Simulation and optimization for airdrop adaptability of overweight equipment

XU Jian, LI Qiang, YANG Zhen

(College of Mechatronic Engineering, North University of China, Taiyuan 030051, China)

徐 健， 李 強， 楊 臻

(中北大學 機電工程學院， 山西 太原 030051)

?

Simulation and optimization for airdrop adaptability of overweight equipment

XU Jian, LI Qiang, YANG Zhen

(CollegeofMechatronicEngineering,NorthUniversityofChina,Taiyuan030051,China)

Airbag buffer process was analyzed with the aid of aerodynamic and thermodynamic methods. Based on the current structure of the airbag, the terminal velocity was too high. Therefore, the research on the diameter and height of the airbag was done and the feasible design area was found. With the optimized structure parameters, the airbag buffer experiment under normal conditions was conducted. Furthermore, the residual height and internal pressure of the airbag as well as the terminal velocity and acceleration of the airdrop were obtained. The experiment results show that the optimized airbag is feasible for 20 t cargo airdrop.

airdrop adaptability； airbag； terminal velocity

0 Introduction

Airbag buffer system is one of the most important airdrop systems, and its main function is to reduce the collision and impact during the landing process and to moderate the collision velocity between equipment and the ground. Thus it is widely used in reentry capsule landing, weapons airdropping, emergency rescue, etc. For example, in the earthquake rescue process, if heavy-type engineering machine can be put in the suitable place by airdrop, the road can be repaired quickly by rapid clean-up of barrier lake and seldom dam-break.

The buffer airbag has a great variety of types. It can be divided into single airbag and joint airbag according to structure. And it also can be divided into active air inflation airbag and natural inflation airbag, or closed airbag and exhaust airbag. According to current index request, at the initial landing velocity of 8 m/s, the maximum overload will not exceed 20 g and the terminal buffer velocity will not surpass 3 m/s.

For current airbag systems are few, airdrop mass is not big enough, ranging from mostly 2 t to 9 t[1-3], only a few systems are over 10 t, and 20 t airdrop systems are few. An increase in airdrop mass in the process of airdrop not only makes it possible to airdrop heavy-duty equipment, but also increases the combat effectiveness.

1 Airbag working principle

The cargo platform is similar to the flat board on which the equipment is fixed. The airbags are folded in the cross beam and longitudinal beam of the cargo platform by ropes. The airdrop system contains 6 airbags and every two airbags form one group. The single airbag and six-airbag combination are represented in Fig.1 and Fig.2, respectively.

Eight holes are uniformly distributed on the upper part of the airbags, as shown in Fig.1. Four holes have constant area, but the other four holes are made of rubbers and can be expanded due to increase of inner gas pressure.

In the appropriate time after the airplace takes off from the cargo platform, the folded airbags are released. The airbags expand along the height direction inflated by the exterior air. When the airbags touch the ground, they begin to be compressed and the gas is also blown off.

Fig.1 Single airbag

Fig.2 Six-airbag combination

2 Basic assumption

Airbags are made of polyester canvas, and several steel wires are fixed in the cylindrical area to protect the airbag radius dimension from enlargement. In the process of thermodynamic modeling[4-5], some assumptions are given as follows:

1) The airbag wall has non-elastic behavior and does not deform in the radius direction, thus the contact area remains constant between the airbags and the ground as well as between airbags and cargo platform;

2) The pulling force from the parachute ropes is ignored, and the buffer is only from the compression action;

3) the air process is adiabatic and isentropic;

4) the gas leakage is ignored except 8 holes.

3 Simulation model

3.1 Modelling

Based on the assumption mentioned above, the airbag’s position at a arbitrary moment can be presented in Fig.3, wheremrepresents the mass of airdrop system, which is shared by one airbag and is one-sixth of the whole mass;his the original height of the airbag;xis the length compressed during the buffer course;Sdis the exhaust area,P0is the air pressure outside,Pyis the current time gas pressure in the airbag andVyis the airbag’s current volume.

Fig.3 Analytical model of airbag

It is supposed that 0 point is origin and the down direction is the positive direction, then the motion equation formcan be written as

(1)

wheregis gravity acceleration, m/s2;Sis the airbag transversal area, m2.

According to the gas state equation,Pycan be presented as the buffer process[6-8],

(2)

whereV0is the airbags initial volume, m3;G0is the air mass before compression, kg;Giis the air mass exhaust during compression, kg;kis air adiabatic exponent.

Calculation ofGineeds to separate the gas flow state into two states: the air exhaustion of the airbag and the air inflation of the airbag. Both the states can also be divided into supercritical state and subcritical state. They are related to the gas pressure ratio, and the formula can be represented as

(3)

Variation of the exhaust areaSdrelies on the four holes which are made of rubber. By means of finite element analysis (FEA), the relationship between rubber hole’s area and inner gas pressure can be got in the form of coordinates. The obtained data can be used for current 9.3 t airdrop system and then be corrected for simulation program by interpolation.

3.2 Sample analysis

Firstly, the analysis was done with the current airbag with the single airbag diameterDof 1 180 mm and the heighthof 1 120 mm. According to the test procedure, the initial landing velocity is 8 m/s. In the whole airdrop system,Mis 20 t and single airbag shares the air drop mass ofm=M/6. The relations among compression displacement, velocity, acceleration, residual air mass and time are represented in Fig.4, and the gas pressure is shown in Fig.5.

Fig.4 Cargo platform motion law and gas mass variation

From Figs.4 and 5, it can be seen that if the airdrop mass is 20 t with the current airbag, the maximum pressure will be 3.2 atm, and the acceleration peak value will be 62.55 m/s2, but the buffer terminal velocity will be 5.1 m/s, which does not meet the requirement of 3 m/s. There obviously are two methods to reduce the buffer terminal velocity: increasing the airbag volume or reducing exhaust area of the airbag. After calculation, it can be known that the latter can reduce the terminal velocity below 3 m/s, but it will cause ultra high airbag pressure, therefore the airbag material needs to be reinforced; at the same time it makes airbag burst easily. For this reason, the method of increasing airbag volume is selected.

Fig.5 Gas pressure law

According to feasible dimension range of the airbag, its diameter is in the range of 1 180-1 300 mm with the step size of 20 mm； the airbag’s height is in the range of 1 120-1 620 mm with the step size of 50 mm. Taking Matlab as the calculation tool, the possible combinations of diameter and height are analyzed, and the results can be drawn by means of the contour function. The maximum pressure, terminal velocity and maximum overload acceleration are shown in Fig.6.

Fig.6 Relationship between D and h resulting in different maximum pressures terminal velocities and maximum overload accelerations

According to terminal velocity in Fig.6(a), the feasible design area can be drawn, as shown in Fig.7.

When the straight line is drawn to represent the feasible area and unfeasible area, in the feasible area the relationship between airbag diameterDand heighthcan be fitted by

(4)

Minimum volume of airbag can be represented by

(5)

The relationship between airbag volume and diameter is shown in Fig.8. It can be seen that the relation in the lower right corner is in accord with the design scheme which has minimum airbag volume, maximum diameter and the minimum height. But in practical design, the balance between height and diameter must be taken into account including the return of airplane cabin on condition that it inclines to the ground and the rail’s width in it. According to Eq.(4), if the diameter is limited to 1 255 mm as its peak value, the height is 1 300 mm. The airbag buffer process is shown in Figs.9 and 10.

Fig.8 Relationship of airbag volume and diameter for airdrop system of 20 t

Fig.9 Cargo platform motion law and gas mass variation at D=1 255 mm and h=1 300 mm

It can be seen that the buffer terminal velocity of the airbag after optimization reduces to 2.67 m/s, less than 3 m/s; The overload acceleration is about 68 m/s2, less than 20 times gravity acceleration. The maximum pressure is about 3.1 atm. It meets the buffer need for overload cargo airdrop.

Fig.10 Gas pressure law

3.3 Experiment

Based on the above-mentioned preparations, the butter airdrop system is set up and then overload experiment is conducted, as shown in Fig.11.

Fig.11 The whole airdrop system before dropping

Fig.12 Displacement at different masses and altitude of 0 m

It is feasible to adjust airbag’s diameter and height for the diameter of 1.06 m, height of 0.9 m and initial landing velocity of 8.0 m/s. In the same way, the airbags at different altitudes are analyzed. Figs.12-14 show the measured displacement, velocity and acceleration. The results are feasible.

Fig.13 Terminal velocity at different masses and altitude of 0 m

Fig.14 Overload acceleration at different masses and altitude of 0 m

4 Conclusions

1)It is feasible for 20 t overweight equipment air drop in theory, the pressure has not remarkable change and the overload acleleration is not greater than 20 times gravity acceleration.

2) In the buffer process of 20 t air drop, the terminal velocity is the key factor and must be paid more attention to. It needs to reduce to 3 m/s after optimization.

3) The optimization program gives the feasible design area which satisfies the buffer terminal velocity, and it is convenient to adjust airbag’s dimension.

[1] WANG Ya-wei, YANG Chun-xin, KE Peng. Airbag cushion process simulation for cargo airdrop system. Journal of System Simulation, 2007， 19(7)： 3176-3179.

[2] FU Xin-hua, LUO Bei-guo, FU Xin-bing. Design on virtual simulation verification platform of airdrop adaptability of airborne equipment. In： Proceedings of International Symposium on Instrumentation & Measurement, Sensor Network and Automation, Toronto, Canada, 2013: 955-958.

[3] HONG Huang-jie， WANG Hong-yan， HAO Gui-xiang. Simulation and analysis of landing cushion process for airborne vehicle and airbag. Journal of Academy of Armored Force Engineering， 2010, 24(4): 33-36.

[4] DU Zhi-qi, SHAO Peng. Dynamic finite element simulation of the aluminum alloy hull at landing. Acta Armamentarii, 2009, 31(1): 1-5.

[5] LU Zhe-yuan, WANG Hong-yan, NIU Si-bo, et al. Study on cushioning characteristics of airbag for heavy equipment recovery system. Journal of Academy of Armored Force Engineering, 2010, 24(1): 25-28.

[6] YIN Han-feng， WEN Gui-lin， HAN Xu. Optimal design of airbag impact attenuation system for airdropping equipment. Journal of System Simulation, 2008, 20(5): 1325-1327.

[7] Lee C T. Adaptive backstepping integral control of a small-scale helicopter for airdrop missions. Asian Journal of Control, 2010, 12(4): 531-541.

[8] Michael W. Real-time system identification for an adaptive MPC autonomous airdrop system. In: Proceedings of the 20th AIAA Aerodynamic Decelerator Systems Technology Conference, Seattle, WA, 2009.

超重裝備空投適應性的仿真與優(yōu)化

采用氣體動力學和熱力學方法對氣囊緩沖過程進行了分析。 基于現(xiàn)有的氣囊結(jié)構， 空投時末端速度過大。 因而， 對氣囊直徑和高度等參數(shù)進行了研究和優(yōu)化， 找到了可行的設計區(qū)域。 利用優(yōu)化后的結(jié)構參數(shù)， 對正常工況下的氣囊緩沖過程進行了實驗， 得到了氣囊高度和內(nèi)壓， 空投速度和加速度。 實驗結(jié)果表明， 利用參數(shù)優(yōu)化后的氣囊實現(xiàn)20 t超重裝備的空投是可行的。

空投適應性； 氣囊； 末端速度

XU Jian, LI Qiang, YANG Zhen. Simulation and optimization for airdrop adaptability of overweight equipment. Journal of Measurement Science and Instrumentation, 2015, 6(3)： 247-252. [

徐 健， 李 強， 楊 臻

(中北大學 機電工程學院， 山西 太原 030051)

10.3969/j.issn.1674-8042.2015.03.008]

Received date： 2015-05-21 Foundation items： National Natural Science Foundation of China (No. 51175481)

XU Jian (Zdp12_0@126.com)

1674-8042(2015)03-0247-06 doi： 10.3969/j.issn.1674-8042.2015.03.008

CLD number： TJ02 Document code： A