Mathematical Models of Tire-Lateral Road Adhesion for Use in Road Vehicle Dynamics Studies

Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.

Mathematical Models of Tire-Longitudinal Road Adhesion and Their Use in the Study of Road Vehicle Dynamics

Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.

Vehicle Dynamics Modeling and Simulation for ACC

A 7 degree-of-freedom （DOF） 4 wheels vehicle dynamics model based on Matlab-Simulink is established,and 7 DOF vehicle dynamics equations in the form of nonlinear state-space standards are given.The characters of the electronic throttle and the active braking system have been analyzed.And the electronic throttle model and the active braking system model are built according to the test results respectively.Off-line simulation results indicate that the model is suitable for the vehicle adaptive cruise control system,and both of the electronic throttle and the active braking system work in a reasonable way.An adaptive cruise control （ACC） example illustrates that the model has a good performance in cruise and distance keeping.

Dynamics Modeling and Simulation of Autonomous Underwater Vehicles with Appendages

To provide a simulation system platform for designing and debugging a small autonomous underwater vehicle＇s （AUV） motion controller, a six-degree of freedom （6-DOF） dynamic model for AUV controlled by thruster and fins with appendages is examined. Based on the dynamic model, a simulation system for the AUV＇s motion is established. The different kinds of typical motions are simulated to analyze the motion performance and the maneuverability of the AUV. In order to evaluate the influences of appendages on the motion performance of the AUV, simulations of the AUV with and without appendages are performed and compared. The results demonstrate the AUV has good maneuverability with and without appendages.

Modeling and Simulation of Automatic Berthing based on Bow and Stern Thruster Assist for Unmanned Surface Vehicle

In order to solve the technical problems of autonomous berthing of the Unmanned Surface Vehicle(USV),this research has met the requirements of maneuverability berthing under different conditions by effectively using the bow and stern thrusters,which is a technological breakthrough in actual production and life.Based on the MMG model,the maneuverability mathematical model of the USV with bow and stern thruster was established.And the motion simulation of USV maneuvering was carried out through the numerical simulation calculation.Then the berthing plan was designed based on the maneuverability analysis of the USV low-speed motion,and the simulation of automatic berthing for USV was carried out.The research results of this paper can be of certain practical significance for the USV based on the support of the bow and stern thruster in the berthing.At the same time,it also provides a certain theoretical reference for the handling of the USV automatic berthing.

Model-Based Approach to Investigate the Influences of Different Load States to the Vehicle Dynamics of Light Electric Vehicles

The need to find alternative urban mobility solutions for delivery and transport has led mobility companies to devote enormous resources for research-based solutions to increase vehicle safety. This paper documents a virtual approach to investigate the influences of different load states to the vehicle dynamic of light electric vehicle. A model basing on a three-dimensional multibody system was used, which consists of five bodies. By applying methods of multibody modelling the generalized equations of motion were generated. To include the behavior within the contact point between road and vehicle a simplified tire models was added. The implementation of the equations allowed a first validation of the model via simulations. In a final modeling step the simulation results were interpreted in respect of plausibility. Afterwards, the model was simulated numerically to investigate different load states of the vehicle, by applying constant steering stimuli and variable velocities. In sum, the investigated model approach is useful to identify safety relevant parameters and shows the effects of load states to the vehicle dynamics. Furthermore, it behaves plausibly regarding general vehicle dynamics. These results prove the general usability of the model for the development controllers and estimators in driver assistances systems.

Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation

The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.

Stochastic dynamic simulation of railway vehicles collision using data-driven modelling approach

Using stochastic dynamic simulation for railway vehicle collision still faces many challenges,such as high modelling complexity and time-consuming.To address the challenges,we introduce a novel data-driven stochastic process modelling(DSPM)approach into dynamic simulation of the railway vehicle collision.This DSPM approach consists of two steps:(i)process description,four kinds of kernels are used to describe the uncertainty inherent in collision processes;(ii)solving,stochastic variational inferences and mini-batch algorithms can then be used to accelerate computations of stochastic processes.By applying DSPM,Gaussian process regression(GPR)and finite element(FE)methods to two collision scenarios(i.e.lead car colliding with a rigid wall,and the lead car colliding with another lead car),we are able to achieve a comprehensive analysis.The comparison between the DSPM approach and the FE method revealed that the DSPM approach is capable of calculating the corresponding confidence interval,simultaneously improving the overall computational efficiency.Comparing the DSPM approach with the GPR method indicates that the DSPM approach has the ability to accurately describe the dynamic response under unknown conditions.Overall,this research demonstrates the feasibility and usability of the proposed DSPM approach for stochastic dynamics simulation of the railway vehicle collision.

Study on Simulation of Remotely Operated Underwater Vehicle Spatial Motion

In order to analyze the spatial maneuverability of the remotely operated underwater vehicle(ROV),the 6-DOF motion mathematic model of the ROV was founded.Hydrodynamics were analyzed by using the Taylor series.The thrusters on the ROV were discussed.This paper considers three cases of motion simulation:vertical motion,rotational motion and Z-shape motion.A series of simulation experiments showed that the 6-DOF motion mathematic model was correct and reliable,and also fit with the scene simulation.

Maneuverability simulation of a mini autonomous underwater vehicle

In order to simulate the under water motion of a mini autonomous underwater vehicle( AUV) and an- alyze its maneuverability,the dynamical characteristic of the mini AUV was researched. The 6-DOF motion equations were founded. Through model experiment with accessory bodies,the hydrodynamics of AUV body including resistance,main inertial and viscous hydrodynamic coefficients was obtained. The hydrodynamics of rudders was gained through theoretical calculation. Simulation computation of the vehicle was carried out through numerical integration of the motion equations. A motion simulation system was constructed. Four typical maneuvers in horizontal and vertical planes were simulated and the maneuverability of the mini AUV was forecasted. The simulation results reflect the basic motion characteristic of mini AUV and validate the feasibility and correctness of the whole system. The simulation system can be a testing platform for the design and debugging of motion controller and an effective tool for the development of AUV.

Global modeling and simulation of vehicle to analyze the inertial parameters effects

This paper mainly studies the comparison of the global vehicle models and the effects of the inertial parameters due to the center of gravity(CG)positions when we consider that the vehicle has only one CG.This paper proposes a new nonlinear model vehicle model which considers both unsprung mass and sprung mass CG.The CG positions and inertial parameters effects are analyzed in terms of the published vehicle dynamics models.To this end,two 14 degree-of-freedom(DOF)vehicle models are developed and compared to investigate the vehicle dynamics responses due to the different CG height and inertial parameters concepts.The proposed models describe simultaneously the vehicle motion in longitudinal,lateral and vertical directions as well as roll,pitch and yaw of the vehicle about corresponding axis.The passive and active moments and the forces acting on the vehicle are also described and they are considered as a direct consequence of acceleration,braking and steering maneuvers.The proposed model M1 takes both the CG of sprung mass,unsprung mass and total vehicle mass into account.The second model M2 assumes that the vehicle is one solid body which has a single CG as reported in majority of literature.The two vehicle models are compared and analyzed to evaluate vehicle ride and handling dynamic responses under braking/acceleration and cornering maneuvers.Simulation results show that the proposed model M1 could offer analytically some abilities and driving performances,as well as improved roll and pitch in a very flexible manner compared to the second model M2.

Modeling and Simulation of Diaphragm Spring Clutch

A model was developed to simulate a vehicle diaphragm spring clutch with the evaluation indicators of jerk degree and friction work.First,the pressing load characteristic of the driven plate of the diaphragm spring clutch was analyzed.Then,the clutch dynamic characteristic under each state was studied according to the basic principles of tribology.Finally,the mathematical model of the clutch was developed.Based on the model,the performance of a vehicle was simulated.The simulation results show that the model can predict the dynamic characteristic of the clutch correctly and evaluate the performance of the clutch engagement effectively.The model can be used for theoretical research of automatic clutch control and can be easily applied to simulate vehicle longitudinal dynamics.

Dynamics Modeling of Heavy Special Driving Simulator

Based on the dynamical characteristic parameters of the real vehicle, the modehng approach ancl procedure of dynamics of vehicles are expatiated. The layout of vehicle dynamics is proposed, and the sub-models of the diesel engine, drivetrain system and vehicle multi-body dynamics are introduced. Finally, the running characteristic data of the virtual and real vehicles are compared, which shows that the dynamics model is similar closely to the real vehicle system.

Modeling COVID-19 Pandemic Dynamics in Two Asian Countries

The current epidemic outbreak COVID-19 first took place in the Wuhan city of China and then spread worldwide.This deadly disease affected millions of people and compelled the governments and other concerned institutions to take serious actions.Around 0.28 million people have died from the COVID-19 outbreak as of May 11,2020,05:41 GMT,and the number is still increasing exponentially.The results of any scientific investigation of this phenomenon are still to come.However,now it is urgently needed to evaluate and compare the disease dynamics to improve the quarantine activities and the level of individual protection,to at least speed up the rate of isolation of infected persons.In the domain of big data science and other related areas,it is always of interest to provide the best description of the data under consideration.Therefore,in this article,we compare the COVID-19 pandemic dynamics between two neighboring Asian countries,Iran and Pakistan,to provide a framework to arrange the appropriate quarantine activities.Simple tools for comparing this deadly pandemic dynamic have been presented that can be adopted to produce the bases for inferences.Most importantly,a new statistical model is developed to provide the best description of COVID-19 daily deaths data in Iran and Pakistan.

Simulation of Restraint System Performance upon the Occupant's Response During Impact

Aim To study the influence of restraint system performance upon the occupant's response during impact, and provide a scientific base for occupant restraint system design. Methods \ In the light of basic theory of multibody system dynamics and impact dynamics on the basis of classical theory of impact, R W method is adopted to construct the vehicle occupant system model consisting of fourteen rigid bodies, thirty seven DOFs and slip joints for the simulation. A software named SVC3D(3 dimensional simulation of vehicle crash) is developed in the FORTRAN language. Results\ The results of simulation have a good coincidence with those of tests and the restraint system with low elongation webbing and equipped with pretensioner provides better restraint effect for the occupant. Conclusion\ The model of vehicle occupant multibody system and SVC3D are suitable for use. Occupant should be belted with low elongation webbing to a certain degree and occupant restraint system should be equipped with pretensioner.

Dynamic Modeling and Analysis of 9-DOF Omnidirectional Legged Vehicle

The omnidirectional legged vehicle with steering-rails has a specific mechanism feature, and it can be controlled flexibly and accurately in omnidirectional motion. Currently there lacks further research in this area. In this paper, the mechanical characteristics of independent walking control and steering control and its kinematics principle are introduced, and a vehicle has a composite motion mode of parallel link mechanism and steering mechanism is presented. The motion direction control of the proposed vehicle is only dependant on its steering rails, so its motion is simple and effective to control. When the relative motion between the walking and steering is controlled cooperatively, the vehicle can walk perfectly. By controlling the steering rails, the vehicle can walk along arbitrary trajectory on the ground. To achieve a good result of motion control, an equivalent manipulator model needs to be built. In terms of the mechanism feature and the kinematic principle, the simplified manipulator model consists of a rail in stance phase, a rail in swing phase, and an equivalent leg. Considering the ground surface slope during walking, a parameter of inclination angle is added. Based on such a RPP manipulator model, the equations of motion are derived by means of Lagrangian dynamic approach. To verify the dynamic equations, the motion of the manipulator model is simulated based on linear and nonlinear motion planning. With the same model and motion parameters, the dynamic equations can be solved by Matlab and the calculation data can be gained. Compared with the simulation data, the result confirms the manipulator dynamic equations are correct. As a result of such special characteristics of the legged mechanism with steering rails, it has a potential broad application prospects. The derivation of dynamics equation could benefit the motion control of the mechanism.

Dynamic Modeling and Investigation of Maneuver Characteristics of A Deep-Sea Manned Submarine Vehicle

A deep-sea Manned Submarine Vehicle （MSV） is usually required to move at a low forward speed and a low rotational speed when it executes investigation tasks. In this condition, the motion is in large drift angles, and the maneuverability hydrodynamic forces cannot be expressed properly in the conventional mathematical model of submersible motion. In this paper, firstly, a general equation of MSV with six-freedom motion is presented, and the numerical simulation of descent/ascent motion and helix motion is conducted to reveal the general maneuver characteristics of MSV. Secondly, according to the data of captive model tests of large drift angles of MSV, the regression analysis of position hydrodynamic forces and rotation hydrodynamic forces is carried out, and the results of regression analysis of maneuverability hydrody- namic characteristics are analyzed to reveal the special maneuver characteristics. Thirdly, a special new mathematical model of MSV with the whole range of drift angles motion is presented, which can be used to predict hydrodynamic performance of motion in the 0° - 180° range of drift angles. The results are applied to the design of maneuverability hydrodynamic forces, development of control system and simulator of a practical MSV.

New Model and Simulation of Condenser for Ship Nuclear Power Plant

A new reasonably perfect dynamic mathematic model has been established for condenser used in ship nuclear power plant according to its structural features and operating principle. The model has been solved by the Runge-Kutta method. And an analysis program has been developed for dynamic numerical simulation under steady operation condition, disturbance condition, and accident condition. The dynamic characteristics of condenser has been calculated and analyzed under several kinds of disturbances, and the results of calculation are in good agreement with the theoretical analysis.

Simulation-based Graphic Method for Dynamic System Modeling

The first step for engineering students to understand the practical system is to describe the system,which means to establish the mathematic model for the considered system.However,traditional mathematical modeling techniques are not readily assimilated by students,because the traditional modeling needs to obey the complicated physical laws for different engineering areas and requires a highly iterative process.In this paper,the simulation-based graphic modeling method is introduced to help students model the system and improve their performance in engineering education.The results from the questionnaire indicate that the simulation-based graphic method can help students to do the modeling of the system and improve their performance compared to the traditional ways.

Mathematical Modelling of Work of Modern Friction-Polymer Shock Absorbers and Determining the Dynamical Force during the Impact

Shock absorbers are main elements into construction of train wagons that secure protection from longitudinal forces which appear during transitional regimes of movement. Besides, development of new constructive solutions for shock absorbers is quite popular development of their working mathematical models. This paper presents modem shock absorber with elastic block made from polymer elements that increase quantity of absorbed energy. This is achieved by increasing the stiffness characteristic of polymer elastic block. The construction is relatively simple and technology used to create the construction is with more or less low price. If there is not enough elastic stiffness of the polymer block, there is a possibility for not meeting the UIC （International Union of Railways） norms for absorbed energy. Therefore, according to the mentioned characteristic, shock absorbers are divided into three groups. The mathematical model presented in this paper allows calculating the necessary elastic characteristic of the polymer block for a short time. Differential equation of movement of the shock absorber elements is presented in this paper. Force change of polymer block for various impact velocities participates in the differential equation of movement where initial velocity V0 and the current meaning of the velocity x are taken into consideration. The presented equation is solved by using program language MATLAB/Simulink by developing a simulation model.