**3. Results**

The aim of this paper is to analyse the wear of a railway turnout with a radius of 3000 m, considering the change in contact area resulting from the variation of normal force. For the guidance mechanism of a wheelset on a through track, if the wheelset is offset to the side, the wheel radii at the wheel contact point are different. Due to the rigid coupling of speeds, one wheel becomes the driving wheel, and the other wheel becomes the braking wheel. This leads to a "steering motion" which drives the wheelset back to the centre of the track. The movement continues past the track axis until the same situation occurs in mirror image to the starting position; then the process starts again. It should be noted that during the passage through the crossing area, there are sleepers laid next to each other that are connected with a change in the substrate stiffness. The next stage of analysis on rail vehicle motion is the passage on a diverging track where, despite the rigid speed coupling between the wheels rolling on the inside and outside of the curve, the wheelset can turn without slipping on curves with large radii. This is possible because the lateral displacement towards the outer rail of the curve turnout results in a difference in wheel radii, which means that the peripheral velocity at the point of contact for the outer wheel is greater than that of the inner wheel. Bearing in mind the discussed phenomena, an attempt has been made to investigate the change in the value of normal force for wear that occurs in railway turnouts.

Using Universal Mechanism and MATLAB software, simulations were performed to determine vertical forces and normal forces for speeds from 100 km/h to 350 km/h, shown in Figures 6–17.

**Figure 6.** Vertical force on wheels at 100 km/h on straight track through a turnout.

**Figure 7.** Vertical force on wheels at 150 km/h on a straight track through a turnout.

**Figure 8.** Vertical force on wheels at 200 km/h on a straight track through a turnout.

**Figure 9.** Vertical force on wheels at 250 km/h on a straight track through a turnout.

**Figure 10.** Vertical force at 300 km/h on a straight track through a turnout.

**Figure 11.** Vertical force at 350 km/h on a straight track through a turnout.

**Figure 12.** Normal force at 100 km/h on a straight track through a turnout.

**Figure 13.** Normal force at 150 km/h on a straight track through a turnout.

**Figure 14.** Normal force at 200 km/h on a straight track through a turnout.

**Figure 15.** Normal force at 250 km/h on a straight track through a turnout.

**Figure 16.** Normal force at 300 km/h on a straight track through a turnout.

**Figure 17.** Normal force at 350 km/h on a straight track through a turnout.

As seen in the figures, the magnitudes of vertical and normal forces increase as velocity increases. Significant changes occur if speeds increase above 100 km/h. For speeds above 250 km/h, the increase in vertical and normal forces occurs mainly within the cross member. The change in these quantities is due to the change in track stiffness. For a straight track without a turnout, the stiffness of the track is usually assumed constant. For a track with a turnout, the stiffness changes along the length as shown in Figure 4. These quantities increase up to 1.5 times the static load.

Next, simulations were performed to determine the vertical and normal forces in straight-track traffic without a turnout. This was done for speeds from 150 km/h to 350 km/h and is shown in Figures 18–27. The value of the force due to the load per wheel is 8.1 × 10<sup>4</sup> N. The alternating loads fluctuate around this value.

From the results presented, there are oscillations of these forces in the movement on the track without turnout, but there is no significant difference. There is an increase of about 1 × 10<sup>4</sup> N in the normal force. These forces are the basis for determining the contact surfaces and the amount of wear.

**Figure 18.** Vertical force at 150 km/h on a straight track without a turnout.

**Figure 19.** Vertical force at 200 km/h on a straight track without a turnout.

**Figure 20.** Normal force at 150 km/h on a straight track without a turnout.

**Figure 21.** Normal force at 200 km/h on a straight track without a turnout.

**Figure 22.** Vertical force at 250 km/h on a straight track without a turnout.

**Figure 23.** Vertical force at 300 km/h on a straight track without a turnout.

**Figure 24.** Normal force at 250 km/h on a straight track without a turnout.

**Figure 25.** Normal force at 300 km/h on a straight track without a turnout.

**Figure 26.** Vertical force at 350 km/h on a straight track without a turnout.

**Figure 27.** Normal force at 350 km/h on a straight track without a turnout.

Next, we proceeded to determine the wear on the wheel and rail. Two works, [12] and [13], were used to consider this topic. Based on them, the following relations can be written:

$$\begin{aligned} \mathcal{W}\_{\text{m}} &= \mathbb{C} \cdot \mathcal{W}\_{f} \\ \mathcal{W}\_{d} &= \mathbb{C}\_{1} \cdot \mathcal{W}\_{f}^{-\text{nr}} \end{aligned} \tag{2}$$

where *Wm* is the mass consumed [μ · g] per unit contact surface, *Wd* is the depth of the wear surface [mm], *C* is constant (for steel ≈0.00124 μ · g/N · mm), *Wf* is the work of friction forces [N · mm], *C*1 is the constant ≈1.55 × 10−<sup>7</sup> [mm/N], and *Wf* −*na* is the work of friction forces per unit contact surface [mm2/Nn].

$$m\_{\mathcal{W}} = \mathbb{C} \cdot \mathcal{W}\_l \tag{3}$$

where *mW* is the mass of consumed material per unit contact area [μ · g /mm2], *C* is the constant (for steel ≈0.00124 μ · g/N · mm), and *Wl* is the work done by friction force per unit area of contact ellipse [mm2/N].

Using the presented relations, *Wl* was determined as the wear factor. The software used to perform the simulation makes it possible to determine the wear factor. Such a test was performed for a straight track with a turnout and for a straight track without a turnout. The test results are shown in Figures 28–37. The figures show wear factors and wheel and rail wear for the passage of a rail vehicle through a turnout with and without a turnout.

**Figure 28.** Wear coefficient at 100 km/h on a straight track with a turnout.

**Figure 29.** Wear coefficient obtained for a straight track without a turnout at 150 km/h.

**Figure 30.** Wear coefficient at 200 km/h on a straight track with a turnout.

**Figure 31.** Wear coefficient obtained for a straight track without a turnout at 200 km/h.

**Figure 32.** Wear coefficient obtained for a straight track with a turnout at 250 km/h.

**Figure 33.** Wear coefficient obtained for a straight track without a turnout at 250 km/h.

**Figure 34.** Wear coefficient obtained for a straight track at 300 km/h with a turnout.

**Figure 35.** Wear coefficient obtained for a straight track without a turnout at 300 km/h.

**Figure 36.** Wear coefficient obtained for a straight track at 350 km/h with a turnout.

**Figure 37.** Wear coefficient obtained for a straight track without a turnout at 350 km/h.

From the simulations presented, when passing through a turnout, the wear coefficients increase in the turnout entry area (needle and resistor) and in the crossover area. For traffic on a track without a turnout, the wear factors vary between 0.0005 and 0.05 N/mm2, while for traffic through a turnout, the factors vary between 0.16 and 12 N/mm2. In traffic on the track without a turnout, the maximum magnitudes come from the normal forces, which increase above the nominal force and decrease when the normal force decreases below the nominal force. The nominal force is 8.1 × 10<sup>4</sup> N.

Simulations of 20,000 train runs on a straight track through a turnout at 200 km/h were performed. The wear results are shown for the left wheel of the wheelset and the wear of the rail by the left wheel. The wear of the left wheel is shown in Figure 38, and the wear of the rail is shown in Figure 39. The wears for the other wheels and rails are identical.

For the same speed of 200 km/h, simulations were performed for wheel and rail wear when the rail vehicle moves on the track without turnout. Wheel wear is shown in Figure 40 and rail wear is shown in Figure 41 for the same conditions.

**Figure 38.** Wear of the first left wheel when a rail vehicle passes a turnout at 200 km/h on a straight track.

**Figure 39.** Wear of rail by the left wheel of the first set when the rail vehicle passes through the turnout at 200 km/h on a straight track.

**Figure 40.** Wheel wear for a straight track without a turnout with constant stiffness obtained at 200 km/h. The maximum wear value is above 0.00014 mm.

**Figure 41.** Rail wear for a straight track without a turnout with constant stiffness obtained at 200 km/h. The maximum value of wear is above 0.0004 mm.

Simulations were then performed for speeds of 300 km/h and 350 km/h for a straight track with a turnout and a straight track without a turnout. The results are shown in Figures 42–49.

**Figure 42.** Wheel wear at 300 km/h for straight-track traffic through a turnout.

**Figure 43.** Wheel wear at 350 km/h for straight-track traffic through a turnout.

**Figure 44.** Rail wear at 300 km/h for straight-track traffic through a turnout.

**Figure 45.** Rail wear for a railroad turnout at 350 km/h for straight-track traffic through the turnout.

**Figure 46.** Wheel wear for a straight track without a turnout with constant stiffness obtained at 300 km/h.

**Figure 47.** Wheel wear for a straight track without a turnout with constant stiffness obtained at 350 km/h.

**Figure 48.** Rail wear for a straight track without a turnout with constant stiffness obtained at 300 km/h.

**Figure 49.** Rail wear for a straight track without a turnout with constant stiffness obtained at 350 km/h.

> From the presented simulation results, it can be clearly seen that the wheel and rail wear when passing through a turnout is many times greater than on a track without a turnout. This coincides with the magnitude of forces and the magnitude of wear factors under the same conditions in relation to lower speeds.

> This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.

> The wear phenomenon itself is related to the way in which the wheelsets are fitted into horizontal curves (circular curves and transition curves). The magnitude of the occurring wheel–track contact forces plays a decisive role. Of course, wear of the rails is accompanied by wear of the rims (Figures 38, 40, 42, 43, 46 and 47). In the presented wear diagrams, the distances between minima and maxima are within 2–3 m, while the distance between axles in the bogie is 1.9 m. The maximum lateral wear occurs at distances of 6–9 m from

each other. These limits correspond to the distance between bogies in a wagon or between the last bogie in the front wagon and the first bogie in the next wagon. The changes in the amount of wear (between successive extremes) can be large and, as shown, occur at relatively short distances from each other. In this way, they can become the cause of sudden changes in track gauge. This, in turn, is directly related to the issue of driving safety. The rolling stock is at risk of derailment if the gradient of the track gauge exceeds the permissible value. During the wear of the side of the grooved head of the outer rail of a straight track turnout and the flange of the outer wheel, the clearance between the side of the inner rail guide and the inner side of the flange of the inner wheel decreases. In a certain state of wear, when the side surfaces rub together, there is simultaneous contact of the flanges of both wheels with the rails. The further interaction of the wheelset with the track depends on multiple factors, such as the position of the bogie when passing through the turnout crossings, the running angle, the value of the steering forces, and the degree of wear on the wheel flanges and rail heads. If the wear of the outer rail head increases, the guidance in the straight track movement of the railway turnout is taken over by the inner wheel, rubbing the inner side of the flange against the guideway, and then all these parameters exceed the acceptable criteria.

A significant influence on the nature and magnitude of lateral wear is exerted by the direction of the vehicle's movement on the straight track, especially on the switch point and the frog, as well as the speed of travel. The obtained diagrams clearly show that wear increases in accordance with the direction of travel. The highest wear is observed on the crossing in the cross member. At this point, a clear irregularity in the path of the last wagons in the rail vehicle formation was observed. The pronounced projections (lateral vibrations) of the last carriage in a tramway formation at these locations are the result of large increments in lateral acceleration. Hence, large lateral forces are transmitted to the outer rail in such a curve. The higher the speed of the vehicle on the straight track, the greater the acceleration. The higher the acceleration, the higher the speed of the vehicle on the straight track.

Apart from contact wear, there is also the phenomenon of corrugation, i.e., corrugated wear. According to the definition given by the UIC (International Union of Railways), corrugated wear is characterised by the occurrence of almost regular irregularities on the rail head surfaces and, on the wheel, running surfaces at intervals of 30 to 80 mm in the form of glossy wave ridges and darkening depressions. Wave wear is an additional source of noise. The course of this phenomenon varies greatly. The conditions conducive to its occurrence are the homogeneity of traffic flow, the type of traffic, and the variable speed of the rail vehicle. It often occurs at sections of rolling stock acceleration and at long straight sections. Railway track construction, as well as differences in the hardness of rails and wheel components of rolling stock, also influence the rate of increase in the phenomenon.
