# Theoretical Study of the Wear of a Reduced-Diameter Wheel for Freight Wagons, Based on Its Diameter
###### Abstract  
This paper presents the development of a numerical analysis model designed to estimate the lifespan of reduced-diameter wheels used in freight wagons based on their diameter, under quasi-static conditions. These wheels are increasingly being used in combined transport applications, where they are installed in various bogie configurations and subjected to different operational environments. However, due to the unique characteristics of reduced-diameter wheels, their lifespan has been scarcely studied. To accurately build this model, an in-depth investigation of the rolling phenomenon was required, addressing key issues in the track-  
A standard wheel typically has a diameter of around 920 mm, whereas a reduced-diameter wheel measures between one-half and one-third of that size. This poses a new problem: if a wheel whose diameter has been halved must roll the same distance as an ordinary-diameter wheel, then the former will have to revolve twice around its rotation axis. Also, its contact angle with the rail will be higher due to its smaller size, and it will have less material to support and withstand the same load. Taking this information into account, it can be foreseen that the reduced-diameter wheel is likely to experience more intense wear and rolling contact fatigue (RCF) than the ordinary-diameter wheel. However, this is only a prediction and must be proved and validated mathematically, taking into account as many factors as possible:  
* [noitemsep,topsep=0 pt]
* Wheel factors: geometry (diameter, conicity, tread width, contact angle), machining (roughness), material (properties), load, and previous wear. * Wagon factors: configuration (bogies or axles distribution and type of bogies), type of suspension, braking system, running speed, and load distribution (axle load). * Railway superstructure factors: track gauge, line layout (curve radii, windiness, sagitta, gradient, etc. ), layout quality (excess or deficiency in cant, transition curves, etc. ), type of rail (welded or with joints), track materials (properties) and track previous degradation (previous rail wear, specially). * External factors: Temperature, humidity, wind, rain, snow, and weather in general. The presence of moisture, leaves, and pollutants (saltpeter, oil, etc.) is important here too. The process involves creating a mathematical model based on behavioral equations derived from existing models that explain wheel degradation, each incorporating a set of assumptions. While the analytical model should account for as many influencing factors as possible, it must also be constrained in size to ensure computational efficiency. This means that additional assumptions will be made to exclude factors with minimal impact on wheel degradation. This study focuses on the Spanish conventional railway network due to the current push for rail motorways in Spain, which faces certain implementation challenges. Specifically, the conventional network has a restrictive loading gauge [3], leading to the use of reduced-diameter wheels. Additionally, the tight curves and steep gradients of this network cause significant wear on these wheels. Figure 2: Conflict illustration. Source: [1]. These wheels are part of wheelsets, which consist of an axle and a pair of wheels. Typically, wheelsets are configured in two-axle (two-wheelset) bogies. According to the same source, two bogies are sufficient for a flat-bed wagon used in rail motorways, making this type of railway vehicle the focus of the wheel degradation analysis. Consequently, this study will concentrate on freight transport within the Spanish national railway network, which has a specific track gauge of 1668 mm. External factors that are highly variable and difficult to predict will be excluded from this analysis. This research paper can be compared to other advanced studies on wheel wear calculation, but it differs in several notable ways. In this paragraph, these differences are discussed in detail: To start with, Refs.