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Crashworthy subfloor structure of civil aircraft via inclined inward-folding composite tubes
Journal Pre-proof Crashworthy subfloor structure of civil aircraft via inclined inward-folding composite tubes Zhefeng Yu, Xin Zhou, Xiang Zhou, Yangyang Zhang, Qiao Zhu PII:
S1359-8368(19)35551-9
DOI:
https://doi.org/10.1016/j.compositesb.2020.107887
Reference:
JCOMB 107887
To appear in:
Composites Part B
Received Date: 20 October 2019 Revised Date:
29 January 2020
Accepted Date: 16 February 2020
Please cite this article as: Yu Z, Zhou X, Zhou X, Zhang Y, Zhu Q, Crashworthy subfloor structure of civil aircraft via inclined inward-folding composite tubes, Composites Part B (2020), doi: https:// doi.org/10.1016/j.compositesb.2020.107887. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Crashworthy Subfloor Structure of Civil Aircraft via Inclined InwardFolding Composite Tubes Zhefeng Yu, Xin Zhou, Xiang Zhou, Yangyang Zhang and Qiao Zhu Aerospace Structure Research Center, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China
Correspondence Information: Zhefeng Yu Associate professor School of aeronautics and astronautics Shanghai Jiao Tong University Email: [email protected] Room A423, Aero-Building, NO.800 Dongchuan Rd., Shanghai, 200240, P.R.China Email: [email protected] Tel & Fax: +86 21 34206387
Pages 33
Figures 19
Tables 2
2
Abstract: This paper describes the design and testing of a shock absorber with an inward-folding composite tube that can be used as a structural component in its normal working state. Although more energy can be absorbed when the hollow of the tube is filled with composite debris, a higher load relative to the initial peak load will be produced. A variable structure based on two inclined energy absorbers was then proposed, and impact tests used to verify the reaction load calculation for two models experimentally. Results indicate that.the variable structure had a greater compression ratio and a flatter load curve, demonstrating its potential for use in the struts of an aircraft cargo floor.
Keywords: shock absorber; inward-folding tube; subfloor; aircraft; variable structure
3
1.
Introduction Structural crashworthiness is an essential requirement in the design of passenger aeroplanes. The failure of
the ring frame and structure under the cargo-floor absorbs the main impact of energy during a crash. The structures involved in the energy absorption include frames [1][2], struts [3][4] and sine wave beams [5]-[8]. Early commercial aircraft were made mostly of aluminium and other metals. Aluminium has a considerable plastic deformation capacity. Metal structures can absorb significant amounts of kinetic energy during a large deformation while maintaining their structural integrity. In recent decades though, composite materials have been used more extensively to build aircraft structures, and as such their crashworthiness needs to be addressed. Components in the fuselage structure serve as energy absorbers in current crashworthy designs for composite fuselages [9][10]. Struts in the fuselage connecting the frame to the passenger floor and the cargo floor, are mostly made from brittle carbon fibre reinforced plastic (CFRP). The triggering mechanism that initiates progressive crushing of a strut can be a chamfer, a “steeple” [11][12], or a “tulip” [4][12] at the end of the strut that will initiate crushing when compressed by a flat surface. When the behaviours of thin-walled hollow squares and circular tubes with chamfer failure triggers are compared to those with steeple failure triggers [12], results show that steeple failure triggers for square tubes are more effective at maintaining a higher sustained crush load than chamfer failure triggers. The opposite effect is observed for circular tubes. The characteristics of geometric shape, fibre architecture, and trigger mechanisms of energy absorbers have been extensively investigated [13]-[15], and testing on various types of tubular structures has shown that composite materials can offer extremely high values of specific energy absorption (SEA) [16]-[20]. The SEA values ues of CFRP generally fall in the range of 50–80 kJ/kg [21]. Honeycomb tubular pipes inspired by bamboo [22][23] and natural fiber reinforced tubes[24][25], are some of the materials being used in bio-inspired composite structures. Examples are a strut with an open thin-walled section being used as a stanchion, though global and local buckling is more likely to occur for such a structure[26][27], where the SEA ranges from 20–60 kJ/kg under a progressive crushing movement [28].
4
To achieve the higher energy absorption and a more stable crush, the failure-triggering method may be adopted in combination during the processing and fabrication of a composite strut that is part of a complex structure. Heimbs [29] presents a solution under axial crushing by cutting composite tubes into strips using a special joint. Tong et al. [30] proposed an external chamfer trigger with a semi-circular cavity. This guides the composite tube towards being fully crushed by increasing the degree of bending of the fibres and squeezing the composite matrix. Siromani et al. [31] conducted a study on the effect of an inward-folding cap on the energy absorption capability of CFRP tubes under axial compression. The cap was not applied to a structure. Ueda et al. [32] designed a double-sided plug to trigger the crushing of a CFRP tube that could be utilized to control SEA by changing its geometric parameters. A crashworthy structure is more likely to be subjected to oblique loadings under real conditions. The peak force and the deformation values decrease as the oblique angle increases [33]. The value of the SEA of a composite tube under a loading angle of 15° will decrease by 20% compared to that with an axial load [34]. The tube could be also subjected to bending load under an oblique load, but if the pivot joint is adopted, the oblique load could be transformed to an axial load. The work of Heimbs [29] also concerned a strut subjected to axial crushing, which avoided the catastrophic failure of the strut. A novel strut system with corrugated composite plate and hinge joints was proposed by Ren et al [35]; the axial impact load would be transferred to the plate during impact process for the hinge joints, which provides the robust progress failure of the composite plate. The energy absorption of a subcomponent of an aircraft structure can be evaluated in two ways. Firstly, the structure is fixed at the base such that the impact is produced when a weight is dropped on it [26][36]. Secondly, the subcomponent, mostly the fuselage section, is lifted and dropped to impact the ground [37][38]; this method is effective to simulate the transference of the load caused by the inertia of the payload and passengers in the fuselage. The authors [39] proposed a shock absorber consisting of a composite tube, crush cap, and pressing cap, and applied it to the legged-landing gear of a drone. In this study the absorbers are experimentally tested by varying the effects of layer configuration. The configuration of the absorber allows debris to fill the hollow
5
tube and enhances energy absorption when the composite tube is crushed to more than half its length, however, the increasing reaction force exerts a higher load on the payload on the structure. A schematic representing the subfloor structure of an aircraft is proposed to demonstrate the utilization of energy absorption of the self-filling effect controlling the high load at this stage. The absorbers were assembled at an angle that inclined away from the impact direction, and while the angle changes as the entire structure crashes, the absorber is subjected to axial load and therefore is crushed steadily. The method of calculating the reaction force was addressed and validated with the crash tests.
2.
Characteristics of the energy absorber
2.1 Configuration of the energy absorber The configuration of the energy absorber is depicted in Figure 1. It consists of a crush cap, a pressing cap, and a composite tube. The composite tube is connected to the two caps with rivets. The caps can be pivotjointed to a structure using lugs. Such a design ensures that the absorber is only subjected to the axial load during a crash thereby avoiding catastrophic failure due to a moment of bending. The pressing cap has a flat inner end-surface that will not destroy the composite tube during the compression load. The crush cap has a triggering fillet with radius Rt that will trigger the failure of the composite tube, and the inverted surface with radius Rf folds the delaminated tube. When the folded tube reaches the pressing cap, the debris will begin to fill the hollow and thereby increase the reaction load. The initial length of absorber is denoted as La0 and that of the composite tube is denoted as Lt0 (Figure 1 (a)). As the composite tube is crushed, the lengths of the absorber and composite tube decrease and are denoted as La and Lt respectively (Figure 1 (b)).
6
(a)
(c)
(b)
Pressing cap
Rivets hole
La
Lt
La0
D
Lt0
tw
Composite tube
Delaminations Rf Rt
Crush cap
Figure 1. Principles of the absorber: (a) structural configuration, (b) scenario when crushing begins, (c) scenario after the crushed composite tube reaches the pressing cap.
2.2 Behaviour of energy absorber under dynamic load The characteristics of the energy absorber under axial impact were demonstrated through a dropping hammer test. The composite tube is made from T700 carbon-fibre/epoxy prepreg unidirectional tape laid in a sequence of [0/90]4, where the tapes at 0° coincide with the axis of the tube. The mechanical parameters provided by the supplier are: tensile modulus is 120 GPa, tensile strength is 2000 MPa, compressive strength is 1050 MPa, interlaminar shear strength is 55 MPa. The composite tubes have an outer diameter D of 30 mm. The thickness of the composite tube is 1.5 mm and the length is 120 mm. The density of the tube is 1.53×103
7
kg/m3. The crush cap with Rt = 3 mm and Rf = 7 mm is made of chrome-plated steel. No lugs were made on the caps for easy installation for the test. The impact tests were conducted with a dropping tower as shown in Figure 2, which is capable of lifting a 500 kg drop hammer to a height of 1.7 m. An optical sensor was used to measure the impact velocity. In this experiment, a drop hammer with a mass of 63 kg was lifted by a pulley to a height of 1.5 m and then released from a quick-release hook. A PCB-200C20 force sensor was mounted on the base to measure the force of the impact.
Quick-release hook Dropping hammer
Linear bears Pulley
Optical sensor Pressing cap Bumper Crush cap
Composite tube
Force Sensor
Figure 2. Impact test setup.
8
The impact force was recorded using a data acquisition instrument sampling at a frequency of 100 kHz, Figure 3 (a). The acceleration of the hammer was calculated from the impact force, and the velocity at time t was obtained by integrating the acceleration over the time using the Simpson algorithm, as follows:
= + −
(1)
where g is acceleration due to gravity, F(t) is the measured impact load, and m is the mass of the hammer. The displacement of the hammer from the location at which it contacts the absorber at time t, i.e. the real-time crush distance of the composite tube, is given by the following equation: = +
−
d d
(2) The plot of the impact force versus crush distance is shown in Figure 3 (b), where the load begins to increase at a crush distance of 60 mm, i.e. half the length of the tube. For convenience of comparing the behaviour of absorbers of different lengths, dimensionless distance is introduced as follows: =
=
(3)
where at bottoming out is also called stroke efficiency (SE) [40]. The impact force was then plotted versus dimensionless distance as shown in Figure 3 (c). There are two main stages apart from the initiation of the tube failure. Stage 1 shows a steady force, while the impact load in stage 2 gradually increases due the tube becoming filled with composite debris. 20
(a)
Load (kN)
15
10
5
tw = 1 .5 mm , R f = 7 m m, R t = 3 mm , D = 3 0 m m 0 0
5
10
15
T im e ( ms )
9
20
25
30
20
(b) Load (kN)
15
10
5
tw = 1 .5 m m , R f = 7 m m , R t = 3 m m , D = 3 0 m m 0 0
20
40
60
80
100
C ru s h d i s t ac n e (m m )
20
(c) 15
Load (kN)
Stage 1 10
Stage 2 5
t w = 1.5 m m, R f = 7 mm , R t = 3 m m, D = 30 m m 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Dimensionle ss cr ush dista nce (1- Lt/Lt0 )
Figure 3. Load curves of the absorber under dynamic load plotted against: (a) time, (b) crush distance and (c) dimensionless crush distance.
One of the characteristics of crash tubes, crush force efficiency (CFE) can be calculated by !" =
#$%& ()*+,& -.)($
#%/ * & %0 (.00%1+$ -.)($
(4)
In Figure 3, the initial peak load is 11.4 kN, and the mean load in stage 1 9.8 kN, hence the CFE is 0.86. This means that the absorber is applicable to situations where the allowable load equals the initial peak if all of the energy can be absorbed in stage 1. In this situation, the SE is less than 0.5. If the allowable load is higher, energy absorption in stage 2 can be utilized, increasing the total energy absorbed. To evaluate the energy absorption due to the filling up of debris, the SEA is calculated with the contact force and the crush distance by:
2"3 =
4
5 6
10
78
(5)
where 9 and 3 are the mass density and cross-sectional area of the composite tube, respectively. The SEA in stage 1 is equal to 47.3 kJ/kg, while it reached 53.3 kJ/kg when stage 2 was included, increasing by 12.7 %. The SE of data in Figure 3 is 0.7. If a high load had been applied, a higher SE would have been obtained until breaking of the tube due to high internal pressure.
2.3 Parametric analysis by experiments Since the materials of construction of the tube parameters affect the performance of the absorber, including layer configuration, wall thickness, Rf and Rt, it is necessary to investigate these before applying the absorber to a structure. Specimens were listed in Table 1, where the each specimen has an outer diameter of 30 mm, and length of 120 mm. Two thicknesses were considered, 2 mm and 1.5 mm. For the 2 mm tube, the effects of layer configuration were studied. The first layer number refers to the first inside layer of the tube. Specimens IF-03 and IF-04 were used to investigate the effect of layer configuration of [45/-45]5 and [15/15]5;, however, considering the stability of the manufacture process, two plies [90/-45] and [90/-15] were laid up on the mould first before other plies were laid up. Table 1. Layer configuration, thickness, Rf and crashworthiness characteristics of the tested specimens.
Specimen
Layer
tw
Rf
Mean load
SEA
configuration
(mm)
(mm)
(kN)
(kJ/kg)
IF-01
[90/-45/0/45]3
2
5
22.7
84.4
IF-02
[90/0]6
2
5
26.3
97.6
IF-03
[90/-45(45/-45) 5]
2
5
17.0
63.1
IF-04
[90/-15(15/-15)5]
2
5
25.7
95.6
IF-05
[90/0]6
2
7
21.0
81.7
IF-06
[90/0]6
2
12
20.0
74.2
11
IF-07
[90/0]4
1.5
5
9.8
47.8
IF-08
[90/0]4
1.5
7
9.6
46.9
IF-09
[90/0]4
1.5
12
9.0
44.0
Our tests show that the tube resisted inward folding and broke up when Rt was less than 3 mm, consequently Rt is equal to 3 mm for all of the specimens. For low velocity crashes, the performance of the composite absorber was evaluated via quasi-static tests that were carried out using an MTS servo-hydraulic system capable of providing a 50 kN static load. The loading was applied under displacement control mode, at a rate of 10 mm/min. As we were most interested in the results of the steady load of stage 1, the test was ceased at the beginning of stage 2. The specimen with layer configuration of [90/0]6 after static test are shown in Figure 4, where the effect of Rf on the folding mode are obvious; the crash cap with smaller Rf bends the tube wall more seriously. The longitudinal cross section of the composite tube after test was shown in Figure 5; the wall of composite tube was delaminated thoroughly and compacted.
12
tw=2 mm, Rf=5 mm
tw=2 mm, Rf=7 mm
tw=2 mm, Rf=12 mm
tw=1.5 mm, Rf=5 mm
tw=1.5 mm, Rf=7 mm
tw=1.5 mm, Rf=12 mm
Figure 4. Post-dynamic-test conditions of the specimen
13
Figure 5. Longitudinal cross-section of the specimen. The effects of layer configuration are shown in Figure 6, where the load of specimens IF-02 is the highest; the loads of IF-04 and IF-02 are similar; the load of IF-01 is lower and that of IF-03 is the lowest. The comparison between the load of IF-03 and IF-04 shows that the load increases magnificently when the layer angle approaches to 0°; IF-01 has more layers in 0° compared with IF-03, so it has a higher load; IF-02 has the most 0° layers, so it has the highest load. 50
Load (kN)
40
30
20
IF-01 IF-02 IF-03 IF-04
10
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dimensionless crush distance (1-Lt/Lt0 )
Figure 6. Load curves of absorbers with different layer configuration under static load. The SEA values were calculated using the steady load in stage 1, as listed in the right-hand column of Table 1. The SEA of a tube with the layer configuration of [90/0]6 is highest in this study. This type of tube is easier to obtain, and thus used more often. The effects of Rf on the absorbers with 1.5 mm and 2 mm thick walls are shown in Figure 7, where all of the tubes have a layer configuration of [90/0]6. The three crush caps have the same Rt, which is 3 mm, and different Rf‘s of 5 mm, 7 mm and 12 mm, respectively. The SEA values of absorbers with tubes of 2-mm wall thickness range from 74.2 kJ/kg to 97.6 kJ/kg, and those of absorbers with tubes of 1.5-mm wall thickness range from 44.0 kJ/kg to 47.8 kJ/kg. This indicates that the effect of Rf on increasing the SEA is more significant for 2 mm tubes than for of 1.5 mm tubes.
14
40
IF-02, tw=2 mm, Rf=5 mm IF-05, tw=2 mm, Rf=7 mm IF-06, tw=2 mm, Rf=12 mm
35
Load (kN)
30 25 20
IF-07, tw=1.5 mm, Rf=5 mm 15
IF-08, tw=1.5 mm, Rf=7 mm IF-09, tw=1.5 mm, Rf=12 mm
10 5 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dimensionless crush distance (1-Lt/Lt0 )
Figure 7. Load curves of absorbers with different Rf under static load.
3.
Variable structures with inclined absorbers
3.1 Principles of the variable structure The schematic of a variable structure, designed to utilize the energy absorption of stage 2 while avoiding the exertion of a higher vertical load on the structure, is shown in Figure 8. The profile drawn as a dashed line represents the initial state. A pair of absorbers are used as stanchions at a θ0 angle inclined to the vertical. The horizontal distance of the two joints of one absorber is denoted W and is assumed to be a constant. When a vertical load Fv caused by the deceleration of the mass on the platform is exerted on it, the platform is vertically deformed because the composite tubes are crushed in their axial direction. The vertical crush distance of the platform is denoted : and can be calculated using Equation (2) as well as , with !; produced by the decelerated payload. The height of the absorber is denoted with H0 and H in the initial and deformed states, respectively. The angle θ0 is then replaced by θ in the deformed state, so that the resultant reaction force of the two absorbers is as follows: !; = 2!/ =>?@
(6)
where Fx is the axial load of the absorber, which is dependent on the dimensionless crush distance for a certain composite tube and crush cap. The angle θ is given by the following:
15
E
@ = sin D F = sin D F
E
G
(7)
As the absorbers become shorter, θ increases. The resultant vertical force decreases to below the axial load in stage 1 and decreases further in stage 2 as θ increases. If the proper parameters are chosen, the resultant force will not exceed the permitted load in stage 2 and the energy absorbed during that stage due to the compacting of composite debris will be utilized effectively for impact mitigation. The method to calculate the vertical reaction load of the platform is given below. The crush distance of the composite tube is then found as follows: = HI − HI = HI −
F
JKL M
= HI −
F G JKL M
(8)
The dimensionless crush distance of the composite tube in the structure is defined in Equation (3). The resultant vertical force of the absorber is then given by Equation (6). If the length of the absorber in the structure is different from that of the single absorber employed in the dynamic test to obtain its load curve, it can be interpolated in terms of the dimensionless crush distance to produce the new load curve. To evaluate the performance of the entire structure as an energy absorption component, its dimensionless crush distance is defined as follows: F F NNN : = FG = F
where : is the vertical crush distance of the platform.
16
(9)
Fv
:
Payload platform Floor beam
F x θ0 H0
Fx
θ W
H
Energy absorber
Frame
Figure 8. Schematic of the variable structure.
3.2 Parametric analysis The resultant vertical force of the inclined absorber is dependent on the initial angle @ and the crush distance. The height of the structure is related to the length of the entire absorber, although only the composite tube can be compressed. Therefore, the ratio of the length of the composite to the absorber, denoted tube ratio Lt0: La0, also affects the behaviour of the platform. In this sub-section, the effects of these parameters are demonstrated. In Figure 9 the vertical forces of one absorber with different values of @ , are plotted versus the dimensionless crush distance of the entire structure, denoted NNN : . The data for @ = 0 was obtained from an axial test on a single absorber with tw = 1.5 mm, Rt = 3 mm, and Rf = 7 mm, as shown in Figure 3. The final dimensionless crush distance of the tube is 0.73. Three ratios of Lt0:La0, i.e. 1:1, 1:1.2, and 1:1.4, were
17
considered in the analysis. The two latter cases represent a situation in which the length of two caps were considered in terms of the total length of the absorber. As θ0 increased, the slope of the load curve decreased and the of the platform increased. In Figure 9 (a), when θ0 = 20° and 30°, NNN δ: reaches 1.0, which indicates that the final angle reached 0° and the residual length La was equal to W. The load curve for absorbers with Lt0:La0 = 1:1.2 and 1:1.4 are shown in Figure 9 (b), and Figure 9 (c), respectively. Due to the total length of the absorber increases when the caps were considered, the angle θ when the tube was crushed was less than that of the absorber with a higher tube ratio. The load curve for θ0 = 20° shown in Figure 9 (b) is flatter than that shown in Figure 7 (a), and then can consume more energy with a load lower than the initial peak. For the curves in which θ0 = 30° in each of the figures, the load at the end of crash is lower than the initial peak, but may be unable to support the gravity of the platform. 20
Ve rtical load (kN)
?0=0°
(a)
18
?0=10°
16
?0=20°
14
?0=30°
12 10 8 6 4 2 0 0. 0
0. 1
0. 2
0. 3
0. 4
0. 5
0 .6
0 .7
0 .8
0 .9
Dime nsionless crush distance (1-H/H 0)
18
1 .0
1 .1
20
Ve rtical load (kN)
? 0= 0°
(b)
18
? 0= 10°
16
? 0= 20°
14
? 0= 30°
12 10 8 6 4 2 0 0. 0
0. 1
0. 2
0. 3
0. 4
0. 5
0 .6
0 .7
0 .8
0 .9
1 .0
1 .1
D ime ns io nless cru sh d istan ce (1 -H /H 0)
20
Ve rtical load (kN)
? 0= 0°
(c)
18
? 0= 10°
16
? 0= 20°
14
? 0= 30°
12 10 8 6 4 2 0 0. 0
0. 1
0. 2
0. 3
0. 4
0. 5
0 .6
0 .7
0 .8
0 .9
1 .0
1 .1
D ime ns io nless cru sh d istan ce (1 -H /H 0)
Figure 9. The vertical loads plotted against the crush distance of platforms with different initial angles and tube ratios: (a) Lt0/La0 = 1:1, (b) Lt0/La0 = 1:1.2, and (c) Lt0/La0=1:1.4. Three tests were carried out on this type of specimen, and the load curves similar to those shown in Figure 9 were obtained. The SEA is calculated for each curve with the initial peak as the allowable load (Table 2). The crush length includes all of stage 1 and the part of stage 2 where the vertical load is lower than the allowable load, and no more energy will be taken into account if La decreases to W. The SEA increases at θ0=10 ° and θ0=20 ° due to the energy in stage 2 is involved. While, the SEA decreases at θ0=30 °for tube
ratios Lt0/La0=1:1 and Lt0/La0=1:1.2, because the final crush distance of the tube decreases due to La decreases to W. As the entire curve was used to calculate the SEA for tube ratio Lt0/La0=1:1.2, including the stage where the load descends, the maximal increment of SEA at 11.3%. 19
Table 2. The SEA of absorber with different initial angles and tube ratios in the situation that the vertical load less than the initial peal load. Lt0/La0 = 1:1
Lt0/La0 = 1:1.2
Lt0/La0 = 1:1.4
Initial angle SEA (kJ/kg)
Increment
Increment
(%)
SEA (kJ/kg)
0
47.9 VX. VW.X
—
10
48.1 VX.[ VX.
20 30
(degree)
4.
Increment
(%)
SEA (kJ/kg)
47.9 VX. VW.X
—
47.9 VX. VW.X
—
0.4
48.0 VX. VW.\
0.2
48.0 VX.D VW.\
0.2
51.4 ^D.^ ^D.
7.3
50.3 ^.^ ^.D
5.0
50.0 ^. V\.X
4.4
47.8 VW.X VW.X
-0.2
49.7 V\.W V\.W
3.8
53.3 ^[.V ^[.D
11.3
(%)
Experiment and Materials
The subcomponent of the cargo floor was fabricated with two absorbers as stanchions, as shown in Figure 10. The metal floor beam and fuselage frame were fixed to the linear bars that support them; similar to the adjacent structures in a fuselage. Both of the absorbers consist of composite tubes with La0 = 327 mm, Lt0 = 237 mm. The two absorbers in this structure were much longer than those in the previous experiment, therefore more energy was needed to crush them. Considering the difficulty in conducting the impact test with higher energy, the absorber with relatively lower crush load was adopted, with tw = 1.5 mm, Rf = 7 mm and Rt = 3 mm. White ticks spaced at 20 mm intervals were drawn on the tubes to indicate the crush distance, but more accurate crush distances were calculated using acceleration demonstrated in sub-section 2.2. Two force sensors were installed on the base to measure the vertical load during the crash. Two steel blocks were put on the top of sensors to transmit the impact load to the sensors. The following two models with different structures and geometric parameters were adopted: model 1 where W = 80 mm, θ0 = 14°, and model 2, where W = 116 mm θ0 = 20°.
20
Linear bear Payload Pivot Floor beam
Pressing cap Absorbers Crush cap Pivot
Fuselage frame
Protecting block Left force sensor
Right force sensor
Figure 10. Crash test setup on a subcomponent of a cargo airplane floor.
The payload had a mass of 180 kg and the dropping height for model 1 was 1.6 m; thus, the impact had a velocity of 5.6 m/s and an energy of 2822 J. In the test for model 2, the dropping height was increased to 1.7 m to increase the compression of the absorber. Bumpers were used to protect the models from being crushed, and the crash procedures were recorded with a high-speed camera.
5.
Results and Discussion High-speed camera photographs of different moments in the two tests are shown in Figure 11 and Figure
12, respectively, demonstrating that the crush procedure was steady and the structure maintained its integrity during the crushing of the composite tubes. The vertical crush distance of the platform, : , shown in Figure 11 and Figure 12, was calculated using the acceleration of the platform based on the impact load. The two absorbers after the testing of model 2 are shown in Figure 13; the rivets of the pressing cap are intact while the rivets on the other ends were severed, and the corresponding ends crushed.
21
0 ms, : =0 mm
15 ms, : = 74 mm
30 ms, : = 130 mm
45 ms, : = 166 mm
Figure 11. High-speed camera photographs of the crash test on model 1.
0 ms, : =0 mm
13 ms, : =77 mm
26 ms, : =138 mm
39 ms, : =181 mm
Figure 12. High-speed camera photographs of the crash test on model 2.
22
Crushed ends
Rivets
Figure 13. Post-dynamic-test conditions of the two absorbers of model 2. The impact loads measured by the two sensors are shown in Figure 14 and Figure 15. The initial load is high as a result of the hard contact between the metal fuselage frame and the protecting block. The load histories of the left- and right-hand sensors were similar. For model 1, all of the kinetic energy was absorbed by the composite tube, where the descent of the loads at the end of the crash is depicted by the dashed line in Figure 14. In the test on model 2, where higher impact energy was applied, the platform made contact with the polyurethane bumpers before stopping, depicted by the dashed line in Figure 15. The dashed curves could not be predicted based on the axial load obtained from the axial impact test on the single composite tube, therefore these parts of the data will not be incorporated in the analysis.
23
40
Right Left
35
Vertical load (kN)
30 25 20 15 10 5
The end of impact 0 0
10
20
30
40
50
60
Time (ms) Figure 14. Impact load measured by the left- and right-hand sensors of model 1.
30
Right Left
Vertical load (kN)
25
20
15
The declining due to the contact with bumpers 10
5
0 0
10
20
30
40
50
60
70
80
90
100
110
Time (ms) Figure 15. Impact load measured by the left- and right-hand sensors of model 2.
24
The vertical crush distance of the platform, the axial crush distance of the absorbers, and the angle of the absorber can be observed, approximately, from the digital image, with accurate results calculated using the measured force. The crush distance of the platform, 1 , is calculated using the vertical impact force by using Equation (2). The angle and axial crush distances of the absorbers calculated using equations (7) and (8), respectively, are depicted in Figure 16 and Figure 17. The maximum vertical crush distance of the platform was greater than the axial crush distance of the inclined absorber. The difference is more obvious for model 2 due to its initial higher angle. 200 30 180 28 160 26 24
120
22
100
20
80
18
60
16
40
Vertical crush distance of platform Axial crush distance of absorber Angle of absorber
20 0 0
10
20
30
40
50
Angle (degree)
Distance (mm)
140
14 12 10 60
Time (ms) Figure 16. Vertical crush distance of the platform, axial crush distance of the absorber, and angle of the absorber for model 1.
25
200
45
180 40 160
Distance (mm)
120
30
100 25
80 60
Angle (degree)
35
140
20
40
Vertical crush distance of platform Axial crush distance of absorber Angle of absorber
20 0 0
10
20
30
40
15
10 50
Time (ms)
Figure 17. Vertical crush distance of the platform, axial crush distance of the absorber, and angle of the absorber for model 2.
Predicting the vertical load of a composite tube in a structure is meaningful in terms of its design. Given the axial compression ratio of the composite tube in the structure, its vertical load component can be calculated according to the angle θ; and the axial load obtained from the axial impact test on the single composite tube. If the compression ratio of the composite tube in the structural test does not match the reference data, the load can be calculated using an interpolation algorithm. After obtaining θ, the vertical load of the platform is obtained using Equation (7). The ratio of the composite tube length to the length of the entire absorber is 1:1.38 (237:327); therefore, the vertical load here conforms with those shown in Figure 9 (c). The initial angle θ0 of model 1 is 14°; therefore, the vertical component is located approximately between the curves of θ0 = 10° and θ0 = 20°. The initial angle θ0 of model 2 is 20°; therefore, its vertical component may be represented approximately with the curve of θ0 = 20°. The calculated vertical component is then compared with the result of loads measured with the two sensors, as shown in Figure 18 and Figure 19, where the horizontal axis represents the compression ratio of
26
the entire structure. The calculated vertical load decreased with the compression ratio during stage 1, coinciding with the experimental results. The vertical load in Figure 19 is flatter, as the initial angle θ0 of model 2 is greater. More energy can be absorbed in a case where stage 2 crushing is involved, although the vertical load exerted on the platform may be limited, and the increment for the configuration of model 2 equals 6% as interpreted in Table 2. The occurrence of stage 2 causes a lag in the test on the single tube. This may be attributed to the fact that the inertial load was alleviated when transferring from the platform to the sensors, after which the time to compress the absorbers was extended. Nevertheless, the experiment verified the design of the variable structure and the method to calculate the vertical component of absorbers mounted in such a structure. 50
Average vertical load Calculated vertical load
Ve rtical load (kN)
40
30
20
10
0 0. 0
0.1
0 .2
0.3
0.4
0. 5
0.6
Dime nsionless crush distance (1-H/H 0)
Figure 18. Vertical load for model 1.
27
0 .7
50
Average vertical load Calculated vertical load
Ve rtical load (kN)
40
30
20
10
0 0. 0
0.1
0 .2
0.3
0.4
0. 5
0.6
0 .7
Dime nsionless crush distance (1-H/H 0)
Figure 19 Vertical load for model 2
6.
Conclusions This paper presented an energy absorber with an inward-folding composite tube and its application in
forming a crashworthy structure. Experimental results show that the number of layers in 0° or close to 0° increase the crush load magnificently; the effect of Rf is more pronounced when the thickness of the laminate is close to Rf because a smaller Rf tends to destruct the laminate thoroughly. As a result of the absorber configuration, the crush load of increases during the latter half of the crushing due to the hollow tube filling with debris from the composite. This may consume more energy than a conventional structure but is hazardous to other structural components and the human body if the crush load is too high. A variable structure was then designed taking this shortcoming into account. A method to calculate the vertical load of the structure based on the experimental data from the singleabsorber test was demonstrated. The design of the variable structure and the load calculation were validated with impact tests on two models of a subcomponent in the cargo floor. The variable structure had a greater compression ratio and a flatter load curve, thus demonstrating its potential for use in the struts of the cargo floor of an aircraft.
28
Acknowledgments The authors acknowledge the support of the Natural Science Foundation of China (Grant No. 11372192).
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[39] Yu Z, Liu X, Wang J, You Q, Fu Y, Shock absorber with inward-folding composite tube and its application in legged landing gear. International Journal of Crashworthiness, Accepted, dx.doi.org/10.1080/13588265.2020.1718463 [40] Ghasemnejad H, Hadavinia H, Marchant D, Aboutorabi A. Energy absorption of thin-walled corrugated 32
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Conflict of interest statement We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled
Crashworthy Subfloor Structure of
Civil Aircraft via Inclined Inward-Folding Composite Tubes.
S1359-8368(19)35551-9
DOI:
https://doi.org/10.1016/j.compositesb.2020.107887
Reference:
JCOMB 107887
To appear in:
Composites Part B
Received Date: 20 October 2019 Revised Date:
29 January 2020
Accepted Date: 16 February 2020
Please cite this article as: Yu Z, Zhou X, Zhou X, Zhang Y, Zhu Q, Crashworthy subfloor structure of civil aircraft via inclined inward-folding composite tubes, Composites Part B (2020), doi: https:// doi.org/10.1016/j.compositesb.2020.107887. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Crashworthy Subfloor Structure of Civil Aircraft via Inclined InwardFolding Composite Tubes Zhefeng Yu, Xin Zhou, Xiang Zhou, Yangyang Zhang and Qiao Zhu Aerospace Structure Research Center, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China
Correspondence Information: Zhefeng Yu Associate professor School of aeronautics and astronautics Shanghai Jiao Tong University Email: [email protected] Room A423, Aero-Building, NO.800 Dongchuan Rd., Shanghai, 200240, P.R.China Email: [email protected] Tel & Fax: +86 21 34206387
Pages 33
Figures 19
Tables 2
2
Abstract: This paper describes the design and testing of a shock absorber with an inward-folding composite tube that can be used as a structural component in its normal working state. Although more energy can be absorbed when the hollow of the tube is filled with composite debris, a higher load relative to the initial peak load will be produced. A variable structure based on two inclined energy absorbers was then proposed, and impact tests used to verify the reaction load calculation for two models experimentally. Results indicate that.the variable structure had a greater compression ratio and a flatter load curve, demonstrating its potential for use in the struts of an aircraft cargo floor.
Keywords: shock absorber; inward-folding tube; subfloor; aircraft; variable structure
3
1.
Introduction Structural crashworthiness is an essential requirement in the design of passenger aeroplanes. The failure of
the ring frame and structure under the cargo-floor absorbs the main impact of energy during a crash. The structures involved in the energy absorption include frames [1][2], struts [3][4] and sine wave beams [5]-[8]. Early commercial aircraft were made mostly of aluminium and other metals. Aluminium has a considerable plastic deformation capacity. Metal structures can absorb significant amounts of kinetic energy during a large deformation while maintaining their structural integrity. In recent decades though, composite materials have been used more extensively to build aircraft structures, and as such their crashworthiness needs to be addressed. Components in the fuselage structure serve as energy absorbers in current crashworthy designs for composite fuselages [9][10]. Struts in the fuselage connecting the frame to the passenger floor and the cargo floor, are mostly made from brittle carbon fibre reinforced plastic (CFRP). The triggering mechanism that initiates progressive crushing of a strut can be a chamfer, a “steeple” [11][12], or a “tulip” [4][12] at the end of the strut that will initiate crushing when compressed by a flat surface. When the behaviours of thin-walled hollow squares and circular tubes with chamfer failure triggers are compared to those with steeple failure triggers [12], results show that steeple failure triggers for square tubes are more effective at maintaining a higher sustained crush load than chamfer failure triggers. The opposite effect is observed for circular tubes. The characteristics of geometric shape, fibre architecture, and trigger mechanisms of energy absorbers have been extensively investigated [13]-[15], and testing on various types of tubular structures has shown that composite materials can offer extremely high values of specific energy absorption (SEA) [16]-[20]. The SEA values ues of CFRP generally fall in the range of 50–80 kJ/kg [21]. Honeycomb tubular pipes inspired by bamboo [22][23] and natural fiber reinforced tubes[24][25], are some of the materials being used in bio-inspired composite structures. Examples are a strut with an open thin-walled section being used as a stanchion, though global and local buckling is more likely to occur for such a structure[26][27], where the SEA ranges from 20–60 kJ/kg under a progressive crushing movement [28].
4
To achieve the higher energy absorption and a more stable crush, the failure-triggering method may be adopted in combination during the processing and fabrication of a composite strut that is part of a complex structure. Heimbs [29] presents a solution under axial crushing by cutting composite tubes into strips using a special joint. Tong et al. [30] proposed an external chamfer trigger with a semi-circular cavity. This guides the composite tube towards being fully crushed by increasing the degree of bending of the fibres and squeezing the composite matrix. Siromani et al. [31] conducted a study on the effect of an inward-folding cap on the energy absorption capability of CFRP tubes under axial compression. The cap was not applied to a structure. Ueda et al. [32] designed a double-sided plug to trigger the crushing of a CFRP tube that could be utilized to control SEA by changing its geometric parameters. A crashworthy structure is more likely to be subjected to oblique loadings under real conditions. The peak force and the deformation values decrease as the oblique angle increases [33]. The value of the SEA of a composite tube under a loading angle of 15° will decrease by 20% compared to that with an axial load [34]. The tube could be also subjected to bending load under an oblique load, but if the pivot joint is adopted, the oblique load could be transformed to an axial load. The work of Heimbs [29] also concerned a strut subjected to axial crushing, which avoided the catastrophic failure of the strut. A novel strut system with corrugated composite plate and hinge joints was proposed by Ren et al [35]; the axial impact load would be transferred to the plate during impact process for the hinge joints, which provides the robust progress failure of the composite plate. The energy absorption of a subcomponent of an aircraft structure can be evaluated in two ways. Firstly, the structure is fixed at the base such that the impact is produced when a weight is dropped on it [26][36]. Secondly, the subcomponent, mostly the fuselage section, is lifted and dropped to impact the ground [37][38]; this method is effective to simulate the transference of the load caused by the inertia of the payload and passengers in the fuselage. The authors [39] proposed a shock absorber consisting of a composite tube, crush cap, and pressing cap, and applied it to the legged-landing gear of a drone. In this study the absorbers are experimentally tested by varying the effects of layer configuration. The configuration of the absorber allows debris to fill the hollow
5
tube and enhances energy absorption when the composite tube is crushed to more than half its length, however, the increasing reaction force exerts a higher load on the payload on the structure. A schematic representing the subfloor structure of an aircraft is proposed to demonstrate the utilization of energy absorption of the self-filling effect controlling the high load at this stage. The absorbers were assembled at an angle that inclined away from the impact direction, and while the angle changes as the entire structure crashes, the absorber is subjected to axial load and therefore is crushed steadily. The method of calculating the reaction force was addressed and validated with the crash tests.
2.
Characteristics of the energy absorber
2.1 Configuration of the energy absorber The configuration of the energy absorber is depicted in Figure 1. It consists of a crush cap, a pressing cap, and a composite tube. The composite tube is connected to the two caps with rivets. The caps can be pivotjointed to a structure using lugs. Such a design ensures that the absorber is only subjected to the axial load during a crash thereby avoiding catastrophic failure due to a moment of bending. The pressing cap has a flat inner end-surface that will not destroy the composite tube during the compression load. The crush cap has a triggering fillet with radius Rt that will trigger the failure of the composite tube, and the inverted surface with radius Rf folds the delaminated tube. When the folded tube reaches the pressing cap, the debris will begin to fill the hollow and thereby increase the reaction load. The initial length of absorber is denoted as La0 and that of the composite tube is denoted as Lt0 (Figure 1 (a)). As the composite tube is crushed, the lengths of the absorber and composite tube decrease and are denoted as La and Lt respectively (Figure 1 (b)).
6
(a)
(c)
(b)
Pressing cap
Rivets hole
La
Lt
La0
D
Lt0
tw
Composite tube
Delaminations Rf Rt
Crush cap
Figure 1. Principles of the absorber: (a) structural configuration, (b) scenario when crushing begins, (c) scenario after the crushed composite tube reaches the pressing cap.
2.2 Behaviour of energy absorber under dynamic load The characteristics of the energy absorber under axial impact were demonstrated through a dropping hammer test. The composite tube is made from T700 carbon-fibre/epoxy prepreg unidirectional tape laid in a sequence of [0/90]4, where the tapes at 0° coincide with the axis of the tube. The mechanical parameters provided by the supplier are: tensile modulus is 120 GPa, tensile strength is 2000 MPa, compressive strength is 1050 MPa, interlaminar shear strength is 55 MPa. The composite tubes have an outer diameter D of 30 mm. The thickness of the composite tube is 1.5 mm and the length is 120 mm. The density of the tube is 1.53×103
7
kg/m3. The crush cap with Rt = 3 mm and Rf = 7 mm is made of chrome-plated steel. No lugs were made on the caps for easy installation for the test. The impact tests were conducted with a dropping tower as shown in Figure 2, which is capable of lifting a 500 kg drop hammer to a height of 1.7 m. An optical sensor was used to measure the impact velocity. In this experiment, a drop hammer with a mass of 63 kg was lifted by a pulley to a height of 1.5 m and then released from a quick-release hook. A PCB-200C20 force sensor was mounted on the base to measure the force of the impact.
Quick-release hook Dropping hammer
Linear bears Pulley
Optical sensor Pressing cap Bumper Crush cap
Composite tube
Force Sensor
Figure 2. Impact test setup.
8
The impact force was recorded using a data acquisition instrument sampling at a frequency of 100 kHz, Figure 3 (a). The acceleration of the hammer was calculated from the impact force, and the velocity at time t was obtained by integrating the acceleration over the time using the Simpson algorithm, as follows:
= + −
(1)
where g is acceleration due to gravity, F(t) is the measured impact load, and m is the mass of the hammer. The displacement of the hammer from the location at which it contacts the absorber at time t, i.e. the real-time crush distance of the composite tube, is given by the following equation: = +
−
d d
(2) The plot of the impact force versus crush distance is shown in Figure 3 (b), where the load begins to increase at a crush distance of 60 mm, i.e. half the length of the tube. For convenience of comparing the behaviour of absorbers of different lengths, dimensionless distance is introduced as follows: =
=
(3)
where at bottoming out is also called stroke efficiency (SE) [40]. The impact force was then plotted versus dimensionless distance as shown in Figure 3 (c). There are two main stages apart from the initiation of the tube failure. Stage 1 shows a steady force, while the impact load in stage 2 gradually increases due the tube becoming filled with composite debris. 20
(a)
Load (kN)
15
10
5
tw = 1 .5 mm , R f = 7 m m, R t = 3 mm , D = 3 0 m m 0 0
5
10
15
T im e ( ms )
9
20
25
30
20
(b) Load (kN)
15
10
5
tw = 1 .5 m m , R f = 7 m m , R t = 3 m m , D = 3 0 m m 0 0
20
40
60
80
100
C ru s h d i s t ac n e (m m )
20
(c) 15
Load (kN)
Stage 1 10
Stage 2 5
t w = 1.5 m m, R f = 7 mm , R t = 3 m m, D = 30 m m 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Dimensionle ss cr ush dista nce (1- Lt/Lt0 )
Figure 3. Load curves of the absorber under dynamic load plotted against: (a) time, (b) crush distance and (c) dimensionless crush distance.
One of the characteristics of crash tubes, crush force efficiency (CFE) can be calculated by !" =
#$%& ()*+,& -.)($
#%/ * & %0 (.00%1+$ -.)($
(4)
In Figure 3, the initial peak load is 11.4 kN, and the mean load in stage 1 9.8 kN, hence the CFE is 0.86. This means that the absorber is applicable to situations where the allowable load equals the initial peak if all of the energy can be absorbed in stage 1. In this situation, the SE is less than 0.5. If the allowable load is higher, energy absorption in stage 2 can be utilized, increasing the total energy absorbed. To evaluate the energy absorption due to the filling up of debris, the SEA is calculated with the contact force and the crush distance by:
2"3 =
4
5 6
10
78
(5)
where 9 and 3 are the mass density and cross-sectional area of the composite tube, respectively. The SEA in stage 1 is equal to 47.3 kJ/kg, while it reached 53.3 kJ/kg when stage 2 was included, increasing by 12.7 %. The SE of data in Figure 3 is 0.7. If a high load had been applied, a higher SE would have been obtained until breaking of the tube due to high internal pressure.
2.3 Parametric analysis by experiments Since the materials of construction of the tube parameters affect the performance of the absorber, including layer configuration, wall thickness, Rf and Rt, it is necessary to investigate these before applying the absorber to a structure. Specimens were listed in Table 1, where the each specimen has an outer diameter of 30 mm, and length of 120 mm. Two thicknesses were considered, 2 mm and 1.5 mm. For the 2 mm tube, the effects of layer configuration were studied. The first layer number refers to the first inside layer of the tube. Specimens IF-03 and IF-04 were used to investigate the effect of layer configuration of [45/-45]5 and [15/15]5;, however, considering the stability of the manufacture process, two plies [90/-45] and [90/-15] were laid up on the mould first before other plies were laid up. Table 1. Layer configuration, thickness, Rf and crashworthiness characteristics of the tested specimens.
Specimen
Layer
tw
Rf
Mean load
SEA
configuration
(mm)
(mm)
(kN)
(kJ/kg)
IF-01
[90/-45/0/45]3
2
5
22.7
84.4
IF-02
[90/0]6
2
5
26.3
97.6
IF-03
[90/-45(45/-45) 5]
2
5
17.0
63.1
IF-04
[90/-15(15/-15)5]
2
5
25.7
95.6
IF-05
[90/0]6
2
7
21.0
81.7
IF-06
[90/0]6
2
12
20.0
74.2
11
IF-07
[90/0]4
1.5
5
9.8
47.8
IF-08
[90/0]4
1.5
7
9.6
46.9
IF-09
[90/0]4
1.5
12
9.0
44.0
Our tests show that the tube resisted inward folding and broke up when Rt was less than 3 mm, consequently Rt is equal to 3 mm for all of the specimens. For low velocity crashes, the performance of the composite absorber was evaluated via quasi-static tests that were carried out using an MTS servo-hydraulic system capable of providing a 50 kN static load. The loading was applied under displacement control mode, at a rate of 10 mm/min. As we were most interested in the results of the steady load of stage 1, the test was ceased at the beginning of stage 2. The specimen with layer configuration of [90/0]6 after static test are shown in Figure 4, where the effect of Rf on the folding mode are obvious; the crash cap with smaller Rf bends the tube wall more seriously. The longitudinal cross section of the composite tube after test was shown in Figure 5; the wall of composite tube was delaminated thoroughly and compacted.
12
tw=2 mm, Rf=5 mm
tw=2 mm, Rf=7 mm
tw=2 mm, Rf=12 mm
tw=1.5 mm, Rf=5 mm
tw=1.5 mm, Rf=7 mm
tw=1.5 mm, Rf=12 mm
Figure 4. Post-dynamic-test conditions of the specimen
13
Figure 5. Longitudinal cross-section of the specimen. The effects of layer configuration are shown in Figure 6, where the load of specimens IF-02 is the highest; the loads of IF-04 and IF-02 are similar; the load of IF-01 is lower and that of IF-03 is the lowest. The comparison between the load of IF-03 and IF-04 shows that the load increases magnificently when the layer angle approaches to 0°; IF-01 has more layers in 0° compared with IF-03, so it has a higher load; IF-02 has the most 0° layers, so it has the highest load. 50
Load (kN)
40
30
20
IF-01 IF-02 IF-03 IF-04
10
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dimensionless crush distance (1-Lt/Lt0 )
Figure 6. Load curves of absorbers with different layer configuration under static load. The SEA values were calculated using the steady load in stage 1, as listed in the right-hand column of Table 1. The SEA of a tube with the layer configuration of [90/0]6 is highest in this study. This type of tube is easier to obtain, and thus used more often. The effects of Rf on the absorbers with 1.5 mm and 2 mm thick walls are shown in Figure 7, where all of the tubes have a layer configuration of [90/0]6. The three crush caps have the same Rt, which is 3 mm, and different Rf‘s of 5 mm, 7 mm and 12 mm, respectively. The SEA values of absorbers with tubes of 2-mm wall thickness range from 74.2 kJ/kg to 97.6 kJ/kg, and those of absorbers with tubes of 1.5-mm wall thickness range from 44.0 kJ/kg to 47.8 kJ/kg. This indicates that the effect of Rf on increasing the SEA is more significant for 2 mm tubes than for of 1.5 mm tubes.
14
40
IF-02, tw=2 mm, Rf=5 mm IF-05, tw=2 mm, Rf=7 mm IF-06, tw=2 mm, Rf=12 mm
35
Load (kN)
30 25 20
IF-07, tw=1.5 mm, Rf=5 mm 15
IF-08, tw=1.5 mm, Rf=7 mm IF-09, tw=1.5 mm, Rf=12 mm
10 5 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dimensionless crush distance (1-Lt/Lt0 )
Figure 7. Load curves of absorbers with different Rf under static load.
3.
Variable structures with inclined absorbers
3.1 Principles of the variable structure The schematic of a variable structure, designed to utilize the energy absorption of stage 2 while avoiding the exertion of a higher vertical load on the structure, is shown in Figure 8. The profile drawn as a dashed line represents the initial state. A pair of absorbers are used as stanchions at a θ0 angle inclined to the vertical. The horizontal distance of the two joints of one absorber is denoted W and is assumed to be a constant. When a vertical load Fv caused by the deceleration of the mass on the platform is exerted on it, the platform is vertically deformed because the composite tubes are crushed in their axial direction. The vertical crush distance of the platform is denoted : and can be calculated using Equation (2) as well as , with !; produced by the decelerated payload. The height of the absorber is denoted with H0 and H in the initial and deformed states, respectively. The angle θ0 is then replaced by θ in the deformed state, so that the resultant reaction force of the two absorbers is as follows: !; = 2!/ =>?@
(6)
where Fx is the axial load of the absorber, which is dependent on the dimensionless crush distance for a certain composite tube and crush cap. The angle θ is given by the following:
15
E
@ = sin D F = sin D F
E
G
(7)
As the absorbers become shorter, θ increases. The resultant vertical force decreases to below the axial load in stage 1 and decreases further in stage 2 as θ increases. If the proper parameters are chosen, the resultant force will not exceed the permitted load in stage 2 and the energy absorbed during that stage due to the compacting of composite debris will be utilized effectively for impact mitigation. The method to calculate the vertical reaction load of the platform is given below. The crush distance of the composite tube is then found as follows: = HI − HI = HI −
F
JKL M
= HI −
F G JKL M
(8)
The dimensionless crush distance of the composite tube in the structure is defined in Equation (3). The resultant vertical force of the absorber is then given by Equation (6). If the length of the absorber in the structure is different from that of the single absorber employed in the dynamic test to obtain its load curve, it can be interpolated in terms of the dimensionless crush distance to produce the new load curve. To evaluate the performance of the entire structure as an energy absorption component, its dimensionless crush distance is defined as follows: F F NNN : = FG = F
where : is the vertical crush distance of the platform.
16
(9)
Fv
:
Payload platform Floor beam
F x θ0 H0
Fx
θ W
H
Energy absorber
Frame
Figure 8. Schematic of the variable structure.
3.2 Parametric analysis The resultant vertical force of the inclined absorber is dependent on the initial angle @ and the crush distance. The height of the structure is related to the length of the entire absorber, although only the composite tube can be compressed. Therefore, the ratio of the length of the composite to the absorber, denoted tube ratio Lt0: La0, also affects the behaviour of the platform. In this sub-section, the effects of these parameters are demonstrated. In Figure 9 the vertical forces of one absorber with different values of @ , are plotted versus the dimensionless crush distance of the entire structure, denoted NNN : . The data for @ = 0 was obtained from an axial test on a single absorber with tw = 1.5 mm, Rt = 3 mm, and Rf = 7 mm, as shown in Figure 3. The final dimensionless crush distance of the tube is 0.73. Three ratios of Lt0:La0, i.e. 1:1, 1:1.2, and 1:1.4, were
17
considered in the analysis. The two latter cases represent a situation in which the length of two caps were considered in terms of the total length of the absorber. As θ0 increased, the slope of the load curve decreased and the of the platform increased. In Figure 9 (a), when θ0 = 20° and 30°, NNN δ: reaches 1.0, which indicates that the final angle reached 0° and the residual length La was equal to W. The load curve for absorbers with Lt0:La0 = 1:1.2 and 1:1.4 are shown in Figure 9 (b), and Figure 9 (c), respectively. Due to the total length of the absorber increases when the caps were considered, the angle θ when the tube was crushed was less than that of the absorber with a higher tube ratio. The load curve for θ0 = 20° shown in Figure 9 (b) is flatter than that shown in Figure 7 (a), and then can consume more energy with a load lower than the initial peak. For the curves in which θ0 = 30° in each of the figures, the load at the end of crash is lower than the initial peak, but may be unable to support the gravity of the platform. 20
Ve rtical load (kN)
?0=0°
(a)
18
?0=10°
16
?0=20°
14
?0=30°
12 10 8 6 4 2 0 0. 0
0. 1
0. 2
0. 3
0. 4
0. 5
0 .6
0 .7
0 .8
0 .9
Dime nsionless crush distance (1-H/H 0)
18
1 .0
1 .1
20
Ve rtical load (kN)
? 0= 0°
(b)
18
? 0= 10°
16
? 0= 20°
14
? 0= 30°
12 10 8 6 4 2 0 0. 0
0. 1
0. 2
0. 3
0. 4
0. 5
0 .6
0 .7
0 .8
0 .9
1 .0
1 .1
D ime ns io nless cru sh d istan ce (1 -H /H 0)
20
Ve rtical load (kN)
? 0= 0°
(c)
18
? 0= 10°
16
? 0= 20°
14
? 0= 30°
12 10 8 6 4 2 0 0. 0
0. 1
0. 2
0. 3
0. 4
0. 5
0 .6
0 .7
0 .8
0 .9
1 .0
1 .1
D ime ns io nless cru sh d istan ce (1 -H /H 0)
Figure 9. The vertical loads plotted against the crush distance of platforms with different initial angles and tube ratios: (a) Lt0/La0 = 1:1, (b) Lt0/La0 = 1:1.2, and (c) Lt0/La0=1:1.4. Three tests were carried out on this type of specimen, and the load curves similar to those shown in Figure 9 were obtained. The SEA is calculated for each curve with the initial peak as the allowable load (Table 2). The crush length includes all of stage 1 and the part of stage 2 where the vertical load is lower than the allowable load, and no more energy will be taken into account if La decreases to W. The SEA increases at θ0=10 ° and θ0=20 ° due to the energy in stage 2 is involved. While, the SEA decreases at θ0=30 °for tube
ratios Lt0/La0=1:1 and Lt0/La0=1:1.2, because the final crush distance of the tube decreases due to La decreases to W. As the entire curve was used to calculate the SEA for tube ratio Lt0/La0=1:1.2, including the stage where the load descends, the maximal increment of SEA at 11.3%. 19
Table 2. The SEA of absorber with different initial angles and tube ratios in the situation that the vertical load less than the initial peal load. Lt0/La0 = 1:1
Lt0/La0 = 1:1.2
Lt0/La0 = 1:1.4
Initial angle SEA (kJ/kg)
Increment
Increment
(%)
SEA (kJ/kg)
0
47.9 VX. VW.X
—
10
48.1 VX.[ VX.
20 30
(degree)
4.
Increment
(%)
SEA (kJ/kg)
47.9 VX. VW.X
—
47.9 VX. VW.X
—
0.4
48.0 VX. VW.\
0.2
48.0 VX.D VW.\
0.2
51.4 ^D.^ ^D.
7.3
50.3 ^.^ ^.D
5.0
50.0 ^. V\.X
4.4
47.8 VW.X VW.X
-0.2
49.7 V\.W V\.W
3.8
53.3 ^[.V ^[.D
11.3
(%)
Experiment and Materials
The subcomponent of the cargo floor was fabricated with two absorbers as stanchions, as shown in Figure 10. The metal floor beam and fuselage frame were fixed to the linear bars that support them; similar to the adjacent structures in a fuselage. Both of the absorbers consist of composite tubes with La0 = 327 mm, Lt0 = 237 mm. The two absorbers in this structure were much longer than those in the previous experiment, therefore more energy was needed to crush them. Considering the difficulty in conducting the impact test with higher energy, the absorber with relatively lower crush load was adopted, with tw = 1.5 mm, Rf = 7 mm and Rt = 3 mm. White ticks spaced at 20 mm intervals were drawn on the tubes to indicate the crush distance, but more accurate crush distances were calculated using acceleration demonstrated in sub-section 2.2. Two force sensors were installed on the base to measure the vertical load during the crash. Two steel blocks were put on the top of sensors to transmit the impact load to the sensors. The following two models with different structures and geometric parameters were adopted: model 1 where W = 80 mm, θ0 = 14°, and model 2, where W = 116 mm θ0 = 20°.
20
Linear bear Payload Pivot Floor beam
Pressing cap Absorbers Crush cap Pivot
Fuselage frame
Protecting block Left force sensor
Right force sensor
Figure 10. Crash test setup on a subcomponent of a cargo airplane floor.
The payload had a mass of 180 kg and the dropping height for model 1 was 1.6 m; thus, the impact had a velocity of 5.6 m/s and an energy of 2822 J. In the test for model 2, the dropping height was increased to 1.7 m to increase the compression of the absorber. Bumpers were used to protect the models from being crushed, and the crash procedures were recorded with a high-speed camera.
5.
Results and Discussion High-speed camera photographs of different moments in the two tests are shown in Figure 11 and Figure
12, respectively, demonstrating that the crush procedure was steady and the structure maintained its integrity during the crushing of the composite tubes. The vertical crush distance of the platform, : , shown in Figure 11 and Figure 12, was calculated using the acceleration of the platform based on the impact load. The two absorbers after the testing of model 2 are shown in Figure 13; the rivets of the pressing cap are intact while the rivets on the other ends were severed, and the corresponding ends crushed.
21
0 ms, : =0 mm
15 ms, : = 74 mm
30 ms, : = 130 mm
45 ms, : = 166 mm
Figure 11. High-speed camera photographs of the crash test on model 1.
0 ms, : =0 mm
13 ms, : =77 mm
26 ms, : =138 mm
39 ms, : =181 mm
Figure 12. High-speed camera photographs of the crash test on model 2.
22
Crushed ends
Rivets
Figure 13. Post-dynamic-test conditions of the two absorbers of model 2. The impact loads measured by the two sensors are shown in Figure 14 and Figure 15. The initial load is high as a result of the hard contact between the metal fuselage frame and the protecting block. The load histories of the left- and right-hand sensors were similar. For model 1, all of the kinetic energy was absorbed by the composite tube, where the descent of the loads at the end of the crash is depicted by the dashed line in Figure 14. In the test on model 2, where higher impact energy was applied, the platform made contact with the polyurethane bumpers before stopping, depicted by the dashed line in Figure 15. The dashed curves could not be predicted based on the axial load obtained from the axial impact test on the single composite tube, therefore these parts of the data will not be incorporated in the analysis.
23
40
Right Left
35
Vertical load (kN)
30 25 20 15 10 5
The end of impact 0 0
10
20
30
40
50
60
Time (ms) Figure 14. Impact load measured by the left- and right-hand sensors of model 1.
30
Right Left
Vertical load (kN)
25
20
15
The declining due to the contact with bumpers 10
5
0 0
10
20
30
40
50
60
70
80
90
100
110
Time (ms) Figure 15. Impact load measured by the left- and right-hand sensors of model 2.
24
The vertical crush distance of the platform, the axial crush distance of the absorbers, and the angle of the absorber can be observed, approximately, from the digital image, with accurate results calculated using the measured force. The crush distance of the platform, 1 , is calculated using the vertical impact force by using Equation (2). The angle and axial crush distances of the absorbers calculated using equations (7) and (8), respectively, are depicted in Figure 16 and Figure 17. The maximum vertical crush distance of the platform was greater than the axial crush distance of the inclined absorber. The difference is more obvious for model 2 due to its initial higher angle. 200 30 180 28 160 26 24
120
22
100
20
80
18
60
16
40
Vertical crush distance of platform Axial crush distance of absorber Angle of absorber
20 0 0
10
20
30
40
50
Angle (degree)
Distance (mm)
140
14 12 10 60
Time (ms) Figure 16. Vertical crush distance of the platform, axial crush distance of the absorber, and angle of the absorber for model 1.
25
200
45
180 40 160
Distance (mm)
120
30
100 25
80 60
Angle (degree)
35
140
20
40
Vertical crush distance of platform Axial crush distance of absorber Angle of absorber
20 0 0
10
20
30
40
15
10 50
Time (ms)
Figure 17. Vertical crush distance of the platform, axial crush distance of the absorber, and angle of the absorber for model 2.
Predicting the vertical load of a composite tube in a structure is meaningful in terms of its design. Given the axial compression ratio of the composite tube in the structure, its vertical load component can be calculated according to the angle θ; and the axial load obtained from the axial impact test on the single composite tube. If the compression ratio of the composite tube in the structural test does not match the reference data, the load can be calculated using an interpolation algorithm. After obtaining θ, the vertical load of the platform is obtained using Equation (7). The ratio of the composite tube length to the length of the entire absorber is 1:1.38 (237:327); therefore, the vertical load here conforms with those shown in Figure 9 (c). The initial angle θ0 of model 1 is 14°; therefore, the vertical component is located approximately between the curves of θ0 = 10° and θ0 = 20°. The initial angle θ0 of model 2 is 20°; therefore, its vertical component may be represented approximately with the curve of θ0 = 20°. The calculated vertical component is then compared with the result of loads measured with the two sensors, as shown in Figure 18 and Figure 19, where the horizontal axis represents the compression ratio of
26
the entire structure. The calculated vertical load decreased with the compression ratio during stage 1, coinciding with the experimental results. The vertical load in Figure 19 is flatter, as the initial angle θ0 of model 2 is greater. More energy can be absorbed in a case where stage 2 crushing is involved, although the vertical load exerted on the platform may be limited, and the increment for the configuration of model 2 equals 6% as interpreted in Table 2. The occurrence of stage 2 causes a lag in the test on the single tube. This may be attributed to the fact that the inertial load was alleviated when transferring from the platform to the sensors, after which the time to compress the absorbers was extended. Nevertheless, the experiment verified the design of the variable structure and the method to calculate the vertical component of absorbers mounted in such a structure. 50
Average vertical load Calculated vertical load
Ve rtical load (kN)
40
30
20
10
0 0. 0
0.1
0 .2
0.3
0.4
0. 5
0.6
Dime nsionless crush distance (1-H/H 0)
Figure 18. Vertical load for model 1.
27
0 .7
50
Average vertical load Calculated vertical load
Ve rtical load (kN)
40
30
20
10
0 0. 0
0.1
0 .2
0.3
0.4
0. 5
0.6
0 .7
Dime nsionless crush distance (1-H/H 0)
Figure 19 Vertical load for model 2
6.
Conclusions This paper presented an energy absorber with an inward-folding composite tube and its application in
forming a crashworthy structure. Experimental results show that the number of layers in 0° or close to 0° increase the crush load magnificently; the effect of Rf is more pronounced when the thickness of the laminate is close to Rf because a smaller Rf tends to destruct the laminate thoroughly. As a result of the absorber configuration, the crush load of increases during the latter half of the crushing due to the hollow tube filling with debris from the composite. This may consume more energy than a conventional structure but is hazardous to other structural components and the human body if the crush load is too high. A variable structure was then designed taking this shortcoming into account. A method to calculate the vertical load of the structure based on the experimental data from the singleabsorber test was demonstrated. The design of the variable structure and the load calculation were validated with impact tests on two models of a subcomponent in the cargo floor. The variable structure had a greater compression ratio and a flatter load curve, thus demonstrating its potential for use in the struts of the cargo floor of an aircraft.
28
Acknowledgments The authors acknowledge the support of the Natural Science Foundation of China (Grant No. 11372192).
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Conflict of interest statement We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled
Crashworthy Subfloor Structure of
Civil Aircraft via Inclined Inward-Folding Composite Tubes.