Research on the Energy-Absorbing and Cushioning Performance of a New Half-Bowl Ball Rubber Body in Tunnel Support

Abstract

As coal mine underground operating conditions are harsh, strengthening and optimizing the support structure is conducive to the safety of mining work and personnel. Currently, underground support devices face problems such as poor environmental adaptability and unbalanced performance of shockproof and energy absorption. At the same time, the energy absorption mechanism and impact dynamic analysis of the support structure are still imperfect. This paper proposes a simple and effective bionic half-bowl spherical rubber energy-absorbing structure based on the actual production needs of coal mines, with energy-absorbing rubber as the main structural interlayer. A combination of experimental testing and simulation was used to reveal the dynamic response and mechanism of simulated energy absorption of a half-bowl-shaped rubber layer under different working conditions. Abaqus software was used to simulate and analyze the dynamic response of the half-bowl spherical rubber structure under the impact condition, and the simulation data were compared with the experimental results. In addition, the relationship between energy absorption and stress at the rubber structure and the base plate under different impact velocities was investigated. The results show that the simulated and experimental results of the rubber structure have almost the same pressure vs. time trend within 0.1 s at an impact velocity of 64 m/s, and there is no significant wear on the rubber surface after impact. Due to the energy-absorbing effect of the rubber structure, the maximum stress of the bottom member plate-2 of the mechanism is lower than 9 × 10⁴ N. The maximum amount of compression of the half-bowl ball is 37.56 mm at an impact velocity of 64 m/s. The maximum amount of compression of the half-bowl ball is 37.56 mm.

1. Introduction

Approximately 87% of rock burst incidents in coal mines occur in tunnels [1,2,3]. Current tunnel support technology primarily uses a combination of advanced hydraulic support groups and anchoring systems to support the surrounding rock [4,5]. During the advancement of the working face, mining disturbances and rock bursts can easily cause the failure of the support capacity of the equipment and mismatches in the support force between various support components [6]. This severely impacts the service life of support equipment such as advanced hydraulic supports. Especially during rock bursts, it is difficult for hydraulic supports to withstand the strong impact loads [7]. The dynamic response time of safety valves is insufficient, and fluid resistance losses in long-distance protection element pipelines cause serious damage to equipment, such as bending, fracturing, and bursting of hydraulic support columns, leading to safety accidents [8,9,10].

Therefore, exploring impact protection and energy-absorbing structures that allow advanced hydraulic support groups to adapt to initial supporting pre-pressure, buffer initial pressure, periodic pressure, and rock bursts can effectively enhance the service life of support equipment by adding a shield to hydraulic supports and other support equipment. This, in turn, reduces safety accidents and greatly improves production efficiency, making it a new direction for the development of safe and efficient support technology for advanced hydraulic supports.

The design of the impact protection and energy absorption structure of hydraulic supports is mainly based on the rock burst pressure received by the tunnel roof. By analyzing and modeling the pressure within the tunnel, theoretical support can be provided for the design of support materials. Researchers have summarized the typical responses of blocky, moderately jointed, and highly jointed rock masses to increasing stress levels in tunnels. Additionally, a case study has been introduced where advanced modeling techniques were used to improve ground support performance by optimizing the timing and stiffness of the ground support system at the CSA mine in Cobar, New South Wales [11].

The choice of support materials for underground mines is a prerequisite for the design of support structures [12,13,14]. Dmytro Babets [15] proposed the use of a dry mixture “BI-lining” additive, which is fed through a monorail system into a mixer and mixed with water. The resulting mixture is then inserted into an industrial fiber material, which ultimately increases the strength of the support itself. Volodymyr Bondarenko [16] has paid great attention to the possibility of using composite materials (especially carbon fiber-reinforced plastics) as fastening elements and has carried out a comparative analysis of the physico-mechanical properties of carbon fiber-reinforced plastics and low-alloy steels, which have traditionally been used in the manufacture of frame supports. The results show that the comparative analysis of stress intensities confirms the advantages of the proposed frame support made of composite materials in limiting the region of maximum values. The complexity of the support environment also provides direction for the study of impact protection and energy absorption structures. By studying three-phase composite materials as substitutes for two-phase composite materials, the impact of the matrix and reinforcing materials on the energy absorption capacity of composite structures was detailed. The results showed that fillers and matrix materials have a significant impact on the energy absorption capacity of polymer composites [17]. Additionally, a new type of multilayer composite material was proposed, and its NPR (negative Poisson’s ratio) effect and mechanical properties under quasi-static compression were studied and compared with the NPR effect and mechanical properties of pure polyurethane foam and non-expanding composite materials [18]. Furthermore, by performing structural design on impact-resistant materials, the energy absorption performance of the materials can be further improved. Through bionic structure design on the material surface combined with a highly ductile and high-strength carbon glass fiber skin, simulation analysis showed that the introduction of composite structures can enhance the impact resistance and energy absorption performance of materials [19,20,21].

In addition, researchers have performed analyses based on the environment around the mine. A study on the disaster mechanisms of three types of rock bursts—deep strain type, fault slip type, and hard roof type—has led to the proposal of two new indices: the coal–rock combined impact energy velocity index and the unloading confining pressure impact energy velocity index. A coal–rock impact tendency evaluation system, corresponding to the different types of rock bursts, was established [22]. This system has helped identify the precursor information characteristics of the three types of rock bursts in deep mining. Moreover, the high-temperature environment in tunnels also affects the internal structure of coal and rock. To study the physical and mechanical properties of coal and rock under impact loads after different temperature treatments, dynamic compression experiments were conducted using a split-Hopkinson pressure bar (SHPB). The experiments showed that the internal structure of coal and rock is gradually damaged under high temperatures [23]. However, the energy evolution of coal and rock mainly goes through four stages: initial energy damage, energy hardening, energy softening, and failure. With the increase in strain rate, the total energy and elasticity at the peak point under uniaxial compression gradually decrease, while under triaxial compression, the total energy, elastic energy, and dissipative energy at the peak point first increase and then decrease [24,25].

By analyzing the environment of supporting materials and underground coal mine rocks, the development of programs adapted to different environments will further enhance the supporting effect [26,27,28,29]. Zhang [30] analyzed the existence conditions and damage characteristics of the surrounding rocks in the west-wing traffic lane, as well as the structural characteristics and mechanical properties of the anchor-grouted flexible anchors, combines the analysis of elasticity–plasticity and superposition arch theory, and establishes the theoretical model of a superposition community to propose the superposition joint support scheme of “anchor rods (ropes) + anchor net + anchor grouted flexible anchors + grouting support”. Li [31] proposed a support parameter selection scheme with allowable deformation as the control objective and applied it to the Muziling highway tunnel in Minxian County, Dingxi City, Gansu Province. Through theoretical analysis, five factors affecting prestressing anchorage were determined. The inverse analysis method is used for the selection of rock mechanical parameters. Compared with the measured data, the maximum displacement error of the numerical simulation results was only 0.07 m.

In addition, Wang [32] proposed a temporary support system to improve the efficiency and safety of underground roadway excavation in coal mines for the detection and installation of support equipment underground. Jiang [33] selected the calculation method for the bearing capacity of a restrained lightweight concrete structure by comparing the test results with the theoretical calculation results of restrained concrete. The design method of restrained lightweight concrete support structure was established and successfully applied in the extra-large mine, the Lime Strip Tower Coal Mine.

In response to the impact protection issues of advanced support systems, this paper conducts a study on the mechanical properties of advanced hydraulic supports under complex impact loads. Based on actual support conditions, energy transfer mechanisms, and energy absorption effects, new high-damping, high-elasticity, impact-resistant, energy-absorbing functionally graded materials/microstructures are utilized to design periodic filling impact-resistant energy-absorbing structures. A simple and effective bionic half-bowl spherical rubber energy-absorbing structure is proposed with energy-absorbing rubber as the main structural interlayer according to the actual production needs of a coal mine and the roadway environment. The energy-absorbing structure is prepared by one-piece molding technology, and the dynamic response of the half-bowl spherical rubber structure under different impact conditions is simulated and analyzed using Abaqus 6.14-4 software, and the simulated data are compared with the experimental results. The relationship between the energy absorption and stress of the rubber structure and the base plate under different impact velocities was also investigated. A coupled dynamic model of rock burst tunnel surrounding rock-advanced hydraulic support group–periodic filling impact-resistant energy-absorbing structure-anchoring system is constructed to obtain the dynamic energy-absorbing characteristics of the periodic filling impact-resistant energy-absorbing structure and its impact protection effect on the coupled system. This research provides theoretical guidance and practical support for advancing coal mining into deeper parts of the Earth and towards intelligent and green development.

2. Materials and Methods

2.1. Cushion Energy Absorber Structure

To effectively tackle the intricate support challenges encountered in tunnels, particularly those requiring advanced protective measures, this paper introduces an innovative energy-absorbing buffer device, the design of which is depicted in Figure 1. This device boasts dimensions that span 1400 mm in length, 340 mm in height, and 810 mm in width (Figure 1a), ensuring a compact yet efficient form factor for tunnel installation.

At the heart of this device lies a meticulously crafted rubber energy-absorbing component, sourced from Qingdao Huaxia Co., Ltd., Qingdao, China. This nitrile rubber formulation is specifically engineered to excel in impact resistance and energy dissipation, playing a pivotal role in mitigating the shockwaves generated during tunnel excavation or seismic activities. As depicted in Figure 1c, the rubber’s inherent properties allow it to deform strategically, absorbing and dissipating the energy of impact, thereby protecting the tunnel’s structural integrity.

To further enhance the device’s robustness and prevent unwanted deformation of the rubber structure under extreme conditions, a clever integration of telescopic disc spring columns and alloy steel plates has been employed. These components, as illustrated in Figure 1b, provide a robust framework that not only supports the rubber component but also constrains its deformation within safe limits, ensuring consistent and reliable performance.

Moreover, the advanced support system showcased in Figure 1d underscores the device’s scalability and versatility. The upper section of the support framework incorporates multiple instances of the energy-absorbing devices, arranged in a strategic configuration to distribute impact forces evenly and maximize overall protection. This modular design allows for easy customization and adaptation to varying tunnel sizes and support requirements, underscoring the device’s potential for widespread adoption in the tunneling industry.

2.2. Half-Bowl-Shaped Energy-Absorbing Rubber Structure

The utilization of soft, insect-inspired bowl-shaped protrusions as energy-absorbing surfaces has garnered significant attention in various applications, notably serving as landing platforms for space probes [34] and as nanoscale components in energy-dissipating systems [35]. In this research endeavor, a strategic selection was made to employ a flexible rubber structure, where the upper and lower contact interfaces were designed in a half-bowl configuration, as illustrated in Figure 2.

Figure 2 showcases the intricate arrangement of these half-bowl structures, with a precise spacing of 159.6 mm between the centers of adjacent formations. The smaller circular diameter, which interfaces with the upper steel plate, measures 106.4 mm, while the larger diameter spans 133 mm, creating a unique geometry that optimizes energy absorption.

Upon the application of impact pressure from the upper plate, the half-bowl structures undergo a controlled deformation process. This deformation serves as a transformative mechanism, converting the kinetic energy of the impact into potential energy stored within the deformed rubber. This conversion not only mitigates the impact force but also effectively absorbs and dissipates the energy, thereby enhancing the overall impact resistance and energy-absorbing capabilities of the structure [36].

Furthermore, the strategic inclusion of gaps between the half-bowl structures is a pivotal design feature. These gaps act as deformation reservoirs, allowing the rubber to expand and contract freely during the absorption process. This flexibility not only maximizes the energy absorption potential but also ensures the structural integrity of the system by preventing undue stress concentrations. In essence, this innovative design represents a harmonious blend of form and function, tailored to excel in energy-absorbing applications.

2.3. Dynamical Model

Numerical Modeling

The impact load imposed on the roof plate of an underground coal mine support system is a complex phenomenon intricately linked to various factors such as the characteristics of the overlying rock strata, geological formations, and mining activities. Collaborating closely with the mining company, it has been determined that the support equipment designed in this study must endure an impact energy range of 10⁴ J to 10⁵ J. To address this challenge, plate-0, the primary component exposed to the impact, has been meticulously dimensioned at 1280 mm × 250 mm × 20 mm and crafted from alloy steel, a material renowned for its high density (~7.82 kg/m³), strength, and durability.

Sandwiched between plate-1 and plate-2 lies a half-bowl spherical rubber structure, as depicted in Figure 3, which serves as a crucial energy-absorbing layer. This innovative design element is pivotal in mitigating the impact forces and protecting the underlying support system. Utilizing the principles of kinetic energy, the potential velocity range of plate-0 under the specified impact energy can be calculated. Given the energy range of 10⁴ J to 10⁵ J, the corresponding velocity of plate-0 ranges from approximately 20 m/s to 64 m/s. This wide velocity spectrum underscores the dynamic nature of the impact load and the importance of designing a robust support system that can withstand such variations.

In the simulation modeling phase, meticulous attention is paid to the application of pressure and velocity on plate-0. These parameters are accurately simulated to replicate real-world conditions, ensuring the validity and reliability of the results. Additionally, the contact time between plate-0 and the subsequent layers is set to 0.1 s, reflecting the brevity of the impact event and the need for swift and effective energy dissipation.

The nature of the interaction between the rubber interlayer and the plates is “general contact” with a friction coefficient of 0.3 and hard contact is the normal behavior of the tangential behavior of the penalized friction formula. In order to reduce the computational cost, the stabilization time of the explicit solver is reduced by the mass scaling method. In order to reduce the simulation time and to ensure that the loads remain in the quasi-static region without any penetration, the kinetic energy is assumed to be 5% smaller than the internal energy of the structure.

2.4. Impact Test

We designed an energy-absorbing impact protection device to characterize the effects of different impact forces on the energy absorption device, as shown in Figure 4. To compare with the simulation results, we added pressure sensors to the corresponding half-bowl structure locations of plate-1 and plate-2 shown in Figure 3 to obtain surface pressure and energy transfer information. We controlled the magnet with an electromagnetic device to ensure the impact plate struck the energy absorption device at a predetermined speed. Specifically, Figure 4a shows the overall structure of the impact test, which mainly includes the electromagnet block, the impact plate, and the upper and lower guards of the impact architecture. Among them, the electromagnet is controlled by a solenoid valve to realize the process of applying different impact speeds. The impact energy is applied to the rubber sandwich through the impact plate, which is designed to simulate the impact form of the roof plate of the roadway. The movement of the impact plate is mainly controlled by four screws, which always ensure the verticality of the impact speed. In order to analyze the pressure change of the upper and lower plates of the energy-absorbing structure, 15 pressure sensors are added in the middle of the upper and lower plates of the rubber sandwich structure to extract the impact pressure. Limit sensors are embedded at the edge of the upper plate to measure the compression of the rubber sandwich surface structure. Based on the above, a physical drawing of the test device is produced, as shown in Figure 4b.

3. Results and Discussion

3.1. Dynamic Response of Rubber Structures under Different Impact Energies

Qualified protective structures need to be able to withstand maximum impact. Figure 5 shows the stress cloud of the rubber structure at a maximum impact velocity of 64 m/s. It can be seen from the figure that the incorporation of the rubber structure can withstand the impact force and at the same time will produce a rebound effect. In Figure 5a, every part of the overall structure is in contact with each other and the impact force will be directly applied to the rubber structure in a vertical direction. At this point, the upper half of the rubber structure’s half-bowl structure carries most of the stress, and the half-bowl structure in contact with its lower plate has less stress. As the number of simulation steps increases, the stress reconstruction on both sides of the rubber structure increases, as shown in Figure 5b. However, due to the elastic qualities of the rubber itself, the upper and lower plates appear to leave the rubber structure [37], and this phenomenon is the rebound phase, when elastic stresses exist within the rubber, as shown in Figure 5c. During the rebound phase, the stresses are concentrated on the contact surface of the half-bowl ball and transferred to plate-1 and plate-0, as shown in Figure 5d.

In the same published literature [38,39], the pressure on the surface of the rubber structure at larger impact velocities is mainly concentrated on the surface of the half-bowl ball, which suggests that the surface structure can disperse the impact stresses better. However, the difference is that the half-bowl ball structure absorbs energy and also stores it briefly with the upper surface of the rubber, which helps to protect the lower part of the support structure from the huge pressure on the hydraulic system.

Figure 6 shows the stress versus time curves for the half-bowl spherical rubber structure. From the figure, it can be seen intuitively that the stress of the rubber structure with the time of the impact load first increases and reaches the highest point and then decreases, which is the nature of the compound rubber elastomer [40]. Unlike the simulation data, the experimental data show a fluctuating region in the rising phase, which is mainly attributed to the vibration of the experimental bench. In addition, when the stress reaches its maximum, the experimental data show abrupt changes directly. This is due to the fact that the rubber layer bounced the top and bottom plates apart during the experiment, and the pressure sensor at the half-bowl spherical structure was unable to detect the change in stress; hence, the stress was zero [41].

In addition, by observing the surface morphology of the rubber after the experiment, it was found that the half-bowl spherical structure was relatively intact, with no obvious tearing or wear, which indicated that the rubber structure was able to withstand the maximum impact energy [42]. This is the difference between the rubberized energy-absorbing structures covered in this paper and the foam concrete-filled PE pipe [43] and the diamond-shaped special predeformed alloy pipe [39]. Solid rubber does not excessively achieve energy absorption by sacrificing its own compression variables. The foam concrete-filled PE pipe and the diamond-shaped special predeformed alloy pipe will deform maximally under impact pressure, which is the reason for their more similar simulation and experimental data.

3.2. Transmission Effects of Pressure

The propagation journey of the stress wave within the intricate energy-absorbing structure unfolds in a precise sequence, traversing from the initial impact on the top plate-0, sequentially permeating through plate-1, encountering the crucial rubberized interlayer, and finally reaching the bottom plate-2. This orchestrated progression underscores the pivotal role of the rubberized interlayer in mitigating stress concentrations, particularly in the bottom plate-2, thereby safeguarding the integrity and functionality of the entire structural system against potential failure.

Figure 7 provides a vivid illustration of the dynamic stress evolution in plate-2 under peak impact energy conditions. Here, both the simulated and experimental data converge, exhibiting a distinctive pattern characterized by two pronounced peaks (A and B) punctuated by a pronounced trough (C). This synchronized trend underscores the reliability of the simulation model in capturing the intricate stress–strain interactions within the composite structure [44].

As the impact event unfolds, the stress on plate-2 escalates almost linearly towards a threshold maximum (point A). This swift rise is a direct consequence of the efficient transfer of the impact load through the preceding layers, demonstrating the material’s ability to swiftly respond to external forces. Following this initial surge, however, the stress profile experiences a notable dip at point C, marking a pivotal moment in the energy dissipation process. This decrement is attributed to the remarkable energy-absorbing capabilities of the rubber sandwich, where a substantial portion of the incoming impact energy undergoes rapid attenuation as it traverses the multi-layered assembly. Simultaneously, a significant fraction of this energy is harnessed and stored within the rubber in the form of deformation potential energy, providing a resilient buffer against further structural stress.

The subsequent rise in stress, culminating at point B, represents a distinct phase in the energy release cycle. Here, the accumulated deformation potential energy within the rubber layer is gradually released, contributing to a secondary stress peak. Notably, the magnitude at point B is observed to be lower than that at the initial peak (A). This disparity stems from the fact that while the release of rubber deformation energy contributes to the stress rise, it does so in a more gradual and controlled manner, mitigating the intensity of the stress wave and its potentially detrimental effects on the structural integrity.

By examining the combined insights from Figure 6 and Figure 7, it becomes evident that the strategic integration of the rubberized interlayer within the energy-absorbing structure represents a highly effective strategy for mitigating the adverse effects of impact loads. By efficiently dissipating and storing impact energy, this design significantly enhances the overall stability and resilience of the structure, significantly reducing the risk of catastrophic failure and ensuring the continued safe performance of the system.

3.3. Energy Absorption in Half-Bowl Ball Rubber Structures

The performance of cushioning and energy-absorbing materials varies according to their structure and impact energy [45,46]. The energy-absorbing properties of the materials are mainly investigated by simulation, based on the rated impact energy mentioned in Section Numerical Modeling, different impact speeds are set, and the corresponding data of energy and speed are shown in Table 1.

In order to deeply investigate the energy-absorbing effect of the rubber structure proposed in this paper, the effects of different impact velocities on the performance of this structure were investigated, as shown in Figure 8. It is worth noting that the energy data on the y-axis in Figure 8 are not equidistant, which is mainly to analyze and compare the trend of energy absorption of the rubber structure under different impact velocities. In the figure, it can be seen that the absorption of energy by the rubber structure shows a trend of first rising and then falling to finally reach equilibrium. In particular, when the impact velocity is 20 m/s, the energy absorption curve shows an obvious decreasing trend from 0.1 s onwards. This indicates that the rubber half-bowl ball structure will gradually absorb the external impact energy in the pre-impact period and convert it into internal deformation energy.

Figure 9 shows the maximum deformation energy of the half-bowl rubber structure under different impact force conditions in relation to the maximum stress of plate-2. With the increase in impact velocity, the compression height gradually increases. However, when the impact velocity exceeds 50 m/s, the change in compression height of the rubber structure shrinks, as shown in Figure 9a. This is due to the strength and compression limit properties of the rubber structure itself [47]. The change in compression height is similar to the trend of maximum stress change in the bottom plate-2, and the larger the impact velocity, the more the maximum stress change in the plate-2 decreases, as shown in Figure 9a,b. The impact energy is converted into elastic potential energy and deformation energy with the contact between the energy-absorbing structures, and the increase in the impact force leads to the increase in the compression height of the rubber [48,49], which absorbs more energy, which is consistent with the analyzed results in Figure 8. Currently, one of the energy-absorbing damping options is the use of mechanical metamaterials, especially corrugated wall structures with a negative Poisson’s ratio. This structure allows for more exaggerated deformations and energy-absorbing damping through a volatile mesh structure [50]. However, this deformation can lead to pressure inhomogeneity, while the structure is more prone to damage. The half-bowl structure rubber sandwich is more likely to maintain a certain compression ratio under greater impact pressure while having the effect of equalizing the pressure.

4. Conclusions

In this study, a bionic half-bowl spherical rubber energy-absorbing structure customized for underground coal mining applications was designed and analyzed. The primary goal was to enhance the energy absorption and impact resistance of support equipment in harsh mining environments. Utilizing the versatility and toughness of energy-absorbing rubber as the primary sandwich material, a structure was developed that significantly improves the overall performance of the support system. A combination of simulations and experiments were used to evaluate the dynamic response of a half-bowl spherical rubber structure under various impact conditions. These simulations provide valuable insights into the behavior of the structure. The accuracy and reliability of the model was confirmed by comparing the simulated data with the experimental results. The following conclusions are made:

• (1). The results of this study show that the half-bowl spherical rubber structure is very effective in absorbing external impact energy. Specifically, at 10⁵ J of impact energy, the structure exhibits excellent performance to meet the stringent requirements of mining operations.

• (2). The energy-absorbing effect of the rubber structure is mainly realized by converting the impact energy into elastic potential energy, which is then stored in the rubber structure.

• (3). An analysis of the relationship between energy absorption, stress distribution, and deformation of the rubber structure and the base plate at varying impact velocities revealed that when the impact speed is within the range of 35 m/s to 50 m/s, the compression amount of the half-bowl structure undergoes the most significant changes. This observation underscores the critical importance of controlling the impact velocity within this range to optimize energy absorption and minimize stress concentrations.

Half-bowl ball rubber construction is designed to address the topmost impact forces of the roadway. The rubber sandwich combines with disc spring support and is able to form compression against impact forces, thus performing an energy-absorbing and shock-absorbing function. It reduces the impact stress on the vulnerable hydraulic components of the overall support structure and improves the load carrying capacity of the support equipment. In addition, the rubber structure is simple and easy to replace, which is conducive to improving the service life of the support equipment. Currently, the rubberized energy-absorbing structure is being tested in the Jisan mine in Jining, China, and is expected to be extended to coal mines in eastern China in the future.

Author Contributions

Conceptualization, J.M. and K.Z.; methodology, Y.X.; software, B.M.; validation, C.Z. and X.H.; formal analysis, K.Z.; investigation, D.T.; resources, M.D.; data curation, K.Z.; writing—original draft preparation, J.M.; writing—review and editing, J.M; funding acquisition, K.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Dataset available on request from the authors.

Conflicts of Interest

Authors Jian Ma and Kun Zhang were employed by the company Shandong Energy Group Co., Ltd. Author Yaomeng Xiao was employed by the company Yankuang Energy Group Co., Shandong Energy Group Co., Ltd. Author Bin Ma was employed by the company Wangwa No.2 Mine of Ningxia Wangwa Coal Industry Co., Ltd. Author Canguang Zheng was employed by the company Yankuang Energy Group Co., Ltd. Author Xiangpeng Hu was employed by the company Tiandi Ningxia Support Equipment Co., Ltd. Author Dan Tian was employed by the company Yankuang Xinjiang Energy Chemical Co., Ltd. The remaining author declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

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Figures and Table

Figure 1. Buffer energy-absorbing device overall structure and assembly: (a) cushioning energy absorbers; (b) secondary telescopic disc spring-cushioned monolithic columns; (c) half-bowl-shaped cushioning and energy-absorbing structures; (d) overall installation effect diagram.

Figure 2. Half-bowl rubber energy-absorbing structure.

Figure 3. Energy-absorbing simulation model.

Figure 4. Impact test bench: (a) schematic diagram of the impact instrument; (b) physical diagram of the impact instrument.

Figure 5. Stress diagram of the rubber structure at plate-0 velocity of 64 m/s: (a) Step 2; (b) Step 20; (c) Step 30 and its (d) top view.

Figure 6. Stress versus time curves for half-bowl spherical rubber structures.

Figure 7. Stress versus time curves for plate-2.

Figure 8. Variation of absorbed energy in rubber structures at different impact velocities.

Figure 9. Maximum deformation of the half-bowl rubber structure under different impact force conditions: (a) the relationship between the rubber compression height and the stress of plate-2; (b) simulation diagram of rubber compression height.

Table 1

The corresponding data of energy and speed.

Impact Energy (J)	1 × 104	4 × 104	7 × 104	1 × 105
Speed (m/s)	~20 m/s	~35 m/s	~50 m/s	~64 m/s

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