated to fit for the computer programming and calculation. To improve the estimation accuracy, the Newton method is modified with reference to Simulated Annealing algorithm by introducing the Metropolis Principle to control the fluctuation during the estimation process and escape from the local minima.