The role of the contact geometry in wheel–rail impact due to wheel flats: Part II

A classification of wheel flats according to the different stages of their growth is given, along with the characteristic features of the dynamic wheel–rail interaction for each category. Mathematical expressions and frequency spectra of the corresponding wheel mass trajectories are derived. Difference is made between the subcritical and the transcritical speed regime. A criterion is derived for contact loss for worn flats. Simulations show that the dynamic wheel–rail interaction is governed by the track stiffness for low train speeds or long flat lengths; for high speeds and/or short flat lengths the interaction is governed by the inertial properties of the wheel and the rail. For a given flat geometry, nonlinearities in the relationship between the impact magnitude and the train speed occur in the stiffness-dominated speed domain, whereas this relationship is approximately linear in the inertia-governed domain. In the latter domain, the impact magnitude is found to be linearly dependent upon the maximum trajectorial curvature or inversely linearly dependent on the minimum circumferential wheel tread curvature. The above relationships are valid for the subcritical speed regime, in which no contact loss occurs. Different contributions from the literature are compared with respect to the established relationship between impact magnitude and speed. Significant differences are found, due to insufficiently defined parameters and conditions. Conditions are derived for a consistent application of the so-called equivalent rail indentation in experiments with wheel flats, and the indirect strain registration method for measuring dynamic wheel–rail contact forces is reviewed.     

The Added Value of Accounting For Users’ Flexibility and Information on the Potential of a Station-Based One-Way Car-Sharing System: An Application in Lisbon,Portugal

Car-sharing systems are an alternative to private transportation whereby a person may use an automobile without having to own the vehicle. The classical systems in Europe are organized in stations scattered around the city where a person may pick up a vehicle and afterward return it to the same station (round trip). Allowing a person to drop off the vehicle at any station, called one-way system, poses a significant logistics problem because it creates a significant stock imbalance at the stations, which means that there will be times when users will not have a vehicle available for their trip. Previous mathematical programming formulations have tried to overcome this limitation by optimizing trip selection and station location in a city in order to capture the best trips for balancing the system. But there was one main limitation: The users were assumed to be inflexible with respect to their choice of a station, and held to use only the one closest to their origin and destination. If the user is willing to use the second or even the third closest station the user could benefit from using real-time information on vehicle stocks at each station and be able to select the one with available capacity. In this article we extend a previous model for trip selection and station location that takes that aspect into account by considering more vehicle pick-up and drop-off station options and then apply it to a trip origin–destination matrix from the Lisbon region in Portugal. Through the extended formulation we were able to conclude that user flexibility allied with having information on vehicle stocks increases the profit of the company, as people will go directly to a station with a vehicle available, thus making the use of the fleet more efficient. Observing the size of the stations resulting from the model, we also concluded that the effect of information is enhanced by large car-sharing systems consisting of many small stations.