Thermo-mechanical coupling characteristics of the shearer’s guiding shoe during the friction | Scientific Reports

Scientific Reports volume 14, Article number: 24825 (2024) Cite this article

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The reliability and longevity of the guiding shoe are crucial for the proper functioning of coal mining machines. The heavy wear of the sliding surface under thermal stress coupling is the primary factor influencing the service life of the guiding shoe. To reveal the heat flow distribution patterns and the thermo-stress coupling mechanisms of the guiding surface, a thermo-mechanical coupling model of the guiding shoe and the pin row is established. The transient thermodynamic behavior of the guiding shoe under different load and speed conditions is studied using the coupled temp-displacement analysis method in Abaqus. The results indicate that the overall temperature of the guiding shoe friction surface experiences a rapid increase during the initial running-in phase, followed by a progressively slower temperature increase over time. Temperature and stress concentration regions on the friction surface primarily localize at the corners of the shoe groove, and the distribution of temperature and stress shows a strong coupling. Furthermore, elevated traction speed and mechanical load exacerbate the thermo-elastic instability of the guiding shoe, consequently augmenting thermal stress on the friction surface. The increase in support load results in significant thermal shock on the lower area of the left side of the guiding shoe. The research provides a reference for exploring the fatigue failure and wear mechanisms of the guiding shoe while considering thermal effects.

The double drum coal mining machine plays a vital role in coal mining. As a crucial component of the shearer’s traction system, the reliability and stability of the guiding shoe directly impact the mining efficiency of the longwall face1,2. During operation, the guiding shoe moves forward with the shearer. It supports and guides the shearer by frictional contact with the pin row on the scraper conveyor3,4. During the sliding contact between the guiding shoes and the pin row, most of the mechanical energy is converted into frictional heat, while some is converted into deformation energy. The contact surface between the guiding shoe and the pin row is not smooth. Under the combined effects of high temperature and heavy load, the contact surface may experience deformation, wear, and even failure5,6. This will seriously affect the normal operation between the guiding shoe and the pin row. Therefore, it is necessary to analyze the thermo-mechanical coupling mechanism and heat flow distribution of the friction contact surface between the guiding slipper and the pin row.

Many scholars, both domestically and internationally, have conducted thermo-mechanical coupling analyses on the key components of coal mining machines and have studied the heat generation mechanisms of the sliding shoe and its contact body. Jaśkowiec et al.7 conducted experimental research on the wear characteristics and mechanisms of the traction system of coal mining machines. They found that elevated temperatures lead to increased wear on the traction wheel. Chen et al.8 considered the friction coefficient under the influence of multiple factors on transmission gears and found that the environmental temperature is directly proportional to the temperature rise during gear engagement and inversely proportional to the temperature difference. Mao Jun et al.9 used the load of the smooth shoe test as an excitation to analyze the solid-thermo-mechanical coupling characteristics of the smooth shoe and found that the highest temperature of the smooth shoe is located at the center of its prismatic joint. Huang et al.10,11 developed a thermo-mechanical coupling friction model for elastic rough bodies. They discovered that at the moment of sliding and during the formation of flash temperatures, the Von Mises equivalent stress on the surface of the rough body undergoes significant changes. Andreas Draganis12 used a finite element model to study the distribution of transient temperature fields in rigid body motion. Hong Min et al.13 conducted friction tests on 40CrMo samples under different conditions and found that the average friction temperature ranged from 45 to 110 °C during relative motion speeds of 0.327–0.980 m/s. Gu et al.14 constructed a simplified frictional heat generation model for the guiding shoe and found that the instantaneous temperature during friction could reach 650 °C, while the maximum continuous working temperature could reach 136.7 °C. Gui et al.15 proposed a simulation method for thermo-mechanical-friction coupling in dry sliding systems. They found that material wear and thermal expansion affect the contact characteristics of contacting objects, indirectly influencing temperature and stress. Lestyán et al.16 established a three-dimensional rough surface model and used numerical simulation methods to calculate the temperature distribution on the contact surfaces. Pyung Hwang et al.17 found that the temperature and stress distributions on the disc are consistent and pointed out that asymmetric contact pressure is a significant factor leading to asymmetric temperature fields.

Currently, research on traction components of coal mining machines focuses primarily on dynamic performance, reliability assessment, and structural optimization. There is relatively little research on the frictional thermal effects of the guiding shoe and the pin row during operation, which hinders the understanding of the guiding shoe´s failure mechanisms under actual working conditions. Due to the non-smooth contact surface between the guiding shoe and pin row, fluctuations in interface contact pressure and shoe deformation during operation alter the contact state, resulting in significant thermal expansion of the sliding friction pair with localized contact. This can lead to thermal-elastic instability of the guiding shoe, causing localized differences in deformation and wear mechanisms at the contact surface. Therefore, the novelty of this manuscript lies in the development of a thermo-mechanical coupling model between the guiding shoe and the pin row, clarifying the differences in heat flow distribution and stress distribution patterns across different regions of the friction surface.

During the thermo-mechanical coupling process, the temperature field and stress field of an object interact with each other. The significant heat generated by the friction between the guiding shoe and the pin row causes the temperature to rise. This temperature increase leads to thermal deformation of the guiding shoe, which in turn affects the contact state of the friction pair and the distribution of thermal stress.

In finite element studies considering the thermo-mechanical coupling process, there are primarily two methods: the direct coupling method and the indirect coupling method. During the interaction between the guiding shoe and the pin row, friction generates uneven temperature and stress fields on the contact surface, resulting in varying contact pressures. The direct coupling method considers both the influence of temperature fields on thermal deformation of objects and the impact of thermal deformation on the contact status of friction pairs. Therefore, using the direct coupling method can more accurately simulate the interactions among temperature, stress, and load-bearing capacity of the guiding shoe during the traction process. The transient thermodynamic behavior of the guiding shoe is studied using the coupled temp-displacement analysis method in Abaqus. The computational process of the direct coupling method in finite element analysis is illustrated in Fig. 1.

Thermo-mechanical coupling calculation flowchart.

During the working process of the coal mining machine, the guiding shoe moves forward with the machine and causes sliding friction with the pin row. The primary source of energy dissipation in guiding shoes stems from the generation of frictional heat energy at the contact interface. This phenomenon can be quantified by the heat flux density at the frictional interface, which can be expressed as9,11:

Where qc represents the frictional heat flow on the friction surface, η is the heat energy conversion ratio, µf is the friction coefficient, p denotes the contact-specific pressure on the friction surface, v is the traction speed of the shearer, and x, y, z denotes the coordinates of the friction surface, t is the relative motion time of the guiding shoe and the pin row.

Assuming isotropic material properties for the guiding shoe and neglecting heat loss due to material wear during the frictional process of the shoe. The temperature field of the guiding shoe in the Cartesian coordinate system can be characterized by a three-dimensional unsteady thermal conductivity differential equation:

Where k represents the thermal conductivity of the guiding shoe, ρ denotes the density of the guiding shoe, c signifies the specific heat capacity of the guiding shoe, and T represents the guiding shoe’s temperature.

In addition to the heat generated by friction between the guiding shoe and the pin row, there is also the convection heat transfer and radiation heat release process in the contact and non-contact areas. Therefore, the thermal boundary condition of the guiding shoe can be determined by assuming the initial ambient temperature Tf is 20 ℃.

The convective heat transfer of the surface of the guiding shoe not in contact with the pin row can be expressed as:

The convective heat transfer of the surface of the guiding shoe in contact with the pin row can be expressed as:

Where ni is the normal unit vector of the non-friction contact surface of the shoes, nj is the normal unit vector of the friction contact surface of the shoes, hi is the convection heat transfer coefficient of the non-friction contact surface of the shoes, hj is the convection heat transfer coefficient of the friction contact surface of the shoes.

In addition, there is radiation heat transfer on the surface of the guiding shoe, and the formula for calculating heat flux can be expressed as:

Where qr is the radiation heat flux density, ω denotes the emissivity of the object, which ranges between 0 and 1.

Assuming that only elastic deformation occurs in the guiding shoe during friction. The temperature rise induces a temperature gradient and thermal deformation within the guiding shoe. Assuming the guiding shoe is isotropic and homogeneous, thermal expansion only produces linear strain, resulting in identical extensional strains in all directions. Temperature changes do not induce shear strain18:

Where εx2, εy2, εz2 represent the linear strains caused by temperature, while γxy2, γyz2, γxz2 represent the shear strains caused by temperature, α is the coefficient of thermal expansion of the guiding shoe.

Incorporating thermal deformation into the generalized Hooke’s law, the strain matrix ε of the guiding shoe, resulting from both temperature and stress, can be expressed as follows19:

Where εx, εy, εz are the linear strains of the guiding shoe, and γxy, γyz, γxz are the shear strains, E is the modulus of elasticity, µ is the Poisson’s ratio, σx, σy, σz are the normal stresses, and τxy, τyz, τxz are the shear stresses.

From Eq. (8), the stress components can be expressed in terms of strain components, as follows:

Where σ represents the total stress matrix of the guiding shoe. e is the volumetric strain, λ is the Lame constant, G is the shear modulus, β is the thermal stress coefficient.

The MG650/1620 shearer and SGZ1000/2 × 700 scraper conveyor were studied using the finite element software Abaqus 2021 to construct a frictional contact model between the guiding shoe and the pin row. During the load-bearing process, the ear plate hole of the guiding shoe and its connection with the shoe often become a crucial area of stress concentration20. However, considering that the focus of this article is on the thermal coupling effect of the frictional contact surface between the guiding shoe and the pin row. The structure of the guiding shoe was simplified by removing the ear plate structures on both sides to mitigate potential interference from stress concentration at the ear plate position on the research results. The main dimensions of the guiding shoes are shown in Fig. 2. Assuming isotropic elastic materials for both the guiding shoe and pin row, Table 1 presents the basic material properties of each component. In Abaqus, material properties can be defined with temperature-dependent parameters. The material parameters from.

Schematic diagram of the main dimensions of the guiding shoe.

Table 2 are imported into the material property settings of the guiding shoe in tabular format. It is assumed that the material properties of the pin row remain constant with temperature due to the short contact time between the pin row and guiding shoe within the same section.

The thermo-mechanical coupling model of the guiding shoe and the pin row is shown in Fig. 3. During operation, the pin row is fixed on the scraper conveyor, and the guiding shoe undergoes relative motion with the pin row driven by the walking wheel. Therefore, in the model, apply fixed constraints to the lower surface of the pin row, allowing the guiding shoe to undergo relative sliding along the x-axis direction with respect to the pin row. The translational degrees of freedom along the x, y, z axes of the guiding shoe have been released, while all rotational degrees of freedom have been constrained, allowing relative sliding between the guiding shoe and the pin assembly along the x-axis. As the study focuses on the thermo-mechanical coupling of the guiding shoe, the model mesh employs hexahedral elements (C3D8RT) with temperature degrees of freedom included. Mesh refinement is applied to the contact area between the guiding shoe and the pin row to enhance simulation accuracy. The guiding shoe is divided into 141,730 units, while the pin row is divided into 34,255 units. For defining friction surface behavior, the normal behavior is set as hard contact, indicating no penetration in the normal direction, with a friction coefficient of 0.15. The guiding shoe primarily bears the self-weight of the shearer and the cutting force of the drum. The support load is set to 120 kN, applied uniformly along the negative y-axis direction on the outer upper surface of the guiding shoe. The lateral load is 110 kN, applied uniformly on the outer left surface of the guiding shoe. The traction speed is 0.15 m/s, and the total simulation duration is 10 s22. Thermal boundary conditions include an ambient temperature of 20 ℃, a surface convective heat transfer coefficient of 12, and a thermal radiation emissivity of 0.2 for the object surface14. Simulations are performed on a computer equipped with an Intel(R) Xeon(R) CPU E5-2620 v3 processor, 32GB of RAM, and running Windows 7 Professional.

Thermo-mechanical coupling simulation model.

Before delving into the thermal coupling mechanisms of the guiding shoe, it is necessary to validate the accuracy of the finite element model. Since there are differences in the temperature values of the guiding shoe under different working conditions, it is difficult to verify the validity of the model by comparing the temperature values. Therefore, the Spearman correlation coefficient23 is introduced to quantify and analyze the temperature data obtained from this model and the model or experimental data from other literatures. The Spearman correlation coefficient can reflect the correlation of the changing trends between different data, as follows:

where xi is the rank of the ith data of the random variable x, yi is the rank of the ith data of the random variable y,‾x and‾y denote the expectations of x and y, respectively.

In terms of the trend of temperature changes, Fig. 4a illustrates the variation in the maximum contact temperature on the friction surface of the guide shoe over time, as calculated based on the model established in section “Development of a finite element model for theguiding shoe”. It indicates a rapid increase in temperature during the initial contact stage, followed by a gradual slowing of the upward trend. This trend aligns with the results obtained from the simplified heat transfer model based on the moving heat source method, as shown in Fig. 4b−d. Table 3 lists the Spearman correlation coefficients for each comparison group. For multiple sets of data in literature9 and literature13, the Spearman correlation coefficients of each set of data relative to the model data were calculated and averaged. The Spearman correlation coefficients of each group of data exceeded 0.8. This strongly supports the reliability of the temperature trend analysis between this model and other models. Additionally, literature24 utilized ANSYS finite element software to simulate the temperature distribution during the operation of the guide shoe and found that the temperature peak on the left side is concentrated in the central lower region. This observation is consistent with the temperature distribution depicted in Fig. 5a. These results effectively validate the accuracy of this model in temperature prediction.

Temperature curve.

Temperature and stress cloud map of guiding shoe.

In terms of the distribution of stress, literature25 and literature26 both emphasize that the upper guiding surface and the inner corner of the guiding shoe are the weakest areas where stress concentration is most significant and most prone to damage. This conclusion is visually confirmed in the equivalent stress distribution shown in Fig. 5b. It can be observed from Fig. 5b that the maximum stress on the friction contact surface does not exceed 50 MPa, which is supported by the results in literature25. These agreements demonstrate the reliability of the thermo-mechanical coupling model presented in terms of stress analysis.

Provide further analysis on Fig. 4a. According to the differences in the rate of temperature rise on the friction surface, the heating process can be subdivided into three stages for detailed exploration. Firstly, during the rapid heating stage, from 0 to 2 s, the peak temperature of the guiding shoe friction surface quickly rises from 20 to 56.5 °C. This phenomenon occurs because of the delayed heat conduction, resulting in heat accumulation on the friction surface during the initial sliding stages, leading to a rapid increase in the maximum contact temperature.

Secondly, the period from 2 to 5 s constitutes the slow heating stage, during which the peak temperature on the friction surface rises from 56.5 to 65.8 °C. Due to the constant generation rate of frictional heat flux, the rate of temperature rise on the friction surface begins to slow down under the influence of heat conduction and convective heat transfer to the air. Finally, in the slow heating stage, from 5 to 10 s, the peak temperature on the friction surface increases only slightly from 65.8 to 71.5 °C. It is predicted that over time, the rate of temperature rise on the friction surface will further decelerate and gradually approach stability. The deformation and thermal expansion of the guiding shoe affect the contact status of the contact surface, causing changes in the numerical value and location of the maximum contact pressure, thereby influencing the temperature field distribution on the friction surface. Therefore, the maximum contact temperature will appear at different contact points, with corresponding fluctuations in values.

Stress cloud map of guiding shoe.

Temperature cloud map of guiding shoe.

Diagram of path selection.

During the sliding contact between two entities, the combined effects of mechanical stress caused by external loads, thermal stress due to temperature unevenness, and friction are referred to as equivalent stress (Von Mises stress). This stress is closely related to wear, end-face failure, and damage of the contact surface. According to the above division of the heating stages of the guiding shoe, the cloud maps of equivalent stress and temperature of the guiding shoe at the end of each stage are shown in Figs. 6 and 7. There is a strong coupling between the stress and temperature distribution on the friction contact surface, with both distributions highly consistent. High temperature and stress concentration regions are primarily located at the corners of the grooves. Furthermore, with time, both the temperature and stress of the guiding shoe show a gradually increasing trend. This is because the heat flux generated by friction accumulates over time, leading to an increase in the temperature of the friction surface. The temperature rise on the friction surface causes the thermal expansion of the guiding shoe, while the constraint effect of the low-temperature regions of the shoe on the thermal expansion of the friction area results in thermal stress within the shoe. When the temperature gradient inside the shoe increases, the thermal stress also increases accordingly.

To further explore the coupling relationship between the stress field and temperature field of the guiding shoe, the most significant stress and temperature concentration positions on the contact surface of the guiding shoe are divided into four regions. Four representative paths are selected in each region for analysis. Due to the symmetry of the guiding shoe, only the side with the more severe friction contact state was selected for analysis. The selected area and path division are shown in Fig. 8. All four paths take the end face of the guiding shoe as the coordinate origin, and d is the distance from the node on the path to the end face of the shoe. path 1 and path 4 are located on the upper contact surface of the guiding shoe, while path 2 and path 3 are on the left contact surface.

Temperature and stress at different positions along each path.

The average temperature and average stress of each path.

Figure 9 shows the variations in temperature and stress along the four paths in the frictional region at different times. It can be observed that the temperature and stress variations along the same path exhibit a high degree of consistency. This suggests that thermal stress resulting from temperature gradients significantly impacts the total stress of the guiding shoe.

As shown in Fig. 9a and b, for path 1, the temperature of the nodes gradually decreases as the distance from the nodes to the end face of the guiding shoe increases. Moreover, this path has a significant coupling relationship between stress and temperature. This reflects that the interface near the end face of the guiding shoe bears higher contact pressure during the friction process between the guiding shoe and the pin row. The guiding shoe generates a temperature gradient along the contact surface in the direction of relative sliding, resulting in significant pressure stress along the direction of relative sliding on the friction surface. This uneven thermal coupling effect may induce surface cracks in this area.

As shown in Fig. 9c and d, for path 2, the temperature of the nodes initially decreases and then increases with increasing distance from the nodes’ position to the end face of the guiding shoe. The lowest temperature along the path is approximately 230 mm from the end face of the guiding shoe. At 10 s, the trends of stress and temperature variation along the distance of the nodes are consistent. However, there are differences in the variation patterns of stress and temperature at 2 s and 5 s. This may be because the temperature in this friction region is lower at the end of 2 s and 5 s, thus thermal deformation and thermal stress are less pronounced. As the temperature of the friction surface continues to rise, thermal deformation changes the contact status of the surface in the range of 180–230 mm from the end face of the shoe, which causes a change in the position of stress concentration along the path. This indicates that the stress distribution, particularly the stress concentration position in the upper area of the left side of the guiding shoe, is significantly affected by the thermal effect of the friction surface.

As shown in Fig. 9e and f, the temperature and stress distribution along path 3 stabilize after 5 s. This indicates that the lower area of the left side of the shoe experiences uniformly distributed contact pressure during the stable friction contact stage between the guiding shoe and the pin row, and the difference in contact status along the entire path is relatively small.

As shown in Fig. 9g and h, for path 4, the temperature of nodes exhibits a trend of increasing and then decreasing with the increasing distance from the node position to the end face at different time points. The frictional heat flux mainly occurs and distributes within the range of 0–200 mm from the end face in this area, which is also the reason for stress concentration. Figure 10 shows the average stress and temperature of each path at 10 s. It can be observed that the average temperature and stress of nodes on path 1 are the highest, indicating that the average contact pressure on the upper side of the guiding shoe is greater than that on other paths, and the thermal effect in this area is the most significant.

The above analysis indicates the presence of significant frictional heating behavior on the friction surface of the guiding shoe. The overall temperature trend of the friction surface is rapid heating during the initial running-in period and slow heating during the stable friction stage. The degree of thermal effect varies in different regions of the friction surface, leading to varying impacts on the guiding shoe. The thermal effect is most pronounced on the upper side of the guiding shoe, where the thermal stress coupling effect is also most apparent. The stress distribution on the upper part of the left side of the guiding shoe is most sensitive to the frictional thermal effect.

With the continuous development of fully mechanized mining technology, the demand for high-speed traction of coal mining machines is becoming increasingly urgent in coal mining. However, the influence of traction speed on the thermal stress coupling characteristics of the guiding shoe is still not fully understood. Therefore, to reveal the mechanism of speed influence, temperature and stress distribution data for each path were obtained for seven sets at traction speeds ranging from 0.1 m/s to 0.2 m/s, as shown in Fig. 11.

The variation of temperature and stress along each path with traction speed.

Figure 11 shows the variations trends of stress and temperature on four different paths of the friction surface of the guiding shoe with traction speed, the curve 0.1T represents the temperature of the path at 0.1 m/s, the curve 0.1 S represents the stress of the path at 0.1 m/s, and so on for the rest. As the traction speed increases, the temperature of the guiding shoe’s contact surface continuously rises. This is because the increasing traction speed leads to a higher heat flux density. The rising temperature of the friction surface increases the internal temperature gradient of the guiding shoe, resulting in greater thermal stress. The total stress on the guiding shoe is far below the material’s yield strength. However, the high temperatures induced by high speeds exacerbate the thermal elastic instability of the guiding shoe, resulting in increased internal thermal stresses. This significantly reduces the fatigue cycle count and lifespan of the guiding shoe’s wear-resistant layer. Therefore, in the design and usage of the guiding shoe, careful consideration should be given to the influence of traction speed on the temperature and stress distribution of the friction surface to optimize performance and prolong lifespan.

Figure 11 shows the varying sensitivity of temperature and stress responses at different positions of the guiding shoe to changes in traction speed. Therefore, to investigate the differential impact of traction speed on the thermal stress coupling characteristics of different contact regions of the guiding shoe, the temperature peaks and stress peaks concerning traction speed were separately obtained for different paths, as depicted in Fig. 12.

The variation of peak temperature and peak stress of each path with increasing traction speed.

Figure 12(a) shows a linear regression analysis of the acquired stress and temperature data. The results indicate that the temperature peak of path 1 is the highest, followed by path 4. The temperature rise rates of paths 1 and 4 are nearly identical and greater than those of paths 2 and 3. This indicates that with increasing speed, the temperature accumulation on the upper contact surface of the shoe is the most severe. The thermal effect on the upper side is the most sensitive to changes in speed. This is attributed to the fact that the y-axis support load of the guiding shoe is greater than the z-axis load, and the contact area on the upper side of the shoe is smaller than that on the left side, resulting in greater contact pressure on the upper side and hence a higher heat flux density generated by friction. As shown in Fig. 12(b), The stress peak growth rate on path 1 is significantly higher than that of the other paths. This indicates that changes in speed cause the temperature gradient increase to be the greatest in the left part of the upper side of the guiding shoe, leading to more significant thermal stresses. This rapid temperature rise and stress variation may cause material delamination on the left side of the upper surface of the guiding shoe.

When the shearer encounters hard coal, gangue, uneven coal quality areas, or when the cutting depth increases, the cutting resistance of the drum will significantly increase, leading to an increase in the support load of the guiding shoe. Therefore, to study the effect of supporting load on the guiding shoe and the pin row’s thermal stress coupling characteristics of the guiding shoe under support loads ranging from 50 to 120 kN were obtained.

The variation of temperature and stress along each path with supporting load.

Figure 13 shows the variations trends of stress and temperature within four paths on the friction surface of the guiding shoe under different support loads, the curve 60T represents the temperature of the path at 60kN, the curve 60 S represents the stress of the path at 60kN, and so on for the rest. It can be observed that the temperature and stress along each path exhibit highly consistent trends, both increasing with the rise in support load. The increased stress at the nodes along the paths is partly due to the amplified mechanical stress on the shoe caused by the increased support load. Additionally, the greater support load enhances the contact force on the friction surface, accelerating wear and releasing more heat. The resulting intense temperature rise on the friction surface leads to significant localized thermal stress.

Furthermore, as shown in Fig. 13c, significant fluctuations are observed in the temperature of path 3. This fluctuation is also slightly manifested in paths 1 and 2. Such fluctuations are caused by the combined effect of heat generation from friction, heat conduction, thermal convection, and thermal radiation18,27. This thermal shock effect occurs because the increased support load causes mechanical deformation and thermal expansion of the guiding shoe, disrupting the contact between the lower region of the left side of the guiding shoe and the pin row. The change in contact state prevents some nodes of the guiding shoe from maintaining stable contact with the pin row, which results in continuous fluctuations in contact pressure and frictional heat flux. This repetitive thermal shock can induce thermal fatigue damage to the lower area of the left side of the shoe, which significantly reduces the service life of the guiding shoe.

The variation of peak temperature and peak stress of each path with increasing supporting load.

Temperature and stress peak values are obtained for different paths under varying support loads and subsequently subjected to linear fitting, as shown in Fig. 14. The results indicate that all four paths’ peak stresses and temperatures exhibit an almost linear increase with increasing support load. The rate of increase in the peak stress and temperature values is highest for path 1, followed by path 4. The growth rate of peak stress and temperature values in paths 1 and 4 is significantly faster than in paths 2 and 3. This indicates that the supporting load has a greater impact on the contact of the upper side than the left side. This is because the supporting load is mainly borne by the upper contact surface of the guiding shoe. An increase in support load leads to greater deformation and contact pressure in this area, resulting in a significantly faster increase in temperature and stress than in other areas. Prolonged exposure to high temperatures, high stress, and thermal shock may cause the failure and peeling of the wear-resistant layer on the upper side of the shoe, leading to a reduction in its thickness.

When the coal mining machine operates in an upward or oblique cutting condition, the lateral force acting on the guiding shoe will increase. Excessive lateral force can disrupt the stability of the traction system and accelerate the damage to the components of the walking mechanism. Therefore, to investigate the influence of lateral force on the thermal stress coupling between the guiding shoe and the pin row, the thermal stress coupling characteristics of the guiding shoe were obtained under lateral forces ranging from 40 to 110 kN.

The variation of temperature and stress along each path with lateral force.

Figure 15 shows the variations in stress and temperature along four paths within the friction surface of the guiding shoe under different lateral loads, the curve 50T represents the temperature of the path at 50kN, the curve 50 S represents the stress of the path at 50kN, and so on for the rest. The results indicate that the stress and temperature of nodes in paths 2 and 3 significantly increase, while the stress and temperature of nodes in paths 1 and 4 change slightly. This is because paths 2 and 3 are located on the left side of the guiding shoe, where the lateral load has a greater impact on the contact force of the guiding shoe’s left side. Additionally, as shown in Fig. 15c, thermal shock effects caused by load fluctuations persist on path 3, making the shoe’s left side the most vulnerable to fatigue damage.

The variation of peak temperature and peak stress of each path with increasing lateral force.

With the increase in support load, the peak temperatures and peak stresses for different paths were obtained and linearly fitted, as shown in Fig. 16. It can be observed that, compared to paths 2 and 3, the temperature and stress of paths 1 and 4 are less sensitive to changes in lateral load. However, both the peak stress and peak temperature of paths 2 and 3 increase linearly with the increase of lateral. The peak stress and temperature of path 3 are greater than those of path 2. This could be attributed to the larger proportion of lateral load borne by the lower area of the left side of the guiding shoe. On the other hand, considering the analysis of Fig. 15c, the significant temperature fluctuations on path 3 lead to higher thermal stresses than path 2.

A thermo-mechanical coupled finite element model of the guiding shoe and the pin row was constructed to reveal the thermal flux distribution patterns on the guiding surface of the guiding shoe and the mechanism of thermal stress coupling. The effects of different traction speeds and mechanical loads on the thermal flux and stress distribution on the friction surface of the guiding shoe were discussed separately, and the research findings are as follows:

At the initial stage of sliding friction of the guiding shoe, the contact temperature of the friction surface rapidly increases due to the sudden change in relative sliding speed. Subsequently, under the effects of heat conduction and convective heat transfer, the rate of increase in the maximum contact temperature of the friction surface slows down.

The thermal effect is most significant on the upper side of the guiding shoe, with the highest temperature rise within the same time frame. The frictional thermal effect notably impacts the stress distribution in the upper area of the left side of the shoe, where temperature changes can alter the location of stress concentration.

The traction speed significantly affects the frictional thermal effect on the guiding shoe, with an increase in traction speed exacerbating the thermoelastic instability in various contact areas of the shoe. The temperature accumulation and stress increase are most significant on the upper contact surface of the guiding shoe. The temperature and stress sensitivity to velocity changes is highest in the left contact area on the upper side.

The temperature and stress on the friction surface increase with the load of the guiding shoe bears. The supporting load has a greater impact on the thermal effect and equivalent stress of the upper side of the guiding shoe compared to the left side, while the lateral load has a greater impact on the left side than the upper side. The increase in supporting and lateral loads causes mechanical deformation and thermal expansion of the guiding shoe, leading to significant thermal shock effects in the lower left side area of the shoe.

This study provides an important reference for elucidating the fatigue failure mechanism and wear mechanism of guiding the shoe’s friction surfaces under thermal effects. However, the impact of cutting load on the thermal effects of the guiding shoe has yet to be considered in this study. To reveal the performance and failure mechanisms of the shoe more comprehensively under actual operating conditions, subsequent research could further explore the influence of the time-varying characteristics of cutting load on the thermo-mechanical coupling characteristics of the guiding shoe.

The data used to support the findings of this study are available from the corresponding author upon request.

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This research was funded by the Natural Science Foundation of China (Grant No. U23A20599; 52274132); the central government guides local funds for science and technology development (YDZX2022013); the Postdoctoral Fellowship Program of CPSF (GZC20240948); Qingdao postdoctoral project (QDBSH20240102076). Shandong Postdoctoral Science Foundation (SDCX-ZG-202400230).

College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

Lirong Wan, Jinwei Wang, Dejian Ma & Qingliang Zeng

College of Safety and Environmental Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

Dejian Ma

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L.W. and D.M. are mainly responsible for conceptualizing, structuring, establishing theoretical models, analyzing results, and writing manuscripts. J.W.is mainly responsible for solving the model of the manuscript and writing the original manuscript. Q.Z. is mainly responsible for providing financial support.

Correspondence to Dejian Ma.

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Wan, L., Wang, J., Ma, D. et al. Thermo-mechanical coupling characteristics of the shearer’s guiding shoe during the friction. Sci Rep 14, 24825 (2024). https://doi.org/10.1038/s41598-024-76505-8

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Received: 17 April 2024

Accepted: 14 October 2024

Published: 22 October 2024

DOI: https://doi.org/10.1038/s41598-024-76505-8

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