Dynamic modelling and stability analysis of articulated frame steer vehicles

Crack kinking in brittle materials

This study presents a seven degree of freedom, dynamic model for a two-axle vehicle which is used to analyse the influence of road profile on the vehicle's rollover capabilities and ride characteristics. Non-linear elements are included due to the air suspension featured in the vehicle. Road roughness is represented as a Power Spectral Density (PSD) function acting as an exciting force on the unsprung masses of the seven degree of freedom model, and solved numerically for both rollover simulation and lane change manoeuvre. Results indicate that road surface does have a significant impact in a vehicle's performance since it may prompt the vehicle to flip over below its rollover threshold.

Because of the complexity of vehicle steering motion, the classical linear two degrees of freedom lateral dynamics model of vehicle has been unable to meet well the research needs of the active steering control system. In order to make better use of the chassis control technology to improve the safety when vehicle turning and the vehicle-handling stability at high speeds, it is necessary to establish a more complex new dynamic model which not only fully reflect the steering characteristics of the vehicle, but also meet the needs of the control system design. In this paper, the active four-wheel steering vehicle is regarded as the research object; the modeling method of a eight degrees of freedom nonlinear dynamics model of this active four-wheel steering vehicle is discussed based on the comprehensive analysis of kinetic and kinematic; the differential equations for each degree of freedom of motion are derived step by step; and the modeling and solving methods are also illustrated by means of the Simulink software. In addition, the model accuracy is also verified effectively by contrast with ADAMS vehicle multi-body dynamics model. Verification results show that the established model has a relatively high accuracy and can be applied to the research and analysis for different active chassis control systems of the vehicle.

Hybrid pump-controlled asymmetric cylinder drive systems are implemented for energy saving purposes in applications that do not require fast responses. Under low-velocity and low-pressure conditions, the friction influence in the hybrid pump-controlled system is evident. Researchers have developed various models to describe friction. These friction models are implemented based on the relative motion of the contact surfaces, and they can be categorized into static friction and dynamic friction models. For example, dynamic friction models are suitable for simulating the friction in hydraulic cylinder seals under lubrication conditions. Among the dynamic models, the LuGre model can capture almost all static and dynamic friction behaviors at the macroscopic level; for example, stiction, the Stribeck effect, and hysteresis. Thus, the LuGre model is suitable for describing the friction in hydraulic cylinders. Because the friction force in the hydraulic cylinder is mainly from the cylinder seal and seal deformation occurs under pressure due to its flexibility, the friction in a hybrid pump-controlled hydraulic system is affected by the relative motion of the contact surfaces. Therefore, to investigate factors that affect the friction other than the relative motion of the contact surfaces, the friction behaviors of a hybrid pump-controlled hydraulic system are studied. Pressure difference and acceleration terms are introduced in the LuGre friction model, and the simulated friction results of the updated LuGre model are compared with the measured experimental results to validate the new friction model.

Aiming at the issue of inaccurate design of multistage spiral pair structures due to the inaccuracy of the traditional transmission efficiency calculation formula for double-screw swinging hydraulic cylinders, which are used in steering gear, a new transmission efficiency calculation formula for these cylinders is proposed through mathematical modeling and dynamic analysis. Corresponding flexible dynamic and rigid dynamic simulation models of the double-screw swinging hydraulic cylinder are established to investigate the output characteristics, load startup characteristics, and maximum torque of the spiral pair. The accuracy of the flexible dynamic model and the rigid dynamic model is compared, and an experimental validation is conducted using a hydraulic test bench. The following conclusions are drawn: the calculation accuracy of the new transmission efficiency formula is improved by 21% compared to the traditional formula; under rated load pressure, the output torque accuracy of the flexible dynamic simulation model is improved by 55%. The flexible dynamic simulation model's closer alignment with experimental results proves its necessity. The research offers new simulation tools and a theoretical basis for the development of high-precision efficiency prediction models, holistic design, and optimization of double-helical oscillating hydraulic cylinders for underwater equipment.

This is the third in a series of four papers (Parts 1 to 4) looking at the application of computer-based analysis methods to model vehicles and simulate vehicle handling. The material contained in these papers is based on a study carried out in order to investigate the influence of suspension and tyre modelling on the outputs predicted by vehicle handling simulations. The papers deal with analysis methods, vehicle modelling (both in the previous Issue), tyre modelling and handling simulation. In this paper an overview of the use of tyre models in vehicle dynamics is provided. This is followed by a more detailed description of three tyre modelling approaches that can be used for handling simulations. A description is also provided of a computer-based modelling system where FORTRAN routines represent the various models and a computer model of a tyre test rig is used to interrogate the models and data before integrating these into a full vehicle handling simulation. The use of this system to compare the accuracy of the tyre models under consideration is also presented. The examples used to illustrate the concepts explained throughout this series of papers have been generated using the ADAMS (Automatic Dynamic Analysis of Mechanical Systems) program.

In this paper, a robust tracking control problem for underactuated underwater vehicles in horizontal motion is investigated. The presented control scheme that performs the trajectory tracking task is a combination of the backstepping technique and the integral sliding mode control method using the inertial quasi velocities (IQVs) resulting from the inertia matrix decomposition. Unlike many known solutions, the proposed approach allows not only trajectory tracking, but also, due to the fact that IQV includes dynamic and geometric model parameters, allows us to obtain additional information about changes in vehicle behavior during movement. In this way, some insight into its dynamics is obtained. Moreover, the control strategy takes into account model inaccuracies and external disturbances, which makes it more useful from a technical point of view. Another advantage of this work is to indicate problems occurring during the implementation of trajectory tracking in algorithms with a dynamics model containing a diagonal inertia matrix, i.e., without inertial couplings. The theoretical results are illustrated by simulation tests conducted on two models of underwater vehicles with three degrees of freedom (DOF).

It is shown how a formally exact classical analog can be defined for a finite dimensional (in Hilbert space) quantum mechanical system. This approach is then used to obtain a classical model for the electronic degrees of freedom in a molecular collision system, and the combination of this with the usual classical description of the heavy particle (i.e., nuclear) motion provides a completely classical model for the electronic and heavy particle degrees of freedom. The resulting equations of motion are shown to be equivalent to describing the electronic degrees of freedom by the time-dependent Schrödinger equation, the time dependence arising from the classical motion of the nuclei, the trajectory of which is determined by the quantum mechanical average (i.e., Ehrenfest) force on the nuclei. Quantizing the system via classical S-matrix theory is shown to provide a dynamically consistent description of nonadiabatic collision processes; i.e., different electronic transitions have different heavy particle trajectories and, for example, the total energy of the electronic and heavy particle degrees of freedom is conserved. Application of this classical model for the electronic degrees of freedom (plus classical S-matrix theory) to the two-state model problem shows that the approach provides a good description of the electronic dynamics.

Recursive subdivision schemes have been extensively used in computer graphics and scientific visualization for modeling smooth surfaces of arbitrary topology. Recursive subdivision generates a visually pleasing smooth surface in the limit from an initial user-specified polygonal mesh through the repeated application of a fixed set of subdivision rules. In this paper, we present a new dynamic surface model based on the Catmull-Clark (1978) subdivision scheme, which is a very popular method to model complicated objects of arbitrary genus because of many of its nice properties. Our new dynamic surface model inherits the attractive properties of the Catmull-Clark subdivision scheme as well as that of the physics-based modeling paradigm. This new model provides a direct and intuitive means of manipulating geometric shapes, a fast, robust and hierarchical approach for recovering complex geometric shapes from range and volume data using very few degrees of freedom (control vertices). We provide an analytic formulation and introduce the physical quantities required to develop the dynamic subdivision surface model which can be interactively deformed by applying synthesized forces in real time. The governing dynamic differential equation is derived using Lagrangian mechanics and a finite element discretization. Our experiments demonstrate that this new dynamic model has a promising future in computer graphics, geometric shape design and scientific visualization.

The dynamic model of a counterbalance forklift truck is established, and the validations under various operational conditions are studied. The roll motion of the counterbalance forklift is expressed by four degrees of freedom with consideration given to the independent roll motion between the body and chassis, the variation of the roll axis, and the contact between the body limit block and rear axle. Furthermore, testing under turning on firm ground and driving over obstacle conditions are conducted for verifying the dynamic response characteristic of the established model. In addition, numerical simulations are performed to investigate the effect of forklift structural parameters and road roughness excitation on the roll dynamics of forklifts. Finally, the rationality of evaluating the forklift roll state by load transfer ratio (LTR) is discussed. Simulation results are well in harmony with experiment results, suggesting that the proposed dynamic model can be an effective tool for stability analysis of counterbalance forklift trucks. This work provides theoretical foundations for the development of improved anti-rollover control, ultimately leading to enhanced stability and safety of forklifts.

This paper introduces an efficient and flexible hair modeling method to develop intricate hairstyle dynamics. A prominent contribution of the present work is that it proposes an evaluation approach for the spring coefficient, i.e., spring coefficient can be obtained through a combination of the large deflection deformation model and spring hinge model. This is based on the fact that there is a directly proportional relationship between the spring coefficient and stiffness coefficient, a variable determined by hair shape. What is more, the damping coefficient is no longer regarded as a constant, but a function of hair density, and this treatment has turned out to be successful in solving the problem of hair-hair collision. As a result, a dynamic model, which fits a great variety of hairstyles, is proposed.

Mathematical modeling of Electric vehicles - A survey

The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-geostrophic, baroclinic flow is investigated. Period-doubling cascades and Shil'nikov bifurcations lead to chaos in this model. The low dimension of the chaotic attractor suggests the possibility to reduce the model to three degrees of freedom. In a physically comprehensible limit of the parameters this reduction is done explicitly. The bifurcation diagram of the reduced model in this limit is compared to the diagram of the six degrees of freedom model and agrees well. A numerical implementation of the graph transform is used to approximate the three-dimensional invariant manifold away from the limit case. If the six-dimensional model is reduced to a linearisation of the invariant manifold about the Hadley state, the Lorenz-84 model is found. Its parameters can then be calculated from the physical parameters of the quasi-geostrophic model. Bifurcation diagrams at physical and traditional parameter values are compared and routes to chaos in the Lorenz-84 model are described.

The present paper investigates the aerodynamic performances variations of straight-blades DARRIEUS wind turbine in two-dimensional steady flow with different low Reynolds numbers (30k, 40k, 55k and 80k). The numerical 6DOF approach (six degrees of freedom) is used to predict sequentially the angular positions according to the wind turbine mass properties (mass and moment of inertia) in real time. The numerical optimization requires a transient dynamic mesh technique for one degree of freedom around the rotation axis. The self-starting ability of the H-Darrieus wind turbine is expressed by increasing the inlet wind velocity, independently to the wind direction (angles of attack: 0°, 10°, and 20°). A 2D unsteady shear stress transport (SST k- ω) model has been employed to perform the present simulation. The various results of performance coefficients (lift and torque) obtained by a two blades design show a significant agreement with the available experimental data, as well as, an important increase in lift and torque according to the increase of the free stream wind velocity. However, the static stall still at the same azimuthal position (about 11°). That is a consequence of the appropriate modelling of the rotational speed, as well as, the stability that characterizes the 6DOF approach. The tangential force is maximum (wind turbine acceleration), where the blades axis are normal to the velocity field, and neglected at the braking position 0°.

With the development of the global automotive industry, environmental pollution and driving safety have been major problems. This paper focuses on a novel integrated cooperative antilock braking system (ABS) controller, which is used for antilock regenerative braking systems (ARBS) and antilock mechanical braking systems (AMBS) for hybrid electric vehicles (HEV) driving on different road surfaces. An intelligent tire system is utilized to detect varying road surfaces to obtain friction information and optimal operation slip ratio. In addition, the HEV eight‐degree‐of‐freedom dynamics model is developed for ABS control, which includes the LuGre tire model. Adaptive backstepping and finite state machine controllers are explored to maintain optimal wheel slip and regenerate energy, based on wheel slip, battery state of charge (SOC), motor capability torque, and vehicle velocity, and to develop the switching rules of regenerative and mechanical braking systems. In order to evaluate the performance of regenerative and mechanical braking systems on harvesting energy and driving safety, the HEV and LuGre dynamic tire models are developed in MATLAB SIMULINK /SimDriveline. The estimation results of different road surfaces and slip controller effects are tested via the experiments and simulations, finding good braking performances and high regenerative efficiency in different maneuvers.