HOU Yu，ZHANG Ming，NIE Hong*

1.Key Laboratory of Fundamental Science for National Defense?Advanced Design Technology of Flight Vehicle，Nanjing University of Aeronautics & Astronautics，Nanjing 210016，P.R.China；2.State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China

Abstract: A buffer bag mechanism is designed，which can provide axial impact protection under small displacement.The stiffness characteristics of the structure under impact load are studied.The stiffness of the mechanism and the internal pressure change of the buffer bag are compared and analyzed，when the filling materials are liquid and gas respectively. Finally，the influence of initial fluid bag pressure，bulk modulus and shell thickness on the stiffness of the mechanism and the change of bag pressure are studied. The results show that the stiffness of the liquid bag is better than that of the gas bag when the filler is liquid and gas；the liquid bag has obvious pressure rise after the mechanism is subjected to axial force by 300 kN，and the gas bag has almost no pressure rise；the change of bulk modulus，which is 1 000，1 500，2 000 and 2 500 MPa，has an obvious effect on the liquid bag，and it is positively correlated with the stiffness of the mechanism. The change of gas modulus，which is 28 and 44，has little effect on the stiffness of the mechanism；the thickness of the buffer bag，which is 5，10 and 15 mm，also has an obvious effect on the stiffness.The stiffness of the liquid bag is greater，and the protection for flexible joint is better in the same condition.

Key words：buffer bag；flexible joint；axial protection；liquid bag；gas bag

0 Introduction

With the continuous growth of industrial de?mand，the research and application of buffer at home and abroad is becoming more and more ma?ture［1-3］. Traditional hydraulic buffer has such a com?plex structure that cannot support large load under small displacement and deformation，which limits its application in practice. The traditional shock ab?sorber is not suitable for small displacement and small deformation. Therefore，a new type of buffer bag is designed to provide small displacement and deformation of axial impact protection in the mecha?nism［4］. Buffer bag is a kind of non-metallic buffer which is filled with fluid in a flexible closed contain?er and uses the buffer property of fluid to work. The buffer bag can absorb a lot of energy in small defor?mation and recover quickly. The flexible and easy to deform composite material is used in the contact part of the buffer device and the mechanism，which can fit well with the mechanism under the impact load，so as to prevent the damage of the mechanism caused by stress concentration. So far，liquid buffer bag has been rarely investigated at home and abroad. However，buffer airbag and air spring simi?lar to liquid buffer bag have been studied in depth［5-10］. The rigid and unique characteristics of the gas bag and the liquid bag are better，and need to be further studied under the same condition，as well as the buffer performance of them［11］.

In this paper，a kind of buffer bag cushion is chosen，and the influence of different filling materi?als on the stiffness characteristics of the buffer bag is studied when the filling is gas or liquid. The axial stiffness characteristics of the buffer bag are further addressed.

1 Working Process of Buffer Bag

1.1 Buffer bag shock absorber

The mechanism of shock absorber is mainly composed of two parts：one is rubber joint，and the other is buffer bag，as shown in Fig.1（a）. When the mechanism works，a large axial upward impact load is exerted at the bottom of the mechanism［12］.

The flexible joint is composed of laminated elastic layer and metal layer. The metal plate and rubber layer are bonded together，and thus there is no large axial static displacement. Otherwise，the flexible joint may fail and cause the mechanism fail?ure. Therefore，it is necessary to use large stiffness damper to protect the rubber joint axially. It is as?sumed that there is absolute adhesion between the elastic layer and the metal one. The schematic dia?gram of the flexible joint is shown in Fig.1（b）.

Fig.1 Buffer bag shock absorption mechanism

As shown in Fig.2（a），the buffer bag is a kind of conical ring flexible sealing container filled with incompressible fluid. The real buffer bag is not con?nected in the loop upward，and the head end and tail end of the buffer bag have a closed ring，which is in?serted with a hinge pin to lock the buffer bag in the mechanism. The pressure pipe is connected with the joint and the bottom of the buffer bag to realize the charging of the buffer bag，and the joint is connect?ed with the pressure filling device.

The pressure of the buffer bag can be adjusted to a predetermined value，and the buffer bag can be placed between the inner and outer shells of the mechanism，which can greatly reduce the load trans?mitted to the rubber joint through the contact area between the inner and outer shells. The simplified model of the buffer bag is shown in Fig.2（b）.

Fig.2 Schematic of buffer bag and its simplified model

1.2 Numerical method for analyzing buffer bag

When the liquid reaches the static equilibrium state in the buffer bag，there is no tension and tan?gential force between the liquid particles，as well as between the liquid and buffer bag. Only the normal pressure exists，which is the hydrostatic pressure of the fluid［13］. The hydrostatic pressure of the liquid acting on any point of the buffer bag is the same in each direction，and it is not related to the normal di?rection of the pressure action surface，that is，not re?lated to the shape of the buffer bag. Since the liquid in the buffer bag is a continuous medium，the hydro?static pressure is a continuous function related to the spatial coordinate. Hence，the following equation can be obtained.

A small parallelepiped is randomly selected from the liquid in the buffer bag. The sides of the six faces are dx，dy and dz，which are parallel to the three coordinate axes. Let the projection of unit mass force on the coordinate axis be fx，fy，fz. The components of mass force in x，y and z axes are ρfxdxdydz，ρfydxdydz，and ρfzdxdydz. The surface force is hydrostatic pressure. If the hydrostatic pres?sure of the fluid at any point in the hexahedron is p，the hydrostatic pressure at the center of the two sur?faces parallel to the x-axis in the normal direction is divided into

The hexahedron is a small hexahedron. There?fore，the average hydrostatic pressure in the plane can be regarded as equal to the pressure at the cen?tral point. Therefore，the hydrostatic pressure of the fluid on these two surfaces are

Since the sum of all the external force vectors acting on the hexahedron is 0，it can be known that for the x-axis

After simplification，the following results can be obtained.

Similarly，similar results can be obtained on the y and z axes. Then，when the liquid in the buf?fer bag is in equilibrium，the differential equations are as follows

According to Eq.（6），when the liquid in the buffer bag is at rest，the change rate of hydrostatic pressure along any axis is equal to its unit mass force. In the buffer bag，compared with the external force，the pressure change caused by the liquid mass force is negligible. In Eq.（6），fx，fy，fzcan thus be regarded as 0. Therefore，the following results are obtained.

This means that the change rate of hydrostatic pressure of the liquid in the buffer bag along any ax?is is 0，that is，the pressure in the buffer bag is equal everywhere. The shell and liquid of the buffer bag are divided into fine grids by finite element method. Since the liquid pressure is equal every?where，the pressure of each liquid unit is also the same. The volume（density）of liquid is related to temperature and pressure. In this paper，all the liq?uid units form a set，and set a reference point（RP）for this set. The initial pressure and density of all liq?uid units are given at the RP，and then the real simu?lation of the buffer bag is completed.

2 Stiffness Analysis of Buffer Bag

2.1 Finite element model for buffer bag mecha?nism analysis

2.1.1 Coupling of buffer bag and material prop?erties

According to the structural characteristics of the buffer bag damping mechanism，the mechanical analysis model of the buffer bag cushion system is established by using ABAQUS［14］. S4R mesh is used to define buffer bag，inner shell and shell，and C3D8 element is used to define flexible joint. It is assumed that both the mass and temperature of the fluid in the bag remain unchanged［15］. The fluid cavi?ty method is used to couple the buffer bag at the RP［16］. The fluid cavity method in ABAQUS can be used to calculate the gas（liquid）-structure interac?tion based on the surface defined fluid strength（the filling can be liquid or gas）. When defining the fluid cavity，the properties of the filling in the fluid cavity can be defined by the RP，where the RP has cou?pling with the fluid cavity. Subsequently，set the properties of the liquid at RP-1，as shown in Fig. 3.The material of buffer mechanism is high strength steel. The buffer bag is made of rubber fiber. Table 1 is relevant material properties.

Fig.3 Coupling whit fluid cavity method

Table 1 Material properties of model

2.1.2 Simulation of contact

When the buffer bag is compressed，the con?tact states among inner，outer shell and buffer bag change with its deformation. In ABAQUS，this kind of contact is treated as finite-sliding interaction between deformable bodies，where separation and sliding of finite amplitude and arbitrary rotation of the surfaces may arise. Defining possible contact conditions by identifying and pairing potential con?tact surfaces，the appropriate contact elements are generated automatically. To define a sliding inter?face between two surfaces，one of the surfaces is the“slave”surface. The other surface is the“mas?ter”surface. Two contact pairs were defined in this paper. The first contact pair，the outer surface of in?ner shell，i.e.，the master surface，and inner diame?ter surface of bag，i. e.，the slave surface，are shown in Fig.4. The second contact pair，the inner surface of outer shell，i.e.，the master surface，and outer diameter surface of bag，i.e.，the slave sur?face，are shown in Fig.5.

Fig.4 Master surface and slave surface for the first contact pair

Fig.5 Master surface and slave surface for the sec?ond contact pair

2.1.3 Boundary conditions and mesh indepen?dence test

In the real working state of the buffer bag，the mechanism will be subjected to strong impact load.Typical external input curve is shown in Fig.6. The load is exerted on the bottom of the mechanism in a short period of time，and gradually decreases after?wards. The concentrated load is set to act on the bottom of the inner shell，and the load acts on the load coupling reference node in the model，so that the load is distributed on the bottom surface of the inner shell，as shown in Fig.7. The initial pressure of the buffer bag is 1.5 MPa，and the impact load on the bottom of inner shell is 300 kN. Before the formal loading，the buffer bag was pressurized to 1.5 MPa. Then，the inner shell was released and the impact load was formally applied.

Fig.6 External input curve

Fig.7 Finite element model

Mesh independence test is an important task of FEA. Table 2 shows the analysis of mesh inde?pendence test. Considering the accuracy and time，10 mm mesh size is chosen.

Table 2 Mesh independence test

2.2 Result analyses of different filling materi?als

2.2.1 Result analysis of gas bag

As shown in Fig.8，the stress map of the gas bag and the displacement map of the flexible joint can be obtained by analyzing the mechanical charac?teristics of the gas bag buffer system after establish?ing the real simulation model of the gas bag system.It can be seen from Fig.8（a）that under the action of load，the inner shell axis moves upward，the gas bag deforms with the axial displacement of the inner shell，and the stress map is evenly distributed in the circumferential direction. On the surface of the gas bag，the stress is concentrated in the lower part of the inner side of gas bag and the upper part of the outer side of gas bag. The maximum stress is locat?ed in the top part of the outside of gas bag，as shown in Fig. 8（b）. In the process of impact load?ing，it can be seen that the displacement of flexible joint is small，and it is well protected in the whole deformation process.

The dynamic stress map of gas bag within 0.0—1.1 s after applied the impact load is shown in Fig.9. The results show that during the dynamic de?formation process，the stress map is evenly distrib?uted in the circumferential direction，and the stress is larger in the lower and upper parts of the gas bag.During the loading process of impact load，the stress of gas bag increases gradually and reaches its peak value about 0.5 s. Then the stress on the gas bag decreases.

Fig.8 Stress map of the gas bag and displacement map of the flexible joint

Fig.9 Stress map of gas bag dynamic process

Fig.10 is the stress curve of the node with the largest stress value in the gas bag from 0.0 s to 1.1 s.The results show that in the initial stage of 0.0—0.1 s，the process is the filling stage of convective bag. When the pressure of fluid bag increases from 0.0 MPa to 1.5 MPa，the node stress will rapidly in?crease to a fixed value；In the stage of 0.1—0.3 s，due to the existence of initial pressure of 1.5 MPa，the stress is in dynamic oscillation state at this stage with the increase of load，and the stress does not in?crease significantly. At the stage of 0.3—0.5 s，the stress of the node increases with the increase of load，and reaches the maximum value at 0.5 s，where the load is also maximal. At the stage of 0.5—1.1 s，the load began to decrease，and the stress of the joint also began to decrease. At 1.1 s，the load becomes half of the maximum value，and the stress value of the node is smaller than the value in the oscillation stage.

Fig.10 Maximum stress curve of gas bag element

2.2.2 Result analysis of liquid bag

Fig.11 is the stress map of the liquid bag and the displacement map of the flexible joint，where the filler is water. It can be seen that the liquid bag deforms with the axial displacement of the inner shell. Compared with Fig.8（a），the stress map is al?so uniformly distributed in the circumferential direc?tion，and the position of the maximum stress on the surface of the liquid bag is on the outer edge at the top of the outside of liquid bag. It can be seen from Fig.11（b）that the displacement map is uniformly distributed in the circumferential direction after the impact load. The maximum displacement position is also close to the interior，and the external displace?ment is small. It implies that the buffer liquid bag has strong resistance to deformation.

Fig.11 Stress map of liquid bag and displacement map of flexible joint

The dynamic stress map of liquid bag within 0.0—1.1 s after applied the impact load is shown in Fig.12. Compared with Fig.9，it shows that during the dynamic deformation process，the stress map is evenly distributed in the circumferential direction，and the stress is larger in the lower and upper parts of the fluid bag. During the loading process of im?pact load，the stress of fluid bag increases gradually and reaches its peak value of 0.5 s approximately.Then the stress on the fluid bag decreases.

Fig.13 is the stress curve of the node with the largest stress value in the fluid bag from 0.0 s to 1.1 s.Compared with Fig.10，it shows that in the initial stage of 0.0—0.1 s，the process is the filling stage of convective bag. When the pressure of fluid bag in?creases from 0.0 MPa to 1.5 MPa，the node stress will rapidly increase to a fixed value，which is same as Fig.10. In the stage of 0.1—0.3 s，due to the ex?istence of initial pressure of 1.5 MPa，the stress is in dynamic oscillation state at this stage with the in?crease of load，and the stress does not increase sig?nificantly，which is same as Fig.10. At the stage of 0.3—0.5 s，compared with Fig.10，the stress of the node increases slowly with the increase of load，and reaches the maximum value 22 MPa at 0.5 s and the load at the same time. At the stage of 0.5—1.1 s，the load began to decrease，and the stress of the joint also began to decrease. At 1.1 s，the load be?comes half of the maximum value. Compared with Fig.10，the stress value of the node returns to the same value as that of the oscillation stage.

Fig.12 Stress map of fluid bag dynamic process

Fig.13 Maximum stress curve of liquid bag element

Fig.14 is the simulated distance of the buffer bag under impact load. By comparing with the rele?vant experimental data obtained by Zhang et al.［4］，it can be found that the simulation model is in good agreement with the experimental structure.

Fig.14 Simulated and experimental distance of gas bag and liquid bag

2.3 Influence of different parameters on stiff?ness of buffer bag

2.3.1 Influence of initial pressure of buffer bag

The axial displacement of the flexible joint is calculated when the initial pressure of the buffer bag is 1.5，2.0，2.5 and 3.0 MPa，and the calculation re?sults are shown in Fig.15（a）. It can be seen from Fig.15（a）that when the internal fillers are gas and liquid，the external load and axial displacement are in positive proportion. When the initial pressure is different，the axial displacement decreases with the increase of initial pressure. Compared with gas and liquid，the axial displacement of liquid bag is small?er than that of gas bag under the same conditions，that is，the stiffness of the liquid bag is larger and deformation is smaller.

When the initial pressure of the buffer bag is different，the internal pressure change of the buffer bag is calculated，and the results are shown in Fig.15（b）. According to Fig.15（b），when the inter?nal filling material is liquid，the internal pressure of the liquid bag increases with the increase of external load，and the increase is more obvious. When the in?ner filler is gas，the internal pressure of the gas bag hardly changes with the increase of external load.

2.3.2 Influence of bulk modulus of buffer bag

Fig.15 Influence of initial pressure of buffer bag

The axial displacement of the flexible joint is calculated when the initial pressure of the buffer bag is 1.5 MPa，the gas modulus is 28 and 44，and the liquid elastic modulus is 1 000，1 500，2 000 and 2 500 MPa. The calculation results are shown in Fig.16（a）. When the filler is gas，the geometry of the stiffness curve does not change when the gas modulus is different. that is，the influence of the gas modulus on the stiffness of the mechanism can be ig?nored. When the filler is liquid，the stiffness of the mechanism increases with the increase of the elastic modulus of the liquid，showing a positive correla?tion. Comparing the stiffness curves of gas and liq?uid，it is found that the stiffness of liquid is greater than that of gas.

When the initial pressure is 1.5 MPa，the inter?nal pressure changes of the buffer bag under differ?ent gas modulus and different liquid elastic modulus are calculated. The calculation results are shown in Fig.16（b）. When the internal filler is liquid，the in?ternal pressure of the liquid bag increases with the increase of the elastic modulus of the liquid，and the increased value is nonlinear. When the inner filler is gas，the internal pressure of the gas bag hardly changes with the increase of external load.

Fig.16 Influence of bulk modulus of buffer bag

2.3.3 Influence of buffer bag thickness

The initial pressure is 1.5 MPa，and the thick?ness is 5，10 and 15 mm. The stiffness of the buffer bag with different thickness is calculated，and the calculation results are shown in Fig.17（a）. When the initial pressure is the same and the filler is gas and liquid，the stiffness of the structure will increase with the increase of the thickness. Compared with gas and liquid，the axial stiffness of liquid bag is greater than that of gas bag.

The initial pressure is 1.5 MPa，and the pres?sure change of buffer bag with different thickness is calculated. The calculation results are shown in Fig.17（b）. When the internal filling material is liq?uid，the pressure of the liquid bag increases with the increase of the thickness，and the relationship is non?linear. When the inner filling is gas，the pressure of the gas bag almost does not change with the in?crease of the thickness.

3 Conclusions

Fig.17 Influence of buffer bag thickness

In this paper，the mechanical properties of buf?fer bag are studied. The influence of gas bag and liq?uid bag on the stiffness of the buffer mechanism is analyzed. Finally，the effects of initial pressure，bulk modulus and thickness on the stiffness of the mechanism are studied

（1） After the mechanism is impacted by 300 kN，the displacement change is very small，which indicates that the buffer bag has a good pro?tection on the flexible joint under the impact load.After comparing and analyzing the liquid bag and the gas bag，it is found that after the mechanism is subjected to axial force，the liquid bag has obvious pressure rise，and the internal pressure of the gas bag hardly changes.

（2）The influence of initial pressure，bulk mod?ulus and thickness of buffer bag on the stiffness of the mechanism are discussed. It is found that the change of bulk modulus（1 000，1 500，2 000 and 2 500 MPa）has an obvious effect on the liquid bag，so it is positively correlated with the stiffness of the mechanism. The change of gas modulus（28 and 44）has little effect on the stiffness of the mecha?nism. The thickness of the buffer bag （5 mm，10 mm and 15 mm）also has an obvious effect on the stiffness. The gas bag and the liquid bag show different changing rules under different thickness conditions.

（3）Through the overall stiffness analysis and observation of the pressure change of the buffer bag，it can be known that the stiffness of the liquid bag is greater under the same condition，and it has better protection for flexible joint.