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Study on buffering performance of thin-walled metal tube with different angles
Defence Technology xxx (2018) 1e7
Contents lists available at ScienceDirect
Defence Technology journal homepage: www.elsevier.com/locate/dt
Study on buffering performance of thin-walled metal tube with different angles Qun Liu*, Wen-tao Wang, Wen-feng Zhang Beijing Institute of Space Mechanics and Electricity, Beijing, China
a r t i c l e i n f o
a b s t r a c t s
Article history: Received 10 February 2018 Received in revised form 1 June 2018 Accepted 9 June 2018 Available online xxx
High frequency shock load is often generated during pyrotechnic device working, which is detrimental to spacecraft structures and electric devices. Therefore, it is valuable to reduce the shock load in pyrotechnic device design. Actually, there are several ways to decrease pyroshock loads, such as reduction of powder, installation of buffering structure, insulation of damageable devices, and so on. Considered assuring the function of pyrotechnic device and minimum of structure modification, shock absorbing structure is more propitious to be introduced in pyrotechnic device. In this paper, based on the method of thinwalled metal tube diameter-expanding, a thin-walled tube shock buffering structure was designed on a separate bolt. Built on the simplified structure of a separate bolt, the model of cone piston impacting thin-walled tube absorber was established, and the thin-walled tube shock absorbing characteristics and the relation between cone angles and absorber performance were analyzed. The results showed that the change of buffering force of thin-walled tube could be divided into four phases, and each phase was correspondent to the cone piston structure. In addition, as the cone angle increases, the max shock acceleration changes in the style of decrease-increase-decrease-increase, which is the result of coupled effects of cone piston max enter depth, buffering force and energy loss. In short, these results could establish the relationships between thin-walled tube absorbing performance and its structure, which is of significance to develop low-shock pyrotechnic device. © 2018 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Pyroshock Shock absorbing Thin-walled metal tube
1. Introduction Pyrotechnic devices are widely used by the aerospace and defense industries, and consist of a broad family of sophisticated devices using self-contained energy sources such as explosives and/ or pyrotechnic compositions. When the pyrotechnic compositions are initiated, pyroshock rarely causes damage to structural members, but it can easily cause failures in electronic and optical components that are sensitive to high frequency energy [1]. Pyroshock mainly comes from three aspects: explosive explosion, impact of components and release of preload, among which impact of components is the main source of pyroshock. Therefore, it is significantly valuable to use shock absorbers to decrease pyroshock in pyrotechnic device design. A shock absorber is a system that converts, totally or partially, kinetic energy into another form of energy. Since the second half of
* Corresponding author. E-mail address: [email protected] (Q. Liu). Peer review under responsibility of China Ordnance Society
last century, a great number of shock absorbers aiming at absorbing the majority of the kinetic energy of impact within the device itself in an irreversible manner were investigated, such as steel drums [2], circular tubes [3], tubular rings [4], square tubes [5e7], corrugated tubes [8], multicorner columns [9], frusta [10], struts [11], honeycomb cells [12], sandwich plates [13] and some other special shapes such as stepped circular thin-walled tubes [14] and top-hat thin-walled metal tubes [15]. Each shock absorber system has its own characteristics and special features which one needs to be familiar with in order to be able to understand how metallic structures respond to impulsive loads. Because of the extreme complexities of impact mechanisms, some of these performance characteristics were determined only through experimental procedures [16]. Consequently, the resulting empirical relations are confined to limited applications. In this paper, thin-walled metal tube shock absorber was insert into the pyrotechnic device to investigate its characteristics to decrease the pyroshock. The thin-walled metal tube method has many advantages such as smaller space to install, more efficient energy to utilize, and less unsteady to shock buffer, which is much
https://doi.org/10.1016/j.dt.2018.06.008 2214-9147/© 2018 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: Liu Q, et al., Study on buffering performance of thin-walled metal tube with different angles, Defence Technology (2018), https://doi.org/10.1016/j.dt.2018.06.008
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applicable to be used in the pyrotechnic devices [1718]. The “pioneer” Venus probe, the Soviet Union's Mars 39, Mars 6 and Venus probe use this kind of buffer [19]. It is also used in the China's Shenzhou five manned spacecraft re-entry module seat buffer, and the impact speed is 8 m/s [20]. The buffering characteristics of thin-walled metal tubes have a great relationship with the impact velocity. In the impact velocity bellow 10 m/s, the deformation of tube is quasi-static load, and it is low-velocity impact [21]. With the velocity between 10 m/s and 100 m/s, the strain rate of tube is from 1 to 103, which is defined as medium-velocity impact [21]. With the velocity between 100 m/s and 800 m/s, the strain rate of tube is from 103 to 105, which is named as high-velocity impact [21]. Quasi static retarding of thinwalled metal tubes is studied theoretically by Refs. [22e24]. The properties of energy absorption under quasi static state are studied experimentally by Refs. [25e27]. The previous research of the thin-walled metal tube focus on the impact at low speed (impact velocity is less than 10 m/s) or quasistatic study. However, the structure will produce the dynamic load effect at medium and high velocity impact, including the effects of stress wave and strain rate. In this case, the dynamic strength of some materials is two times or more than that under low strain rate, which has a significantly influence on the buffering performance of thin-walled metal tube. However, the research of buffer characteristics under the impact of medium and high speed were not seen. Considering the impact in the pyrotechnic device is at the medium velocity, it is of great value to understand its buffering characteristics at medium impact speed for the low-shock pyrotechnic device design. The thin-wall metal tube shock absorbing structure is comprised of thin-walled metal tube and cone piston, and its shock absorbing effect is determined by material and structure design. In this paper, based on the non-linear dynamics, the calculation model of cone piston impacting metal tube was established, and the characteristics of its shock absorbing was analyzed. In the end, the relation between shock absorbing and cone angle was obtained, which is extremely useful to low shock pyrotechnic device design.
2. Principle of thin-walled metal tube shock buffering
thin-walled metal tube. The cone piston is divided into three sections, varying diameter section, equal diameter section and smaller diameter section. The thickness of thin-walled metal tube is equal, and its inner diameter is a little bigger than the top of cone piston. When the piston impacts the tube, the diameter of the tube would expand, and the shock energy of piston is converted into the deformation energy and friction heat of tube to decrease the shock. The performance of a thin-walled metal tube shock absorbing is mainly determined by buffer force. When the force is too small, the absorbing energy of tube is relatively low to decrease shock. However, when the force is too big, the shock load during impact between piston and tube is so high that the effect of absorbing is unsatisfied. Therefore, proper buffer force is significantly important to increase the buffer effect of thin-walled metal tube structure.
3. Simulation of thin-walled metal tube shock absorbing process 3.1. Geometry Fig. 2 is the schematic structure of a separate bolt. Initially, the separate bolt is fixed on the satellite, and the piston and nut are the components of separate bolt that connects the baseboard with the satellite. When the separate bolt is on fire, the piston would move out of the bolt and impact the baseboard and drive the baseboard separate from the satellite. The impact of piston and baseboard would generate impact shock, which is harmful to the electric equipments near the baseboard. Fig. 3 is the schematic structure of an improved separate bolt. The piston in the improved bolt changes from cylinder into cone, and thin-walled metal tube is installed between the piston and baseboard, which is used to decrease the shock load. Based on the improved bolt structure, the calculation model was established. Considering the shock load of bolt coming from the impact of piston and baseboard, the calculation model is simplified to only include piston, tube and baseboard, see in Fig. 4. The varying diameter section is in cone shape, the top diameter is 8 mm, the height of cone is 5 mm, and the bottom diameter is determined by the cone angle. The diameter of equal section is the same as the bottom diameter of cone, and the height is 3 mm. The diameter of
The shock load in the impact between cone piston and thin tube is depleted by the plastic deformation and friction work during diameter expansion. Fig. 1 is the scheme of thin-walled metal shock absorbing structure. The structure is comprised of cone piston and
Fig. 1. The scheme of thin-walled metal tube shock absorbing structure.
Fig. 2. The schematic structure of a separate bolt.
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Fig. 3. The schematic structure of an improved separate bolt.
Fig. 5. Mesh model of the structure.
Fig. 4. Model of piston impacting thin walled tube.
small section is 8 mm, and the height is 37 mm. The inner diameter of thin tube is 8.05 mm, the thickness is 0.8 mm, and the height is 15 mm. The diameter of baseboard is 40 mm, and the height is 15 mm. Fig. 5 is the mesh model of the structure. The cone piston is meshed in tetrahedron with the mesh side length 1 mm. The tube and baseboard are meshed in hexahedral with the mesh side length 0.3 mm and 1 mm respectively. In calculation, the piston impacts the baseboard with the velocity of 20 m/s, the mass of the piston is 20 g.
The material of piston is stainless steel 14Cr17Ni2, weight 20 g, the tube is Aluminum alloy 5A06, and the baseboard is stainless steel 14Cr17Ni2. All these materials are described by Plastic-Kinetic material model [28]. The plastic kinematic model is suited to model isotropic and kinematic hardening plasticity with the option of including rate effects. It is a very cost effective model and is available for solid elements. It is widely used in automobile collision simulation, and is suitable for the calculation of impact energy absorption. The formulation of this model is
"
1 # ε_ P s0 þ bEP εeff P C
m ¼ md þ ðms md Þecjvj
(2)
Where c is a decay constant. 3.3. The results of calculation
3.2. Material model
sY ¼ 1 þ
predetermination of where and how contact will take place may be difficult. For this reason, the automatic contact options are chosen as these contacts are non-oriented, meaning they can detect penetration coming from either side of an element. Contact friction is based on a Coulomb formulation and uses the equivalent of an elastic-plastic spring. Friction is invoked by giving non-zero values for the static and dynamic friction coefficients, ms ¼ 0.2 and md ¼ 0.1, respectively, in the input. An exponential interpolation function smooths the transition between the static ms and dynamic md, coefficients of friction where v is the relative velocity between the contact surface:
(1)
s0 is initial yield stress, ε_ is strain rate;C and P are parameters of Cowper-Symond strain rate, εPeff is effective plastic strain, EP is plastic hardness modulus. Table 1 summarizes the material parameters. In impact analysis, the deformations can be very large and
3.3.1. The characteristics of thin-walled metal tube shock absorbing Fig. 6 is the Mises stress contour during the impact between piston in cone angle 4 and tube at different time. At 160 ms, the varying diameter section has inserted into the tube, which caused the top of tube generate plastic deformation. At 560 ms, the varying and equal section both entered the tube, the plastic deformation area of the tube was enlarged. At 1240 ms, the piston has inserted into the deepest length of the tube, but not touching on the baseboard. At 1345 ms, the velocity of baseboard was high enough to separate from the piston and tube. Fig. 7 is the buffer force curve of the tube during the impact. The force curve could be divided into four phases. In the first phase, the buffer force increased to 340 N rapidly, which was caused by the large deformation of the tube during the entry of varying diameter section into the tube. The duration of this phase was corresponding to that of varying section entering into the tube, so this phase can be called varying section entry phase. In the second phase, the buffer force decreased initially and increased lately. In this phase, the equal section piston started to enter into the tube, and the tube
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Table 1 The material parameters. Material
Density r/(kg$m3)
Young's Modulus E/GPa
Poisson Ratio m
Yield Stress ss/MPa
14Cr17Ni2 5A06
7800 2700
206 69.8
0.3 0.33
500 200
Fig. 8 is the shock acceleration curve on the baseboard in the cases of (a) non-buffer and (b) buffer. Under no buffer structure, the max shock acceleration of the baseboard was up to 310000 g, while with buffer structure, it was down to 4800 g. This showed that the thin-walled metal tube was extremely beneficial to decrease the shock load. In addition, the moment of peak shock acceleration under buffer structure was at 470 ms, which was the time of the equal section entering into the tube entirely.
Fig. 6. The Mises stress contour during impact at different time.
Fig. 7. Buffer force curve of the tube during impact.
could not contact with the equal section piston immediately because of the inertance of dynamic expanding, which leads to the buffer force decreased. As disappearance of dynamic expanding of tube, the tube contact with the equal section again, which leads to the increase of friction between the tube and the piston. The duration of this phase was equal to the equal section entering into the tube, so this phase could be called equal section entry phase. In the third phase, the buffer force was equally constant. In this phase, the cone piston has entered into the tube entirely, so the contact area between piston and tube was constant, and the deformation mode of tube was stable, both of which lead to the buffer force constant. This phase can be called the stead entry phase. In the fourth phase, the buffer force decreases rapidly because the piston decelerated and stop in the tube, which could be called stop phase.
3.3.2. The relation between cone angle and shock absorbing performance The pistons with 2 ,4 and 6 cone angles impacting tube were calculated to obtain the relation between cone angles and shock absorbing performance. Fig. 9 is the shock acceleration curve in different impact cases (the result in 4 angle showed in Fig. 8 with buffer) on the baseboard. The max shock accelerations under three cases were 160000 g、4800 g and 24000 g respectively, namely the cone piston with 4 angle had the best shock absorbing performance. To understand the relation between the cone angles and shock absorbing performance, the max enter depth, buffer force and energy loss during the impacts were analyzed. Fig. 10 is the max enter depth graph of piston in different cone angles. In the 2 angle case, the piston entered across the tube, and impacted the baseboard directly. The max enter depth of this case was 15 mm. In the 4 and 6 angles cases, the piston entered and stop at the middle of the tube, and the max enter depth were 13.5 mm and 8.6 mm respectively. Therefore, max enter depth decreased as the cone angle increased. Fig. 11 is the buffer force curve of different cone angles. The max buffer forces under different angles were 135 N, 340 N and 510 N respectively, and the buffer force increased rapidly. The energy loss of the cone piston during impact could be calculated by integrating the buffer force with the displacement. Fig. 12 is the energy loss history curve of different impact cases. The original kinematic energy of cone piston was 4 J, and the energy loss of different cases were 1.52 J, 3.49 J and 3.47 J respectively, namely the energy loss rate was 38%, 87.25% and 86.75%. The above analysis showed that the characteristics of max enter depth, buffer force and energy loss had different characteristics from the shock acceleration of the baseboard, and it could be considered that the shock acceleration results were the coupled effects of above three aspects, and the main factor was different in various cone angles. In order to understand the influence of cone angles on the shock absorbing performance, pistons in ten cone angles impacting tube were calculated. With the increase of cone angles, the shock acceleration of baseboard changed in the style of decrease-increasedecrease-increase, see in Fig. 13, namely the shock absorbing performance changed as increase -decrease-increase-decrease. These characteristics were analyzed as follows: Shock acceleration decrease phase: when the cone angle was small, the buffer force of tube was so little that the cone piston could impact the baseboard directly, which cause extremely large shock. With the angle increasing, the buffer force and energy loss became bigger, see in Fig. 14 and Fig. 15, and the shock acceleration of baseboard decreased significantly. Until the piston stops at the interface of tube and baseboard, the shock acceleration decreased
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Fig. 8. The shock acceleration curve on the baseboard.
Fig. 9. The shock acceleration curve in different impact cases.
Fig. 12. The energy loss curve of different impact cases.
Fig. 10. The max enter depth graph of piston at different cone angles.
Fig. 13. Max shock acceleration with different cone angles.
Fig. 11. The buffer force history curve of different cone angles.
to the least of this phase. Therefore, the buffer force and the energy loss were the key factors of shock absorbing performance. Shock acceleration increase phase: after last phase, the source of the max shock source converted from the impact between piston and baseboard to that between piston and tube. In this case, the shock acceleration increased with the bigger cone angle because that the impact was becoming more rigid with the buffer force increased. As the angle has increased to the case that the equal section of the piston just inserted into the tube, the shock acceleration increased to the maximum of this phase, see in Fig. 16. Therefore, max enter depth is the key factor of shock absorbing performance.
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absorbing were changing, which is determined by max enter depth, buffer force and energy loss. 4. Conclusion
Fig. 14. Max buffering force with different cone angles.
Based on the diameter expansion method of thin-walled metal tube, the model of piston impacting tube was established, the performance of tubes on shock absorbing were analyzed, and the relation between the cone angles and shock absorbing performance was obtained. The results showed the thin-walled metal tube could reduce the shock load significantly. The buffer force during impact could be divided into four phases, which was corresponding to the structure of the cone piston. In addition, with the increase of cone angles, the shock acceleration of baseboard changed in the style of decrease-increase- decrease-increase, and this characteristics were the coupled effects of max enter depth, buffer force and energy loss, and the main factor was different in various cone angles. References
Fig. 15. Max enter depth with different cone angles.
Fig. 16. Energy loss rate with different cone angles.
Shock acceleration decrease phase again: previous analysis showed that the max shock acceleration occurred at moment of equal section entering into the tube. Based on this conclusion, with the cone angle increasing further, the equal section of piston could not enter into the tube, which lead to the decrease of max shock acceleration until the max enter depth was equal to varying section height. Therefore, the max enter depth is the key factor of shock absorbing performance. Shock acceleration increase phase again: when the varying section of piston could not insert the tube entirely as the angle increases, the energy loss of cone piston decreased, see in Fig. 15, which lead to the shock load of impact increased because the impact between piston and tube is head-on impact approximately. Therefore, the energy loss is the key factor of shock absorbing performance. In short, as the cone angle increased, the characteristics of shock
[1] Bi WH, Yan N, He CQ, et al. Measurement of pyroshock for explosive initiating device used in spacecraft. Metrol Meas Technol 2009;29(3):14e8. [2] Carney III JF, Pothen S. Energy dissipation in braced cylindrical shells. Int J Mech Sci 1988;30(3/4):203e16. [3] Alexander JM. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Quart J Mech Appl Math. 1960;13(1):10e5. [4] Reid SR, Austin CD, Smith R. Tubular rings as impact energy absorber. In: Davies G, Morton J, editors. Structural impact and crashworthiness. New York: Elsevier; 1984. p. 555e63. [5] Langseth M, Hopperstand OS. Static and dynamic axial crushing of square thin-walled aluminum extrusions. Int J Impact Eng 1996;18(7/8):949e68. [6] Langseth M, Hopperstand OS, Berstad T. Crashworthiness of aluminum extrusions: validation of numerical simulation, effect of mass ratio and impact velocity. Int J Impact Eng 1999;22(8):829e54. [7] Nannucci PR, Marshall NS, Nurick GN. A computational investigation of the progressive buckling of square tubes with geometric imperfections. In: 3rd asiaepacific conference on shock and impact loads on structures. Singapore, 24e26 November; 1999. [8] Singace AA, El-Sobky H. Behaviour of axially crushed corrugated tubes. Int J Mech Sci 1997;39(3):249e68. [9] Wierzbicki T, Abramowicz W. On the crushing mechanics of thin-walled structures. J Appl Mech 1983;50(4):727e34. [10] Mamalis W, Johnson W. The quasi-static crumpling of thin-walled circular cylinders and frusta under axial compression. Int J Mech Sci 1983;25(9/10): 713e32. [11] Harris JA, Adams RD. An assessment of the impact performance of bonded joints for use in high energy absorbing structures. Proc Inst Mech Eng 1985;199(C2):121e31. [12] Wierzbicki T. Crushing analysis of metal honeycombs. Int J Impact Eng 1983;1(2):157e74. [13] Corbett GG, Reid SR. Local loading of simply-supported steelegrout sandwich plates. Int J Impact Eng 1993;13(3):443e61. [14] Stangl PK, Meguid SA. Experimental and theoretical evaluation of a novel shock absorber for an electrically powered vehicle. Int J Impact Eng 1991;11(1):41e59. [15] White MD, Jones N. Experimental quasi-static axial crushing of top-hat and double-hat thin-walled sections. Int J Mech Sci 1999;41:179e208. [16] Carney III JF, Veillette JR. Impact response and energy characteristics of stiffened metallic tubes. In: Davies G, Morton J, editors. Structural impact and crashworthiness. New York: Elsevier; 1984. p. 564e75. [17] Abramowicz W. Thin-walled structures as impact energy absorbers. ThinWalled Struct 2003;4l(1):91e107. [18] Salehghafari S, Panahipoor M. Controlling the axial cm shing of circular metal tubes using all expanding rigid ring press fitted on top of the structure. Int J Crashworthiness 2010;15(3):251e64. [19] Gibson LJ, Ashby MF. Cellular solid: structure and properties. Carnbridge: Cambridge University Press; 1997. [20] Xiangfu Wang. Absorbed energy of astronauts seat. Aeronaut Sci Technol 2007;3(4):33e5. [21] Yu Tongxi, Qiu Xinming. Impact dynamics. Beijing: Tsinghua University Press; 2011. p. 39e41 [in Chinese]. [22] Wenbin Xu, Peiqi Ge, Pengshun Zhang. Calculation of forming pressure in thin wall tube press expansion. Forging Stamping Technol 1996;3(1):19e21 [inChinese]. [23] Weizhong Niuu. Analysis of the stress an d wall-thickness on stampingexpanding of connoid thin-wailed cylindrical-tube workpiece. J Huazhong Univ Sci Technol Nat Sci Ed 2004;32(4):13e37 [in Chinese]. [24] nianjun Hu, da wei Lin. Deformation analysis of tube expanding process. Journal of Plasticity Engeerring 2006;13(3):52e5 [in chinese].
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Q. Liu et al. / Defence Technology xxx (2018) 1e7 [25] Changjie Luo, Rongqian Liu, Zongquan Dang, et al. Experimental investigations of an energy absorber based on thin-walled metal tube’s plastic deformation. J Vib Shock 2010;29(4):101e6 [in Chinese]. [26] Shakeri M, Salehghafari S. Expansion of circular tubes by rigid tubes as impact energy absorbers: experimental and theoretical investigation. Int J Crashworthiness 2007;5(3):493e501.
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[27] Azizi R, Salehghafari S. Energy absorption in plastic expansion of circular metal tubes. Comput Plast X-Fund Appl 2009;28(3):68e76. [28] LS-DYNA User’s manual (nonlinear dynamic analysis of structures in three dimensions). University of California, Lawrence Livermore National Laboratory; 2001.
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Contents lists available at ScienceDirect
Defence Technology journal homepage: www.elsevier.com/locate/dt
Study on buffering performance of thin-walled metal tube with different angles Qun Liu*, Wen-tao Wang, Wen-feng Zhang Beijing Institute of Space Mechanics and Electricity, Beijing, China
a r t i c l e i n f o
a b s t r a c t s
Article history: Received 10 February 2018 Received in revised form 1 June 2018 Accepted 9 June 2018 Available online xxx
High frequency shock load is often generated during pyrotechnic device working, which is detrimental to spacecraft structures and electric devices. Therefore, it is valuable to reduce the shock load in pyrotechnic device design. Actually, there are several ways to decrease pyroshock loads, such as reduction of powder, installation of buffering structure, insulation of damageable devices, and so on. Considered assuring the function of pyrotechnic device and minimum of structure modification, shock absorbing structure is more propitious to be introduced in pyrotechnic device. In this paper, based on the method of thinwalled metal tube diameter-expanding, a thin-walled tube shock buffering structure was designed on a separate bolt. Built on the simplified structure of a separate bolt, the model of cone piston impacting thin-walled tube absorber was established, and the thin-walled tube shock absorbing characteristics and the relation between cone angles and absorber performance were analyzed. The results showed that the change of buffering force of thin-walled tube could be divided into four phases, and each phase was correspondent to the cone piston structure. In addition, as the cone angle increases, the max shock acceleration changes in the style of decrease-increase-decrease-increase, which is the result of coupled effects of cone piston max enter depth, buffering force and energy loss. In short, these results could establish the relationships between thin-walled tube absorbing performance and its structure, which is of significance to develop low-shock pyrotechnic device. © 2018 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Pyroshock Shock absorbing Thin-walled metal tube
1. Introduction Pyrotechnic devices are widely used by the aerospace and defense industries, and consist of a broad family of sophisticated devices using self-contained energy sources such as explosives and/ or pyrotechnic compositions. When the pyrotechnic compositions are initiated, pyroshock rarely causes damage to structural members, but it can easily cause failures in electronic and optical components that are sensitive to high frequency energy [1]. Pyroshock mainly comes from three aspects: explosive explosion, impact of components and release of preload, among which impact of components is the main source of pyroshock. Therefore, it is significantly valuable to use shock absorbers to decrease pyroshock in pyrotechnic device design. A shock absorber is a system that converts, totally or partially, kinetic energy into another form of energy. Since the second half of
* Corresponding author. E-mail address: [email protected] (Q. Liu). Peer review under responsibility of China Ordnance Society
last century, a great number of shock absorbers aiming at absorbing the majority of the kinetic energy of impact within the device itself in an irreversible manner were investigated, such as steel drums [2], circular tubes [3], tubular rings [4], square tubes [5e7], corrugated tubes [8], multicorner columns [9], frusta [10], struts [11], honeycomb cells [12], sandwich plates [13] and some other special shapes such as stepped circular thin-walled tubes [14] and top-hat thin-walled metal tubes [15]. Each shock absorber system has its own characteristics and special features which one needs to be familiar with in order to be able to understand how metallic structures respond to impulsive loads. Because of the extreme complexities of impact mechanisms, some of these performance characteristics were determined only through experimental procedures [16]. Consequently, the resulting empirical relations are confined to limited applications. In this paper, thin-walled metal tube shock absorber was insert into the pyrotechnic device to investigate its characteristics to decrease the pyroshock. The thin-walled metal tube method has many advantages such as smaller space to install, more efficient energy to utilize, and less unsteady to shock buffer, which is much
https://doi.org/10.1016/j.dt.2018.06.008 2214-9147/© 2018 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: Liu Q, et al., Study on buffering performance of thin-walled metal tube with different angles, Defence Technology (2018), https://doi.org/10.1016/j.dt.2018.06.008
2
Q. Liu et al. / Defence Technology xxx (2018) 1e7
applicable to be used in the pyrotechnic devices [1718]. The “pioneer” Venus probe, the Soviet Union's Mars 39, Mars 6 and Venus probe use this kind of buffer [19]. It is also used in the China's Shenzhou five manned spacecraft re-entry module seat buffer, and the impact speed is 8 m/s [20]. The buffering characteristics of thin-walled metal tubes have a great relationship with the impact velocity. In the impact velocity bellow 10 m/s, the deformation of tube is quasi-static load, and it is low-velocity impact [21]. With the velocity between 10 m/s and 100 m/s, the strain rate of tube is from 1 to 103, which is defined as medium-velocity impact [21]. With the velocity between 100 m/s and 800 m/s, the strain rate of tube is from 103 to 105, which is named as high-velocity impact [21]. Quasi static retarding of thinwalled metal tubes is studied theoretically by Refs. [22e24]. The properties of energy absorption under quasi static state are studied experimentally by Refs. [25e27]. The previous research of the thin-walled metal tube focus on the impact at low speed (impact velocity is less than 10 m/s) or quasistatic study. However, the structure will produce the dynamic load effect at medium and high velocity impact, including the effects of stress wave and strain rate. In this case, the dynamic strength of some materials is two times or more than that under low strain rate, which has a significantly influence on the buffering performance of thin-walled metal tube. However, the research of buffer characteristics under the impact of medium and high speed were not seen. Considering the impact in the pyrotechnic device is at the medium velocity, it is of great value to understand its buffering characteristics at medium impact speed for the low-shock pyrotechnic device design. The thin-wall metal tube shock absorbing structure is comprised of thin-walled metal tube and cone piston, and its shock absorbing effect is determined by material and structure design. In this paper, based on the non-linear dynamics, the calculation model of cone piston impacting metal tube was established, and the characteristics of its shock absorbing was analyzed. In the end, the relation between shock absorbing and cone angle was obtained, which is extremely useful to low shock pyrotechnic device design.
2. Principle of thin-walled metal tube shock buffering
thin-walled metal tube. The cone piston is divided into three sections, varying diameter section, equal diameter section and smaller diameter section. The thickness of thin-walled metal tube is equal, and its inner diameter is a little bigger than the top of cone piston. When the piston impacts the tube, the diameter of the tube would expand, and the shock energy of piston is converted into the deformation energy and friction heat of tube to decrease the shock. The performance of a thin-walled metal tube shock absorbing is mainly determined by buffer force. When the force is too small, the absorbing energy of tube is relatively low to decrease shock. However, when the force is too big, the shock load during impact between piston and tube is so high that the effect of absorbing is unsatisfied. Therefore, proper buffer force is significantly important to increase the buffer effect of thin-walled metal tube structure.
3. Simulation of thin-walled metal tube shock absorbing process 3.1. Geometry Fig. 2 is the schematic structure of a separate bolt. Initially, the separate bolt is fixed on the satellite, and the piston and nut are the components of separate bolt that connects the baseboard with the satellite. When the separate bolt is on fire, the piston would move out of the bolt and impact the baseboard and drive the baseboard separate from the satellite. The impact of piston and baseboard would generate impact shock, which is harmful to the electric equipments near the baseboard. Fig. 3 is the schematic structure of an improved separate bolt. The piston in the improved bolt changes from cylinder into cone, and thin-walled metal tube is installed between the piston and baseboard, which is used to decrease the shock load. Based on the improved bolt structure, the calculation model was established. Considering the shock load of bolt coming from the impact of piston and baseboard, the calculation model is simplified to only include piston, tube and baseboard, see in Fig. 4. The varying diameter section is in cone shape, the top diameter is 8 mm, the height of cone is 5 mm, and the bottom diameter is determined by the cone angle. The diameter of equal section is the same as the bottom diameter of cone, and the height is 3 mm. The diameter of
The shock load in the impact between cone piston and thin tube is depleted by the plastic deformation and friction work during diameter expansion. Fig. 1 is the scheme of thin-walled metal shock absorbing structure. The structure is comprised of cone piston and
Fig. 1. The scheme of thin-walled metal tube shock absorbing structure.
Fig. 2. The schematic structure of a separate bolt.
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Fig. 3. The schematic structure of an improved separate bolt.
Fig. 5. Mesh model of the structure.
Fig. 4. Model of piston impacting thin walled tube.
small section is 8 mm, and the height is 37 mm. The inner diameter of thin tube is 8.05 mm, the thickness is 0.8 mm, and the height is 15 mm. The diameter of baseboard is 40 mm, and the height is 15 mm. Fig. 5 is the mesh model of the structure. The cone piston is meshed in tetrahedron with the mesh side length 1 mm. The tube and baseboard are meshed in hexahedral with the mesh side length 0.3 mm and 1 mm respectively. In calculation, the piston impacts the baseboard with the velocity of 20 m/s, the mass of the piston is 20 g.
The material of piston is stainless steel 14Cr17Ni2, weight 20 g, the tube is Aluminum alloy 5A06, and the baseboard is stainless steel 14Cr17Ni2. All these materials are described by Plastic-Kinetic material model [28]. The plastic kinematic model is suited to model isotropic and kinematic hardening plasticity with the option of including rate effects. It is a very cost effective model and is available for solid elements. It is widely used in automobile collision simulation, and is suitable for the calculation of impact energy absorption. The formulation of this model is
"
1 # ε_ P s0 þ bEP εeff P C
m ¼ md þ ðms md Þecjvj
(2)
Where c is a decay constant. 3.3. The results of calculation
3.2. Material model
sY ¼ 1 þ
predetermination of where and how contact will take place may be difficult. For this reason, the automatic contact options are chosen as these contacts are non-oriented, meaning they can detect penetration coming from either side of an element. Contact friction is based on a Coulomb formulation and uses the equivalent of an elastic-plastic spring. Friction is invoked by giving non-zero values for the static and dynamic friction coefficients, ms ¼ 0.2 and md ¼ 0.1, respectively, in the input. An exponential interpolation function smooths the transition between the static ms and dynamic md, coefficients of friction where v is the relative velocity between the contact surface:
(1)
s0 is initial yield stress, ε_ is strain rate;C and P are parameters of Cowper-Symond strain rate, εPeff is effective plastic strain, EP is plastic hardness modulus. Table 1 summarizes the material parameters. In impact analysis, the deformations can be very large and
3.3.1. The characteristics of thin-walled metal tube shock absorbing Fig. 6 is the Mises stress contour during the impact between piston in cone angle 4 and tube at different time. At 160 ms, the varying diameter section has inserted into the tube, which caused the top of tube generate plastic deformation. At 560 ms, the varying and equal section both entered the tube, the plastic deformation area of the tube was enlarged. At 1240 ms, the piston has inserted into the deepest length of the tube, but not touching on the baseboard. At 1345 ms, the velocity of baseboard was high enough to separate from the piston and tube. Fig. 7 is the buffer force curve of the tube during the impact. The force curve could be divided into four phases. In the first phase, the buffer force increased to 340 N rapidly, which was caused by the large deformation of the tube during the entry of varying diameter section into the tube. The duration of this phase was corresponding to that of varying section entering into the tube, so this phase can be called varying section entry phase. In the second phase, the buffer force decreased initially and increased lately. In this phase, the equal section piston started to enter into the tube, and the tube
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Table 1 The material parameters. Material
Density r/(kg$m3)
Young's Modulus E/GPa
Poisson Ratio m
Yield Stress ss/MPa
14Cr17Ni2 5A06
7800 2700
206 69.8
0.3 0.33
500 200
Fig. 8 is the shock acceleration curve on the baseboard in the cases of (a) non-buffer and (b) buffer. Under no buffer structure, the max shock acceleration of the baseboard was up to 310000 g, while with buffer structure, it was down to 4800 g. This showed that the thin-walled metal tube was extremely beneficial to decrease the shock load. In addition, the moment of peak shock acceleration under buffer structure was at 470 ms, which was the time of the equal section entering into the tube entirely.
Fig. 6. The Mises stress contour during impact at different time.
Fig. 7. Buffer force curve of the tube during impact.
could not contact with the equal section piston immediately because of the inertance of dynamic expanding, which leads to the buffer force decreased. As disappearance of dynamic expanding of tube, the tube contact with the equal section again, which leads to the increase of friction between the tube and the piston. The duration of this phase was equal to the equal section entering into the tube, so this phase could be called equal section entry phase. In the third phase, the buffer force was equally constant. In this phase, the cone piston has entered into the tube entirely, so the contact area between piston and tube was constant, and the deformation mode of tube was stable, both of which lead to the buffer force constant. This phase can be called the stead entry phase. In the fourth phase, the buffer force decreases rapidly because the piston decelerated and stop in the tube, which could be called stop phase.
3.3.2. The relation between cone angle and shock absorbing performance The pistons with 2 ,4 and 6 cone angles impacting tube were calculated to obtain the relation between cone angles and shock absorbing performance. Fig. 9 is the shock acceleration curve in different impact cases (the result in 4 angle showed in Fig. 8 with buffer) on the baseboard. The max shock accelerations under three cases were 160000 g、4800 g and 24000 g respectively, namely the cone piston with 4 angle had the best shock absorbing performance. To understand the relation between the cone angles and shock absorbing performance, the max enter depth, buffer force and energy loss during the impacts were analyzed. Fig. 10 is the max enter depth graph of piston in different cone angles. In the 2 angle case, the piston entered across the tube, and impacted the baseboard directly. The max enter depth of this case was 15 mm. In the 4 and 6 angles cases, the piston entered and stop at the middle of the tube, and the max enter depth were 13.5 mm and 8.6 mm respectively. Therefore, max enter depth decreased as the cone angle increased. Fig. 11 is the buffer force curve of different cone angles. The max buffer forces under different angles were 135 N, 340 N and 510 N respectively, and the buffer force increased rapidly. The energy loss of the cone piston during impact could be calculated by integrating the buffer force with the displacement. Fig. 12 is the energy loss history curve of different impact cases. The original kinematic energy of cone piston was 4 J, and the energy loss of different cases were 1.52 J, 3.49 J and 3.47 J respectively, namely the energy loss rate was 38%, 87.25% and 86.75%. The above analysis showed that the characteristics of max enter depth, buffer force and energy loss had different characteristics from the shock acceleration of the baseboard, and it could be considered that the shock acceleration results were the coupled effects of above three aspects, and the main factor was different in various cone angles. In order to understand the influence of cone angles on the shock absorbing performance, pistons in ten cone angles impacting tube were calculated. With the increase of cone angles, the shock acceleration of baseboard changed in the style of decrease-increasedecrease-increase, see in Fig. 13, namely the shock absorbing performance changed as increase -decrease-increase-decrease. These characteristics were analyzed as follows: Shock acceleration decrease phase: when the cone angle was small, the buffer force of tube was so little that the cone piston could impact the baseboard directly, which cause extremely large shock. With the angle increasing, the buffer force and energy loss became bigger, see in Fig. 14 and Fig. 15, and the shock acceleration of baseboard decreased significantly. Until the piston stops at the interface of tube and baseboard, the shock acceleration decreased
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Fig. 8. The shock acceleration curve on the baseboard.
Fig. 9. The shock acceleration curve in different impact cases.
Fig. 12. The energy loss curve of different impact cases.
Fig. 10. The max enter depth graph of piston at different cone angles.
Fig. 13. Max shock acceleration with different cone angles.
Fig. 11. The buffer force history curve of different cone angles.
to the least of this phase. Therefore, the buffer force and the energy loss were the key factors of shock absorbing performance. Shock acceleration increase phase: after last phase, the source of the max shock source converted from the impact between piston and baseboard to that between piston and tube. In this case, the shock acceleration increased with the bigger cone angle because that the impact was becoming more rigid with the buffer force increased. As the angle has increased to the case that the equal section of the piston just inserted into the tube, the shock acceleration increased to the maximum of this phase, see in Fig. 16. Therefore, max enter depth is the key factor of shock absorbing performance.
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absorbing were changing, which is determined by max enter depth, buffer force and energy loss. 4. Conclusion
Fig. 14. Max buffering force with different cone angles.
Based on the diameter expansion method of thin-walled metal tube, the model of piston impacting tube was established, the performance of tubes on shock absorbing were analyzed, and the relation between the cone angles and shock absorbing performance was obtained. The results showed the thin-walled metal tube could reduce the shock load significantly. The buffer force during impact could be divided into four phases, which was corresponding to the structure of the cone piston. In addition, with the increase of cone angles, the shock acceleration of baseboard changed in the style of decrease-increase- decrease-increase, and this characteristics were the coupled effects of max enter depth, buffer force and energy loss, and the main factor was different in various cone angles. References
Fig. 15. Max enter depth with different cone angles.
Fig. 16. Energy loss rate with different cone angles.
Shock acceleration decrease phase again: previous analysis showed that the max shock acceleration occurred at moment of equal section entering into the tube. Based on this conclusion, with the cone angle increasing further, the equal section of piston could not enter into the tube, which lead to the decrease of max shock acceleration until the max enter depth was equal to varying section height. Therefore, the max enter depth is the key factor of shock absorbing performance. Shock acceleration increase phase again: when the varying section of piston could not insert the tube entirely as the angle increases, the energy loss of cone piston decreased, see in Fig. 15, which lead to the shock load of impact increased because the impact between piston and tube is head-on impact approximately. Therefore, the energy loss is the key factor of shock absorbing performance. In short, as the cone angle increased, the characteristics of shock
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