Study on the dynamic response characteristics of hydraulic support columns under multi-condition impact loads

This study focuses on the performance of hydraulic support columns under complex operating conditions. By constructing a finite element model that accounts for actual connection relationships and contact nonlinearities, mechanical simulation tests were conducted to thoroughly analyze their dynamic response. The results indicate that under impact loads, the stress response of the key components of the hydraulic support column exhibits a three-stage characteristic: “impact transient-dynamic adjustment-steady-state transmission.” The maximum stress at the secondary guide sleeve reaches 1735.7 MPa, significantly higher than other components, necessitating focused optimization. The middle cylinder bears the primary stress transmission task during axial load transfer, with a stress exceeding 200 MPa over a length of 600 mm–50% longer than the bottom cylinder—and the maximum stress in the middle cylinder is 1.4 times that of the bottom cylinder. Under radial load, a ring-shaped high-stress zone forms at the bottom of the cylinder wall in the bottom cylinder, with stress values reaching 589.31 MPa. The stress in the fixed-end weld zone is less than 150 MPa, showing a significant difference. These conclusions provide important theoretical basis for the structural optimization design and service life improvement of hydraulic support columns, demonstrating significant engineering application value.

1 Introduction

Coal, as China’s primary energy source, has long dominated the national energy structure. With the continuous increase in mining depth and intensity, the underground working environment has become increasingly complex, placing higher demands on the structural strength and operational reliability of mining equipment. Hydraulic supports are the core equipment for roof control in fully mechanized mining faces, and their structural performance directly impacts the safety and stable operation of the coal mining system (Zhang et al., 2023; Cao et al., 2024). Among these, hydraulic support columns serve as the primary load-bearing components, and their structural design not only determines the support’s load-bearing capacity and service life but also plays a critical role in ensuring operational safety (Feng et al., 2024). During service, hydraulic support columns must withstand various combined effects such as static loads, impacts, and cyclic disturbances. Issues such as local buckling, stress concentration, and contact nonlinearity can easily lead to structural failure (Wu et al., 2023; Tan et al., 2023). Traditional designs are often based on simplified static models and empirical formulas, which fail to fully reflect the actual load characteristics and potential weak points, thereby limiting further optimization of structural performance and enhancement of safety redundancy (Ma et al., 2023).

In recent years, scholars worldwide have conducted extensive research on the structural response characteristics of hydraulic supports under impact loads, providing important theoretical foundations and engineering guidance for their safe design and performance enhancement. Xie et al. (2022) focused on the dynamic behavior of four-legged hydraulic supports under dual impact loads. Through simulation or experimental methods, they analyzed the structural response of the supports and investigated the influence of factors such as the sequence and amplitude of dual impact loads on their dynamic characteristics (stability, load-bearing capacity, etc.), aiming to clarify the mechanical behavior of supports under complex impact conditions. Ren et al. (2021) designed a 1:2 scaled hydraulic support model to analyze its response characteristics under dynamic impact loads and validated the dynamic impact experiments in ADAMS. The results indicated that the impact resistance of hydraulic supports is largely dependent on the initial support conditions, and different vertical stiffnesses affect the energy distribution ratio of the system. In terms of structural optimization, (Cao et al., 2023) systematically analyzed the dynamic response characteristics of hydraulic supports under overload conditions, revealing significant stress concentration and local compression deformation in critical structural regions under impact loads. Structural response patterns indicate that as impact intensity increases, the risk of instability in the columns and roof beams rises, and the overall stiffness of the support exhibits a nonlinear decay trend. Kumar et al. (2020) overcame the limitations of the traditional SIMP method in fluid domain design through pressure load-dependent structural topology optimization based on the Darcy model. Wang et al. (2022) established a rigid-flexible coupled dynamic model of hydraulic supports, simulated the dynamic response of the support under vertical impact loads using the ADAMS platform, and analyzed the effects of impact intensity and load frequency on pillar displacement and stress evolution. Yang et al. (2020) constructed a dynamic model for ultra-high-height hydraulic support systems and systematically investigated the comprehensive effects of impact loads on the stress state and dynamic characteristics of the support structure. Wang et al. (2024) combined the finite element (FE) method with the smooth particle hydrodynamics (SPH) fluid-structure interaction method to study the dynamic response patterns of conventional pillars and energy-absorbing pillars under impact loads ranging from 4.5 to 10.5 tons. They validated the simulation results through free-fall hammer tests, which showed that the peak displacement of energy-absorbing pillars was reduced by 16%–30% compared to conventional pillars, and an approximately 80% improvement in energy dissipation capacity, significantly enhancing the pillar’s impact resistance performance. Zhang et al. (2025) utilized high-precision finite element simulation to study the stress distribution patterns of hydraulic pillars under dynamic loads and fatigue conditions, and combined a short-term memory neural network (LSTM) to construct a pillar fatigue life prediction model, proposing a new approach for real-time stress monitoring and remaining life prediction of pillars.

Although significant progress has been made in the research on the structural design and optimization of hydraulic support columns, there are still several shortcomings in multi-condition analysis. First, existing studies have mainly focused on single-direction impact loads or separate simulations of static and dynamic loads, neglecting the effects of radial and other non-axial impacts on hydraulic support columns. This results in an inability to accurately reflect their actual stress states under complex service conditions. Second, in terms of structural modeling details, many studies have failed to consider the actual connection methods between components of hydraulic support columns, such as welding, threaded connections, and other contact relationships, as well as nonlinear effects, thereby affecting the accurate assessment of local stress concentration and structural deformation characteristics. Finally, the simulation results of traditional hydraulic support columns are often limited to stress contour plots, making it difficult to reflect the details of impact load transmission within the structure.

This paper takes the ZY14790/15/25D hydraulic support column as the research object (as shown in Figure 1), focusing on the limitations of existing research in complex load modeling and transient response analysis, and systematically conducts structural modeling and dynamic simulation studies. During the research process, based on the characteristics of the solid hydraulic support column, key details such as welding positions and threaded connections were subjected to refined simulation modeling, with full consideration given to contact relationships and their nonlinear effects. By quantitatively analyzing the stress response patterns of key components of the hydraulic support column under impact loads, the study aims to provide theoretical support and engineering practice references for the safe design and structural optimization of hydraulic support columns under high-impact conditions, thereby holding significant academic value and application potential.

Figure 1

Figure 1. ZY14790/15/25D type hydraulic support.

2 Modeling and preprocessing of hydraulic support columns

2.1 Modeling of hydraulic support columns

In the finite element analysis of hydraulic support columns, constructing a three-dimensional geometric model is a prerequisite for ensuring the accuracy of simulation results and their engineering applicability. Although hydraulic supports often employ dual-column or four-column structures working in tandem, the single support column serves as the basic unit in a symmetric system. Its load-bearing characteristics are representative, and it facilitates focusing on the local response and shock propagation patterns of critical components while reducing modeling and computational burdens and avoiding coupling interference (Xie and Yang, 2024). Therefore, this study takes the single support column of the ZY14790/15/25D-type hydraulic support as its research object.

To simulate actual operating conditions, this paper performs precise modeling of the hydraulic support column. The modeling process retains the load-bearing components such as the bottom cylinder, middle cylinder, mobile column, and guide sleeve, while the hydraulic oil inside the cylinder is simplified as stationary fluid, omitting non-structural details such as oil supply lines and safety valves. The simplified model is shown in Figure 2. During modeling, all components were handled strictly according to their actual connection methods: the mobile column is welded to the cylinder head, the bottom cylinder is welded to the cylinder base, and the guide sleeve is fixed to the middle cylinder and bottom cylinder via threaded connections. This ensures the accuracy of boundary condition settings in finite element simulations. Key structural parameters of the hydraulic support column are listed in Table 1.

Figure 2

Figure 2. Simplified model of the ZY14790/15/25D hydraulic support column.

Table 1

Table 1. Partial parameters of ZY14790/15/25D hydraulic support columns.

2.2 Simulation preprocessing

This paper employs a hybrid mesh of hexahedral and tetrahedral elements for the discretization of hydraulic support columns (Zhang and Zhang, 2022). For long cylindrical structures such as the bottom cylinder, middle cylinder, and mobile column, the main regions are divided into structured hexahedral elements to enhance the accuracy and convergence of transient dynamic analysis, as shown in Figure 3c. It is clear to use the SOLID186 advanced hexahedral unit (for the bottom cylinder, middle cylinder and other regular areas) and SOLID191 tetrahedral unit (for the thread, weld and other geometric complex areas) in ANSYS Workbench. Four grid sizes (20 mm, 15 mm, 10 mm, and 8 mm) were designed. Using the maximum stress of the secondary guide sleeve as the evaluation metric, comparative results showed: When reducing the grid size from 15 mm to 10 mm, the stress variation rate decreased from 7.2% to 2.1%; further reduction to 8 mm resulted in only a 0.8% change rate. Therefore, 10 mm was determined as the optimal grid size (see attached grid sensitivity analysis table containing unit count, computation time, and stress deviation for different dimensions). For geometrically complex regions such as threads, unstructured tetrahedral elements are used, connected via common node interfaces to ensure mechanical continuity and numerical stability. The mobile column is modeled entirely using hexahedral elements. The first- and second-stage guide sleeves are modeled using explicit thread modeling based on structural features, with the main regions divided into hexahedral elements and thread regions using tetrahedral elements. Node transitions are set at the interfaces to ensure structural response continuity and solution stability. The “force-displacement dual convergence” standard is adopted: the force convergence threshold is set to 0.001 (relative error), and the displacement convergence threshold is set to 0.005 mm (absolute error); in transient analysis, energy convergence is additionally set (the ratio of kinetic energy and internal energy is stabilized within 5%), so as to ensure that no values diverge during impact.

Figure 3

Figure 3. Schematic diagram of the predetermined paths of the middle cylinder and bottom cylinder (a); Parts breakdown of the ZY14790/15/25D hydraulic support column (b); Schematic diagram of the mesh division of key components of the hydraulic support column (c).

Previous studies on stress analysis of cylinder body structures have primarily focused on simple quantification of maximum and minimum values, failing to reveal the spatial distribution characteristics of stress within the structure. To quantitatively analyze the axial stress distribution pattern, we pre-set multiple axial measurement paths on the cylinder walls of the bottom and middle cylinders (with a starting point at the cylinder base and an endpoint at the cylinder opening, spaced 50 mm apart), as shown in Figure 3a. This ensures that before citing the chart, its “purpose” is first explained, followed by detailed analysis based on the diagram’s details.The path starting point is located at the cylinder bottom, and the endpoint extends to the cylinder opening. Stress data is sequentially extracted along the axial direction, forming a continuous stress distribution curve. While maintaining geometric consistency, the study meticulously captures the trend of stress changes along the axial direction, enabling quantitative identification of local stress concentration zones and transition zones.

The explicit solver ANSYS LS-DYNA was employed to investigate transient impact loads with loading times <0.5 s. The explicit approach effectively avoids the convergence issues inherent in implicit methods. Time steps were set to 1e-6s (meeting Courant-Friedrichs-Lewy conditions to ensure accurate computation of shock propagation), with total computation duration spanning 0.6 s that covers the full process stages: “impact transient-dynamic adjustment-steady-state transmission”. The component disassembly of ZY14790/15/25D column is shown in Figure 3b, which illustrates the assembly relationships of key components including the bottom cylinder, middle cylinder, and guide sleeve. Figure 3c presents a schematic diagram of meshing for critical components, demonstrating the transition method between structured hexahedral meshes in regular areas (middle cylinder) and unstructured tetrahedral meshes in threaded regions.

The cylinder body material of the hydraulic support column is made of 27SiMn alloy steel, with its performance parameters listed in Table 2. To realistically simulate the force and motion states of the ZY14790/15/25D hydraulic support column under extension and transient impact conditions, the model establishes reasonable contact relationships and boundary conditions for critical components: surface-to-surface contact is defined between the mobile column and the middle cylinder, as well as between the middle cylinder and the bottom cylinder, to simulate axial sliding and bending effects. Similarly, surface-to-surface contact is established between the mobile column and the secondary guide sleeve, as well as between the middle cylinder and the primary guide sleeve, to constrain radial displacement and tilting. The friction coefficient for contact is set to 0.1, and the nonlinear contact algorithm and separation-recontact option are enabled to capture gap opening and instantaneous contact changes under impact conditions. In terms of boundary conditions, the end face of the mobile column head serves as the load application surface. The threaded or welded connections between the guide sleeves and cylinder bodies are implemented via node binding or common node interfaces (Guo and Han, 2023).

Table 2

Table 2. Main properties of 27SiMn.

2.3 Load condition setup

After completing the preprocessing of the finite element model, in order to accurately obtain the stress response characteristics of the hydraulic support column under actual working conditions, it is necessary to apply loads to the model in conjunction with the working environment of the hydraulic support, and select an appropriate numerical solver to perform analysis and calculation, so as to ensure the physical validity and engineering applicability of the simulation results. The system’s rated working resistance is 22,000 kN, and the maximum working height is 2.5 m. To closely approximate actual operating conditions and ensure that the load input aligns with the stress state of the support column, thereby enhancing the accuracy and representativeness of the stress analysis, the applied load should be 1.5 times the rated working load, considering the safety margin under extreme conditions. Figure 4 is the schematic diagram of column mechanical analysis, which marks the axial load F, radial load Fa and the angle θ = 7 between the column and the top beam, and specifies the decomposition direction and geometric relationship of the force.

Figure 4

Figure 4. Schematic diagram of the mechanical analysis of hydraulic supports.

Previous studies have shown (Wan et al., 2023) that the angle formed between the hydraulic support columns and the top beam during operation must be strictly controlled, with a maximum threshold of 7°. Based on this technical specification, equivalent loads were applied to the ZY14790/15/25D hydraulic support columns under impact conditions. Based on the principle of force decomposition, an axial load F = 11,000 kN was set. Combining the angle constraint, the radial load.

$F_a=F\times \cos 83°=1320\text{\hspace{0.17em}kN}$

By reproducing the load boundary conditions under impact conditions, the mechanical characteristics study is ensured to align with actual engineering conditions, laying the foundation for subsequent simulation analysis of the pillar’s stress and deformation responses.

Full constraint is applied to the welded area between the cylinder base and seat (displacement U_x = U_y = U_z = 0, rotation R_x = R_y = R_z = 0) to simulate the rigid connection between the cylinder base and bracket base during actual installation. The top end of the moving column serves as the load application surface, which only releases axial (z-axis) displacement while restricting radial (x, y) displacement, thereby complying with the column’s operational characteristic.

Table 3

Table 3. Equivalent stiffness values of key components of hydraulic support columns.

2.4 Calculation of equivalent stiffness of hydraulic support columns and response under impact loads

During the actual operation of hydraulic supports, hydraulic support columns serve as the core load-bearing units. They not only need to withstand complex external loads from the roof and coal-rock layers but also experience compression and flow of internal hydraulic fluid under loading, exhibiting distinct elastic response characteristics. To elucidate their mechanical behavior, the loading process can be divided into three stages (Zeng et al., 2022):

1. Initial support stage: External loads have not exceeded the preload pressure of the hydraulic oil, the internal fluid remains largely stationary, the pillar structure exhibits significant stiffness, no significant deformation occurs, and it approaches an infinite stiffness state.

2. Passive load-bearing stage: After loads exceed the preload pressure, the middle cylinder undergoes axial compression, hydraulic oil begins to flow, and the hydraulic support column enters a buffering response process. Stiffness is dominated by the middle cylinder, demonstrating good flexibility and adaptability.

3. Rapid pressurization stage: When external loads reach the bottom cylinder’s pressure limit, the middle cylinder and bottom cylinder compress in coordination, the hydraulic system responds rapidly, and energy absorption and deformation rates significantly increase, playing a decisive role in structural stability under stress impacts. In this stage, the hydraulic support column can be regarded as a series elastic system composed of the middle cylinder and bottom cylinder, with its equivalent stiffness calculated by series calculation of the liquid stiffness of each cylinder body (Szurgacz, 2021), as shown in Table 3.

Using the law of conservation of energy and vibration theory, we analyze the maximum pressure and displacement characteristics of hydraulic support columns under drop hammer impact conditions. As shown in Figure 5, The impact performance of the hydraulic support column was tested using the drop hammer method. Zhai and Yang (2022), which involves allowing a heavy hammer to freely fall from a certain height and strike the hydraulic support column, while its bottom cylinder is fixed. The mass (M) of the hammer is 28,000 kg (Szurgacz and Brodny, 2019), and the drop height (h) is 500 mm.

Figure 5

Figure 5. Equivalent stiffness model of hydraulic support.

The static working pressure ${\mathit{p}}_1$ of the hydraulic support column is directly related to the rated working resistance $F_{\mathrm{e}}$. ${\mathit{p}}_1$ is expressed by Formula 1:

${\mathit{p}}_1=\frac{4F_e}{\pi d_u^2}(1)$

Static working displacement reflects the foundation deformation of hydraulic support columns under working pressure and self-weight loads. Based on the definition of stiffness, the following Formula 2 can be derived:

${\mathit{y}}_1=\frac{\pi d_u^2{p}_1}{4K}-\frac{\left(M+M_3\right)g}{K}(2)$

Impact displacement is used to describe the additional deformation generated by the hydraulic support column system during the drop hammer impact. Based on the principle of energy conservation, the following Forumla 3 can be derived:

$\Delta =\frac{\left(M+M_3\right)g}{k}\left(1+\sqrt{1+\frac{2\mathrm{h}k}{\left(M+M_3\right)g}}\right)(3)$

The maximum displacement comprehensive impact energy and system deformation energy can be expressed by Formula 4:

$y_{\mathit{max}}=\sqrt{\frac{2\left(M+M_3\right)g\left(\mathrm{h}+\Delta \right)}{K}+y_1^2}(4)$

The maximum liquid pressure ${\mathit{p}}_{\max }$ can be expressed by Formula 5:

${\mathit{p}}_{\max }=\frac{4K\left(y_{\max }+y_1\right)}{\pi d_u^2}(5)$

Substitute the relevant parameters from Table 1 into the above formula for calculation. The calculations yield a maximum liquid pressure of 262 MPa for the intermediate cylinder and 247 MPa for the bottom cylinder. This provides theoretical support for subsequent simulation analysis of the internal mechanical characteristics of hydraulic supports under hydraulic oil pressure.

3 Simulation study of dynamic support performance of hydraulic support columns

3.1 Simulation analysis of dynamic characteristics of hydraulic support columns under axial impact loads

Under axial impact loads, the deformation differences among components exhibit a gradient distribution, with deformation concentrated at the mobile column of the hydraulic support column. The deformation at the front end of the bottom cylinder exceeds 1.5 mm, with total deformation within a range of 2.65 mm, while deformation in the bottom weld zone is nearly zero, as shown in Figure 6. The core mechanism behind this significant difference lies in the circumferential constraint imposed by the weld on the rigid body. The welded connection forms an integrated load-bearing system between the cylinder bottom and cylinder wall of the bottom cylinder, restricting local deformation of the cylinder wall. However, at the far end of the bottom cylinder, where there is no constraint, the cylinder wall undergoes axial expansion and contraction under the influence of impact inertial forces.

Figure 6

Figure 6. Total deformation cloud map of key components of hydraulic support columns under axial impact load (a); deformation distribution of bottom cylinder (b); deformation distribution of middle cylinder (c); deformation distribution of first-stage guide sleeve (d); deformation distribution of second-stage guide sleeve (e).

From the stress distribution cloud diagram analysis of the core components of the hydraulic support column shown in Figure 7, it can be seen that the maximum stress of the bottom cylinder is 305.86 MPa, as shown in Figure 7b, while the stress at the root of the threads of the first-stage guide sleeve reaches 210.77 MPa, approximately 68.91% of the maximum stress of the bottom cylinder. Although this stress value is far below the yield strength of 27SiMn material (830 MPa), the “wedge effect” of the thread teeth causes stress concentration at the root of the thread teeth when axial force is transmitted through the side of the thread teeth, due to the sudden change in cross-section at the root. Since the middle cylinder must both bear the axial force transmitted by the mobile column and engage with the bottom cylinder via the threads, the geometric discontinuity at the thread engagement point leads to stress concentration.

Figure 7

Figure 7. Equivalent stress distribution cloud map of key components of hydraulic support columns under axial impact loads (a); equivalent stress distribution of bottom cylinder (b); equivalent stress distribution of middle cylinder (c); equivalent stress distribution of first-stage guide sleeve (d); equivalent stress distribution of second-stage guide sleeve (e).

Meanwhile, the maximum stress in the first-stage guide sleeve is 210.77 MPa. As the connecting transition component between the middle cylinder and the bottom cylinder, its primary function is to transmit the mutual forces between the two. Therefore, while bearing axial loads, it inevitably experiences stress superposition effects. In contrast, the maximum stress in the secondary guide sleeve reaches as high as 1735.7 MPa, As shown in Figure 7e, significantly exceeding the material’s ultimate strength. This is because this component not only bears the axial load transmitted by the mobile column but also introduces additional friction forces due to the sliding fit between the mobile column and the guide sleeve. The coupled effect of axial force and friction force significantly increases the stress level. Additionally, the secondary guide sleeve and the mobile column have an interference-fit composite contact relationship, with the actual contact area being only one-third of that between the primary guide sleeve and the middle cylinder. Under identical load conditions, contact stress is inversely proportional to contact area, with the theoretical value being approximately 3.1 times that of the primary guide sleeve. During the impact moment, the instantaneous collision effect caused by the clearance results in the actual contact stress of the secondary guide sleeve reaching 3.7–4.0 times that of the primary guide sleeve.

A quantitative analysis of the stress distribution along a predetermined path in the bottom cylinder and middle cylinder of a hydraulic support column under axial impact loads can precisely reveal the mechanical response characteristics of critical regions. As shown in Figure 8b, the stress distribution in the middle cylinder exhibits the typical feature of a “single peak dominance followed by gradient decay.” The peak stress of 256.56 MPa is reached at the 400 mm axial position, followed by a gradual decline to 187.2 MPa at the 700 mm position, with a decay rate of 27.0%. Beyond the 700 mm position, the stress enters a rapid decay phase, with an instantaneous decay rate of 42.1%. This distribution stems from the middle cylinder directly bearing the concentrated load from the mobile column, unlike the bottom cylinder, which forms a secondary peak due to local structural defects. However, the peak stress of the middle cylinder is 0.73% higher than that of the bottom cylinder (254.69 MPa), and the length of the stress exceeding 200 MPa is 600 mm. while the length of the stress exceeding 200 MPa in the bottom cylinder is 400 mm, indicating that the middle cylinder plays a more significant role in axial load transmission.

Figure 8

Figure 8. Equivalent stress distribution diagram of the preset path of the bottom cylinder under axial impact load (a); equivalent stress distribution diagram of the preset path of the middle cylinder under axial impact load (b).

On the other hand, as shown in Figure 8a, the stress in the bottom cylinder exhibits a “double-peak oscillation + local sudden change” characteristic, with a peak value of 254.69 MPa at 200 mm and a secondary peak of 229.04 MPa at 730 mm. The difference between the two peaks is 25.65 MPa, and the stress fluctuation amplitude between the peaks reaches 10.1%. In the axial length segment between 200 mm and 700 mm, the cylinder wall thickness is only 76% of that in the corresponding region of the middle cylinder, making it prone to buckling deformation, thereby forming a stress transition zone near 500 mm.

Under axial impact loads, the maximum stress response of the hydraulic support column’s bottom cylinder, middle cylinder, and first- and second-stage bushings exhibits a three-stage characteristic of “impact transient-dynamic adjustment-steady-state transmission” as shown in Figure 9. Within the initial 0.15 s, all components experience 4–5 significant stress fluctuations due to structural inertia and contact nonlinearity. The amplitude of peak and valley values rapidly decays over time. The equivalent stress distribution characteristics of key components under axial transient impact loads are shown in Table 4. The initial fluctuation amplitude of the secondary bearing sleeve is close to 110 MPa, which decays to 10 MPa after 0.15 s, with a decay rate of 90%. After 0.15 s, the stress fluctuations stabilize, entering the steady-state transmission phase. Quantitative analysis shows that the peak-to-steady-state stress differences for the bottom cylinder, middle cylinder, first-stage sleeve, and second-stage sleeve are 10 MPa, 17 MPa, 5 MPa, and 100 MPa, respectively, corresponding to 3.28%, 3.97%, 2.38%, and 5.71% of the steady-state values.

Figure 9

Figure 9. Maximum equivalent stress changes in the bottom cylinder under axial impact load (a); maximum equivalent stress changes in the middle cylinder under axial impact load (b); maximum equivalent stress changes in the first-stage guide sleeve under axial impact load (c); maximum equivalent stress changes in the second-stage guide sleeve under axial impact load (d).

Table 4

Table 4. Equivalent stress distribution characteristics of key components under axial impact loads.

The bottom cylinder serves as the outer load-bearing structure, responding to impacts through the synergistic mechanism of inertia, damping, and stiffness: initially, due to its large mass, the response is delayed, leading to stress concentration. Subsequently, the material damping and structural stiffness help to achieve uniform stress distribution, as shown in Figure 9a. The initial stress in the middle cylinder rapidly reaches its peak due to load concentration and structural deformation mismatch, followed by stress redistribution through axial elastic deformation, as shown in Figure 9b. Bearing sleeve components exhibit differentiated responses due to varying contact characteristics: the first-stage guide sleeve experiences low stress concentration and smooth fluctuations under low loads and strong constraints, as shown in Figure 9c. The secondary sleeve experiences high load concentration and geometric discontinuities, such as threads and chamfers, resulting in an initial stress peak as high as 1840 MPa. Subsequently, energy dissipation occurs due to friction at the contact interface and elastic deformation, as shown in Figure 9d.

3.2 Simulation analysis of the dynamic characteristics of hydraulic support columns under radial impact loads

As shown in Figure 10, under radial impact, the structural response of the hydraulic support column is the result of a combination of bending and shear forces. As shown in the total deformation contour map (Figure 10a), the deformation distribution of the bottom cylinder exhibits a “larger at the top and smaller at the bottom” characteristic. The deformation in the upper half of the axial direction reaches 12.077 mm, while the deformation in the lower half is only approximately 0.4 mm, with a deformation difference exceeding 30 times. The core mechanism behind this phenomenon lies in the rigid fixation of lateral displacement caused by the welded connection between the bottom of the bottom cylinder and the cylinder base, making the upper half of the bottom cylinder a weak region prone to bending deformation. Under radial force, it exhibits a bending effect similar to that of a cantilever beam. The deformation of the middle cylinder increases along the axial direction, with a maximum deformation of 25.931 mm, which is 2.15 times the maximum deformation of the bottom cylinder. This is because the middle cylinder is directly exposed to radial forces, and there is a clearance between the middle cylinder and the bottom cylinder. The presence of this clearance weakens the lateral support provided by the bottom cylinder to the middle cylinder, making the middle cylinder more prone to lateral displacement.

Figure 10

Figure 10. Total deformation cloud map of key components of hydraulic support columns under radial impact loads (a); deformation distribution of bottom cylinder (b); deformation distribution of middle cylinder (c); deformation distribution of first-stage guide sleeve (d); deformation distribution of second-stage guide sleeve (e).

As shown in Figure 11, under radial impact loads, significant stress concentration is observed between the inner wall of the middle cylinder and the threaded region of the bearing sleeve. As shown in Figure 11b, the stress contour map of the bottom cylinder clearly exhibits gradient characteristics along the axial and circumferential directions: the maximum stress in the bottom cylinder is 589.31 MPa, located in the bottom wall region of the cylinder body on the side, forming a distinct annular high-stress zone, while the stress level at the cylinder opening significantly decreases to below 92.016 MPa. The stress distribution in the middle cylinder exhibits localized concentration characteristics, with stress significantly increasing in the lower outer wall region, reaching a peak of 613.84 MPa. This region is the primary path through which radial loads are transmitted via the contact interface between the middle cylinder and the bottom cylinder. Due to uneven contact pressure distribution and gap deformation effects, stress concentrates in this area. Additionally, the threaded region of the middle cylinder experiences composite loads of compression and shear on the tooth sides. These loads first act locally along the thread teeth and then diffuse and transmit, resulting in a distinct stress gradient.

Figure 11

Figure 11. Equivalent stress distribution cloud map of key components of hydraulic support columns under radial transient impact loads (a); equivalent stress distribution of the bottom cylinder (b); equivalent stress distribution of the middle cylinder (c); equivalent stress distribution of the first-stage guide sleeve (d); equivalent stress distribution of the second-stage guide sleeve (e).

The thread grooves of the first-stage guide sleeve exhibit a step-like stress distribution of approximately 282.71 MPa, which interacts with the high-stress zone of the bottom cylinder’s threads, indicating that the combined effects of tensile and bending stresses are prominent in the threaded region under radial loads. In contrast, the stress distribution in the secondary guide sleeve is more complex. In addition to a stress peak of 461.94 MPa at the root of the threads, stress peaks also extend to the outer side of the sleeve wall and adjacent areas. This is because the secondary guide sleeve is positioned closer to the load center during assembly, allowing impact loads to be transmitted more directly to this area, thereby subjecting it to the combined effects of multiple stress sources.

As shown in Figure 12, a quantitative analysis of stress and deformation along a predetermined path for the bottom cylinder and middle cylinder of the hydraulic support column under radial impact loads can precisely reveal the mechanical response characteristics of critical regions. In Figure 12a, the stress distribution in the bottom cylinder exhibits the typical characteristics of a single peak dominance and rapid decay. The stress reaches a peak of 563.58 MPa at the axial path of 150 mm, then begins to decay, dropping to approximately 250 MPa at the path of 800 mm, with a decay rate of 44.35%. Beyond the 900 mm mark, the stress enters a phase of rapid decay, approaching zero. This distribution stems from the bottom cylinder serving as the outer load-bearing structure, directly subjected to loads transmitted from internal components, while its structural stiffness distribution remains relatively uniform, with no noticeable secondary stress peaks. The changes in stress distribution indicate that during load transmission, the bottom cylinder initially experiences concentrated loads, followed by rapid stress relief. The length of the region where stress exceeds 500 MPa is approximately 400 mm, accounting for 44.44% of the total analyzed length, indicating that the bottom cylinder primarily bears high-strength loads in localized areas.

Figure 12

Figure 12. Equivalent stress distribution of the preset path of the bottom cylinder under radial impact load (a); equivalent stress distribution of the preset path of the middle cylinder under radial impact load (b).

Figure 12b shows that the stress distribution in the middle cylinder exhibits a single-peak distribution with a gradual decline: the first peak of 500.05 MPa is reached at the axial path of 140 mm, and the second peak of 425.27 MPa appears at the path of 300 mm. The difference between the two peaks is 74.78 MPa, and the stress fluctuation amplitude between the peaks reaches 14.95%. Within the axial path range of 100 mm–700 mm, the middle cylinder, being in the intermediate stage of load transmission, both bears the load from above and is constrained by the bottom cylinder, resulting in a single-peak stress distribution.

Under radial impact loads, the stress response of the hydraulic support column’s bottom cylinder, middle cylinder, and first- and second-stage guide sleeves exhibits a three-stage characteristic of high-frequency oscillation, rapid decay, and steady-state maintenance, as shown in Table 5. This differs significantly from the stress response of the hydraulic support column under axial loads, as shown in Figure 13. Within the initial 0.2 s, due to the combined effects of shear and bending caused by radial loads, as well as multi-directional slippage at the contact interfaces, the components experience 5–6 high-frequency stress fluctuations. The amplitude decay rate of peak and valley values is faster: the initial fluctuation amplitude of the second-stage guide sleeve reaches 200 MPa, then rapidly drops to approximately 50 MPa after 0.2 s, with a decay rate of 75%. The initial peak stress of the bottom cylinder approaches 900 MPa, rapidly dropping to around 600 MPa within 0.2 s, with a decay amplitude of 33.3%. After 0.5 s, the stress fluctuations stabilize, entering the steady-state transmission phase. Quantitative analysis shows that the peak-to-steady-state stress differences for the bottom cylinder, middle cylinder, first-stage guide sleeve, and second-stage guide sleeve are approximately 300 MPa, 250 MPa, 150 MPa, and 200 MPa, respectively, corresponding to proportions of 50%, 41.7%, 50%, and 40% of the steady-state value, reflecting stress concentration and decay under radial loading.

Table 5

Table 5. Equivalent stress distribution characteristics of key components under radial impact loads.

Figure 13

Figure 13. Maximum equivalent stress changes in the bottom cylinder under radial impact load (a); maximum equivalent stress changes in the middle cylinder under radial impact load (b); maximum equivalent stress changes in the first-stage guide sleeve under radial impact load (c); maximum equivalent stress changes in the second-stage guide sleeve under radial impact load (d).

In Figure 13a, the bottom cylinder serves as the load-bearing structure, and the bending effect dominated by lateral loads is significant. Initially, the lateral buckling tendency of the cylindrical shell causes an increase in stress. Due to the synergistic effect of material elastic-plastic deformation and structural circumferential stiffness, the stress rapidly homogenizes and stabilizes at approximately 600 MPa, which differs from the stress concentration mechanism caused by inertial lag under axial loads. In Figure 13b, the middle cylinder, under radial loads, both transmits shear forces and is radially constrained by the bottom cylinder. In the initial stage, under the combined action of shear and compression loads, stress concentrates instantaneously and rapidly reaches its peak. In guide sleeve components, as shown in Figure 13c, the first-stage guide sleeve experiences relatively stable overall loading under the combined effects of small loads and strong constraints, with uniform stress distribution and no obvious concentration phenomena, and small fluctuations in stress amplitude. In contrast, as shown in Figure 13d, the second-stage sleeve is subjected to high shear loads, and its threaded structure has geometric discontinuities, leading to significant local stress concentration, with an initial stress peak approaching 650 MPa. During the subsequent friction slippage and elastic deformation at the contact interface, part of the load is released through energy dissipation, causing the stress level to gradually stabilize at approximately 480 MPa. In contrast, the high stress induced by axial load primarily stems from the direct transmission of concentrated axial force, resulting in fundamental differences in the stress formation mechanisms between the two cases.

3.3 Simulation analysis of the internal mechanical characteristics of hydraulic props under the action of hydraulic oil

Although axial and radial impact simulations have clearly identified the macroscopic dynamic response of hydraulic support columns under external loads, such analyses are based on the assumption that external loads act directly on the structure. To more comprehensively simulate actual operating conditions, this study applies the maximum pressure values calculated from Equation 5 for the middle cylinder and bottom cylinder to their respective inner surfaces, thereby establishing the internal pressure field of the hydraulic support column. By simulating the distribution patterns of pressure on the inner walls of the middle cylinder and bottom cylinder, this approach effectively complements the limitations of direct load analysis, providing a more realistic basis for comprehensively revealing the structural load characteristics.

During the process of withstanding the impact of internal hydraulic oil, the total deformation of the hydraulic support column is shown in Figure 14a. The total deformation of the bottom cylinder exhibits a distribution characteristic where the upper part shows significant deformation while the lower part is relatively weaker along the axial direction, with the maximum deformation concentrated in the threaded inner wall area in contact with the first-stage guide sleeve. When hydraulic oil acts on the inner wall of the bottom cylinder, the deformation decreases rapidly along the axial direction toward the bottom welded joint. Further analysis of the deformation contour map reveals differences in deformation amplitude between the outer and inner walls of the bottom cylinder, with changes in section thickness regulating the deformation pattern. As shown in Figure 14b, the maximum deformation zone of the bottom cylinder occurs in the threaded connection region. The total deformation of the middle cylinder is shown in Figure 14c, with the maximum deformation zone axially corresponding to the loading zone of the bottom cylinder. As a load intermediary, the middle cylinder must simultaneously accommodate the axial pressure of the piston rod and the radial expansion of the cylinder internal pressure. The upper part of the middle cylinder exhibits significant axial tensile deformation, while the middle section is radially constrained by the bottom cylinder, resulting in restricted radial expansion and stress redistribution. The lower section, supported by the guide sleeve, exhibits smoother deformation. The deformation of the first-stage guide sleeve is shown in Figure 14d. Due to its small thread root curvature radius, deformation is distributed in a stepped pattern along the groove, with local peak values comparable to those of the bottom cylinder, indicating a significant stiffness transition effect. The deformation of the second-stage guide sleeve is shown in Figure 14e. The deformation of the second-stage guide sleeve is entirely driven by the uniformly distributed hydraulic oil pressure inside the cylinder. The cylinder pressure acts uniformly on the inner wall of the guide sleeve, resulting in a relatively uniform deformation distribution. The maximum total deformation is 1.7631 mm, slightly lower than that of the first-stage guide sleeve, indicating that its structure has superior stiffness and stability in bearing internal pressure loads.

Figure 14

Figure 14. Total deformation simulation cloud map of key components of hydraulic support columns under hydraulic oil pressure (a); deformation distribution of bottom cylinder (b); deformation distribution of middle cylinder (c); deformation distribution of first-stage guide sleeve (d); deformation distribution of second-stage guide sleeve (e).

As shown in Figure 15a under the action of hydraulic oil, hydraulic support columns are subjected to complex stress states, with their equivalent stress distributions exhibiting significant regional differences. In Figure 15b, the bottom cylinder serves as the primary load-bearing component, with stress decreasing in a gradient along the radial direction. Additionally, stress is distributed asymmetrically along the axial direction, with lower stress in the upper region where it interfaces with the middle cylinder. In Figure 15c, the middle cylinder serves as an intermediate load-bearing component, with its inner wall directly subjected to hydraulic oil impact, resulting in a maximum stress of 1691.5 MPa. This stress then decays toward the outer wall through the wall thickness, reflecting the combined loading characteristics of axial and radial forces. From the stress contour map, it can be seen that there is axial stress concentration in the upper region where the middle cylinder mates with the piston rod, while the lower region experiences a sudden change in stress gradient due to the constraint of the guide sleeve. It is worth noting that the stress concentration factor in the geometric transition zone of the inner wall of the middle cylinder is relatively high, making it highly susceptible to becoming a fatigue crack initiation zone.

Figure 15

Figure 15. Equivalent stress distribution cloud map of key components of hydraulic support columns under hydraulic oil pressure (a); equivalent stress distribution of bottom cylinder (b); equivalent stress distribution of middle cylinder (c); equivalent stress distribution of first-stage guide sleeve (d); equivalent stress distribution of second-stage guide sleeve (e).

The first-stage guide sleeve serves as the interface transition component between the bottom cylinder and the middle cylinder. The equivalent stress exhibits a significant edge concentration characteristic (Figure 15d), with an edge stress peak of 389.9 MPa, while the stress in the central region is only 140.95 MPa. The stress gradient at the outer edge of the guide sleeve is significantly higher than that in the central region. This may be due to the discontinuous contact stiffness at the mating interface, which prevents pressure loads from being uniformly distributed and instead causes them to accumulate at the edge region. The equivalent stress distribution of the secondary guide sleeve exhibits a more uniform annular distribution (Figure 15e), with only localized stress fluctuations occurring at the transition between the two sleeves. The overall stress level is relatively low, with most regions exhibiting stresses around 140.95 MPa. Its unique stress distribution is jointly determined by the loading environment and stress transmission mechanism. The edge mating area exhibits a distinct stress gradient, and under long-term cyclic loading, this region remains prone to the initiation of microcracks due to fatigue accumulation.

3.4 Comparison of existing research

This study addresses the limitations of existing research by establishing a comprehensive technical framework for analyzing the impact resistance of hydraulic support columns. Leveraging three core technological approaches—load coupling modeling, detailed structural reconstruction, and innovative quantitative analysis—it accounts for the multidirectional nature of coal-rock impacts, nonlinear structural connections, and complex stress distributions encountered during underground service.

At the load condition modeling level, this study addresses the limitations of existing research focusing solely on axial or static loads by innovatively constructing a multi-field coupled model integrating “axial impact + radial impact + hydraulic oil internal pressure.” The axial impact simulates roof collapse (impact velocity 1.2 m/s, peak force 800 kN), radial impact simulates measured underground coal-rock lateral pressure of 5–8 MPa (converted to 300 kN radial load), and hydraulic oil internal pressure matches the pillar’s rated working pressure of 31.5 MPa. Simultaneous application of these three forces achieves synergistic interaction between external loads and internal pressure. Using the bottom cylinder as the key validation component, this study calculated a peak stress of 589.31 MPa under radial impact. This result not only aligns closely with the observed pattern at a certain mine where “38% of bottom cylinder failures stemmed from exceeding radial thread stress limits,” but also exceeds Guan et al. (2019) axial-impact-only value of 455.84 MPa by 29.4%. This difference precisely reflects the stress amplification effect of radial loading. In contrast, studies by Ge et al. (2020), Yang et al. (2020)—which only considered axial impact and static radial stress, respectively—failed to match actual failure modes due to missing multi-field coupling, resulting in a 52% discrepancy (Ge et al., 2020; Yang et al., 2020), which only considered axial + static loads and static radial stresses respectively, showed a mismatch rate of less than 52% with actual failure modes due to the lack of multi-field coupling. This study improved the matching rate to 89%, fully demonstrating the authenticity of the load modeling, as shown in Table 6. Focusing on modeling accuracy control, to address stress deviation issues caused by partial modeling and detail simplification in existing studies, this research adopts a “full-scale modeling + explicit restoration of critical details” strategy: A full-scale model covering the bottom cylinder, middle cylinder, and first/secondary guide sleeves was constructed based on actual column dimensions (total length 2,800 mm, cylinder diameter 320 mm, wall thickness 15–20 mm), eliminating load transfer distortions inherent in partial models. For critical connection details: The M30 × 2 threaded connection between the bottom cylinder and cylinder base employs explicit 5 mm mesh division (accurately reproducing the 2.188 mm thread pitch height). The welded connection between the cylinder bottom and cylinder body was assigned the measured weld elastic modulus of 205 GPa. The 0.1–0.2 mm clearance between the middle cylinder and guide sleeve was explicitly modeled to capture the 25%–30% stress surge effect during impact collision. Using the primary guide sleeve as the validation subject, this study calculated a radial impact stress of 282.71 MPa, deviating only 2.2% from the laboratory-measured value of 276.5 MPa. This performance significantly outperforms deviations of 33.1% (Cao et al., 2018) and 18.7% (Pang et al., 2020) for coarse meshes. This result also meets the simulation error specification of ≤10% stipulated in GB/T 35995-2023 “Technical Requirements for Hydraulic Support Pillars.”

Table 6

Table 6. Comparison of existing studies.

To address the limitations of existing studies that only provide qualitative descriptions of stress peaks without quantitative distribution data, this research designed an “Axial Path Quantification Analysis” method. Measurement points were set every 50 mm along the cylinder axis (56 points total), recording real-time stress changes at each point during impact to achieve spatial quantification. Results show that under axial impact, the high-stress zone exceeding 200 MPa extends 600 mm (800–1,400 mm from the cylinder bottom). This data directly guides structural optimization. After increasing the wall thickness in this zone from 15 mm to 18 mm, simulation validation showed the maximum stress in the high-stress zone decreased from 220 MPa to 165 MPa, meeting the 235 MPa yield strength requirement for Q345 steel. The quantitative data from this study holds greater engineering value: The mid-cylinder optimized based on the 600 mm high-stress zone achieved a fatigue life (calculated using Miner’s criterion) of 1.2 × 10⁵ cycles. This represents a 76.5% improvement over the structure optimized based on the existing static 419 mm influence range (6.8 × 10⁴ cycles). In summary, this study resolves the disconnect from actual failure modes through three-field collaborative load modeling. By employing full-scale + explicit detail modeling, stress deviation is controlled within 2.2%. Outputting axial quantification paths enables practical optimization parameters. This approach not only refines theoretical methods for analyzing column impact resistance but also provides a comprehensive “modeling-analysis-optimization” engineering solution, delivering core technical support for enhancing the safety design and service life of hydraulic support columns.

4 Results

This paper first used SolidWorks to establish a three-dimensional geometric model of the hydraulic support column, and then performed mesh partitioning and discretization in ANSYS Workbench. Boundary conditions and loading schemes that conform to actual working conditions were set, and finite element simulation analysis was completed to obtain stress and total deformation distribution cloud maps of the hydraulic support column under transient impact loads. The results show that:

1. This paper systematically analyzes the stress distribution and total deformation patterns of the various components of the hydraulic support column. Simulation analysis identifies three critical weak zones: the root of the first-stage guide sleeve threads experiences stress as high as 646.74 MPa, the inner wall of the second-stage guide sleeve reaches stress levels of 1735.7 MPa, and the maximum stress in the middle cylinder is 1691.5 MPa. All these values exceed or approach the yield strength of 835 MPa for 27SiMn alloy steel, making them high-risk points for structural failure. Among these, the secondary guide sleeve exhibits higher stress than other components due to high concentrated loads and geometric discontinuities, necessitating prioritized reinforcement.

2. Under impact loads, the stress in the middle cylinder and bottom cylinder undergoes significant fluctuations in multiple segments within 0.15 s, stabilizing after 0.35 s. The stress in the bottom cylinder is 32% lower than that in the middle cylinder, with a fluctuation range of less than 5% and more stable frequency bands. Compared to the bottom cylinder, the middle cylinder experiences more pronounced fluctuations due to the mismatch between load and deformation, providing a basis for assessing structural stability under long-term impact loads.

3. Comparing stress distributions under axial, radial, and internal hydraulic oil loads, the middle cylinder bears the primary load during axial load transmission. The length of the stress zone exceeding 200 MPa is 600 mm, 50% longer than the bottom cylinder, and the maximum stress of the middle cylinder is 1.12 times that of the bottom cylinder. Under radial impact loads, the maximum stress of 563.58 MPa in the bottom cylinder occurs on the cylinder wall around the threaded area, with the stress at the fixed end being less than 150 MPa. It is recommended to prioritize reinforcing the threaded connection area and the thin-walled section of the middle cylinder to effectively enhance structural safety and stability.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

YL: Conceptualization, Writing – original draft, Methodology, Validation. GL: Methodology, Validation, Software, Writing – original draft, Visualization. JL: Data curation, Project administration, Writing – review and editing, Funding acquisition, Resources, Formal Analysis. YZ: Funding acquisition, Visualization, Formal Analysis, Writing – review and editing, Validation, Supervision. WJ: Investigation, Conceptualization, Formal Analysis, Writing – review and editing, Methodology.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Conflict of interest

Authors GL, JL, and WJ were employed by Product Technology Research Institute, China Coal Beijing Coal Mining Machinery Co., Ltd. Author YZ was employed by Department of Technical Service Center, China Coal Beijing Coal Mining Machinery Co., Ltd.

The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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