Keywords

1 Introduction

The braking system is the safety guarantee for the operation of the train. Among all the braking methods, disc braking is widely used in high-speed train braking due to its advantages of safety, stability and good heat dissipation performance. During braking, the braking system converts kinetic energy of the train into thermal energy, thus slowing or stopping the train [1]. Experimental research has shown that for every doubling of the train speed, the required braking power increases eight times [2]. During emergency braking, more kinetic energy of the train is converted into thermal energy of the brake disc through friction, and the temperature of the brake disc rises rapidly. As one of the important devices to ensure the safety of trains, the braking system will bring great potential safety hazards to the operation of the train if the heat generated by the brake disc cannot be dissipated in a timely and effective manner [3, 4].

Therefore, this article starts from the temperature changes of the brake disc during the entire braking process in a flow field environment, and studies the simulation method of heat dissipation. This article uses the ANSYS-FLUENT software to simulate it. Assuming that the brake disc is in an open flow field environment, and studies the temperature distribution law of the brake disc surface and the heat dissipation of surface under emergency braking conditions with an initial speed of 400 km/h, and obtains the factors that affect the temperature rise of the brake disc.

2 Simulation Model

2.1 3D Model and Grid Division

This article analyzes the shaft-mounted brake disc used in high-speed trains. Using SOLIDWORKS software for modeling, and in order to save computational costs and facilitate the generation of meshes, the brake disc is reasonably simplified, ignoring subtle features that have a small impact on the simulation results. The main dimensions of the brake disc are shown in the following Table 1.

Table 1. Main dimensions of brake disc
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The actual brake disc model is completely symmetrical and consists mainly of friction rings, heat dissipation ribs, etc. During train braking, the friction ring surface comes into direct contact with the brake pads, generating strong frictional resistance that slows or stops the train. Although the train and other structures are also neglected here, the brake disc is not placed separately in the flow field for calculation [5], which will result in the brake disc being close to the axis region of the inner ring, that is, the axle position is also filled with air, making the original leeward area of the disc surface become windward. Based on the above considerations, when establishing the solid calculation domain model of the brake disc, the disc claw and a section of the axle connected to the brake disc are retained. Figure 1 is a three-dimensional solid model of the brake disc for calculation, where the right side is a section model of the brake disc cut along the symmetrical section. As can be seen from the figure, the interior of the brake disc mainly contains several cylindrical heat dissipation ribs with equal diameter and uniform arrangement. The uniform arrangement of the heat dissipation ribs can make the temperature rise of the brake disc friction surface consistent under the action of friction heat generation, and the thermal stress on the friction ring is equal [6].

Fig. 1.
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Three-dimensional model of solid computational domain

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Based on the three-dimensional model of the brake disc, a fluid-solid coupling model containing a fluid calculation domain is created. In fluid calculation, in order to prevent the boundary from affecting the research object, it is required to have an infinite flow field, but it is difficult to achieve in actual grid generation [7]. The fluid region established in this article is mainly to simulate the physical environment in which the brake disc works. However, because the single brake disc heat dissipation simulation calculation is mainly used for the principle verification analysis of brake disc heat transfer, to study the heat transfer characteristics of the brake disc, and to compare and verify with the model simulation of the complex structure of the high-speed train head, in order to save computational costs, it is assumed that the brake disc is in an open and unobstructed fluid environment, that is, the fluid domain is simplified to a rectangular region with a size of 7 m * 3.5 m * 3.5 m. The calculation model is shown in the Fig. 2(a). The processed model is meshed, and the meshed grid is shown in the Fig. 2(b).

Fig. 2.
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(a). Fluid-solid coupling calculation model (b). Grid division of brake disc

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2.2 Working Conditions and Material Parameters

The braking condition used in the simulation is that the initial braking speed is 400 km/h. The deceleration during braking is as Table 2. The parameters of the brake disc materials used in the simulation are shown in Table 3. The physical parameters of air are shown in Table 4.

Table 2. Braking condition
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Table 3. Parameters of brake disc material
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Table 4. Parameters of air
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The loading of thermal flow on the surface of the brake disc is using an equivalent friction heat calculation method. The emergency braking of a train with a initial speed of 400 km/h takes a total of 101 s from the application of braking to the complete stop of the train. The calculated set duration is 120 s, which includes the entire process from the application of braking to the end of braking at the time of 101 s, as well as the 19 s of the train’s stationary state after completing braking. The simulation results mainly focus on the temperature variation law of the brake disc and the dynamic convection heat dissipation of the brake disc surface, and study the temperature rise law and influencing factors of the brake disc.

3 Fluid-Solid-Thermal Coupling Simulation Results

3.1 Law of Brake Disc Solid Temperature Rise

Fig. 3.
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Temperature curve of brake disc friction surface

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The surface of the brake disc comes into direct contact with the outside air, so there is both thermal conduction between solids and convection between fluids on the surface. As shown in Fig. 3, the maximum and average temperatures of the brake disc friction surface vary with time. It can be clearly seen from the figure that the disc surface temperature rises first and then falls with time. This is because the heat flow input at the initial node is greater than the output, resulting in an increase in the node temperature. At around 60 s, the temperature curve rises abruptly, which is due to changes in the deceleration of the train and the work done by the friction force, resulting in a sudden change in the input heat flow. When the heat flow input and output reach equilibrium, the node temperature reaches its maximum, and then the heat flow input at the node is less than the output, and the temperature begins to decrease. This calculation condition reaches its maximum disc surface temperature of 1103.08 K at around 72 s.

Figure 4 shows the temperature cloud maps of the brake disc surface at different times. It can be seen from the figure that the temperature distribution of the brake disc friction surface along the circumferential direction has little difference, and it generally shows an upward trend along the radial direction. The surface temperature of the heat dissipation ribs gradually increases with time, mainly due to the heat conduction between solids, where heat is transferred from the higher temperature friction surface to the lower temperature area, especially through the comparison of the temperature cloud maps at different times. It can be seen that with the increase of time, the temperature difference between the friction surface and the heat dissipation ribs decreases significantly.

Fig. 4.
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Cloud map of brake disc surface temperature at different times

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3.2 Convection Heat Dissipation on the Surface of the Brake Disc

Distribution of Air Velocity Flow Field Around the Brake Disc

During emergency braking, the running speed of the train decreases continuously as the braking time increases. At the same time, the rotational motion of the brake disc will interfere with the surrounding air flow, causing the flow velocity of the air to change continuously, which in turn leads to a corresponding change in the convective heat transfer coefficient of the brake disc surface. Therefore, air convection, as a major mode of heat dissipation of the brake disc, analyzing the distribution of the air flow field around the brake disc plays an important role in studying the temperature rise law of the brake disc [8].

In this simulation, the distribution of air flow around the brake disc is relatively simple. As time changes, the flow field speed gradually decreases, but the distribution law of the flow field around the brake disc remains basically unchanged. Therefore, only the flow field at the time of emergency braking for 20 s is analyzed here. Figure 5 shows the instantaneous velocity distribution cloud map of the air flow field at the z-x symmetric section position of the brake disc, which is similar to the temperature distribution of the air flow field.

Fig. 5.
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(a). Cloud map of air velocity; (b). Temperature cloud map of the air domain

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From the air velocity cloud map around the brake disc, it can be seen that during the braking process of the train, the air blown in from the front interacts with the airflow generated by the rotation of the brake disc, reducing the air flow velocity in front of the brake disc. The air flow velocity above and below the brake disc increases due to rotation. However, behind the brake disc, the air flow velocity decreases due to the obstruction of the brake disc.

In order to better analyze the flow pattern of air around the brake disc and in the channels near the cooling ribs under two different conditions: train operation and brake end, the distribution of air velocity around the brake disc and streamline diagram are output. Figure 6(a) shows the results during the braking process (time 20 s), when the train is still running. Correspondingly, Fig. 6(b) shows the results when the train is at a standstill (time 120 s).

From the velocity streamline diagram at time 20 s, it can be seen that some of the air flowing in from the inlet enters a complex channel consisting of heat dissipation ribs, and the flow velocity of the air inside the brake disc decreases significantly. Due to the multi-scale complex motion formed by the rotation of the brake disc and the horizontal travel of the train, as well as the complex structure of the brake disc, multiple flow phenomena with vortex structures appear around the brake disc, including near the heat dissipation ribs.

Fig. 6.
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Velocity streamline diagram around the brake disc

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From the velocity streamline diagram at time 120 s, it can be seen that after the braking is completed, the train and the brake disc are in a stationary state, and the air is not completely static or in irregular motion, but generally shows an upward trend, which is due to natural convection. Natural convection is a spontaneous heat transfer process that occurs due to the spontaneous motion of fluids participating in heat transfer due to their different densities [9]. From the previous analysis, it can be seen that after the emergency braking of the train is completed, the temperature of the solid brake disc is high, and the air around it will also be affected. Although the train is in a stationary state, due to uneven temperature distribution, the air around the brake disc has a low density of high temperature air, and the density difference causes fluid motion under the influence of gravity.

Coefficient of Convective Heat Dissipation on the Surface of Brake Disc

Thermal convection can be divided into forced convection and natural convection. The heat dissipation of trains under braking and running conditions belongs to forced convection, while the heat dissipation after the completion of braking belongs to natural convection [10]. In this simulation, the shape of the brake disc remains unchanged, and the convective heat transfer coefficient is mainly related to the flow state of the fluid. During the braking process, the spatial position of each point on the brake disc changes continuously and periodically, which causes the magnitude of the convective heat transfer coefficient at each point on the surface of the brake disc to also vary periodically. When a point on the disc surface rotates to a position with high air flow velocity in the flow field, the convective heat transfer coefficient at that point increases accordingly. Conversely, when a point on the surface rotates to a position with low air flow velocity in the flow field, the convective heat transfer coefficient at that point decreases accordingly.

By extracting the heat dissipation power of each part of the brake disc, it can be found through comparison that the heat dissipation power of the heat dissipation ribs is significantly lower than that of the brake disc friction surface, and the decrease in heat dissipation power of the cooling ribs compared to the brake disc friction surface has a significant lag. This is because, except for the contact surface, the input heat flow in the axial direction is mainly from the heat conduction of the upper nodes, and according to the principle of heat transfer, the heat conduction distance is proportional to the required time, so it takes a certain amount of time for the heat conducted from the upper layer to be transmitted to the lower nodes. Therefore, during braking, the temperature of the cooling ribs is always lower than that of the friction surface, and the numerical difference in heat dissipation power between the cooling ribs and the friction surface is mainly due to the temperature difference.

4 Conclusions

This article analyzes the simulation results of brake disc thermal dissipation under a simplified flow field environment, and obtains the general rules of brake disc temperature rise and heat dissipation process:

  1. (1)

    The surface of the brake disc is greatly affected by the heat flux density and air convection. The surface temperature of the brake disc is mainly affected by heat conduction and heat convection. The temperature of the friction surface rises first and then falls with time. Under emergency braking conditions with an initial speed of 400 km/h, the temperature of the brake disc reaches a maximum of 829.93 °C at time 72 s;

  2. (2)

    The convective heat transfer coefficient of the disc surface changes dynamically with time and space during braking, the air flow field distribution around the brake disc can be roughly divided into two different situations: the train running stage and the train stationary state. During the running process, the air flow velocity around the brake disc can be regarded as the superposition of the brake disc rotation and the air inlet velocity, and the flow field at the cooling rib is complex. After braking, the air flow is mainly caused by air convection generated by temperature difference in the stationary state of the train.