Marginal cost pricing of ferry transportation: a practical application

In this paper, in which the author attempts to redress the lack of attention by economists to ferry operation, a simple pricing model, based on marginal cost pricing, is developed.     

Dynamic and Vibration Analysis of a Vehicle Rear Axle System

A detailed finite element model for the rear axle system of a sport utility vehicle is developed in this investigation. The axle system is treated as a multibody system that consists of nine bodies that include the input shaft, two output shafts, the carrier and tube system, four control arms and a track bar. The rotating input and output shafts are mounted on the carrier and tube system using six bearings. The four control arms and the track bar are connected to the carrier system and the frame of the vehicle using rubber bushings. In the model developed in this investigation, three dimensional beam elements are used to develop the finite element model for the input and output axle shafts, the control arms, and the track bar. A non-conventional finite element formulation is used to develop the equations of motion of the rotating input and output shafts in order to account for the effect of their angular velocities. These equations are expressed in terms of inertia shape integrals that depend on the assumed displacement field. The inertia shape integrals are first evaluated for each finite element. The inertia shape integrals of the rotating shafts are obtained by assembling the inertia shape integrals of its finite elements using a standard finite element assembly procedure. A conventional finite element formulation is used for the control arms and the track bar. The model developed in this investigation includes the effect of the bearing stiffness, the effect of the stiffness of the helical springs of the suspension system, and the effect of the stiffness of the tires. Using the Lagrangian dynamics and the finite element method, the equations of motion of the axle system are developed and expressed in terms of the nodal coordinates of the shafts, the control arms and the track bar as well as the degrees of freedom of the carrier. This finite dimensional model is used to determine the mode shapes and the natural frequencies of the axle system. The discrepancies between several of the natural frequencies predicted using the dynamic model developed in this investigation and natural frequencies determined experimentally are found to be less than 2%. A parametric study is performed in order to investigate the effect of the axle system parameters on the natural frequencies and mode shapes. Using the modal transformation, a set of differential equations of motion of the axle system is developed and used to examine the system dynamics under given loading conditions. The solutions of the resulting equations of motion are obtained using numerical methods.     

Effect of Frame Compliance on the Lateral Dynamics of Motorcycles

The lateral dynamics of an uncontrolled motorcycle, running on a straight, level road surface, is investigated in this paper. The structural compliances in the front and the rear frames of the motorcycle are taken into account by introducing additional degrees of freedom in the analysis. The kinematics of the tires is represented by linear differential equations which are based on the taut-string model of pneumatic tires. The linear differential equations of motion are solved to yield the eigensolutions of the system. Numerical results, obtained for parameters corresponding to a Honda CB750 motorcycle, are presented and discussed.     

The Influence of Tire Factors on the Stability of Trucks and Tractor Trailers

The mechanical properties of tires and trucks are contrasted with comparable properties of the motor car to explain why the motor truck and the tractor-trailer can exhibit fixed-control instability at moderate levels of lateral acceleration. The (1) rearward bias in the distribution of roll stiffness, (2) large ratio of e.g. height to track, and (3) low torsional stiffness of the parallel-rail frame (as typically employed in heavy commercial vehicles) are found to be the major factors implicated in this phenomenon. Experimental and analytical evidence is provided to show how tire inflation pressure and mixes of (a) tire-carcass construction and (b) tread design also influence stability at moderate levels of lateral acceleration. Conclusions relating to the safety of commercial vehicle operations are drawn.     

Aerodynamics of Road- and Rail Vehicles

The technical state-of-the-art of aerodynamics of ground transportation vehicles is reviewed. Currently available theoretical calculation methods and experimental simulation techniques as well as typical results illustrating the impact of aerodynamics on vehicle performance and running characteristics are summarized and the interactions between vehicle system dynamics and aerodynamics are adressed. Correlation of theoretical and experimental data show the present potential of vehicle aerodynamics and point to fields in which further research work is necessary.     

Design of a Stroke Dependent Damper for the Front Axle Suspension of a Truck Using Multibody System Dynamics and Numerical Optimization

Summary A stroke dependent damper is designed for the front axle suspension of a truck. The damper supplies extra damping for inward deflections rising above 4 cm. In this way the damper should reduce extreme suspension deflections without deteriorating the comfort of the truck. But the question is which stroke dependent damping curve yields the best compromise between suspension deflection working space and comfort. Therefore an optimization problem is defined to minimize the maximum inward suspension deflection subject to constraints on the chassis acceleration for three typical road undulations. The optimization problem is solved using sequential linear programming (SLP) and multibody dynamics simulation software. Several optimization runs have been carried out for a small two degree of freedom vehicle model and a large full-scale model of the truck semi-trailer combination. The results show that the stroke dependent damping can reduce large deflections at incidental road disturbances, but that the optimum stroke dependent damping curve is related to the acceleration bound. By means of vehicle model simulation and numerical optimization we have been able to quantify this trade-off between suspension deflection working space and truck comfort.     

Aeroelastic Effects in Multibody Dynamics

To enable a realistic assessment of the aeroelastic phenomena of aircraft, a simultaneous application of computational fluid dynamics (CFD), computational structural mechanics and flight mechanics has to be performed. Each discipline has developed powerful specialized tools which have to be adapted for multidisciplinary applications. The combination of CFD and elastic multibody systems is well suited for the simulation of a range of aircraft applications, especially for aircraft ground dynamics. Approaches to a coupling of elastic multibody systems and computational fluid dynamics have been performed using close coupling, that is a modal approach, and loose coupling, that is by co-simulation. In the article the applied programs and the coupling methods are presented. Advantages and limits of using multibody simulation as compared to the direct use of FEA methods for the representation of structural dynamics are discussed. Results of coupled steady and unsteady simulations are presented. Finally, an approach to the aeroelastic trim problem is shown.     

Overview of Coupling of Multibody and Control Engineering Tools

The role of Computer Aided Engineering in vehicle development has been significantly increased during the last decade. Specialised simulation tools became very complex, however, growing demands on complexity and particularly interdisciplinarity of vehicles and their simulation models have led to a number of approaches trying either to develop multidisciplinary simulation tools or to connect various specialised simulation tools by interfaces. This paper addresses some aspects of interconnection of the specialised simulation tools as one possibility for simulating complex mechatronic vehicle systems. It classifies the interfaces between specialised software packages in general, mentions some historical development of the interfacing and further discusses the examples of the implemented couplings between the Multibody System codes and Computer Aided Control Engineering tools. Finally, the performance of selected interfaces is compared on an example simulation of a controlled vehicle suspension.