Research into the Possibilities of Improving the Adhesion Properties of a Locomotive

Abstract

Locomotives are important vehicles, which serve for towing wagons, i.e., trains. Many factors influence the safe and cost-effective operation of locomotives and trains in general. One of these factors is adhesion at the wheel/rail contact. The adhesion determines how much power the locomotive can deliver and how the braking system will ensure that the train stops. The main way to improve adhesion is to use sand at the wheel/rail contact point. The aim of this study is to improve the efficiency of the sand system of the locomotive. For this purpose, a new sand system nozzle mounting design was proposed. The newly proposed sanding system is equipped with a nozzle mounted to the axlebox unlike the original one, which uses the nozzle attached to the bogie frame. To compare the proposed and existing design, simulation calculations were performed in Simpack software 2024.3. For the simulation computation of the locomotive bogie, two types of railway tracks were chosen. A straight track section with two angular frequencies and three amplitudes of track irregularities was created, and a real track section corresponding to several kilometers of track was modeled in the Simpack software. During the simulations, it was determined that the proposed nozzle mounting design has a smaller amplitude of motion, compared to the existing one; therefore, there is a more accurate and efficient operation of the sand system. This in turn has a favorable effect on the adhesion of the wheel with the rail. It was found out that the newly designed sanding system has a significant positive economic effect regarding saving sand. There is no sand loss during sandblasting compared with the original sanding system. This directly relates to saving costs during locomotive operation.

1. Introduction

The railway transport serves for the transportation of goods and passengers in many countries. As it is an important kind of transport, the rail vehicles should be safe, effective and reliable [1,2]. During the operation of rail transport, its safety and technical and economic characteristics are influenced by many factors. Such factors include the wheel and rail adhesion in the wheel/rail contact [3,4]. The adhesion between the wheel and rail is the property of the transmission of longitudinal tangential forces (traction and braking forces) by the wheel/rail contact point during the rolling of a vertically loaded wheelset on the rails [5,6,7]. The traction force is important in the technical and economic pertinent data because it determines the maximum permissible weight of a train. As the freight-traffic volume increases, so do the requirements for the adhesion between the wheel and rail. Exceeding the maximum allowable value of adhesion can lead to wheel slippage, thereby increasing the wear and tear on the rolling surface of the wheels and rails [4,8,9,10]. The train’s safety also depends on adhesion since the adhesion influences the realization of braking forces and the length of the braking distance. If the train loses adhesion during braking, it can lead to wheel blockage and, consequently, to a flat spot on the wheel tread, which increases the dynamic loads of the rail vehicle and the rail bed many times over [11,12].

During a train’s movement, many factors influence adhesion. These factors can also be caused by faults of construction in the vehicle, as well as by external factors. When the rolling surfaces are clean and dry, maximum adhesion is achieved. The presence of oil films, moisture, dust, fallen leaves, and other types of contamination significantly reduces the adhesion in the wheel/rail [13,14,15]. Many researchers conducted studies of the influence of contaminants on adhesion. According to the results of these research studies, fallen leaves, because of their crushing and mixing with moisture, have lubricating properties that negatively affect adhesion. The rolling surface is cleaned during abundant rain, resulting in a higher adhesion value. However, with prolonged exposure to moisture, an oxide film can form on the rolling surface, which reduces the traction of the wheel with the rail. The presence of moisture caused by dew or condensation also causes low adhesion values. Based on these studies, the most unfavorable period that has a propensity for a decrease in adhesion is autumn/winter [16,17,18] although the tendency to reduce adhesion is present at any time of the year, regardless of the weather. In this regard, the issue of improving the coupling properties of trains is relevant and in demand.

The main method of increasing adhesion is the use of sand in the wheel/rail contact. Several types of loose abrasive materials, namely, sand, zinc oxide, spinel, and alumina, were studied [18,19]. As a result of the study, it was found that the value of adhesion is affected by the crush strength. Studies have indicated that the higher the value of the particle strength, the better the adhesion value. However, the harder particle leads to a greater wear and tear on the rolling surfaces. The use of sand showed the most favorable results in terms of adhesion and wheel/rail wear and tear. However, the use of sand has several disadvantages. The presence of excess sand in the wheel/rail contact can cause the isolation of the wheel from the rail [20,21]. Also, the excessive amount of sand hurts the track facilities, and, due to track ballast contamination, moisture drainage deteriorates. Passive resistance increases, resulting in higher fuel and energy costs. Excessive amounts of sand negatively affect the environment and safety near railway tracks. When the train is in motion, sand particles are crushed, and the dust from them can remain suspended in the atmosphere for a long time.

In this regard, it is necessary to ensure the high accuracy of the sanding system, as well as supply the minimum required amount of sand to the point of wheel/rail contact for its most efficient and safe operation. There is research that investigates the ways of reducing and adjusting the amount of sand supply to the point of wheel/rail contact. The article [8] proposes a method of electrification of the abrasive bulk material, which provides an equilibrium distribution of sand on the rolling surface of the rail. The work [22] states the principle of adjusting the amount of sand with an adaptive system based on a relay or microcontroller. However, not only is the amount of sand supplied important but also the accuracy of its supply to the point of the wheel/rail contact. During the movement of the locomotive, it is affected by various dynamic loads. The wheelset moves on a complex track; therefore, some sand spills out past the point of the wheel/rail contact.

Despite these disadvantages, the main method for improving the locomotive’s adhesion properties is still the use of sand in the wheel/rail contact. The all-weather capability of rail transport is ensured precisely because of the use of sand. This is the case especially when the train moves on a big slope and, further, when it accelerates or decelerates in the autumn and winter season. The study of this issue is still relevant and necessary to understand the impact of sand on adhesion properties. These properties play an important part in the technical and economic performance and safety of rail transport in general.

The main contribution of the presented research is a design of a sanding system, which includes a nozzle mounted to an axlebox. It was considered that such a technical solution of a sanding system is able to improve the efficiency of sand distribution to the wheel/rail contact area without excessive sand losses during operation. This idea is investigated by means of the created multibody model of the locomotive bogie equipped with the designed sanding system. The preformed simulation analysis showed that the suggested idea is right. The numerical values of the nozzle amplitudes during locomotive operation as well as a comparison of the findings with the existing technical solutions are presented below.

2. A Description of a Sanding System

As it is described above, the sanding system is designed to prevent the skidding of the wheelset of a locomotive in traction mode, as well as to prevent the occurrence of skids during braking [23,24,25,26].

All electric locomotives as well as other types of locomotives have devices that supply sand to the rails in the wheel/rail contact [27,28,29,30]. As a result, the coefficient of adhesion in the wheel/rail contact and, therefore, the traction force of the locomotive significantly increases [14,31,32].

The sand used in the devices of the sand system of the electric locomotive must flow freely and evenly through the pipes; therefore, it must have grains with a size of 0.1 to 0.2 mm and also have sufficient hardness and strength. The last property is determined by the amount of quartz in the sand. Normal quality sand should have at least 70% quartz, and high-quality sand should have at least 90%. Sand should not change its qualities when heated in drying ovens and easily release the moisture contained in it. Sanding systems of locomotives consist of a hopper, a nozzle and pipes that carry sand to the wheel/rail contact. A neck with a mesh net and a lid is in the upper part of the hopper, which is sealed with a rubber gasket. In the lower part of the hopper, a sand outlet fitting is located in which a sand pipe is screwed using a union nut with a sealing gasket. There is a hole for loosening on the side surface of the hopper. The hole is covered with a cover with a rubber gasket using six bolts. The bunker is filled with sand through hatches with a net located on the roof of the locomotive. Sand enters the nozzle from the hopper through the pipeline. How the sand supply system works on an eight-axle locomotive is shown in Figure 1. When the manual valve (3) of the sandbox is pressed, air from the supply line (4) flows through the disconnect valve (2) and the switching valve (5) to the nozzle (6). At the same time, sand is supplied only under the first pair of wheels of that section of the electric locomotive, which is controlled from a locomotive cabin.

When it is necessary to distribute and supply sand to improve the wheel/rail contact adhesion under several wheelsets of a locomotive or when a locomotive works on a system of many units, the control of sand devices is carried out using electropneumatic valves (1). These valves receive power from the sandbox switches installed in the driver’s cabins through blocking the reverser. After their inclusion, air from the supply line through the disconnecting taps, valve (1) and switching valve (5) enters the nozzles of sandboxes I, III, VII and VIII of the electric locomotive wheelsets.

The nozzle (Figure 2) has an opening (I) for the entrance and an opening (II) for the exit of sand through the pipes. Pipes are connected to the nozzle body (6) with nuts (4) with sealing rings (5). The opening is intended for cleaning the nozzle and is closed with a cover (3), screwed with bolts (1) and sealed with a rubber gasket (2). Air coming from the supply line through the hole in the nozzle body with the adjusting bolt (9) enters the nozzle (7). A certain amount of the air flows through canal “B” into chamber “A” to loosen the sand. The air from the nozzle (7) enters chamber “B”, captures the sand from chamber “A”, flows along with the sand through the pipes to the rails. By turning the bolt (9), adjust the sand supply—400 to 500 g per 1 min per nozzle. Through the channel (with plug (8)), air passes around the outer surface of the nozzle, which increases the pressure in chamber “B”. At the same time, the speed of sand outflow increases but without increasing its consumption.

The analysis of patent documentation on the designs of sandboxes of locomotives showed that there are currently many options for their construction. Let us consider some of them.

The publication [33] proposed the design of a locomotive sandbox, which includes a control unit, a locomotive speed sensor and a case with sand supply and discharge channels. In the cavity of the sandbox housing, the working wheel is fixed on the shaft of the electric motor, and the blades are placed on its cylindrical surface. At the same time, the center of the rotation of the wheel is shifted relative to the geometric center of the cavity in such a way that the wheel and the lower part of the cavity create a gap that increases in the direction of the rotation of the impeller. The disadvantage of this sandbox design is the inability to ensure rational sand consumption when feeding it onto the rails.

A new design of the sandbox of the locomotive was also proposed in [34]. Such a sandbox contains a control unit, a locomotive speed sensor, a case with sand supply and discharge channels. In the cavity of the sandbox body, an impeller is fixed on the shaft of the electric motor on the cylindrical surface of which there are tangential blades oriented against the natural movement of sand under the influence of gravity. The center of the rotation of the impeller is shifted horizontally, relative to the geometric center of the cavity, so that the impeller and the lower part of the cavity forms a wedge-shaped gap that increases in the direction of the rotation of the impeller, while the channels for the supply and removal of sand are located with horizontal displacement from each other on different sides of the body cavity. The author noted that the use of the invention will lead to a reduction in the intensity of the wear of the working surfaces of the wheel and the cavity and a reduction in the possibility of jamming of the working wheel. However, the presented invention does not allow one to control the flow of sand onto the working surface of a rail.

The team of authors in the work [35] proposed a locomotive sandbox design in which a central conductor, a cylinder-shaped electrode, a power source, an electropneumatic multi-position valve connected to a speedometer, a control system connected to a receiver and a measuring voltmeter are placed in front of the nozzle. Additionally, behind the nozzle, there is a regulated power source connected to the electrodes located on the pipeline. However, this sandbox design does not allow for a rational supply of sand to the rails.

To improve the operation of the sandbox of the locomotive, an improvement of its structural elements is proposed in [36]. At the same time, its cutter is fixed by welding in the additional groove of the striker at an angle of 98° to the axis of the elastic plate. However, this solution does not limit the sandbox’s own degree of freedom in the horizontal plane. This contributes to unnecessary losses of sand when feeding it onto the rails.

The work [37] proposed the improvement of the nozzle as one of the most important structural elements of the sandbox of the locomotive. The nozzle of the sandbox of the locomotive contains a case with a loosening cavity in which there are channels for the supply of sand and the removal of the sand–air mixture, an air duct through which compressed air is fed into the nozzle, connected to a guide nozzle and a tube. The body of the nozzle is made with a replaceable insert located at the point where the jet of air directed from the tube hits it. At the same time, the replaceable insert is tightly attached from the outside of the housing wall in the place where the flow of air directed from the tube falls on it. The replaceable insert is made of wear-resistant material.

A similar solution was proposed in [38]. The nozzle of the sandbox of the locomotive contains a case with a loosening cavity, in which there are channels for the supply of sand and the removal of the sand–air mixture, and an air duct through which compressed air is fed into the nozzle, connected to the guide nozzle and the tube. The tube has an end part made at an angle to it, which in turn is directed at an angle to the wall of the case in the direction of the sand in such a way that the compressed air from the end part of the tube falls on the wall of the chamber tangentially to it and then on to the sand.

The sandbox designs presented and described in [38,39] have the same drawback as the one described in [37].

The publication [39] also proposed a new design of the sandbox nozzle of the locomotive. It contains a body with a loosening cavity located between the sand supply and discharge nozzles, as well as a guide nozzle and an air supply channel into the loosening cavity. Additionally, the loosening cavity of the nozzle is made in the form of a cylindrical chamber with a vertical axis, and a cylindrical vertical channel is made between the sand inlet and the loosening cavity, which enters inside the loosening cavity. The air supply channel into the loosening cavity is connected above the level of the outlet opening of the cylindrical vertical channel to the side surface of the loosening cavity. However, such a sandbox also does not allow for a rational supply of sand to the rail.

A similar drawback is the locomotive sandbox described in [40]. It provides an independent regulation of air flow in the nozzles. This allows the possibility for the separate adjustment of the air flow in them, for the precise adjustment of the economic mode of operation of the nozzle and for blowing the pipeline connected to the mouth for the removal of sand for its cleaning. The design of the guide of the first nozzle and the second nozzle is easily replaceable, which allows for their quick replacement or cleaning of dust deposits without disassembling the nozzle.

The design of the locomotive sandbox nozzle proposed in the publication [41] includes a body, a loosening cavity, nozzles for feeding and removing sand, a guide nozzle, a channel for supplying air to the loosening cavity, a conical chamber and a cylindrical chamber. However, the design of such a nozzle does not contribute to the possibility of ensuring optimal sand consumption.

The sandbox nozzle of the locomotive, which was developed by the authors of the work [42], contains the following: a case with a loosening cavity located between the nozzles for feeding and removing sand and made in the form of a cylindrical chamber with a vertical axis; a cylindrical vertical channel located between the mouth for feeding sand and the loosening cavity, which enters the loosening cavity through its air supply channel, connected above the level of the outlet opening of the cylindrical vertical channel to the side surface of the loosening cavity tangentially with the horizontal axis, with a nozzle placed in it; a guide nozzle placed in the cylindrical channel with a neck for sand removal, passing eccentrically, above the level of the outlet opening of the cylindrical vertical channel through the side surface of the loosening cavity. In the cylindrical vertical channel, located between the mouth for feeding sand and the loosening cavity, there is a coaxial cylindrical channel of a smaller diameter for air supply, the outlet of which is located in the loosening cavity below the level of the outlet opening of the cylindrical vertical channel. This sandbox design has the same drawback as the one described in [41].

3. A Description of a Newly Designed Sanding System for a Locomotive Bogie

The working principle of a locomotive sanding system (Figure 3) is as follows. Sand is supplied from a sandbox mounted on a locomotive body or on a locomotive bogie frame. In some types of rail vehicles, the sandbox is mounted inside the vehicles. The sand supply is operated by the train driver or the vehicle’s automatics. Compressed air is used to blow out sand from the nozzle. In most cases, the sand is blown at a constant rate, but some systems allow one to regulate the speed of the sand.

Smaller angles of attack were found to increase the amount of sand falling into the contact point between the wheel and the rail. Most locomotives use a design to attach the sanding nozzle to the locomotive’s bogie frame or a main frame. The disadvantages of this design are inefficiency and increased sand consumption because the nozzle positioning does not allow one to ensure a constant angle of attack of its position concerning the point of the wheel/rail contact since the wheelset moves along a composite path, especially when moving in curves, which leads to the spillage of abrasive material out of wheel/rail contact, increased sand consumption and the excessive pollution of the environment with sand and its dust. One of the nozzles works while the locomotive runs in a straight track section, and the other is activated in a curved track section. This design ensures a more accurate sand supply, but its disadvantage is the need for two nozzles, as well as a controlling system to switch between the nozzles of the sanding system.

The authors of this research propose a nozzle mounting construction. The proposed design (Figure 4) is based on increasing the efficiency of the sanding system, reducing the sand consumption by making the nozzle (5) attachment in the form of an adaptive system using a bracket (4), which is bolted (3) to the axlebox (2), and using a pipe (6) attached at one end to the bogie frame 1, which in effect allows the movement of the nozzle (5) relative to the bogie frame (1). As a result, the sand-supplying device follows all the movements of the wheelset (7), allowing the sand to be supplied at an optimum constant angle to the wheelset (7).

A simulation model of a two-axle bogie of a locomotive (Figure 5) operated on a railway track was created in the Simpack software. It is licensed software for the simulation of multibody systems (MBSs), which allows one to simulate the movement of any mechanical system, including railway transport. Details of the created MBS model of the locomotive bogie with the nozzles are depicted in Figure 6.

The shunting locomotive bogie was chosen because shunting locomotives have an increased tendency to decrease or lose adhesion. This is because, during operation, shunting locomotives often start the run or break. Also, on many industrial and station tracks, there is an increased contamination of the rolling surface of the rail in comparison with the main lines. The simulation model is composed of several bodies (a bogie frame, an axlebox units and wheelsets), which are connected by employing massless force elements. The Simpack software also implements algorithms, allowing one accurately to determine the parameters of the wheel/rail contact [43,44] (Figure 7).

These parameters have a major impact on the dynamic performance of the rail vehicle while running on a track. The first simulation model is the original, i.e., the nozzle is attached to the bogie frame. The second simulation model represents a design novelty, i.e., the nozzle attachment to an axlebox by using an adaptive system.

The bogie input parameters for the Simpack software are listed in

Table 1. A list of parameters of the locomotive bogie.

Parameter	Value	Note
Mass of the bogie	6580 kg	Without wheelsets +1/3 traction motor
Mass of the wheelset	3575 kg	+2/3 traction motor
Mass of the traction motor	1860 kg
Mass of the axlebox	129 kg
Wheel diameter	1100 mm
Wheelbase	2400 mm
Primary suspension spring stiffness	808,800 N/m	Vertical direction
Moment of inertia of the bogie relative to the x-axis	3946 kg·m2	Without traction motor, +½ primary suspension
Moment of inertia of the bogie relative to the y-axis	4571 kg·m2	Without traction motor, +½ primary suspension
Moment of inertia of the bogie relative to the z-axis	7297 kg·m2	Without traction motor, +½ primary suspension
Moment of inertia of the wheelsets relative to the x-axis	1983 kg·m2	+traction motor
Moment of inertia of the wheelsets relative to the y-axis	298 kg·m2
Moment of inertia of the wheelsets relative to the z-axis	2498 kg·m2	+traction motor
Moment of inertia of the axleboxes relative to the y-axis	36 kg·m2

.

In the railway industry, simulation calculations play a crucial role in predicting the behavior of rail vehicles and ensuring their safe operation. However, to obtain accurate simulation results, it is necessary to determine several essential parameters, such as the profile of the track and its irregularity. The track profile refers to the longitudinal shape of the rail, which includes the railhead’s height and width and the track’s vertical alignment [3,20,45,46]. The track profile can vary depending on several factors, such as the type of rail, the type of sleeper and the design of the track. The input parameters of the track are as follows: the track gauge—1435 mm, the rail head profile UIC60 (Figure 8) and the rail cant—1:40.

Track irregularities refer to any deviations from the standard track profile, such as bumps, dips and twists. These irregularities can occur due to various reasons, such as poor maintenance, weather conditions and wear and tear. The track irregularity can affect the behavior of the rail vehicle, leading to increased wear and tear on the vehicle’s components and decreased safety [47,48].

The track irregularity (Figure 9) function is given by the formula:

$$h\left(t\right)=h_0\cdot \sin \left({\omega }_t\cdot t\right)$$

(1)

where h(t)—the height of the track irregularity [m], h₀—the track irregularity amplitude [m], ω_t—the angular frequency [rad/s], t—time [s] and T—time period [s]. The predefined track irregularities are valid for the lateral direction as the lateral movement of the nozzle relating to the rail centerline is the main objective of the performed research.

The research was performed for the locomotive bogie running on the straight track section and on the real track section. The real track section profile corresponds to the section between the two Slovak towns Prievidza and Chrenovec. The longitudinal geometry of the track together with its curvatures is shown in Figure 10.

The railway tracks are modeled with a rigid foundation. It is a common approach for modeling a railway track. Moreover, track flexibility influences the vehicle dynamics by the fact that the modeled viscoelastic elements eliminate the vibration, i.e., the amplitudes of vibrations are smaller. It means that the rigid track foundation approach represents a stricter approach to the modeling.

Once the track profile and irregularity data are obtained, they can be used to accurately simulate the rail vehicle’s behavior. The simulation results can help to identify potential safety issues and optimize the vehicle’s design to improve its safety and efficiency.

In conclusion, determining the track profile and its irregularity is crucial for accurate simulation calculations in the railway industry. The track profile and irregularity data can help to predict the behavior of rail vehicles accurately and identify potential safety issues. The use of advanced measurement techniques can provide precise data and help to enhance rail safety and efficiency and reduce maintenance costs.

4. Results and Discussion of the Research

The simulations described in this study were conducted to investigate the impact of track irregularities on the motion of the sandbox nozzle in rail vehicles. The simulations were performed using Simpack software, which is a multibody dynamics simulation tool designed for analyzing complex mechanical systems. The results of the research are presented for the track irregularity amplitude of h₀ = 0.002 and 0.003 m and for the angular frequency ω_t = 2, 3 and 5 rad/s. These chosen angular frequencies relate to the frequency characteristics of the solved locomotive bogie.

To evaluate the motion of the nozzle and its impact on the performance of the locomotive sand system, the results of the simulations were processed using Simpack Post software, which provides a visualization and analysis of simulation data. Graphical dependencies were plotted to compare the motion of the sandbox nozzle in the transverse direction between when it was attached to the axlebox and when it was attached to the bogie frame.

The results are shown in the form of the waveform of the lateral motion of the nozzle relating to the longitudinal axis of the symmetry of a rail y_rS (Figure 11). Further, these graphs include blue lines, which are referred to in the legend as the “Running surface of the rail” (Figure 11). This means that these lines define the effective rail width.

Figure 12 shows the results of the simulation computation of the locomotive running on the straight track section with the track irregularity amplitude of h₀ = 0.002 m and for the angular frequency of ω_t = 2 rad/s, 3 rad/s and 5 rad/s.

It can be recognized that sand distributed to the wheel/rail contact by the nozzle mounted on the axlebox is concentrated only in the running surface of the rail. It is valid for all three types of angular frequencies. Further, it is possible to see that the higher value of the angular frequency causes even lower values of the amplitude motion of the nozzle mounted on the axlebox. Such a finding is not observed for the nozzle mounted on the bogie frame. It can be explained by the fact that the unsprung masses (the nozzle mounted on the axlebox) act directly to the nozzle motion.

Regarding the quantitative evaluation of the results, the maximal value of the nozzle lateral motion mounted on the axlebox is of 0.027 m for the irregularity amplitude of 0.002 m and for the frequency of 2 rad/s (Figure 12a). However, this value is reached only at the beginning of the bogie motion. For the rest of the motion, the maximal amplitude is up to the value of 0.020 m. It is within the range marked by the running surface of the rail. The minimal value of the nozzle is reached for the design when the nozzle is attached to the axlebox for the frequency of 5 rad/s (Figure 12c). This minimal value is of 0.004 m.

The results of the simulation computation of the nozzle lateral motion for the irregularity amplitude of 0.003 m and the frequency of 2 rad/s and 3 rad/s are shown in Figure 13.

As can be seen from Figure 13, the lateral oscillating motion of the nozzle has a very similar tendency as in the previous case. The maximal value of the lateral motion is also about 0.022 m at the beginning of the motion, and, during the rest of the motion, it is within the running surface of the rail. The higher angular frequency of the irregularity leads to lower values of the lateral oscillation of the nozzle, and these values are up to the value of 0.015 m. Only at the beginning of the motion, they are higher but still under the wanted limits.

The additional simulation computations were focused on the evaluation of the efficiency of the newly designed nozzle attachment on the real track section. The locomotive bogie was running on the real track section with the length of 5400 m. The achieved results are presented in Figure 14.

The simulation analyses on the real track section show that the designed improved sanding system has better operational properties than the system, which uses the nozzle mounted on the bogie frame. The nozzle mounted to the axlebox is within the running surface of the rail during the entire track section. The original sanding system with the nozzle attached on the bogie frame has a disadvantage that, on curves, the sand is distributed out of the wanted rail surface. It leads to lower efficiency of the system. The maximal value of the lateral displacement of the nozzle mounted to the axlebox is 0.023 m, while the maximal value of the observed parameter of the nozzle mounted on the bogie frame is over 0.035 m. This is identified for almost all curves excluding four curves in the time interval from 475 s to 680 s.

The simulations revealed that the amplitude of the motion of the sandbox nozzle in the transverse direction was lower when it was attached to the axlebox compared to when it was attached to the bogie frame. This finding is significant because the amplitude of the nozzle motion affects the economic and environmental performance of the locomotive sand system. In the transverse direction, excessive nozzle motion causes the emission of a large amount of sand outside the wheel/rail contact area, resulting in unnecessary sand usage and environmental pollution. Therefore, the lower amplitude of nozzle motion observed when it was attached to the axlebox could be beneficial in reducing sand consumption and environmental pollution.

These results indicate that the proposed construction of attaching the nozzle to the axlebox using an adaptive system can significantly reduce the amplitude of nozzle movement relative to the wheel/rail contact point, resulting in a more stable position of the nozzle and reduced sand consumption and pollution.

When attaching the nozzle to the axlebox, there is a more stable position relative to the point of wheel/rail contact. In this case, the nozzle’s motion is reduced, resulting in less sand spillage beyond the point of wheel/rail contact. Consequently, attachment of the nozzle to the axlebox leads to a more stable position relative to the point of wheel/rail contact, ultimately resulting in reduced sand consumption and pollution.

The nozzle’s movement is reduced, and it results in less sand spillage beyond the point of the wheel/rail contact when it is attached to the axlebox. In contrast, when the nozzle is attached to the bogie frame, excess sand is spilt onto the track beyond the point of the wheel/rail contact. This causes environmental pollution and excessive sand consumption.

The attachment of the nozzle to the axlebox leads to a more stable position relative to the point of the wheel/rail contact, ultimately resulting in reduced sand consumption and pollution.

The quantitative evaluation of the advantages of the newly designed sanding system comes from the findings of the preformed research. Simulation analyses revealed a real improvement of the system in comparison with the existing sanding system currently used in practice. The research was performed for a locomotive with the normal track gauge, i.e., 1435 mm. A wheel profile was S1002, and a rail profile was UIC60. The efficient working width of this rail can be considered 52 mm. It is marked by the blue color in Figure 11, Figure 12, Figure 13 and Figure 14. It means, that a suitable sand distribution is within this width. When the results of the simulations were analyzed, it was found out that the original solution with the nozzle attached on a bogie frame distributes sand out of this range. This led to the loss of sand. For the track irregularity amplitude h₀ = 0.002 m (2 mm) and the angular frequency ω_t = 2 rad/s, the amplitude of the original system is 74 mm. The new system has the amplitude for ω_t = 2 rad/s only 30 to 34 mm. The original system has practically the same amplitude also for ω_t = 3 and 5 rad/s. However, the new sanding system has for ω_t = 3 rad/s the amplitude 26 to 30 mm, and, for the angular frequency ω_t = 5 rad/s, this amplitude is only 16 mm. This is depicted in Figure 12. It is evident that the newly designed sanding system is more effective than the system currently used.

Further, the track irregularity with the amplitude of h₀ = 0.003 m (3 mm) and with the angular frequency ω_t = 2 and 3 rad/s is the amplitude of the sanding system nozzle 80 mm. The amplitude of the nozzle of the newly designed system is 40 mm for the angular frequency ω_t = 2 rad/s, and, for the angular frequency ω_t = 3 rad/s, the nozzle amplitude is 30 mm. These results are shown in Figure 13, and they prove again the effectiveness of the sanding distribution by the newly designed sanding system.

The simulation analyses also allowed us to investigate and compare the behavior of the nozzle sanding system for the real railway track (Figure 14). As was found out, the original sanding system leads to the maximal amplitude of 80 mm and the newly designed system only to the maximal amplitude of 46 mm. It can be strongly assumed that the newly designed sanding system will have better operational properties in a real operation.

The achieved finding and results regarding the maximal amplitudes of the newly designed sanding system are concluded and listed in

Table 2. A quantitative comparison of the original sanding system and the newly designed sanding system.

			Maximal Amplitude of the Nozzle [mm]
Irregularity Amplitude h0 [mm]	Irregularity Angular Frequency ωt [rad/s]	Rail Working Width [mm]	Original System	Newly Designed System
2	2	52	74	34
	3		74	30
	5		74	16
3	2	52	80	40
	3		80	30
Real track	-	52	80	46

.

The absolute values of the nozzle deviations of the original and newly designed sanding system can be also expressed in percentages. It can be more illustrative for the assessment of the system effectiveness. When the rail working width of 52 mm is considered, the nozzle amplitude of the original sanding system of 74 mm leads to ineffective or unused sand in the rail contact. In this case, i.e., for h₀ = 2 mm and ω_t = 2 rad/s, 42.3% sand is unused. For h₀ = 3 mm, these losses are even 53.8% during operation. This is listed in

Table 3. Evaluation of sand losses for the original sanding system.

		Maximal Amplitude of the Nozzle
Irregularity Amplitude h0 [mm]	Irregularity Angular Frequency ωt [rad/s]	Original System—Losses	Newly Designed System—Reserve
2	2	42.3%	34.6%
	3	42.3%	42.3%
	5	42.3%	69.2%
3	2	53.8%	23.1%
	3	53.8%	42.3%
Real track	-	53.8%	11.5%

. On the contrary, the newly designed sanding system is able to save sand, and it is able always to distribute sand effectively, i.e., always 100% of sand is used for adhesion. In the other words, lost sand caused by the original sanding system is saved by the newly designed sanding system. This is how the 4th column of Table 3 should be understood. The word “reserve” for the newly designed sanding system expresses a possibility of higher nozzle amplitude (e.g., due to higher track irregularities) without sand loss.

An economical contribution of the newly designed system can be assessed from the operation point of view as well as from the engineering design point of view. In the case of a newly produced locomotives, the considered costs are negligible because the locomotive and its bogie design would be adapted already in the development stage. A modification of the existing locomotives requires a deeper assessment of the advantages of the new system and the operational costs. They mainly relate to the sand losses. Even though the price of the abrasive material is not fixed for a long time period, it is still possible to calculate the cost savings when using the original and newly designed sanding system. The current price of sand (January 2025, Slovak Republic) suitable for a locomotive is EUR 38 to 42 per 1 ton. Based on experiences of the Slovak freight railway operator, the average annual sand consumption for the locomotives’ fleet is 390 tons. The average sand price is considered EUR 40 per 1 ton. It means that the total costs for sand are EUR 15,600 per year. An application of the newly designed system would lead to saving sand consumption. This sand consumption would no longer be 390 tons per a year, but it would decrease according to the calculated sand losses (Table 3). The calculated saved costs for sand in the case of the application of the newly designed sanding system are listed in

Table 4. Average saved costs for sand for the newly designed sanding system calculated for the examined running conditions. The average sand price is EUR 40 per 1 tone.

Irregularity Amplitude h0 [mm]	Saved Sand [%]	Saved Sand [tons]	Saved Costs [EUR/Year]
2	42.3%	164.97	6598.8
3	53.8%	209.82	8392.8
Real track	53.8%	209.82	8392.8

.

As is obvious form Table 4, the newly designed sanding system significantly saves operational costs for locomotives. It can be assumed that railway operators who operate locomotives in mountainous countries (in comparison to the Slovak Republic) with a stronger need to use the sanding system during locomotive operations can save much more money.

The results and findings of the research are compared with the existing results in this field. In comparison to the works [18,19], the proposed solution is focused on wheel/rail adhesion improvement of which a new design of the sanding system is suggested. It should be noted that various adhesion materials could be applied in the future with the aim to assess how this will manifest in a combination with the new designed sanding system.

In contrast with the work [20,21], a particular practical contribution focused on the wheel/rail adhesion is suggested. The mentioned works [20,21] only describe a problem of adhesion importance.

When the presented research and the designed technical solution of the sanding system were compared with the work [8], the main advantage of the designed system consists in minimizing the sand losses. Similarly, the work [22] also presents only a regulation of the sand amount. We have designed a system so that sand is not lost from the rail working surface.

Any of the analyzed patents [33,34,35,36,37,38,39,40,41,42] were not aimed at the improvement of the nozzle position or dosing using it. They are aimed at the improvement of the designs as a whole, i.e., sand amount regulation, reduction in the wedging surface, reduction in a wheel sliding on a rail, a modification of a pipeline and similar.

The deficiencies of the presented research consider the fact that we did not investigate the dynamics of the train set, i.e., that a locomotive would be a part of a rail vehicle set with the applied sanding system. Further, it is a research limit that the system was investigated only for the track gauge of 1435 mm. Although it is widely used in Europe, a significant part of the railway infrastructure uses the track gauge of 1520 mm. These described disadvantages of the research are being considered to be solved as a continuation of the research in the near future. We also plan to perform experimental measurements on a real locomotive. For now, this is under development. The presented investigation will continue for the locomotive and railway transport as a whole.

5. Conclusions

Rail vehicles are equipped with a sanding system, i.e., they use sand in the wheel/rail contact to increase the adhesion between the wheels and the rails. Therefore, it is necessary to realize more traction effort when starting the run and acceleration. Also, sand should be supplied under the wheels during braking to ensure the most efficient implementation of braking forces and for traffic safety. In this research, the principle of the locomotive sand system was reviewed, and examples of an existing solution to the issues under investigation were given. The main point of the presented research was to propose a design of a sanding system to improve the efficiency of the sanding system. It is proposed that the nozzle of the sanding system is attached to the axlebox instead of being attached to the bogie frame. This system allows a more stable nozzle movement relative to the wheel/rail contact point while the rail vehicle is in movement both on a straight as well as on curved railway track sections.

A simulation model of the locomotive bogie was created to study the properties of the proposed sanding system design and to compare its properties with the existing design in the MBS Simpack software 2024.3. The values of the amplitude of the irregularity of the track are equal to 0.002 m and 0.005 m.

Based on the results of simulation calculations, graphs of the amplitude waveforms of the sanding system nozzle motion relative to the wheel/rail contact were plotted. Based on the analysis of the obtained graphs, the following results were achieved:

• The maximum peaks of nozzle movement relative to the wheel/rail contact attached with the adaptive system to the axlebox do not go beyond the running surface of the rail;
• Maximum values of amplitudes of nozzle movement relative to the wheel/rail contact attached by the adaptive system to the axlebox are 0.022 m for the straight track section and 0.023 m for real track section;
• Maximum values of amplitudes of nozzle movement relative to the wheel/rail contact attached to the bogie frame are over 0.040 m for the straight track section and over 0.035 m for the real track section;
• Short radius curves on station or industrial tracks where shunting locomotives operate can lead to excess sand spillage beyond the point of contact between the wheel and rail, causing environmental pollution and excessive sand consumption. The attachment of the nozzle to the axlebox can help to reduce the motion of the nozzle and stabilize its position relative to the point of wheel/rail contact, resulting in reduced sand consumption and pollution;
• The newly designed sanding system with the nozzle attached to the axlebox improves the adhesion properties of the locomotive so that it ensures significantly smaller nozzle amplitudes in comparison with the original sanding system (with the nozzle attached to the bogie frame);
• The newly designed sanding system allows one to save 42.3% to 53.85% of sand during operation in comparison with the original sanding system. Considering the need of a freight railway operator in the Slovak Republic, this would lead to a saving of approximately EUR 6600 to EUR 8400 per year for sand buying costs;
• A disadvantage of the research is that the system was analyzed only on a locomotive bogie and for the track gauge of 1435 mm. It is supposed that the dynamics of the train set during movement and the application of the system of different track gauges (e.g., 1520 mm) will reveal some issues, which should be solved in the future.