Interface - The Journal of Wheel/Rail Interaction

OUT OF ROUND WHEELS

Identifying Causes of Out-of-Round Wheels: Measuring Field Experience Against Simulations
By Bernhard Barkow and Paul Mittermayr • October, 2008

The interface between the wheel and rail represents the central link in railway dynamics. Imperfections, such as out-of-round wheels, have a significant effect on vehicle and track maintenance costs, and on safety and passenger comfort, as well (1).

Much research has been done on the benefits of optimizing life cycle costs in recent years (2). But because of the complexity of the issues, comprehensive studies on out-of-round wheels are scarce. The research presented in this article is based on the use of a new simulation tool that models rolling motion under realistic operating conditions, i.e., the model considers out-of-roundness and wear, among other factors. The simulation results are then verified and calibrated, using real-world measurement data from stationary facilities, in order to predict the system's behavior and possible improvements.

Simulation of the System: the Physical Model

The most important step in modeling a system is to simplify the physical attributes as much as possible. Simplifying a very complex system helps to keep the number and type of errors manageable. The simulation process starts with a simple, one-dimensional model, which consists of a rolling disc on a flat, elastic surface with a coupled load (see Figure 1) (3). This model is then extended to three dimensions by discretizing the wheel surface and implementing detailed contact conditions (see Figure 2). While this is very simplified compared to a vehicle on track, it represents the effects of actual operating conditions quite well.

The second important part to be treated is the wear process, itself. Since it is difficult to accurately simulate the physical processes at the micro-structural level (4), a more phenomenological model was chosen. The Archard wear model proved to be simple but versatile enough, where the wear rate is proportional to the friction in the contact area, with an additional distinction between mild and heavy wear.

Simulating Long-Term Behavior
One of the main challenges of modeling is that wear is a long-term phenomenon, typically occurring over 100,000 kilometers, or more. Wheel/rail contact, on the other hand, occurs rapidly and dynamically, requiring a temporal resolution in the range of milliseconds to reliably compute the forces as they occur.

The different scales make it difficult to treat the system numerically. Unavoidable errors that occur during integration compound quickly, rendering the numerical results useless. To combat this, the system is split into two independent parts that are coupled via a long-term feedback loop. The short-term dynamics are computed precisely under constant parameters (this includes the wheel shape). The forces computed there are used to estimate the wear — the long-term dynamics — which is amplified and fed back into the short-term system dynamics in the form of a modified wheel shape.

This, again, requires the use of a more phenomenological wear model instead of treating the wear processes at the microstructural level, which would require significant cost and computation time — much too long for these processes to show an effect.

Sources of Friction
The type of wear that contributes to out-of-roundness in wheels is caused by friction between wheel and rail, rather than by discontinuous effects such as single impacts or emergency braking.

Since the free wave-like motion of a double cone on two rails (which a wheelset is a good approximation of) is essentially friction-free, other sources of friction must be considered. A good source of friction is found in the bogie. Depending on its stiffness, the bogie forces a modified wavelength on the wheelset’s motion, resulting in a periodic slip and, consequently, periodic friction (see Figure 3). Even if all other components behave ideally, the bogie ensures that there will be wear.

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