# Factors Affecting the Compression and Energy Absorption Properties of Small-Sized Thin-Walled Metal Tubes

Authors: Xiaoqin Hao; Jia Yu; Weidong He; Yi Jiang
Journal: International Journal of Aerospace Engineering
 (2020)

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## Abstract

To solve the problem of the effective cushioning of fast-moving mechanical components in small ring-shaped spaces, the factors affecting the compression and energy absorption properties of small-sized hollow metal tubes were studied. Simulation models were constructed to analyse the influences of tube diameter, wall thickness, relative position, and number of stacked components on the compression and energy absorption properties. The correctness of the simulation method and its output were verified by experiments, which proved the effectiveness of compression and energy absorption properties of small-sized thin-walled metal tubes. The research provides support for the application of metal tube buffers in armament launch technology and engineering practice.


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## Body

## 1. Introduction

With the development of engineering science and technology, the problem of buffer energy absorption caused by mechanical collision in industry has become more prominent. Since the 1970s, attention has been paid to research and development into energy-absorbing structures and materials that dissipate kinetic energy from collisions (or from strong dynamic loads), especially in the automotive and military industries [1]. In recent years, the problem of buffer energy absorption within a narrow space has arisen as an important topic of interest in the aerospace industry. With the development of material science, various types of buffer energy-absorbing materials have been put into use, which has stimulated the creation of different types of buffer energy-absorbing devices. At present, the composite devices with good performance and a wide range of application include metal tube structures, aluminium honeycomb, foamed metal materials, and porous materials used to infill thin-walled structures. These buffer energy absorption devices are all based on the principle of irreversible deformation of materials and absorption of energy through plastic deformation.The common use of thin-walled components as energy-absorbing devices is due to many important aspects including superior performance under dynamic loading, cost-effectiveness, high efficiency, and ease of manufacturing and installation [2]. Thin-walled energy absorbers have been used in many applications including aircraft subfloor structures [3], front structures of cars and trains [4], and rollover protective structures (ROPS) on items of heavy equipment used in agriculture and construction, such as earthmoving machinery and tractors [5].The principal factors that affect the energy absorption capability of such thin-walled components are materials, structural geometry, and load regime. The most commonly used materials for manufacturing a thin-walled energy absorber are metallic, such as aluminium alloy and mild steel, or fibre-reinforced composites (FRCs). The energy dissipating mechanisms of metallic and composite structures are considerably different. The structures made from composite materials are normally brittle and dissipate energy through different combined fracture mechanisms such as delamination, fibre breakage, and matrix cracking [6], whereas the ductility of metallic structures allows them to dissipate energy through progressive plastic deformation [1, 6]. For metallic tubes, both square [7] and circular cross sections have been studied before.The influence factors and behaviour of the buffering energy absorption characteristics of small-sized thin-walled metal tubes were studied in the present research. These kinds of metal tubes are very different from those described above, as they are installed within annular openings with a diameter of 6 to 8 mm; therefore, the diameter of the metal tube is less than 6 mm, and its thickness is 0.8 to 1.2 mm. The metal tubes are annular and are stacked along the axial direction.According to the early research, the axial crushing of circular tubes was extensively studied by many researchers [8–11] interested in their energy absorption capability. Those authors were among the first researchers to develop an analytical model for the axial collapse of a circular tube. The axial crushing of a circular tube involves progressive folding or buckling of the tube with one or more of three main deformation modes: axisymmetric or ring, nonsymmetric or diamond, or a mixed mode [2]. A novel method to improve energy absorption performance of thin-walled circular tubes under quasistatic lateral loading through a preforming process was also investigated [12].A novel solution was established, and the study of the influencing factors and rules of behaviour can be used as a reference to design buffering devices in the narrow space of high-speed mechanical moving parts and provides support for the application of metal tube-type buffering devices in weapon launching technology and aerospace engineering.


## 2. Theory and Model

### 2.1. Geometric Model

The geometry model is shown in Figure1. Under external force, the descending object moves relative to the ascending object at a certain speed to simulate the collision environment. As a result, the metal tube sandwiched between them is compressed and deformed.Figure 1
Compression model for a hollow metal tube. (1) Descending object. (2) Ascending object. (3) Metal tube to be compressed.Ф: outer diameter of the metal tube; t: thickness of the metal tube; d: distance from the outer wall of the metal tube to the wall of the inner moving object.All the materials used in this study were designed by the authors and were manufactured by a collaborating industrial partner.


### 2.2. Material Model

When the changing load acts on the structure at a high speed, it deforms rapidly and the strain rate is higher. A large number of studies have shown that the mechanical properties of materials under a high strain rate are quite different from those governing quasistatic deformation, and the yield limit of materials increases with the strain rate. Among the strain rate-related constitutive relations of various engineering materials, the Cowper-Symonds relationship [13] is the most widely used constitutive model in structural collision simulation. This relation represents an ideal rigid-plastic material whose dynamic yield limit is related to the strain rate.
(1)σsdσs=1+ε̇B1/q,where σsd and σs, respectively, represent the dynamic yield limit and quasistatic yield limit of the material, ε̇ represents the strain rate of the material, and B and q are material parameters used to characterise the rate-dependent sensitivity of the material.In the process of structural collision, the energy absorbed in the elastic stage is negligible and a large amount of energy is dissipated in the plastic deformation stage. Therefore, the buffer material can be approximately abstracted as a rigid-plastic material, and the higher the yield limit, the more energy absorbed by the material. The moving part is made of steel Q345, and the thin-walled tube is made of stainless steel 1Cr18Ni9Ti. The material parameters are summarised in Table1 (all parameters were measured using an MTS testbed in the laboratory).Table 1
Material parameters.
Material
Young’s modulus (E)
Poisson ratio (ν)
Density (ρ)
Tangent modulus (G)
Q345
201 GPa
0.3
7800 kg/m3
1.17 GPa
1Cr18Ni9Ti
184 GPa
0.3
7900 kg/m3
4.13 GPa


### 2.3. Compression Contact Model

A Hertzian-damped model [14, 15] was selected in the study of the compression of metal tubes herein, and a contact unit was introduced to simulate the contact behaviour. The two planes make contact with, and squeeze, the metal tube. The model contains a nonlinear spring and a nonlinear damper to simulate the nonlinearity and energy dissipation of contact stiffness. The collision load can be expressed as
(2)Fc=khδ3/2+chδ̇,δ>0,0,δ≤0,where kh is the contact stiffness, δ is the relative deformation of two objects at the contact point, and δ̇ is the relative deformation velocity of two objects at the contact point. ch represents the damping coefficient, which can be expressed as
(3)ch=λδ3/2,where λ is called the hysteresis damping coefficient, which can be expressed as
(4)λ=3kh1−e24Δu,where Δu is the velocity of the collision contact point at the moment of collision and e is the energy recovery coefficient, which is used to represent the energy loss in the collision process: e=1 represents a completely elastic collision with no energy loss and e=0 represents a completely inelastic collision with the greatest energy loss.The energy recovery coefficient is expressed in(5)e=ΔET−ΦaΔET+Φa,where Φa is the energy lost in the collision compression process and ΔET is the loss of kinetic energy before and after the collision.The contact stiffness is given by(6)kh=43E∗R∗1/2,where E∗ is the equivalent elastic modulus and R∗ is the equivalent radius.The dynamic equation of compression collision is given by(7)Mu¨+Cu̇+Ku=Fu,where M, C, and K, respectively, represent the mass matrix, damping matrix, and stiffness matrix, u is the displacement vector, and F is the external load vector. Except to satisfy the dynamic equation, the condition of the contact boundary must be met. The normal contact boundary condition can be discretised into
(8)Bnu+D0≥0,where Bn is the normal contact constraint matrix and D0 represents the initial normal gap. The tangential contact boundary conditions can be discretised into
(9)Bτut+Δt−ut=0,where Bτ represents the tangential contact constraint matrix and ut and ut+Δt represent displacement vectors at t and t+Δt, respectively. The use of the Lagrange multiplier method, penalty function method, and linear programming is commonplace when introducing the contact condition into the dynamic equation. Here, a penalty function method is adopted, which involves solving the extremum of the functional [16–18], namely:
(10)∏u=E+∫tt+Δt∫ScαBnu+D0TBnu+D0dSdt,where E represents the total potential energy of the system, represents the contact boundary, and α represents the penalty function factor.Through the above analysis, equations (2), (5), (6), (7), and (10) constitute complete kinetic equations of motion in a collision. By introducing an appropriate material constitutive model and finite element discrete method, the whole collision compression contact process can be analysed.


### 2.4. Finite Element Model

The finite element model is shown in Figure2. The load and boundary conditions of moving parts are axisymmetric, so a two-dimensional axisymmetric model is used to reduce the calculation time in the ABAQUS software suite adopted here. Four-noded quadrilateral axisymmetric linear reduced integration units (CAx4R) are used in the mesh, and hourglass control is adopted. The mesh size of ascending and descending parts is 0.8 mm, and the mesh size of the metal tube is 0.1 mm. A predefined vertical upward velocity field is applied to the moving parts, which can provide the initial kinetic energy for the moving part in the collision.Figure 2
Finite element model.


## 2.1. Geometric Model

The geometry model is shown in Figure1. Under external force, the descending object moves relative to the ascending object at a certain speed to simulate the collision environment. As a result, the metal tube sandwiched between them is compressed and deformed.Figure 1
Compression model for a hollow metal tube. (1) Descending object. (2) Ascending object. (3) Metal tube to be compressed.Ф: outer diameter of the metal tube; t: thickness of the metal tube; d: distance from the outer wall of the metal tube to the wall of the inner moving object.All the materials used in this study were designed by the authors and were manufactured by a collaborating industrial partner.


## 2.2. Material Model

When the changing load acts on the structure at a high speed, it deforms rapidly and the strain rate is higher. A large number of studies have shown that the mechanical properties of materials under a high strain rate are quite different from those governing quasistatic deformation, and the yield limit of materials increases with the strain rate. Among the strain rate-related constitutive relations of various engineering materials, the Cowper-Symonds relationship [13] is the most widely used constitutive model in structural collision simulation. This relation represents an ideal rigid-plastic material whose dynamic yield limit is related to the strain rate.
(1)σsdσs=1+ε̇B1/q,where σsd and σs, respectively, represent the dynamic yield limit and quasistatic yield limit of the material, ε̇ represents the strain rate of the material, and B and q are material parameters used to characterise the rate-dependent sensitivity of the material.In the process of structural collision, the energy absorbed in the elastic stage is negligible and a large amount of energy is dissipated in the plastic deformation stage. Therefore, the buffer material can be approximately abstracted as a rigid-plastic material, and the higher the yield limit, the more energy absorbed by the material. The moving part is made of steel Q345, and the thin-walled tube is made of stainless steel 1Cr18Ni9Ti. The material parameters are summarised in Table1 (all parameters were measured using an MTS testbed in the laboratory).Table 1
Material parameters.
Material
Young’s modulus (E)
Poisson ratio (ν)
Density (ρ)
Tangent modulus (G)
Q345
201 GPa
0.3
7800 kg/m3
1.17 GPa
1Cr18Ni9Ti
184 GPa
0.3
7900 kg/m3
4.13 GPa


## 2.3. Compression Contact Model

A Hertzian-damped model [14, 15] was selected in the study of the compression of metal tubes herein, and a contact unit was introduced to simulate the contact behaviour. The two planes make contact with, and squeeze, the metal tube. The model contains a nonlinear spring and a nonlinear damper to simulate the nonlinearity and energy dissipation of contact stiffness. The collision load can be expressed as
(2)Fc=khδ3/2+chδ̇,δ>0,0,δ≤0,where kh is the contact stiffness, δ is the relative deformation of two objects at the contact point, and δ̇ is the relative deformation velocity of two objects at the contact point. ch represents the damping coefficient, which can be expressed as
(3)ch=λδ3/2,where λ is called the hysteresis damping coefficient, which can be expressed as
(4)λ=3kh1−e24Δu,where Δu is the velocity of the collision contact point at the moment of collision and e is the energy recovery coefficient, which is used to represent the energy loss in the collision process: e=1 represents a completely elastic collision with no energy loss and e=0 represents a completely inelastic collision with the greatest energy loss.The energy recovery coefficient is expressed in(5)e=ΔET−ΦaΔET+Φa,where Φa is the energy lost in the collision compression process and ΔET is the loss of kinetic energy before and after the collision.The contact stiffness is given by(6)kh=43E∗R∗1/2,where E∗ is the equivalent elastic modulus and R∗ is the equivalent radius.The dynamic equation of compression collision is given by(7)Mu¨+Cu̇+Ku=Fu,where M, C, and K, respectively, represent the mass matrix, damping matrix, and stiffness matrix, u is the displacement vector, and F is the external load vector. Except to satisfy the dynamic equation, the condition of the contact boundary must be met. The normal contact boundary condition can be discretised into
(8)Bnu+D0≥0,where Bn is the normal contact constraint matrix and D0 represents the initial normal gap. The tangential contact boundary conditions can be discretised into
(9)Bτut+Δt−ut=0,where Bτ represents the tangential contact constraint matrix and ut and ut+Δt represent displacement vectors at t and t+Δt, respectively. The use of the Lagrange multiplier method, penalty function method, and linear programming is commonplace when introducing the contact condition into the dynamic equation. Here, a penalty function method is adopted, which involves solving the extremum of the functional [16–18], namely:
(10)∏u=E+∫tt+Δt∫ScαBnu+D0TBnu+D0dSdt,where E represents the total potential energy of the system, represents the contact boundary, and α represents the penalty function factor.Through the above analysis, equations (2), (5), (6), (7), and (10) constitute complete kinetic equations of motion in a collision. By introducing an appropriate material constitutive model and finite element discrete method, the whole collision compression contact process can be analysed.


## 2.4. Finite Element Model

The finite element model is shown in Figure2. The load and boundary conditions of moving parts are axisymmetric, so a two-dimensional axisymmetric model is used to reduce the calculation time in the ABAQUS software suite adopted here. Four-noded quadrilateral axisymmetric linear reduced integration units (CAx4R) are used in the mesh, and hourglass control is adopted. The mesh size of ascending and descending parts is 0.8 mm, and the mesh size of the metal tube is 0.1 mm. A predefined vertical upward velocity field is applied to the moving parts, which can provide the initial kinetic energy for the moving part in the collision.Figure 2
Finite element model.


## 3. Simulation Calculation

### 3.1. Influence of Outer Diameter Size of a Metal Tube on Compression Energy Absorption Performance

A metal tube with a wall thickness of 1 mm is taken as the research object, and three working conditions with outer diameters of 4 mm, 5 mm, and 6 mm were taken as the research objects.


#### 3.1.1. Comparison of Energy Conversion Performance

The energy changes in the simulation process of each working condition are shown in Figure3. According to the curve in the figure, the energy absorption rate of the metal tube is 59.4% at 6 mm. At 5 mm, the energy absorption rate of the metal tube reaches 93.5%. The energy absorption rate of the metal tube is 87% at 4 mm; therefore, the energy absorption effect of 5 mm thin-walled rings in this model is better than that in the other two working conditions.Figure 3
Energy absorption process for metal tubes of different outer diameters. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done by external load; D: frictional energy consumption; E: total energy of the model.
(a)
6 mm
(b)
5 mm
(c)
4 mm


#### 3.1.2. Comparison of Structural Stress Distribution

The equivalent stress distribution of moving parts under different working conditions is shown in Figure4. From the figure, at 6 mm, the compression of the metal tube is not large and the stress caused by extrusion on the wall of the moving part can reach a maximum of 840 MPa. At 4 mm, the maximum stress on the moving parts can reach 550 MPa. At 5 mm, the maximum stress on the moving parts can reach 440 MPa and the buffering effect is good.Figure 4
Compression equivalent stress for metal tubes of different outer diameters.


#### 3.1.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure5 show the motion of moving parts under the action of metal tubes with different outer diameters. The three curves reach their highest points at three points A, B, and C, respectively. This indicates that the outer diameter of the metal tube is not proportional to the compression time and compression stroke. Among them, when the outer diameter of the metal tube is 5 mm, it can be compressed with the longest buffer time and compression stroke.Figure 5
Comparison of displacement-time curves of the moving object for metal tubes of different outer diameters.


#### 3.1.4. Summary of Results

The performance parameters of the three kinds of metal tubes with different diameters after compression are summarised in Table2. The analysis shows that the compression energy absorption effect of the thin-walled tube with an outer diameter of 5 mm is better than those of 6 mm and 4 mm. Therefore, the metal tube with an outer diameter of 5 mm is selected for subsequent analysis.Table 2
Simulation results: compression and energy absorption process parameters for metal tubes of different diameters.
Outer diameter of the metal tube (mm)
6
5
4
Time of compression and energy absorption (ms)
1.75
2
1.45
Biggest equivalent stress of the moving part (MPa)
840
440
550
Energy absorption ratio (%)
59.4
93.5
87


### 3.2. Influence of the Wall Thickness of Metal Tubes on Compression and Energy Absorption Performance

The metal tube with the outer diameter of 5 mm is taken as the research object. Three working conditions (wall thicknesses of 1.2 mm, 1.0 mm, and 0.8 mm) were studied to compare the effect of different wall thicknesses on buffer performance.


#### 3.2.1. Comparison of Energy Conversion Performance

Energy conversion in the three working conditions is shown in Figure6. At 1.2 mm, the energy absorption rate of the metal tube is 93.8%. At 1.0 mm, the energy absorption rate of the metal tube can reach 93.5%. At 0.8 mm, the energy absorption rate of the metal tube is 87%. This shows that the energy absorption rate of the metal tube with a thickness of 0.8 mm is lower, and there is little difference between the energy absorption rates of the metal tube with a thickness of 1.0 mm and 1.2 mm.Figure 6
Energy conversion curves in the compression and energy absorption process of metal tubes of different wall thicknesses. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done under external load; D: frictional energy consumption; E: total energy of the model.
(a)
1.2 mm
(b)
1.0 mm
(c)
0.8 mm


#### 3.2.2. Comparison of Structural Stress Distribution

The effective stress distribution of the three working conditions is shown in Figure7. The compression of the metal tube with a thickness of 1.2 mm is smaller than that of one of 1.0 mm, and the compression of the metal tube with a thickness of 0.8 mm is the largest. Therefore, the transverse size is larger after compression. At 1.2 mm, the maximum equivalent stress on the side wall of moving parts is 480 MPa; at 1.0 mm, the maximum equivalent stress on the side wall of the moving parts is 440 MPa; at 0.8 mm, the maximum equivalent stress on the side wall of the moving parts is 560 MPa. By contrast, the metal tube with a thickness of 1.0 mm has a better energy absorption effect.Figure 7
Compression of metal tubes of different wall thicknesses (distribution cloud picture of equivalent stress).


#### 3.2.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure8 show the movement of moving parts of metal tubes with different wall thicknesses when they are compressed. The three curves reach their peaks at three points A, B, and C, respectively. This indicates that the thinner the metal tube, the slower the compression (albeit to a greater amount).Figure 8
Comparison of displacement-time curves of the ascending object for tubes of different wall thicknesses.


#### 3.2.4. Summary of Results

The compression energy absorption performance parameters of the three kinds of metal tubes with different wall thicknesses are summarised in Table3. The above analysis shows that the metal tubes with thicknesses of 1.2 mm and 1.0 mm have better energy absorption effects, making the equivalent stress of moving objects smaller, and the energy absorption performance of the two is similar.Table 3
Simulation results: compression and energy absorption parameters of metal tubes of different wall thicknesses.
Wall thickness of the metal tubeD (mm)
1.2
1
0.8
Time of compression and energy absorption (ms)
1.6
2
2.25
Biggest equivalent stress of the moving part (MPa)
480
440
560
Energy absorption ratio of the metal tube (%)
93.8
93.5
87


### 3.3. The Influence of the Relative Position Relationship between the Metal Tube and the Compressed Body on the Compression Energy Absorption Performance

The energy absorption performance of the metal tube is studied in different positions in the clearance of 1 and 2 moving parts. Using the metal tube with an outer diameter of 5 mm and a thickness of 1 mm, making the distance from the outer wall of the metal tube to the wall of the inner moving object 0.75 mm (the metal tube is centred within the available clearance), 0.5 mm (the metal tube deviates from the centreline by 0.25 mm), and 0.25 mm (the metal tube deviates from the centreline by 0.5 mm), the buffer energy absorption over time is calculated.


#### 3.3.1. Comparison of Energy Conversion Performance

Figure9 shows the energy conversion in the process of simulation in different positions on the metal tubes. The energy absorption rate of the metal tube at 0.75 mm is 93.5%. At 0.5 mm, the energy absorption rate of the metal tube reaches 93.4%, and at 0.25 mm, the energy absorption rate of the metal tube is 92.2%. Therefore, there is little difference in the energy absorption rate of metal tubes under the three working conditions analysed here.Figure 9
Energy conversion curves in the process of compression and energy absorption of metal tubes located in different positions. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done by external load; D: frictional energy consumption; E: total energy of the model.
(a)
0.75 mm
(b)
0.5 mm
(c)
0.25 mm


#### 3.3.2. Comparison of Structural Stress Distribution

The stress distribution in each of the three conditions is shown in Figure10. The degree of compression of the metal tube is almost the same, but the equivalent stress distribution on the wall of the moving part varies as follows: at 0.75 mm, the maximum equivalent stress on the wall is 456 MPa; at 0.5 mm, the maximum equivalent stress on the wall is 450 MPa; and at 0.25 mm, the maximum equivalent stress on the wall is 417 MPa.Figure 10
Compression equivalent stress for metal tubes displaced at different locations.


#### 3.3.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure11 show the movement of the ascending part under the action of the metal tube in different positions: the three curves are similar, and the peaks all lie near point A, indicating that the motion of the ascending part is not the same in each case.Figure 11
Displacement-time curves of the ascending object of metal tubes displaced at different places.


#### 3.3.4. Summary of Results

Under the three working conditions in different positions, the compression and energy absorption performance parameters of the metal tube are listed in Table4. From the above analysis, it can be seen that the energy absorption rate of thin-walled tubes under the three conditions varied little, but the stress on the wall is minimised at 0.25 mm, indicating that the extrusion between the tube and the wall is minimised. Therefore, the metal tube has a better cushioning effect when it is close to the outer wall of the inner moving part.Table 4
Simulation results of compression and energy absorption parameters of metal tubes located in different positions.
Location of the metal tubed (mm)
0.25
0.5
0.75
Time of compression and energy absorption (ms)
2
2
2
Biggest equivalent stress of the moving part (MPa)
417
450
456
Energy absorption ratio (%)
92.2
93.4
93.5


### 3.4. The Influence of the Number of Stacked Metal Tubes on the Compression and Energy Absorption Performance

We chose a metal tube with an outer diameter of 5 mm and a wall thickness of 1 mm, placed 0.25 mm from the outer wall of the ascending part. The numbers of superimposed tubes were set to 8, 12, and 16, respectively. The process of buffering energy absorption was simulated, and the effects of different superimposed quantities on compression and energy absorption performance were compared.


#### 3.4.1. Comparison of Energy Conversion Performance

The energy conversion obtained by simulation in different stacking numbers is shown in Figure12: the energy absorption rate of 8 metal tubes is 84.9%, the energy absorption rate of 12 metal tubes is 92.2%, and the energy absorption rate of 16 metal tubes is 94.9%. This shows that the energy absorption rate of the metal tube increases with the number of stacked tubes.Figure 12
Energy conversion curves in the process of compression and energy absorption of different numbers of stacked tubes.
(a)
8 metal tubes
(b)
12 metal tubes
(c)
16 metal tubes


#### 3.4.2. Comparison of Structural Stress Distribution

The finite element simulation results of different stacks of metal tubes which are compressed and collided are shown in Figure13. It shows that the metal tube is compressed to the greatest extent when using 8 tubes (then 12 and 16, in descending order). The maximum stress on the wall of the moving parts is 520 MPa (8 tubes), 417 MPa (12 tubes), and 351 MPa (16 tubes). The more metal tubes are stacked, the lower the compression thereof and the lower the stress on the moving parts.Figure 13
Compression of the metal tube stacks under collision (distribution cloud picture of equivalent stress).


#### 3.4.3. Comparison of Deceleration Performance of Moving Parts

The motion of the ascending part under the action of the metal tubes with different numbers of stacked tubes is shown in Figure14: the more tubes in the stack, the greater the buffer energy absorption and travel and displacement time.Figure 14
Displacement-time curves of the ascending object for stacked tubes. A: 8 metal tubes; B: 12 metal tubes; C: 16 metal tubes.


#### 3.4.4. Summary of Results

The compression and energy absorption performance parameters of the metal tubes under the three different working conditions are listed in Table5. With the increase in the number of the metal tubes, the buffer stroke and time increase, the tube compression decreases, the stress on the moving part decreases, and the energy absorption rate of the thin-walled tube increases; however, from an engineering viewpoint, fewer metal tubes should be selected to meet the needs of engineering practice.Table 5
Simulation results: energy absorption process parameters for different numbers of metal tubes.
Number of metal tubes
8
12
16
Time of compression (ms)
1.48
2
2.38
Displacement of compression and energy absorption (mm)
23.74
30.47
35.82
Biggest equivalent stress on the wall of the moving part (MPa)
520
417
351
Energy absorption ratio of the thin-walled tube (%)
84.9
92.2
94.9


## 3.1. Influence of Outer Diameter Size of a Metal Tube on Compression Energy Absorption Performance

A metal tube with a wall thickness of 1 mm is taken as the research object, and three working conditions with outer diameters of 4 mm, 5 mm, and 6 mm were taken as the research objects.


### 3.1.1. Comparison of Energy Conversion Performance

The energy changes in the simulation process of each working condition are shown in Figure3. According to the curve in the figure, the energy absorption rate of the metal tube is 59.4% at 6 mm. At 5 mm, the energy absorption rate of the metal tube reaches 93.5%. The energy absorption rate of the metal tube is 87% at 4 mm; therefore, the energy absorption effect of 5 mm thin-walled rings in this model is better than that in the other two working conditions.Figure 3
Energy absorption process for metal tubes of different outer diameters. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done by external load; D: frictional energy consumption; E: total energy of the model.
(a)
6 mm
(b)
5 mm
(c)
4 mm


### 3.1.2. Comparison of Structural Stress Distribution

The equivalent stress distribution of moving parts under different working conditions is shown in Figure4. From the figure, at 6 mm, the compression of the metal tube is not large and the stress caused by extrusion on the wall of the moving part can reach a maximum of 840 MPa. At 4 mm, the maximum stress on the moving parts can reach 550 MPa. At 5 mm, the maximum stress on the moving parts can reach 440 MPa and the buffering effect is good.Figure 4
Compression equivalent stress for metal tubes of different outer diameters.


### 3.1.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure5 show the motion of moving parts under the action of metal tubes with different outer diameters. The three curves reach their highest points at three points A, B, and C, respectively. This indicates that the outer diameter of the metal tube is not proportional to the compression time and compression stroke. Among them, when the outer diameter of the metal tube is 5 mm, it can be compressed with the longest buffer time and compression stroke.Figure 5
Comparison of displacement-time curves of the moving object for metal tubes of different outer diameters.


### 3.1.4. Summary of Results

The performance parameters of the three kinds of metal tubes with different diameters after compression are summarised in Table2. The analysis shows that the compression energy absorption effect of the thin-walled tube with an outer diameter of 5 mm is better than those of 6 mm and 4 mm. Therefore, the metal tube with an outer diameter of 5 mm is selected for subsequent analysis.Table 2
Simulation results: compression and energy absorption process parameters for metal tubes of different diameters.
Outer diameter of the metal tube (mm)
6
5
4
Time of compression and energy absorption (ms)
1.75
2
1.45
Biggest equivalent stress of the moving part (MPa)
840
440
550
Energy absorption ratio (%)
59.4
93.5
87


## 3.1.1. Comparison of Energy Conversion Performance

The energy changes in the simulation process of each working condition are shown in Figure3. According to the curve in the figure, the energy absorption rate of the metal tube is 59.4% at 6 mm. At 5 mm, the energy absorption rate of the metal tube reaches 93.5%. The energy absorption rate of the metal tube is 87% at 4 mm; therefore, the energy absorption effect of 5 mm thin-walled rings in this model is better than that in the other two working conditions.Figure 3
Energy absorption process for metal tubes of different outer diameters. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done by external load; D: frictional energy consumption; E: total energy of the model.
(a)
6 mm
(b)
5 mm
(c)
4 mm


## 3.1.2. Comparison of Structural Stress Distribution

The equivalent stress distribution of moving parts under different working conditions is shown in Figure4. From the figure, at 6 mm, the compression of the metal tube is not large and the stress caused by extrusion on the wall of the moving part can reach a maximum of 840 MPa. At 4 mm, the maximum stress on the moving parts can reach 550 MPa. At 5 mm, the maximum stress on the moving parts can reach 440 MPa and the buffering effect is good.Figure 4
Compression equivalent stress for metal tubes of different outer diameters.


## 3.1.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure5 show the motion of moving parts under the action of metal tubes with different outer diameters. The three curves reach their highest points at three points A, B, and C, respectively. This indicates that the outer diameter of the metal tube is not proportional to the compression time and compression stroke. Among them, when the outer diameter of the metal tube is 5 mm, it can be compressed with the longest buffer time and compression stroke.Figure 5
Comparison of displacement-time curves of the moving object for metal tubes of different outer diameters.


## 3.1.4. Summary of Results

The performance parameters of the three kinds of metal tubes with different diameters after compression are summarised in Table2. The analysis shows that the compression energy absorption effect of the thin-walled tube with an outer diameter of 5 mm is better than those of 6 mm and 4 mm. Therefore, the metal tube with an outer diameter of 5 mm is selected for subsequent analysis.Table 2
Simulation results: compression and energy absorption process parameters for metal tubes of different diameters.
Outer diameter of the metal tube (mm)
6
5
4
Time of compression and energy absorption (ms)
1.75
2
1.45
Biggest equivalent stress of the moving part (MPa)
840
440
550
Energy absorption ratio (%)
59.4
93.5
87


## 3.2. Influence of the Wall Thickness of Metal Tubes on Compression and Energy Absorption Performance

The metal tube with the outer diameter of 5 mm is taken as the research object. Three working conditions (wall thicknesses of 1.2 mm, 1.0 mm, and 0.8 mm) were studied to compare the effect of different wall thicknesses on buffer performance.


### 3.2.1. Comparison of Energy Conversion Performance

Energy conversion in the three working conditions is shown in Figure6. At 1.2 mm, the energy absorption rate of the metal tube is 93.8%. At 1.0 mm, the energy absorption rate of the metal tube can reach 93.5%. At 0.8 mm, the energy absorption rate of the metal tube is 87%. This shows that the energy absorption rate of the metal tube with a thickness of 0.8 mm is lower, and there is little difference between the energy absorption rates of the metal tube with a thickness of 1.0 mm and 1.2 mm.Figure 6
Energy conversion curves in the compression and energy absorption process of metal tubes of different wall thicknesses. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done under external load; D: frictional energy consumption; E: total energy of the model.
(a)
1.2 mm
(b)
1.0 mm
(c)
0.8 mm


### 3.2.2. Comparison of Structural Stress Distribution

The effective stress distribution of the three working conditions is shown in Figure7. The compression of the metal tube with a thickness of 1.2 mm is smaller than that of one of 1.0 mm, and the compression of the metal tube with a thickness of 0.8 mm is the largest. Therefore, the transverse size is larger after compression. At 1.2 mm, the maximum equivalent stress on the side wall of moving parts is 480 MPa; at 1.0 mm, the maximum equivalent stress on the side wall of the moving parts is 440 MPa; at 0.8 mm, the maximum equivalent stress on the side wall of the moving parts is 560 MPa. By contrast, the metal tube with a thickness of 1.0 mm has a better energy absorption effect.Figure 7
Compression of metal tubes of different wall thicknesses (distribution cloud picture of equivalent stress).


### 3.2.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure8 show the movement of moving parts of metal tubes with different wall thicknesses when they are compressed. The three curves reach their peaks at three points A, B, and C, respectively. This indicates that the thinner the metal tube, the slower the compression (albeit to a greater amount).Figure 8
Comparison of displacement-time curves of the ascending object for tubes of different wall thicknesses.


### 3.2.4. Summary of Results

The compression energy absorption performance parameters of the three kinds of metal tubes with different wall thicknesses are summarised in Table3. The above analysis shows that the metal tubes with thicknesses of 1.2 mm and 1.0 mm have better energy absorption effects, making the equivalent stress of moving objects smaller, and the energy absorption performance of the two is similar.Table 3
Simulation results: compression and energy absorption parameters of metal tubes of different wall thicknesses.
Wall thickness of the metal tubeD (mm)
1.2
1
0.8
Time of compression and energy absorption (ms)
1.6
2
2.25
Biggest equivalent stress of the moving part (MPa)
480
440
560
Energy absorption ratio of the metal tube (%)
93.8
93.5
87


## 3.2.1. Comparison of Energy Conversion Performance

Energy conversion in the three working conditions is shown in Figure6. At 1.2 mm, the energy absorption rate of the metal tube is 93.8%. At 1.0 mm, the energy absorption rate of the metal tube can reach 93.5%. At 0.8 mm, the energy absorption rate of the metal tube is 87%. This shows that the energy absorption rate of the metal tube with a thickness of 0.8 mm is lower, and there is little difference between the energy absorption rates of the metal tube with a thickness of 1.0 mm and 1.2 mm.Figure 6
Energy conversion curves in the compression and energy absorption process of metal tubes of different wall thicknesses. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done under external load; D: frictional energy consumption; E: total energy of the model.
(a)
1.2 mm
(b)
1.0 mm
(c)
0.8 mm


## 3.2.2. Comparison of Structural Stress Distribution

The effective stress distribution of the three working conditions is shown in Figure7. The compression of the metal tube with a thickness of 1.2 mm is smaller than that of one of 1.0 mm, and the compression of the metal tube with a thickness of 0.8 mm is the largest. Therefore, the transverse size is larger after compression. At 1.2 mm, the maximum equivalent stress on the side wall of moving parts is 480 MPa; at 1.0 mm, the maximum equivalent stress on the side wall of the moving parts is 440 MPa; at 0.8 mm, the maximum equivalent stress on the side wall of the moving parts is 560 MPa. By contrast, the metal tube with a thickness of 1.0 mm has a better energy absorption effect.Figure 7
Compression of metal tubes of different wall thicknesses (distribution cloud picture of equivalent stress).


## 3.2.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure8 show the movement of moving parts of metal tubes with different wall thicknesses when they are compressed. The three curves reach their peaks at three points A, B, and C, respectively. This indicates that the thinner the metal tube, the slower the compression (albeit to a greater amount).Figure 8
Comparison of displacement-time curves of the ascending object for tubes of different wall thicknesses.


## 3.2.4. Summary of Results

The compression energy absorption performance parameters of the three kinds of metal tubes with different wall thicknesses are summarised in Table3. The above analysis shows that the metal tubes with thicknesses of 1.2 mm and 1.0 mm have better energy absorption effects, making the equivalent stress of moving objects smaller, and the energy absorption performance of the two is similar.Table 3
Simulation results: compression and energy absorption parameters of metal tubes of different wall thicknesses.
Wall thickness of the metal tubeD (mm)
1.2
1
0.8
Time of compression and energy absorption (ms)
1.6
2
2.25
Biggest equivalent stress of the moving part (MPa)
480
440
560
Energy absorption ratio of the metal tube (%)
93.8
93.5
87


## 3.3. The Influence of the Relative Position Relationship between the Metal Tube and the Compressed Body on the Compression Energy Absorption Performance

The energy absorption performance of the metal tube is studied in different positions in the clearance of 1 and 2 moving parts. Using the metal tube with an outer diameter of 5 mm and a thickness of 1 mm, making the distance from the outer wall of the metal tube to the wall of the inner moving object 0.75 mm (the metal tube is centred within the available clearance), 0.5 mm (the metal tube deviates from the centreline by 0.25 mm), and 0.25 mm (the metal tube deviates from the centreline by 0.5 mm), the buffer energy absorption over time is calculated.


### 3.3.1. Comparison of Energy Conversion Performance

Figure9 shows the energy conversion in the process of simulation in different positions on the metal tubes. The energy absorption rate of the metal tube at 0.75 mm is 93.5%. At 0.5 mm, the energy absorption rate of the metal tube reaches 93.4%, and at 0.25 mm, the energy absorption rate of the metal tube is 92.2%. Therefore, there is little difference in the energy absorption rate of metal tubes under the three working conditions analysed here.Figure 9
Energy conversion curves in the process of compression and energy absorption of metal tubes located in different positions. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done by external load; D: frictional energy consumption; E: total energy of the model.
(a)
0.75 mm
(b)
0.5 mm
(c)
0.25 mm


### 3.3.2. Comparison of Structural Stress Distribution

The stress distribution in each of the three conditions is shown in Figure10. The degree of compression of the metal tube is almost the same, but the equivalent stress distribution on the wall of the moving part varies as follows: at 0.75 mm, the maximum equivalent stress on the wall is 456 MPa; at 0.5 mm, the maximum equivalent stress on the wall is 450 MPa; and at 0.25 mm, the maximum equivalent stress on the wall is 417 MPa.Figure 10
Compression equivalent stress for metal tubes displaced at different locations.


### 3.3.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure11 show the movement of the ascending part under the action of the metal tube in different positions: the three curves are similar, and the peaks all lie near point A, indicating that the motion of the ascending part is not the same in each case.Figure 11
Displacement-time curves of the ascending object of metal tubes displaced at different places.


### 3.3.4. Summary of Results

Under the three working conditions in different positions, the compression and energy absorption performance parameters of the metal tube are listed in Table4. From the above analysis, it can be seen that the energy absorption rate of thin-walled tubes under the three conditions varied little, but the stress on the wall is minimised at 0.25 mm, indicating that the extrusion between the tube and the wall is minimised. Therefore, the metal tube has a better cushioning effect when it is close to the outer wall of the inner moving part.Table 4
Simulation results of compression and energy absorption parameters of metal tubes located in different positions.
Location of the metal tubed (mm)
0.25
0.5
0.75
Time of compression and energy absorption (ms)
2
2
2
Biggest equivalent stress of the moving part (MPa)
417
450
456
Energy absorption ratio (%)
92.2
93.4
93.5


## 3.3.1. Comparison of Energy Conversion Performance

Figure9 shows the energy conversion in the process of simulation in different positions on the metal tubes. The energy absorption rate of the metal tube at 0.75 mm is 93.5%. At 0.5 mm, the energy absorption rate of the metal tube reaches 93.4%, and at 0.25 mm, the energy absorption rate of the metal tube is 92.2%. Therefore, there is little difference in the energy absorption rate of metal tubes under the three working conditions analysed here.Figure 9
Energy conversion curves in the process of compression and energy absorption of metal tubes located in different positions. A: internal energy of the metal tube; B: kinetic energy of the ascending object; C: work done by external load; D: frictional energy consumption; E: total energy of the model.
(a)
0.75 mm
(b)
0.5 mm
(c)
0.25 mm


## 3.3.2. Comparison of Structural Stress Distribution

The stress distribution in each of the three conditions is shown in Figure10. The degree of compression of the metal tube is almost the same, but the equivalent stress distribution on the wall of the moving part varies as follows: at 0.75 mm, the maximum equivalent stress on the wall is 456 MPa; at 0.5 mm, the maximum equivalent stress on the wall is 450 MPa; and at 0.25 mm, the maximum equivalent stress on the wall is 417 MPa.Figure 10
Compression equivalent stress for metal tubes displaced at different locations.


## 3.3.3. Comparison of Deceleration Performance of Moving Parts

The three displacement-time curves in Figure11 show the movement of the ascending part under the action of the metal tube in different positions: the three curves are similar, and the peaks all lie near point A, indicating that the motion of the ascending part is not the same in each case.Figure 11
Displacement-time curves of the ascending object of metal tubes displaced at different places.


## 3.3.4. Summary of Results

Under the three working conditions in different positions, the compression and energy absorption performance parameters of the metal tube are listed in Table4. From the above analysis, it can be seen that the energy absorption rate of thin-walled tubes under the three conditions varied little, but the stress on the wall is minimised at 0.25 mm, indicating that the extrusion between the tube and the wall is minimised. Therefore, the metal tube has a better cushioning effect when it is close to the outer wall of the inner moving part.Table 4
Simulation results of compression and energy absorption parameters of metal tubes located in different positions.
Location of the metal tubed (mm)
0.25
0.5
0.75
Time of compression and energy absorption (ms)
2
2
2
Biggest equivalent stress of the moving part (MPa)
417
450
456
Energy absorption ratio (%)
92.2
93.4
93.5


## 3.4. The Influence of the Number of Stacked Metal Tubes on the Compression and Energy Absorption Performance

We chose a metal tube with an outer diameter of 5 mm and a wall thickness of 1 mm, placed 0.25 mm from the outer wall of the ascending part. The numbers of superimposed tubes were set to 8, 12, and 16, respectively. The process of buffering energy absorption was simulated, and the effects of different superimposed quantities on compression and energy absorption performance were compared.


### 3.4.1. Comparison of Energy Conversion Performance

The energy conversion obtained by simulation in different stacking numbers is shown in Figure12: the energy absorption rate of 8 metal tubes is 84.9%, the energy absorption rate of 12 metal tubes is 92.2%, and the energy absorption rate of 16 metal tubes is 94.9%. This shows that the energy absorption rate of the metal tube increases with the number of stacked tubes.Figure 12
Energy conversion curves in the process of compression and energy absorption of different numbers of stacked tubes.
(a)
8 metal tubes
(b)
12 metal tubes
(c)
16 metal tubes


### 3.4.2. Comparison of Structural Stress Distribution

The finite element simulation results of different stacks of metal tubes which are compressed and collided are shown in Figure13. It shows that the metal tube is compressed to the greatest extent when using 8 tubes (then 12 and 16, in descending order). The maximum stress on the wall of the moving parts is 520 MPa (8 tubes), 417 MPa (12 tubes), and 351 MPa (16 tubes). The more metal tubes are stacked, the lower the compression thereof and the lower the stress on the moving parts.Figure 13
Compression of the metal tube stacks under collision (distribution cloud picture of equivalent stress).


### 3.4.3. Comparison of Deceleration Performance of Moving Parts

The motion of the ascending part under the action of the metal tubes with different numbers of stacked tubes is shown in Figure14: the more tubes in the stack, the greater the buffer energy absorption and travel and displacement time.Figure 14
Displacement-time curves of the ascending object for stacked tubes. A: 8 metal tubes; B: 12 metal tubes; C: 16 metal tubes.


### 3.4.4. Summary of Results

The compression and energy absorption performance parameters of the metal tubes under the three different working conditions are listed in Table5. With the increase in the number of the metal tubes, the buffer stroke and time increase, the tube compression decreases, the stress on the moving part decreases, and the energy absorption rate of the thin-walled tube increases; however, from an engineering viewpoint, fewer metal tubes should be selected to meet the needs of engineering practice.Table 5
Simulation results: energy absorption process parameters for different numbers of metal tubes.
Number of metal tubes
8
12
16
Time of compression (ms)
1.48
2
2.38
Displacement of compression and energy absorption (mm)
23.74
30.47
35.82
Biggest equivalent stress on the wall of the moving part (MPa)
520
417
351
Energy absorption ratio of the thin-walled tube (%)
84.9
92.2
94.9


## 3.4.1. Comparison of Energy Conversion Performance

The energy conversion obtained by simulation in different stacking numbers is shown in Figure12: the energy absorption rate of 8 metal tubes is 84.9%, the energy absorption rate of 12 metal tubes is 92.2%, and the energy absorption rate of 16 metal tubes is 94.9%. This shows that the energy absorption rate of the metal tube increases with the number of stacked tubes.Figure 12
Energy conversion curves in the process of compression and energy absorption of different numbers of stacked tubes.
(a)
8 metal tubes
(b)
12 metal tubes
(c)
16 metal tubes


## 3.4.2. Comparison of Structural Stress Distribution

The finite element simulation results of different stacks of metal tubes which are compressed and collided are shown in Figure13. It shows that the metal tube is compressed to the greatest extent when using 8 tubes (then 12 and 16, in descending order). The maximum stress on the wall of the moving parts is 520 MPa (8 tubes), 417 MPa (12 tubes), and 351 MPa (16 tubes). The more metal tubes are stacked, the lower the compression thereof and the lower the stress on the moving parts.Figure 13
Compression of the metal tube stacks under collision (distribution cloud picture of equivalent stress).


## 3.4.3. Comparison of Deceleration Performance of Moving Parts

The motion of the ascending part under the action of the metal tubes with different numbers of stacked tubes is shown in Figure14: the more tubes in the stack, the greater the buffer energy absorption and travel and displacement time.Figure 14
Displacement-time curves of the ascending object for stacked tubes. A: 8 metal tubes; B: 12 metal tubes; C: 16 metal tubes.


## 3.4.4. Summary of Results

The compression and energy absorption performance parameters of the metal tubes under the three different working conditions are listed in Table5. With the increase in the number of the metal tubes, the buffer stroke and time increase, the tube compression decreases, the stress on the moving part decreases, and the energy absorption rate of the thin-walled tube increases; however, from an engineering viewpoint, fewer metal tubes should be selected to meet the needs of engineering practice.Table 5
Simulation results: energy absorption process parameters for different numbers of metal tubes.
Number of metal tubes
8
12
16
Time of compression (ms)
1.48
2
2.38
Displacement of compression and energy absorption (mm)
23.74
30.47
35.82
Biggest equivalent stress on the wall of the moving part (MPa)
520
417
351
Energy absorption ratio of the thin-walled tube (%)
84.9
92.2
94.9


## 4. Experimental Verification

Three dynamic compression tests were designed, and metal tubes of 5 mm in diameter and 1 mm in wall thickness were placed in the centre. The three working conditions are set based on the numbers thereof in each stack (condition 1: no tubes, condition 2: 8 tubes, and condition 3: 16 tubes). The experimental results are listed in Table6 and can be seen to be in agreement with the conclusions drawn from the simulation. As is shown in Table 6, the state of moving parts after dynamic compression and metal tube extrusion is as follows: stop-end face fracture occurs in descending parts without a metal tube (as seen in the simulation); with 16 stacked tubes, the ascending part and descending part are in good condition, and most of the metal tubes are compressed and flattened (as seen in the simulation); and with 8 stacked tubes, they are all flattened (as seen in the simulation).Table 6
Comparison of simulation and test results.
Case
Number of stacked tubes
Moving object after dynamic compression
Postcompression squeezing
Simulation results and judgement
Experimental results (descending object)
Simulation results
Test results
1
0
Fractured
Fractured
—
—
2
8
Partially damaged
In good condition
Flattened completely
Flattened completely
3
16
In good condition
In good condition
Flattened to a significant extent
Flattened to a significant extentThe thickness of the compressed metal tube was measured and compared with the simulated results (Table7). The results show that the thickness of the buffered tube in the experiment is slightly larger than that simulated (the discrepancy is within 10%, suggesting that the model should be modified in future research).Table 7
Thickness of metal tubes under compression.
Case
Number of stacked tubes
Total thickness of metal tubes as compressed (mm)
Simulation results
Experimental results
Discrepancy
1
0
—
—
—
2
8
9.78
10.5
6.86%
3
16
20.11
22.3
9.82%


## 5. Conclusion and Discussion

The energy absorption properties of hollow metal tubes in terms of diameter, wall thickness, and relative position were simulated. The behaviour in compression and energy absorption of various metal tubes was described.(1)
The compression and energy absorption properties of metal tubes are affected by their outer diameter, according to the placement space, and a matching outer diameter of a metal tube can be found to play a better effect on buffering and energy absorption
(2)
The compressive and energy absorption properties of the metal tubes are affected by the wall thickness. When other conditions are the same, the smaller the wall thickness, the poorer the energy absorption ability of the metal tube, and the wall thickness increases and the energy absorption ability will increase, but when the wall thickness reaches a certain level, the increase in buffer and energy absorption decreases
(3)
The buffering effect of the metal tube is related to its position within the gap. The closer the metal tube is to the inner compression body, the less damage it inflicts on the structural integrity of the outer compression body and the better the effect of the buffer and energy absorption, but the general influence is limited
(4)
The greater the number of stacked metal tubes, the better the overall buffering and energy absorption properties; however, in practical application, it should be considered comprehensively from the space, weight, and stability of the metal tubes after stacking
(5)
The simulation results and experiment results show that the small-sized metal tubes aligned so as to ameliorate the compaction of the compression process can have significant effects on the motion of bodies in a high-speed collision, and the buffer design needs to be aimed at matching the size and space requirements prevailing in practice



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*Source: 6135925-2020-02-15.xml*