Bond Graphs for Vehicle Dynamics

For the purposes of analyzing the stability and control properties of aircraft, automobiles, and ships, it is convenient to idealize the vehicle as a rigid body and to use a body-centered coordinate frame. A six-port bond graph is first developed which represents the nonlinear dynamics of a rigid body in a coordinate system rotating with the body. It is then shown how the graph simplifies if only lateral or longitudinal dynamics are studied. Finally, bond graphs for the type of stability studies in which the assumption of small perturbations permits linearization are shown for elementary models of automobiles and aircraft.     

Bond Graphs, Normal Modes and Vehicular Structures

Bond graph modeling techniques are used to represent the normal mode dynamic behavior of uniform Bernoulli-Euler beams. The independent beam models are then coupled together to form a distributed system structure of arbitrary complexity. The resulting overall system bond graph is shown to yield the governing state equations in a straightforward manner. Then, through proper ordering of the equations, the normal modes and frequencies of the coupled system are easily obtained

This procedure is demonstrated for a vehicle A-frame structure. In addition, the bond graph model is modified to include primary and secondary suspension dynamics.     

Transient Response Test Procedures for Measuring Vehicle Directional Control

SUMMARY

A comparative study of four different test procedures for quantifying the transient lateral response of automobiles is presented in this paper. Both full-scale testing and analysis have been used in this study. The random steering technique appears to offer several advantages over other procedures in terms of space-requirement and the amount of transient dynamics information generated, whereas the step-steering procedure is more suited to the measurement of steady-state behavior of the automobile.     

Bond Graph Assisted Models for Hydro-Pneumatic Suspensions in Crane Vehicles

SUMMARY

The high weight and critical conditions of wheel load distribution shown by crane vehicle supported on a special chassis, suggest hydro-pneumatic suspensions as most suitable so that they should replace the conventional mechanical types. The Instituto Tecnológico de Aragón, Zaragoza (Spain) in the collaboration with Industrias Luna S.A., Huesca (Spain) has been working on the analysis of hydro-pneumatic suspensions using bond graph techniques, different alternatives to their use being presented in this paper.     

Influence of Liquid Load Shift on the Dynamic Response of Articulated Tank Vehicles

SUMMARY

The influence of the lateral load shift on the dynamic response characteristics of an articulated tank vehicle is investigated assuming inviscid fluid flow conditions. A quasi-dynamic roll plane model of a partially filled cleanbore tank of circular cross-section is developed and integrated to a three-dimensional model of the articulated vehicle, assuming constant forward speed. The destabilizing effects of liquid load shift are studied by comparing the directional dynamics of the partially filled tank vehicle to that of an equivalent rigid cargo vehicle subject to steady steer input. Dynamic response characteristics demonstrate that the stability of a partially filled tank vehicle is adversely affected by the Liquid load shift The distribution of cornering forces caused by the liquid load shift yield considerable deviation of the path followed by the liquid tank vehicle. The influence of the vehicle speed on the dynamics of the liquid tank vehicle is also investigated for variations in the fill levels and fluid density.     

Large motion mountain biking dynamics

A bond graph model of a mountain bike and rider is created to develop baseline predictions for the performance of mountain bikes during large excursion maneuvers such as drops, jumps, crashes and rough terrain riding. The model assumes planar dynamics, a hard-tail (front suspension only) bicycle and a rider fixed to the bicycle. An algorithm is developed to allow tracking of a virtual tire-ground contact point for events that separate the wheels from the ground. This model would be most applicable to novice mountain bikers who maintain a nearly rigid relationship between their body and the bicycle as opposed to experienced riders who are versed in controlling the bicycle independent of the body. Simulations of a steep drop are performed for various initial conditions to qualitatively validate the predictions of the model. Results from this model are to be compared to experimental data and more complex models in later research, particularly models including a separate rider. The overarching goals of the research are to examine and understand the dynamics and control of interactions between a cyclist and mountain bike. Specific goals are to understand the improvement in performance afforded by an experienced rider, to hypothesize human control algorithms that allow riders to perform manoeuvres well and safely, to predict structural bike and body forces from these maneuvers and to quantify performance differences between hard-tail and full suspension bicycles.     

Large motion mountain biking dynamics

A bond graph model of a mountain bike and rider is created to develop baseline predictions for the performance of mountain bikes during large excursion maneuvers such as drops, jumps, crashes and rough terrain riding. The model assumes planar dynamics, a hard-tail (front suspension only) bicycle and a rider fixed to the bicycle. An algorithm is developed to allow tracking of a virtual tire-ground contact point for events that separate the wheels from the ground. This model would be most applicable to novice mountain bikers who maintain a nearly rigid relationship between their body and the bicycle as opposed to experienced riders who are versed in controlling the bicycle independent of the body. Simulations of a steep drop are performed for various initial conditions to qualitatively validate the predictions of the model. Results from this model are to be compared to experimental data and more complex models in later research, particularly models including a separate rider. The overarching goals of the research are to examine and understand the dynamics and control of interactions between a cyclist and mountain bike. Specific goals are to understand the improvement in performance afforded by an experienced rider, to hypothesize human control algorithms that allow riders to perform manoeuvres well and safely, to predict structural bike and body forces from these maneuvers and to quantify performance differences between hard-tail and full suspension bicycles.     

Dynamic Interaction of Railway Train and Bridges

SUMMARY

An analytical method for obtaining the dymanic responses of a train of locomotives moving on bridges is presented. The ratio of dynamic response to maximum static response is called the amplification factor, and its maximum absolute value minus one is called the impact. Each four-axle locomotive is modelled as a rigid body with three degrees of freedom: bounce, pitch and roll, and with a suspension system consisting of springs mounted on wheels. The locomotives are assumed to be connected by frictionless joints to form the train. The bridge is modelled as a three dimensional structure, with the masses lumped at the truss joints. All joints, including the floor beam connections, are assumed to be rigid, except those for the bracing members, which are assumed to be hinged. Vertical displacements are considered as the only dynamic degree of freedom. The mathematical formulation is described briefly, and a numerical example is given. Locomotive and truss member properties, together with stresses in some typical members, are given in the tables. The amplification factors of the responses in some typical bridge members are shown in the figures.     

Heave-Pitch-Roll Dynamics of Flexible Vehicle in Variable Velocity Run

Analysis for response statistics evaluation of a flexible vehicle travelling with variable velocity over nonhomogeneously profiled flexible track is presented with a heave-pitch-roll model. The vehicle body is idealised as a flexible member with variable cross-section, inertia, damping and stiffness distributions. The vehicle may also have variable section slender elastic attachments. Coupled dynamics with rigid body heave-pitch-roll modes and elastic bending-torsion modes of the vehicle body along with coupled bending-torsion modes of the attachments are considered. Equivalent linear suspension system characteristics are employed for developing the analysis. Numerical results are presented for an aircraft with tricycle landing gear arrangements and comparison is made with other models.     

Heave-Pitch-Roll Dynamics of Flexible Vehicle in Variable Velocity Run

Analysis for response statistics evaluation of a flexible vehicle travelling with variable velocity over nonhomogeneously profiled flexible track is presented with a heave-pitch-roll model. The vehicle body is idealised as a flexible member with variable cross-section, inertia, damping and stiffness distributions. The vehicle may also have variable section slender elastic attachments. Coupled dynamics with rigid body heave-pitch-roll modes and elastic bending-torsion modes of the vehicle body along with coupled bending-torsion modes of the attachments are considered. Equivalent linear suspension system characteristics are employed for developing the analysis. Numerical results are presented for an aircraft with tricycle landing gear arrangements and comparison is made with other models.     

Magneto-rheological suspensions for improving ground vehicle’s ride comfort,stability, and handling

ABSTRACT

A state-of-the-art discussion on the applications of magneto-rheological (MR) suspensions for improving ride comfort, handling, and stability in ground vehicles is discussed for both road and rail applications. A historical perspective on the discovery and engineering development of MR fluids is presented, followed by some of the common methods for modelling their non-Newtonian behaviour. The common modes of the MR fluids are discussed, along with the application of the fluid in valve mode for ground vehicles’ dampers (or shock absorbers). The applications span across nearly all road vehicles, including automobiles, trains, semi-trucks, motorcycles, and even bicycles. For each type of vehicle, the results of some of the past studies is presented briefly, with reference to the originating study. It is discussed that Past experimental and modelling studies have indicated that MR suspensions provide clear advantages for ground vehicles that far surpasses the performance of passive suspension. For rail vehicles, the primary advantage is in terms of increasing the speed at which the onset of hunting occurs, whereas for road vehicles – mainly automobiles – the performance improvements are in terms of a better balance between vehicle ride, handling, and stability. To further elaborate on this point, a single-suspension model is used to develop an index-based approach for studying the compromise that is offered by vehicle suspensions, using the H₂ optimisation approach. Evaluating three indices based on the sprung-mass acceleration, suspension rattlespace, and tyre deflection, it is clearly demonstrated that MR suspensions significantly improve road vehicle’s ride comfort, stability, and handling in comparison with passive suspensions. For rail vehicles, the simulation results indicate that using MR suspensions with an on-off switching control can increase the speed at which the on-set of hunting occurs by as much as 50% to more than 300%.     

Railway Vehicles with Perfect Curving Behaviour Which are Asymptotically Stable at Vanishing Speed

SUMMARY

Paper deals with the linear behaviour of a railway vehicle with any arbitrary number of wheelsets, body parts and connecting elements. A vehicle which has both perfect curving properties and asymptotical stability at vanishing speed, has to satisfy a twofold condition, indicated by Wickens in 1978. In the present paper this condition is derived in reliance upon the dimension theorem for linear mappings. How the investigation can be executed in practice, is shown for the case of a two-axled vehicle. At last the behaviour in a transition curve is discussed.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development,Validation and Comparison

SUMMARY

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Decoupled robust control of vehicular platoon with identical controller and rigid information flow

Platoon driving has potential to significantly benefit road traffic. This study presents a decoupled robust control strategy for a vehicular platoon with identical feedback controller and rigid information topology. The node dynamics of vehicle with a lower-level controller is assumed to be covered by a multiplicative uncertainty model. The vehicular platoon control system is skillfully decomposed into an uncertain part and a diagonal system by applying linear transformation and eigenvalue decomposition on information flow graph. Then the requirements of robust stability and distance tracking error are equivalent to the H-infinity norm of decoupled sub-systems. Comparative simulations with a non-robust controller and different communication topologies are conducted to demonstrate the robust stability and distance tracking performances of the proposed method.     

A Modular Computer Model for the Design of Vehicle Dynamics Control Systems1

SUMMARY

This paper describes a multiport approach to computer-aided modeling of vehicle dynamics. The modeling approach produces models that are suitable for the interactive design and evaluation of complex control strategies. The vehicle model which can be used for ride and handling analysis, is built from modular components. The components are programmed using the syntax of the computer aided control system design (CACSD) program EASYS. Seven modeling components are used to create a three-dimensional vehicle dvnamics model. The model is flexible enoug-h to simulate any suspension design with revolute joints.

Each component of the model consists of a FORTRAN subroutine and a main calling module called a macro. To simplify the process of model building, the modeling components in the car model are designed to represent physical elements, such as the spring, damper, link or tire. To create a model, the components, which are represented by blocks, are interconnected through points, located on the blocks, called pons. These ports have been designed to simulate the location of the connection points between the physical elements, as observed in real systems. The construction of multibody models within a CACSD program offers the flexibility of simultaneous interactive simulation of the three-dimensional dvnamics and evaluation of the desien of the controls.

Although modeling of multibody systems using FORTRAN components has been pioneered by Chace, Haug and Orlandea; and bond graph modeling of multibody systems has been investigated by Bos, this approach is novel because:-

The model is included in the control system design program (EASYS). This arrangement allows the designer to exploit the advanced control design tools available in the program. Furthermore, this approach significantly reduces the computation time required for running the model after parameters modification.

The model is built from components that are interconnected by ports which represent the actual physical location of the connection points between the elements. The multiport approach simplifies the model building process for multibody systems. This simplification is achieved by reducing the model of a multibody system to a block diagram form.     

Multibody dynamics modelling of the freight train bogie system

Previous work in the railway technology laboratory at Virginia Polytechnic Institute and State University (Virginia Tech) focused on better capturing the dynamics of the friction wedge, modelled using three-dimensional rigid body dynamics with unilateral contact conditions. The current study extends the previous work to a half-bogie model treated as an application of multibody dynamics with unilateral contact to model the friction wedge interactions with the bolster and the sideframe. The half-bogie model was derived using MATLAB and functions as a three dimensional, dynamic, and multibody dynamics model comprised of four rigid bodies: a bolster, two friction wedges, and a sideframe assembly. This expanded model allows each wedge four degrees of freedom: vertical displacement, longitudinal displacement (between the bolster and sideframe), pitch (rotation around the lateral axis), and yaw (rotation around the vertical axis). The bolster and the sideframe are constrained to have only the vertical degree of freedom. The geometry of these bodies can be adjusted for various simulation scenarios. The bolster can be initialised with a pre-defined yaw (rotation around the vertical axis) and the sideframe may be initialised with a pre-defined pitch/toe (rotation around the lateral axis). The results of the multibody dynamics in half-bogie model simulation are shown in comparison with results from NUCARS^®, an industry standard in train-modelling software, for similar inputs.     

Human Control of Road Vehicles

SUMMARY

This paper reviews the present state of knowledge of human control of road vehicles. Lateral and longitudinal control of motorcycles and automobiles are discussed, whenever information is available. Although knowledge has increased greatly in the last decade, the major part of this concerns lateral control and most is of an ad hoc nature. Adequate mathematical models for longitudinal motion of the vehicle are yet to be developed. Their development is a necessary step in the attainment of a complete understanding of longitudinal control.     

Dynamics of Tracked Vehicles

SUMMARY

This paper provides a brief review of the state-of-the-art of tracked vehicle dynamics, including mobility over soft terrain, ride dynamics over rough surfaces and manoeuvrability. It is found that considerable progress has been made in the development of analytical frameworks for evaluating and predicting tracked vehicle mobility over soft terrain, taking into account the characteristics of terrain response to normal and shear loading. Certain computer simulation models for tracked vehicle mobility have been gaining increasingly wide acceptance by industry and governmental agencies in product development and in procurement. It is also found that most of the research on tracked vehicle ride dynamics and manoeuvrability is confined to operations on rigid surfaces. To achieve a realistic evaluation and prediction of the dynamic behaviour of tracked vehicles in the field, the key is to have a better understanding of terrain response to dynamic vehicular loading, including its dynamic stiffness and damping. Challenges that face vehicle dynamicists in this emerging field are identified.     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

SUMMARY

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.