Degrees Of Freedom Vehicle Model Research Articles

Effect of suspension kinematic on 14 DOF vehicle model

Computer simulations play a major role in shaping modern science and engineering. They reduce time and resource consumption in new studies and designs. Vehicle simulations have been studied extensively to achieve a vehicle model used in minimum lap time solution. Simulation result accuracy depends on the abilities of these models to represent real phenomenon. Vehicles models with 7 degrees of freedom (DOF), 10 DOF and 14 DOF are normally used in optimal control to solve for minimum lap time. However, suspension kinematics are always neglected on these models. Suspension kinematics are defined as wheel movements with respect to the vehicle body. Tire forces are expressed as a function of wheel slip and wheel position. Therefore, the suspension kinematic relation is appended to the 14 DOF vehicle model to investigate its effects on the accuracy of simulate trajectory. Classical 14 DOF vehicle model is chosen as baseline model. Experiment data is collected from formula student style car test runs as baseline data for simulation and comparison between baseline model and model with suspension kinematic. Results show that in a single long turn there is an accumulated trajectory error in baseline model compared to model with suspension kinematic. While in short alternate turns, the trajectory error is much smaller. These results show that suspension kinematic had an effect on the trajectory simulation of vehicle. Which optimal control that use baseline model will result in inaccuracy control scheme.

Energy harvesting from suspension system and self-powered vibration control for a seven degree of freedom vehicle model

Traditionally, a quarter-car model and a sky-hook controller are employed to derive analytical expressions that describe conditions for self-powered operation. The main contribution of this work consists in using a seven degree of freedom vehicle model to determine numerically the condition for self-powered operation of an active suspension system with electromagnetic actuators. The performance of proportional–integral–derivative, linear quadratic regulator, and fuzzy Logic suspension controllers that employ feedback information for heave, pitch, and roll motion is evaluated under self-powered operation. An objective function consisting of a weighted sum of performance measures, including root mean square values for accelerations, road holding, actuator travel, and power regeneration capability, is used to determine equivalent actuator damping values and controller gains that enhance self-powered operation. The resulting optimal designs for each control strategies are compared by means of frequency responses to evaluate their performance and power regeneration capability, as well as to determine the effect of self-powered operation on these characteristics. This investigation shows that the performance of a self-powered active suspension systems, based on heave, pitch, and roll motion information, can be optimized to approach that of an active suspension system with external power supply; the degree of degradation depends on the particular suspension controller and the design objectives that are adopted. The performance improvement compared to a suspension system designed using a quarter car model and a sky-hook controller is also presented.

Sliding Mode Direct Yaw-Moment Control Design for In-Wheel Electric Vehicles

The direct yaw-moment control system can significantly enhance vehicle stability in critical situations. In this paper, the direct yaw-moment control strategies are proposed for in-wheel electric vehicles by using sliding mode (SM) and nonlinear disturbance observer (NDOB) techniques. The ideal sideslip angle at the center of gravity and the yaw rate are first calculated based on a linear two degree of freedom vehicle model. Then, the actual sideslip angle is identified and estimated by constructing a state observer. On this basis, a traditional discontinuous SM direct yaw-moment controller is designed to guarantee that the sideslip angle and the yaw rate will approach the ideal ones as closely as possible. To tackle the chattering problem existing in the traditional SM controller, a second-order sliding mode (SOSM) controller is further designed by taking the derivative of the controller as the new control, which implies that the actual control can be an integration of the SOSM controller. Finally, to avoid the large gains in the derived controllers, by combining the NDOB with the derived controllers, the composite control schemes are also proposed. In comparison with the discontinuous first-order SM controller, the proposed SOSM controller is shown to be more effective.

Study on mixed H2/H∞ robust control strategy of four wheel steering system

Four wheel steering (4WS) technology can effectively improve the vehicle handling stability and driving safety. In order to fully consider the influence of the rear wheel steering, the vehicle dynamics model of 4WS vehicle, including the rear wheel steering by wire and two degrees of freedom vehicle model of 4WS vehicle, is established in this paper. The desired yaw rate is obtained according to the variable transmission ratio strategy. The yaw rate tracking strategy is applied to 4WS vehicle and rear wheel steering resistance moment is taken into account. Based on the robust control theory, H2/H∞ mixed robust controller design is carried to research the stability control of 4WS vehicle. Finally, the closed-loop simulation added driver model based on preview theory is carried out. The simulation results indicate that the designed H2/H∞ mixed robust controller can achieve the stability control.

Improvement of vehicle ride comfort using genetic algorithm optimization and PI controller

In this paper a MATLAB SIMULINK model of seven Degrees Of Freedom (DOF) full vehicle model is developed. Mathematical equations are obtained using Newton’s second law and free body diagram concept. Validation of the SIMULINK model is obtained to ensure that the model is suitable for studying the ride comfort. A Genetic algorithm optimization technique is used to find the optimum values of spring stiffness and damping coefficient for front and rear passive suspension system of the seven DOF vehicle model at variable velocities which improve the performance of the suspension system of the vehicle. Also Proportional Integral (PI) controller is implemented to the model to study its effect on ride comfort. Comparison of the results for body acceleration and sprung mass displacement of the optimized data of suspension parameters and model with PI controller are illustrated. The results show that the optimized parameters and PI controller give significant improvements of the vehicle ride performance over the passive suspension system.

Nonlinear dynamic analysis of a parametrically excited vehicle–bridge interaction system

In this paper, a nonlinear supported Euler–Bernoulli beam under harmonic excitation coupled to a 2 degree of freedom vehicle model with cubic nonlinear stiffness and damping is investigated. The equations of motion are derived by Newton’s law and discretized into a set of coupled second-order nonlinear differential equations via Galerkin’s method with cubic nonlinear terms. Based on the created model, numerical simulations have been conducted using the Runge–Kutta integration method to perform a parametric study on influences of the nonlinear support stiffness coefficient, mass ratio, excitation amplitude and position relation for the vehicle–bridge interaction (VBI) system by using bifurcation diagram and 3-D frequency spectrum. The results indicate that depending on different parameters, a diverse range of periodic motion, quasi-periodic response, chaotic behavior and jump discontinuous phenomenon are observed. And the chaotic regions are scattered between a number of periodic/quasi-periodic motions. The study may contribute to a further understanding of the dynamic characteristics and present useful information to dynamic design and vibration control for the VBI system.

Research on Heavy Truck Dynamic Load Coefficient and Influence Factors

In order to research the vehicle dynamic load coefficient(DLC) and influence factors, high class and low class pavement roughness is tested in fields, 2 degree of freedom vehicle model is built, DLC computing formula is given. Heavy truck is taken as an example, the relationship among DLC and traffic speed, vibrating frequency, loading mass are analyzed. The results show that resonation frequency of heavy truck is about 1HZ and 12HZ, the DLC increases with the increase of traffic speed while decreases with the increase of the loading. The relationship between DLC and travel speed(V) can be described as DLC=0.0047V0.5 for high class road and DLC=0.0102V0.5 for low class road

Vehicle dynamics control using an active third-axle system

This paper introduces the active third-axle system as an innovative vehicle dynamic control method. This method can be applicable for different kinds of three-axle vehicles such as buses, trucks, or even three-axle passenger cars. In this system, an actuator on the middle axle actively applies an independent force on the suspension to improve the handling characteristics, and hence, its technology is similar to slow-active suspension systems. This system can change the inherent vehicle dynamic characteristics, such as under/over steering behaviour, in the linear handling region, as well as vehicle stability in the nonlinear, limit handling region. In this paper, our main focus is to show the potential capabilities of this method in enhancing vehicle dynamic performance. For this purpose, as the first step, the proposed method in both linear and nonlinear vehicle handling regions is studied mathematically. Next, a comprehensive, nonlinear, 10 degrees of freedom vehicle model with a fuzzy control strategy is used to evaluate the effectiveness of this system. The dynamic behaviour of a vehicle, when either uncontrolled or equipped with the active third axle is then compared. Simulation results show that this active system can be considered as an innovative method for vehicle dynamic control.

Quasi-steady-state linearisation of the racing vehicle acceleration envelope: a limited slip differential example

In the motorsport environment, passive limited slip differentials are a well-established means of improving the traction limitation imposed by the open differential. Torque sensing types are highly adjustable, and can alter both the stability and agility of the vehicle in the various cornering phases of a typical manoeuvre. In this paper, an adjustable clutch plate or ‘Salisbury’ differential model is presented, which can significantly alter its torque bias characteristics through adjustments in the drive/coast ramp angle, the number of friction faces and preload. To allow robust evaluation of differential parameter changes on ultimate vehicle performance and handling balance, a unified acceleration or ‘GG’ diagram framework is then described. This builds on traditional GG diagram approaches, by using nonlinear constrained optimisation to define both the vehicle acceleration limits and a ‘feasibility’ region within the performance envelope. By linearising a seven degrees of freedom vehicle model at multiple operating points, eigenvalue and yaw rate response analysis is then used to establish contours of stability and agility throughout the GG envelope. This brings new insights into the way in which handling balance changes below and up to the vehicle's acceleration limits.

Study of Vehicle Handling Stability Based on MATLAB

In this paper, the sideslip angle and yaw velocity as parameters are presented to describing the motion state of the motion state of the vehicle, in which two DOF(degree of freedom) vehicle model is used as the reference model. And car speed is considered as the system step input to building a three DOF vehicle model based on H.B. Pacejka’s tire model. Meanwhile, the sideslip angle and the yaw velocity are taken as the system outputs. And achieve simulated analysis of vehicle handing stability by using Simulink. The results show that the three DOF vehicle model is more accurate in description of transport condition, which provides reference for the study of the vehicle steering stability.

Identification of tire forces using Dual Unscented Kalman Filter algorithm

Nowadays, application of active control systems in vehicles has been developed in order to increase safety and steerability. In these systems, using an appropriate dynamic model can be very effective in increasing the accuracy of simulations and analysis. Tire-road forces are crucial in vehicle dynamics and control since they are the only forces that a vehicle experiences from the ground and have maximum uncertainty on vehicle dynamic model. In order to simulate the non-linear regimes of vehicle motion, the ‘Pacejka’ tire model is being utilized. In this paper, a dynamic model with Dual Unscented Kalman Filter algorithm has been utilized to identify the lateral forces, side slip angle, and normal forces of tires. In order to solve the non-linear least squares problem, these parameters were given as input to the hybrid Levenberg–Marquardt and quasi Newton algorithm to find the Pacejka tire model coefficients in the offline mode. Four degrees of freedom vehicle model combined with Pacejka tire model are used for simulation in various maneuvers. Results show appropriate compatibility with CarSim software.

Parameter Analysis of Vehicle-Bridge Coupling of Half through CFST Arch Bridge due to Vehicle

As a new structure type, arch bridge of concrete filled steel tube (CFST) has many merits and unique dynamic characteristics. Some present researches indicate that the CFST arch bridge has obvious impact effect, but the research on its dynamic performance due to vehicle is relative backward. In this paper, power spectral density function is selected to simulate the roughness of pavement, the dynamic equation of vehicle-bridge is built with seven degrees of freedom vehicle model. Based on separated iterative method, the parameters’ influence of CFST arch bridge on dynamic performance due to vehicle is carried out systematically. The analysis results are useful and helpful for the design theory of impact effect of CFST arch bridge.

Vehicle Collision Avoidance Maneuvers With Limited Lateral Acceleration Using Optimal Trajectory Control

In this paper, the possibility of performing severe collision avoidance maneuvers using trajectory optimization is investigated. A two degree of freedom vehicle model was used to represent dynamics of the vehicle. First, a linear tire model was used to calculate the required steering angle to perform the desired evasive maneuver, and a neighboring optimal controller was designed. Second, direct trajectory optimization algorithm was used to find the optimal trajectory with a nonlinear tire model. To evaluate the results, the calculated steering angles were fed to a full vehicle dynamics model. It was shown that the neighboring optimal controller was able to accommodate the introduced disturbances. Comparison of the resultant trajectories with other desired trajectories showed that it results in a lower lateral acceleration profile and a smaller maximum lateral acceleration; thus the time to perform an obstacle avoidance maneuver can be reduced using this method. A simulation case study of a limited lateral acceleration with constrained direct trajectory optimization shows that using the proposed trajectory optimization technique requires less time than that of trapezoidal acceleration profile for a lane change maneuver.

Design and simulation of the sliding mode controller for the vehicle blow-out process control

During vehicle driving process, the tyre security is very important, but the blow-out is inevitable sometimes, so it is very necessary to control the vehicle stability in order to avoid serious traffic accidents caused by the blowout. In this paper, with the tyre brush model and the seven degree of freedom vehicle model, the vehicle driving system model is modelled, and the front and rear tyres blow-out process was simulated and analysed. The results show that the vehicle will become unstable after the blow-out. In order to ensure the vehicle back to the stable range, the sliding mode controller is designed with the differential braking method, and the yaw rate is controlled by adjusting the braking torque at the opposite side of the blow-out tyre. With simulation, the sliding mode controller can guarantee the vehicle stability, shorten the braking distance and realise the safety brake during the tyre blow-out process.

Simulation of sloshing in tank trucks

Tank trucks dynamics can get worse because of fluid sloshing in partially filled tanks. During braking manoeuvres, fluid sloshing may lead to load transfers causing rear wheels to lock up and loss of directional control, while during turning or lane changes, it may cause rollover. In this paper, a methodology for evaluating the interaction between fluid sloshing and vehicle dynamics is proposed. The fluid and the tank are modelled using the computational fluid dynamics code FLUENT, based on the Navier-Stokes equations and incorporating the Volume of Fluid (VOF) and the moving mesh techniques. The motion of the tank is determined based on the response of a 14 degrees of freedom vehicle model subjected to the forces due to the fluid sloshing. Straight line braking manoeuvres and lane change manoeuvres have been carried out to evaluate the effects of fill level, baffles and tank shape.

Application of Error Analysis Method in the Complex Vehicle Model

A two degree of freedom input vehicle model is set up. Based on driver modeling analytical method of error analysis, step signal is taken as the input of steering angle to complex vehicle model based on CarSim, vehicle lateral acceleration is taken as as output. Meanwhile, the same steering wheel angle is taken as input as equivalent two degrees of freedom vehicle model, vehicle model parameters are optimized based on the minimum objective function. The results show that, in the same kind of speed, for steering wheel angle step input and sinusoidal input , when the input amplitude increases, the equivalent accuracy of the complex vehicle model and two degrees of freedom vehicle model will be reduced.

Influences of the Front Wheel Steering Angle on Vehicle Handling and Stability

In this paper, motion differential equation of the two degrees of freedom (2-DOF) vehicle is established based on the linear two degrees of freedom vehicle model and is derived without simplifying the front wheel steering angle (FWSA), then we analyze the vehicle's steady-state response , transient response and the amplitude-frequency characteristic of yaw velocity under different FWSA with the help of the matlab software and finally compare the results with the simplified ones to determine how the FWSA influences the level of the vehicle handling and stability (VHS). The results show that: while the FWSA is small, it has a less influence on vehicle handling and stability, the FWSA is large, it has a greater influence on vehicle handling and stability.

경사진 노면에서의 차량의 종 속도 추정

Abstract : On-line and real-time information of the longitudinal velocity is the essential factor for the Advanced Vehicle Control Systems such as ABS(Anti-lock Brake System), TCS(Traction Control System), ESC(Electronic Stability Control) etc. However, the longitudinal velocity cannot be easily measured or calculated during braking maneuvering. A new algorithm is presented for the estimation of the longitudinal velocity with the measurements of the vehicle longitudinal/lateral acceleration, steering angle and yaw rate. The algorithm is designed utilizing the Extended Kalman Filter based on the 3 degree of freedom vehicle model. In order to compensate for the biased sensor signal on the inclined road, the inclined angle is also estimated. The performance of the proposed estimation algorithm is evaluated in field tests. Key words : Longitudinal velocity(종 속도), Inclined angle estimation(경사각 추정), Longitudinal acceleration compensation(종 가속도 보정), Extended kalman filter(확장된 칼만필터) Nomenclature

Modeling and Simulation of Electric Power Steering System Based on Multi-Body Dynamics

In order to analyze dynamic characteristic accurately during steering, electric power steering system is selected as research object and dynamic equation of steering system is established. Combined with eleven degrees of freedom vehicle model and tire model at combined conditions of longitudinal slip and side slip, the integral-simulation model of electric power steering system is established. The dynamic response of steering system at different steering wheel angle, control methods, front wheel steering angle and braking force is analyzed. The simulation results show that electric power steering system with neural network control has good stability, tracking performance, assist characteristic and anti-interference ability. The established model can reflect the dynamic characteristic correctly and effectively during steering.

Torque distribution influence on tractive efficiency and mobility of off-road wheeled vehicles

Off-road vehicle performance is strongly influenced by the tire-terrain interaction mechanism. Soft soil reduces traction and significantly modifies vehicle handling; therefore tire dynamics plays a strong role in off-road mobility evaluation and needs to be addressed with ad-hoc models. Starting from a semi-empirical tire model based on Bekker–Wong theory, this paper, analyzes the performance of a large four wheeled vehicle driving on deformable terrain. A 14 degree of freedom vehicle model is implemented in order to investigate the influence of torque distribution on tractive efficiency through the simulation of front, rear, and all wheel drive configuration. Results show that optimal performance, regardless vertical load distribution, is achieved when torque is biased toward the rear axle. This suggests that it is possible to improve tractive efficiency without sacrificing traction and mobility. Vehicle motion is simulated over dry sand, moist loam, flat terrain and inclined terrain.