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A mathematical model of frictional damage to parachute canopy
Author’s Accepted Manuscript A mathematical model of frictional damage to parachute canopy Haishan Teng, D.Y. Li
www.elsevier.com/locate/jtri
PII: DOI: Reference:
S0301-679X(16)30338-3 http://dx.doi.org/10.1016/j.triboint.2016.09.030 JTRI4377
To appear in: Tribiology International Received date: 14 August 2016 Accepted date: 18 September 2016 Cite this article as: Haishan Teng and D.Y. Li, A mathematical model of frictional damage to parachute canopy, Tribiology International, http://dx.doi.org/10.1016/j.triboint.2016.09.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.
1
A mathematical model of frictional damage to parachute canopy Haishan Teng1,2,3, D.Y. Li2* 1
National University of Defense Technology, Changsha, Hunan, China Dept. of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 1H9 3 Beijing Institute of Space Mechanics & Electricity, China 2
*Corresponding author: [email protected] Abstract The damage to parachute canopy caused by friction involves a number of parameters, including material properties, pressure, sliding velocity and surface condition, etc. A theoretical model is proposed to analyze the friction process and help evaluate effects of the parameters on the damage to parachute canopy. Relevant prevent-burn tests were performed to validate the model, which is built with the aim of providing relevant information or clues for parachute design and material selection. Keywords: Parachute, Damage, Friction, Mechanism, Prediction 1. Introduction Parachute is a type of aerodynamic decelerator, which has a wide range of applications. Parachute may fail when is over-loaded, but damage often occurs under lower load conditions. It is noticed that the damage is triggered by local melting or burn caused by frictional heat. Fig.1 illustrates local burned areas on parachute canopies
Fig.1 Local melt or burn is observed on canopies.
2
Although the damage to parachutes is a crucial issue, reported studies in the literature are rather limited. In general, damages may occur mainly during the process of deployment and inflation. When a canopy is pulled out from a bag at a high speed under certain pressure, a considerably large amount of heat could be generated due to the friction between the canopy and the bag as well as that between various parts of the canopy in contact. The frictional heat could markedly raise the local temperature, leading to local melt or burn of the canopy material. Besides, during the initial inflating process, the top of canopy swings quickly and even causes whipping, which may accelerate the canopy’s damage process [1]. Other factors may also contribute to the damage of canopy, such as the friction between parachute and supportingstructure, so-called “ring sail” caused by lateral wind, and twining occurs around the top hole of parachute, etc [2,3]. The present study is focused on the damage to the parachute canopy caused by frictional heating. The canopy’s damage is a complex process, involving various factors, among which the material used to make the parachute is one of key factors. The canopy’s material is generally treated for enhanced anti-burning capability and lowered friction [4]. However, damage to the parachute canopy may not be completely prevented. In order to avoid fatal risk resulting from the parachute damage, efforts must be made to identify factors that affect the friction process and determine critical parameters that can be controlled to prevent damage to parachute. Although research on friction of canopy materials is quite limited, there are many studies on friction of textile reported in the literature. For instance, M.A. Bueno and R.Bocquet built a brush model to predict the friction of hairy textile fabrics [5,6]. V K Kothari and M K Gangal looked into static and kinetic friction processes of some woven farics using different contacting surfaces by [7]. Roughness and frictional properties of cotton and polyester woven fabrics were investigated by V. Sülara [8]. These studies help to understand friction of canopy and associated damages when it is overloaded. There are also some theoretical studies on the whip phenomena [9,10]. However, research on the damage caused by frictional heating is much less and more limited to qualitative analysis. Vasilis Lavrakas described the influence of coefficient of friction [11], which was informative but not sufficient for guiding control of such risk. For example, when analyzing the damage caused by high-speed friction, no information is provided regarding the range of high speeds at which canopy could be overheated and damaged. Without such information on friction, heat generation and transfer, and loading condition, it is difficult to select
3
optimal materials and design reliable parachutes. Due to insufficient understanding of the Canopy’s damage caused by friction, the authors are motivated to conduct this study in order to identify crucial factors that can be controlled to minimize the risk of parachute failure. 2. Theoretical analysis 2.1 Physical processes and model construction The parachute’s opening process consists of canopy deployment and inflation. As shown in Fig.2, the parachute canopy is originally packed in a bag. When the procedure is commenced, the canopy is pulled out from the bag at a high speed. During the pulling process, friction between different portions of the canopy in contact and that between the canopy bag can be high enough to generate a considerable amount of frictional heat, which may burn and damage the canopy.
Fig. 2 Schematic illustration of parachute canopy packing and friction during the opening process.
Based on the physical configurations shown in Fig.2, a model system with a simplified configuration is proposed to deal with the friction between the canopy and the bag as illustrated in Fig.3. Since the fabric is light, compared to the pressure and frictional force, the surfaces in contact are drawn horizontally in order to facilitate relevant analysis. It makes no difference no matter the sliding surface is placed horizontally or with an angle relative to the horizontal plane. The model is general for analyzinge friction between different portions of canopy in contact. When the canopy is pulled out from the bag, friction occurs between the contact areas.
4
Fig. 3 A simplified configuration for modeling friction between folded canopy and bag during the pulling process.
In order to facilitate friction analysis while keeping the generality, the following assumptions are made: 1) Under certain pressure and at high speeds of pulling, the flexibility and deformation of canopy and its counter-face during sliding are ignored. 2) Since the canopy is folded tightly under pressure, air between layers is very little. With little air present, thermal convection and thermal radiation are rather limited, which are thus ignored. 3) The canopy is a network of fibers and the number of fibers in a space of one minimeter is
several dozen. Since a local burning damaged area is usually on the scale of centimeter or at least minimeter, it is assumed that the surfaces under study are continuous and smooth. As for the influence of the surface roughness, this can be reflected by the friction coefficient (measurable). 4) In the present case of dealing with fabrics, the influence of gravity is ignored.
In the model, the bag is denoted as body A and the canopy as body B. They move relative to each other. During the pulling process, body A is always in contact with a moving B, thus it experiences friction for a longer sliding distance than that of body B. Since heat transfer needs to be taken into account, each of A and B consists of two parts as shown in Fig.4; one is the top surface layer under friction action and the other is the layer beneath the top surface layer, which plays a role in heat transfer. For details, A is divided to two layers for analysis, A1 and A2. A1 is in direct contact with its counter-face, in which temperature increases rapidly when subjected to
5
friction. Since it is thin, the difference in temperature within this layer is ignored. A2 is thicker and plays a role in heat conduction. Thus, there is temperature gradient within A2. Similarly, B is also divided to two layers and analyzed in a similar manner. Although canopy can be folded in different ways, the involved friction processes are similar when the canopy is pulled out. Thus, the proposed model is general. Friction occurred at the intersection of layers A1 and B1, and the heat produced by friction is treated as heat-source. The heat was absorbed by A1 and B1, and transfer to the outer layers A2 and B2. We may simplify this process as a one-dimension transfer-heat process. See figure 4.
Fig.4 A simplified model for analyzing friction and heat transfer processes.
In realistic situation, canopy B is the part suffering from damage. Thus, part B is the target object for analysis. For part A, since its heat transfer and dismiss are similar to those of part B, the treatment applied to part A was the same as that for part B. 2.2 Heat equilibrium The heat equilibrium equation for B1 is expressed as Qin _ B1 EB1 Qout _ B1 .............................................................（1）
where ΔEB1 is the increment of internal energy of B1, Qin_B1 the frictional heat entering into B1，and Qout_B1 is the heat that is conducted away from B1. Qin _ B1 QT k B1 .........................................................................（2）
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where QT is the generated heat, kB1 is the heat transfer ratio, defined as the ratio of heat in B1 to the total heat generated during the sliding process. The heat comes from the mechanical work done by the frictional force, part of which results in material’s deformation and the rest is converted to heat as equation (1) expresses:
QT W friction Edef
..............................................................（3）
where Edef is the deformation energy, and Wfriction is the work done by the frictional force, which is expressed as W friction p AB1 v t ...........................................................（4）
where p is pressure, AB1 is the area of contact, μ the coefficient of friction, v the velocity of friction, and t is the duration of the friction process. The increment of B1’s internal energy can be calculated as
EB1 mB1 C p _ B1 TB1 ..........................................................（5） where Cp_B1 is specific heat of B1, ΔTB1 the rise in temperature of B1 and mB1 is the mass of layer B1, where is given as mB1 B1 AB1 B1 ....................................................................（6）
where ρB1 is the density of material (B1), AB1 is the area of contact, and δB1 is the thickness of layer B1. The heat equilibrium equation for B2 is expressed as
Qout_ B1 Qin _ B 2 Qconduct_ B 2 Qconvect _ B 2C ...........................（7） where Qconvect_B2-C is the quantity of heat dismissed through convection from B2. Qconduct_B2 is the quantity of heat conducted away from B2, and we have
Qconduct_ B 2 B 2 AB 2
TB 2
B2
t ................................................（8）
where λB2 is thermal conductivity of B2, AB2 is the area of heat transfer, ΔTB2 the difference in temperature between the two sides of layer B2, δB2 the thickness of B2, and t is the time of heat transfer. As a matter of fact, the conducted heat, Qconduct_B2, is equal to the increment of B2’s internal energy i.e.
Qconduct_ B 2 EB 2 mB 2 C p _ B 2 TB 2
.................................（9）
7
where Cp_B2 is specific heat of B2, ΔTB2 is the rise in temperature of B2 and mB2 is the mass of layer B2., and mB 2 has the following expression: mB 2 B 2 AB 2 B 2 .................................................................（10）
where ρB2 is the density of material (B2), AB2 is the area of contact, and δB2 is the thickness of layer B2. Besides, we have
Qconvect _ B 2C hB 2C AB 2 TB 2C t ............................. ……..........（11） where hB2-C is the convective heat transfer coefficient, AB2 is the area of heat-transfer, and t is the time of heat transfer. Using the derived equations from eq. (1) to eq.(11), one may calculate variations in temperature caused by friction, which is illustrated in the following section using a sample parachute canopy system. 3. Parameters and working conditions for calculation In this section, using a sample parachute canopy system, we analyze influences of various factors on temperature rise and damage to the parachute canopy caused by frictional heating. The influencing factors include pressure, velocity, friction coefficient, specific heat capacity and thermal conductivity. Table 1 lists essential parameters with representative values and working conditions for the calculation. The target material is K59225 nylon fabric, which is one of typical materials for parachute canopy. Table 1 - Parameters for calculation Order number
Typical working Physical quantities
Symbols & units
Range of variety
condition and material’s properties
1
Contact pressure
p(Pa )
50~5×10
5×106
2
Velocity of friction
v( m / s )
0.1~80
50
3
coefficient of friction
0.1~1
0.3 [7,8]
Thermal conductivity of under-
_ B 2 （W/m
friction material
K）
0~1000
0.3 [12]
Specific heat of under-friction
CP-B1 （J/g K）
1.0~4.0
2.0 [12]
4 5
7
8
Order number
Typical working Physical quantities
Symbols & units
Range of variety
condition and material’s properties
material 6 7 8
Sliding distance (or the distance with friction action) Density of under-friction material Thickness of under-friction material
S （mm）
30~300
100
pB1 （g/cm3）
0.5~2.0
1.2 [12]
B1 （mm）
0.1~1.0
0.3[12]
9
Contact length of friction
L （mm）
30
30
10
Contact width of friction
W （mm）
30
30
A2 （W/m K）
0.3
0.3[12]
11
Thermal conductivity of frictional material
12
Density of frictional material
p_ A1 （g/cm3）
1.2
1.2[12]
13
Thickness of frictional material
_ A1 （mm）
0.3
0.3[12]
CP _ A1 （J/g K）
2.0
2.0[12]
hA2 _ C 、 hB 2 _ C
5.0
5.0
14 15
Specific heat of frictional material Convection heat transfer coefficient
4. Results and analysis The objective of the calculation is to investigate how the various factors affect the increase in temperature caused by friction. The factors are classified into three groups: 1) parameters that influence the heat generation such as contact pressure, sliding distance and coefficient of friction; 2) parameters that are related to heat absorption such as heat capacity, density and object dimensions; and 3) parameters that are influence the heat dismissing, including the sliding velocity and thermal conductivity. Although various parameters or factors may synergistically influence the final consequence, it is helpful to analyze effects of individual factors on heat generation and damage first, followed by looking into some synergistic effects. When investigate the effect of a specific parameter on frictional heating and temperature, other parameters are kept constant with typical values given in Table 1.
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4.1 Effects of pressure, frictional coefficient, and sliding distance on temperature Effects of pressure, coefficient of friction, and sliding distance on temperature were analyzed using the proposed model. Results are illustrated in Figs 5, 6 and 7.
350
Rise of Temperature (℃)
100
0 0
2000
4000
6000
8000
300 250 200 150 100 50 0 0.0
10000
0.5
1.0
Pressure (kPa)
Frictional Coefficient
Fig.5 Rise of temperature vs. pressure.
Fig. 6 Rise of temperature vs. friction coefficient.
350
Rise of Temperature (℃)
Rise of Temperature (℃)
200
300 250 200 150 100 50 0 0
50
100
150
200
250
300
Distance of Friction (cm)
Fig.7 Rise of temperature vs sliding distance As shown, temperature increases linearly with pressure, coefficient of friction and sliding distance, respectively. The melting temperature of textile materials used to make parachute is usually above 200C. If set 200C as a critical point (as an input parameter rather than a fixed
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constant in the model) above which the parachute would be melt or damaged, one may estimate critical pressure, frictional coefficient or sliding distance, beyond which the parachute is damaged (other parameters are constant). For instance, according to Fig.5, one may see that the textile would be melted as the pressure reaches 10MPa when friction coefficient (=0.3) and sliding distance (=100mm) have typical values as listed in Table 1. 4.2 Effects of material’s specific heat, density, and thickness Effects of specific heat, density, and thickness of parachute canopy on temperature rise were analyzed using the proposed model. Results of the analysis are presented in Figs. 8, 9 and 10, respectively. Again, in order to determine how a specific parameter affected the rise of temperature, other parameters were kept constant with typical values given in Table 1.
Rise of Temperature (℃)
200 180 160 140 120 100 80 60
200
100
40 0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.4
4.5
Specific Heat (J/g.℃)
0.6
0.8
1.0
1.2
1.6
1.8
Density of Material (g/cm )
Fig.9 Rise of temperature vs material density 700 600 500 400 300 200 100 0 0.0
1.4
3
Fig.8 Rise of temperature vs specific heat
Rise of Temperature (℃)
Rise of Temperature (℃)
220
0.2
0.4
0.6
0.8
Thickness of Material (mm)
1.0
2.0
2.2
11
Rise of Temperature (℃)
Fig.10 Rise of temperature vs thickness of material
100
80
60 0
200
400
600
800
1000
Thermal Conductivity (W/m. C) o
Fig.11 Rise of temperature vs thermal conductivity
As illustrated, these parameters are inversely related to the rise of temperature. These are attributed to the fact that the larger the parameters, the more the absorbed heat. As a result, the rise of temperature is smaller. Thus, increasing the specific heat, density and thickness of the canopy reduces the temperature rise, thus increasing its durability. 4.3 Effects of sliding velocity and material’s thermal conductivity The sliding velocity and material thermal conductivity are of importance to the heat generation and accumulation, respectively. Figs.11 and 12 show how these two factors influence the rise of temperature. As illustrated, temperature increases rapidly as the velocity of sliding between the bag and canopy increases. However, after reaching a certain level around 1 m/s, further increasing the velocity does not further raise temperature. This happens because the fabric material’s thermal conductivity is generally small (usually smaller than 1.0 W/m ℃), so that the heat-generation is much more than heat-dismiss at a high sliding velocity (> 5 m/s). As a result, the friction process could be approximately considered as an adiabatic process. A saturated state is reached as the velocity continuously increases.
Regarding the influence of material’s thermal conductivity on temperature rise, a larger thermal conductivity helps conduct heat away more quickly, thus reducing the temperature rise. As indicated earlier, different parameters may affect the temperature rise synergistically.
12
Since the thermal conductivity affects the heat dissipation while the sliding velocity affects the heat generation, it is of interest to have a look at how these two parameters synergistically affect the temperature rise. Fig.12 illustrates temperature rise with respect to the sliding velocity for two different thermal conductivities ( ), 0.3 and 300 W/m oC. As demonstrated, for =300 W/m oC, a sliding velocity of 200m/s is needed in order to raise temperature by 40oC, while this temperature rise can be achieved at a velocity not higher than 10m/s when the thermal conductivity is equal to 0.3 W/m oC. A lower thermal conductivity results in quick accumulation of heat and consequently a quick rise of temperature. 120
Rise of Temperature (℃)
100
80
λ=0.3 λ=300
60
40
20
0 0
50
100
150
200
Velocity of Friction (m/s)
Figure 12 Rise of temperature with respect to sliding velocity, influenced by the thermal conductivity: 0.3W / m C and 300W / m C .
4.4 Additional effect of the sliding velocity According to above-mentioned data analysis, the burn-damage to canopy occurs under high pressures (see Fig.5). Under the normal condition, such high pressures may not be reached. However, when the canopy is pulled out at a high velocity, the impact between the moving canopy and the canopy bag may generate a large dynamic contact pressure, which may result in large frictional force and rapid increase in temperature, thus damaging the canopy. 5. Testing and model verification In order to verify the model, a series of burn-prevention tests were performed using a testing system shown in Fig.13.
13
Fig.13 A system for burn-prevention tests
In this testing system，one side of the sample (canopy cloth) is fixed, and another side is pulled with a bob-weigh. The sample is in contact with a wheel (friction wheel) which is wrapped with a base cloth (material of canopy bag). During test, the wheel rotates for a certain period of testing time, driven by a motor, to cause friction between the sample cloth and the base cloth. With this apparatus, a number of tests were performed, results of which were compared with results of calculations using the proposed model. During tests, the burning damage was easily viewed. Images of two typical burning situations are illustrated in Fig.14. Results of both testing and calculation are given in Table 2 for comparison. In these tests, the linear velocity is 50 m/s, the contact area is 10mm×10mm. From Table 2, one may see that results of the experimental and computational analyses are consistent, demonstrating the effectiveness of the proposed model, although the comparison is qualitative in the present stage Table 2 Comparison between experimental observation and theoretical analysis Name of Testing Sample A sort of Nylon Ribbon A sort of Nylon Ribbon A sort of Nylon Fabric
Pressure （Pa） 1500 2000 3500 2000 3500 5000 1000 1500 2000 2500
Friction Time （s） 20 20 20 30 30 30 10 10 10 10
Experimental observation No burn No burn Burned No burn No burn Burned No burn No burn No burn 60% No burn，
Predicted temperature rise ( C )
Compliance of Test and Computation
124.15，No burn 158.83，No burn 262.98，Burned 110.11，No burn 177.71，No burn 245.32，Burned 89.45， No burn 124.13，No burn 158.81，No burn 193.59，Close to Burn
Accordance Accordance Accordance Accordance Accordance Accordance Accordance Accordance Accordance Accordance
14
3500 4500 5000
10 10 10
40% Slight burn Burned Burned Burned
262.94，Burned 332.40，Burned 367.07，Burned
Accordance Accordance Accordance
Notice: The material’s melting point is approximately 200 C .
Fig.14 Materials after prevent-burn testing
. A Remark Parachutes are required to be highly reliable. The parachute canopy may fail, triggered by local burn-damage caused by frictional heat. Thus, there is a demand for theoretical tools or models, which can provide useful clues for parachute design and material selection. However, to the authors’ knowledge, research in this specific area is rather limited and there is no such a theoretical tool/model which can be effectively used for parachute design. This article reports an attempt to develop such a theoretical tool. Although in the present stage the proposed model is validated by relevant experiments in a qualitative manner, it provides an approach or methodology for further development. 6. Conclusions Parachute has the risk of being damaged by local burn from frictional heating during its
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opening process. Such damage has not been well investigated in order to identify effective approaches with quantitative information to prevent or minimize it. In this study, we propose a mathematical model to evaluate effects of a number of factors on temperature rise involving heat generation, accumulation and dismissing. These factors include pressure, coefficient of friction, sliding distance with friction, and canopy textile’s properties, including specific heat, density and thickness of involved material components. Although the proposed is a first-stage model, it helps estimate and understand effects of these factors on temperature rise, which is beneficial to parachute design and material selection. Since these factors affect the temperature rise synergistically, there is no an order regarding which factor is more important than another. All these factors need to take account when design parachute systems. The model is verified by performed burn damage tests, results of which are consistent with predictions made using the model. Acknowledgment The authors are grateful for financial support from the National Study Fund Committee (China) and Natural Science and Engineering Research Council of Canada.
References 1. Li, J.,Tang, M.Z.: Improvement and tests of the Shenzhou-8 main parachute. Spacecraft Rec. Rem. Sens. 32(6), 26-32 (2011). 2. G. Watts, George C.: Space shuttle solid rocket booster main parachute damage reduction team report [ R]. NASA TM-4437(1993) 3. Xia, G., Cheng W.K., Qin, Z.Z.: Case study of main parachute malfunction in aerospace recovery，Spacecraft Rec. Rem. Sens. 23(4), 4-8(2002) 4. E. G. Ewing, H. W. Bixby, T. W. Knacke: Recovery systems design guide, Technical Report, FFDL-TR-78-151 (1978) 5. M.A. Bueno, R.Bocquet, M.Tourlonias, R.M. Rossi, S.Derier, Study of friction mechanisms of hairy textile fabrics, J. Wear 303, 343-353(2013) 6. R.Bocquet, M.A. Bueno, M.Tourlonias, R.M. Rossi, S.Derier, Brush model to predict the friction of hairy textile fabrics from indentation measurements, J. Wear 296, 519-527(2012) 7. V. K. Kothari, M. K. Ganga: Assessment of frictional properties of some woven fabrics, Ind.
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J. Fibre Tex. Res. 19, 151-155(1994) 8. V. Sülara, E. Öner, A. Okur: Roughness and frictional properties of cotton and polyester woven fabrics,Ind. J. Fibre Tex. Res. 38, 349-356(2013). 9. Wang, H.T., Qin, Z.Z., Song, X.M., Guo, P., Tao,W.S.: Analysis of the phenomenon of bull whipping in the deployment process of large parachute，J. Natl. Univ. Def. Tech. 32(5), 34-38(2010) 10. Song, X.M., Fan, L., Qin, Z.Z.: “Vent whip” during large parachute deployment, Spacecraft Rec. Rem. Sens. 30(3), 16-21(2009) 11. V. Lavrakas: Frictional forces and lubrication of textile fabrics at high sliding velocities, WADC TR 54-49, 192-208(1954) 12. Yao, M., Zhou, J.F., Huang, S.Z., Shao, L.H.:,An, R.F., Fan, D.Q.: Textile materials science, ISBN 7-5064-0083-9/TS.0083 (1980)
Highlights
A mathematic model is proposed to analyze local burn damage to parachute canopy caused by frictional heat
Evaluate effects of a number of factors, e.g., pressure, friction coefficient, sliding distance with friction, and canopy textile’s properties on temperature rise caused by friction
The theoretical model may provide useful information for parachute design and material selection
www.elsevier.com/locate/jtri
PII: DOI: Reference:
S0301-679X(16)30338-3 http://dx.doi.org/10.1016/j.triboint.2016.09.030 JTRI4377
To appear in: Tribiology International Received date: 14 August 2016 Accepted date: 18 September 2016 Cite this article as: Haishan Teng and D.Y. Li, A mathematical model of frictional damage to parachute canopy, Tribiology International, http://dx.doi.org/10.1016/j.triboint.2016.09.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.
1
A mathematical model of frictional damage to parachute canopy Haishan Teng1,2,3, D.Y. Li2* 1
National University of Defense Technology, Changsha, Hunan, China Dept. of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 1H9 3 Beijing Institute of Space Mechanics & Electricity, China 2
*Corresponding author: [email protected] Abstract The damage to parachute canopy caused by friction involves a number of parameters, including material properties, pressure, sliding velocity and surface condition, etc. A theoretical model is proposed to analyze the friction process and help evaluate effects of the parameters on the damage to parachute canopy. Relevant prevent-burn tests were performed to validate the model, which is built with the aim of providing relevant information or clues for parachute design and material selection. Keywords: Parachute, Damage, Friction, Mechanism, Prediction 1. Introduction Parachute is a type of aerodynamic decelerator, which has a wide range of applications. Parachute may fail when is over-loaded, but damage often occurs under lower load conditions. It is noticed that the damage is triggered by local melting or burn caused by frictional heat. Fig.1 illustrates local burned areas on parachute canopies
Fig.1 Local melt or burn is observed on canopies.
2
Although the damage to parachutes is a crucial issue, reported studies in the literature are rather limited. In general, damages may occur mainly during the process of deployment and inflation. When a canopy is pulled out from a bag at a high speed under certain pressure, a considerably large amount of heat could be generated due to the friction between the canopy and the bag as well as that between various parts of the canopy in contact. The frictional heat could markedly raise the local temperature, leading to local melt or burn of the canopy material. Besides, during the initial inflating process, the top of canopy swings quickly and even causes whipping, which may accelerate the canopy’s damage process [1]. Other factors may also contribute to the damage of canopy, such as the friction between parachute and supportingstructure, so-called “ring sail” caused by lateral wind, and twining occurs around the top hole of parachute, etc [2,3]. The present study is focused on the damage to the parachute canopy caused by frictional heating. The canopy’s damage is a complex process, involving various factors, among which the material used to make the parachute is one of key factors. The canopy’s material is generally treated for enhanced anti-burning capability and lowered friction [4]. However, damage to the parachute canopy may not be completely prevented. In order to avoid fatal risk resulting from the parachute damage, efforts must be made to identify factors that affect the friction process and determine critical parameters that can be controlled to prevent damage to parachute. Although research on friction of canopy materials is quite limited, there are many studies on friction of textile reported in the literature. For instance, M.A. Bueno and R.Bocquet built a brush model to predict the friction of hairy textile fabrics [5,6]. V K Kothari and M K Gangal looked into static and kinetic friction processes of some woven farics using different contacting surfaces by [7]. Roughness and frictional properties of cotton and polyester woven fabrics were investigated by V. Sülara [8]. These studies help to understand friction of canopy and associated damages when it is overloaded. There are also some theoretical studies on the whip phenomena [9,10]. However, research on the damage caused by frictional heating is much less and more limited to qualitative analysis. Vasilis Lavrakas described the influence of coefficient of friction [11], which was informative but not sufficient for guiding control of such risk. For example, when analyzing the damage caused by high-speed friction, no information is provided regarding the range of high speeds at which canopy could be overheated and damaged. Without such information on friction, heat generation and transfer, and loading condition, it is difficult to select
3
optimal materials and design reliable parachutes. Due to insufficient understanding of the Canopy’s damage caused by friction, the authors are motivated to conduct this study in order to identify crucial factors that can be controlled to minimize the risk of parachute failure. 2. Theoretical analysis 2.1 Physical processes and model construction The parachute’s opening process consists of canopy deployment and inflation. As shown in Fig.2, the parachute canopy is originally packed in a bag. When the procedure is commenced, the canopy is pulled out from the bag at a high speed. During the pulling process, friction between different portions of the canopy in contact and that between the canopy bag can be high enough to generate a considerable amount of frictional heat, which may burn and damage the canopy.
Fig. 2 Schematic illustration of parachute canopy packing and friction during the opening process.
Based on the physical configurations shown in Fig.2, a model system with a simplified configuration is proposed to deal with the friction between the canopy and the bag as illustrated in Fig.3. Since the fabric is light, compared to the pressure and frictional force, the surfaces in contact are drawn horizontally in order to facilitate relevant analysis. It makes no difference no matter the sliding surface is placed horizontally or with an angle relative to the horizontal plane. The model is general for analyzinge friction between different portions of canopy in contact. When the canopy is pulled out from the bag, friction occurs between the contact areas.
4
Fig. 3 A simplified configuration for modeling friction between folded canopy and bag during the pulling process.
In order to facilitate friction analysis while keeping the generality, the following assumptions are made: 1) Under certain pressure and at high speeds of pulling, the flexibility and deformation of canopy and its counter-face during sliding are ignored. 2) Since the canopy is folded tightly under pressure, air between layers is very little. With little air present, thermal convection and thermal radiation are rather limited, which are thus ignored. 3) The canopy is a network of fibers and the number of fibers in a space of one minimeter is
several dozen. Since a local burning damaged area is usually on the scale of centimeter or at least minimeter, it is assumed that the surfaces under study are continuous and smooth. As for the influence of the surface roughness, this can be reflected by the friction coefficient (measurable). 4) In the present case of dealing with fabrics, the influence of gravity is ignored.
In the model, the bag is denoted as body A and the canopy as body B. They move relative to each other. During the pulling process, body A is always in contact with a moving B, thus it experiences friction for a longer sliding distance than that of body B. Since heat transfer needs to be taken into account, each of A and B consists of two parts as shown in Fig.4; one is the top surface layer under friction action and the other is the layer beneath the top surface layer, which plays a role in heat transfer. For details, A is divided to two layers for analysis, A1 and A2. A1 is in direct contact with its counter-face, in which temperature increases rapidly when subjected to
5
friction. Since it is thin, the difference in temperature within this layer is ignored. A2 is thicker and plays a role in heat conduction. Thus, there is temperature gradient within A2. Similarly, B is also divided to two layers and analyzed in a similar manner. Although canopy can be folded in different ways, the involved friction processes are similar when the canopy is pulled out. Thus, the proposed model is general. Friction occurred at the intersection of layers A1 and B1, and the heat produced by friction is treated as heat-source. The heat was absorbed by A1 and B1, and transfer to the outer layers A2 and B2. We may simplify this process as a one-dimension transfer-heat process. See figure 4.
Fig.4 A simplified model for analyzing friction and heat transfer processes.
In realistic situation, canopy B is the part suffering from damage. Thus, part B is the target object for analysis. For part A, since its heat transfer and dismiss are similar to those of part B, the treatment applied to part A was the same as that for part B. 2.2 Heat equilibrium The heat equilibrium equation for B1 is expressed as Qin _ B1 EB1 Qout _ B1 .............................................................（1）
where ΔEB1 is the increment of internal energy of B1, Qin_B1 the frictional heat entering into B1，and Qout_B1 is the heat that is conducted away from B1. Qin _ B1 QT k B1 .........................................................................（2）
6
where QT is the generated heat, kB1 is the heat transfer ratio, defined as the ratio of heat in B1 to the total heat generated during the sliding process. The heat comes from the mechanical work done by the frictional force, part of which results in material’s deformation and the rest is converted to heat as equation (1) expresses:
QT W friction Edef
..............................................................（3）
where Edef is the deformation energy, and Wfriction is the work done by the frictional force, which is expressed as W friction p AB1 v t ...........................................................（4）
where p is pressure, AB1 is the area of contact, μ the coefficient of friction, v the velocity of friction, and t is the duration of the friction process. The increment of B1’s internal energy can be calculated as
EB1 mB1 C p _ B1 TB1 ..........................................................（5） where Cp_B1 is specific heat of B1, ΔTB1 the rise in temperature of B1 and mB1 is the mass of layer B1, where is given as mB1 B1 AB1 B1 ....................................................................（6）
where ρB1 is the density of material (B1), AB1 is the area of contact, and δB1 is the thickness of layer B1. The heat equilibrium equation for B2 is expressed as
Qout_ B1 Qin _ B 2 Qconduct_ B 2 Qconvect _ B 2C ...........................（7） where Qconvect_B2-C is the quantity of heat dismissed through convection from B2. Qconduct_B2 is the quantity of heat conducted away from B2, and we have
Qconduct_ B 2 B 2 AB 2
TB 2
B2
t ................................................（8）
where λB2 is thermal conductivity of B2, AB2 is the area of heat transfer, ΔTB2 the difference in temperature between the two sides of layer B2, δB2 the thickness of B2, and t is the time of heat transfer. As a matter of fact, the conducted heat, Qconduct_B2, is equal to the increment of B2’s internal energy i.e.
Qconduct_ B 2 EB 2 mB 2 C p _ B 2 TB 2
.................................（9）
7
where Cp_B2 is specific heat of B2, ΔTB2 is the rise in temperature of B2 and mB2 is the mass of layer B2., and mB 2 has the following expression: mB 2 B 2 AB 2 B 2 .................................................................（10）
where ρB2 is the density of material (B2), AB2 is the area of contact, and δB2 is the thickness of layer B2. Besides, we have
Qconvect _ B 2C hB 2C AB 2 TB 2C t ............................. ……..........（11） where hB2-C is the convective heat transfer coefficient, AB2 is the area of heat-transfer, and t is the time of heat transfer. Using the derived equations from eq. (1) to eq.(11), one may calculate variations in temperature caused by friction, which is illustrated in the following section using a sample parachute canopy system. 3. Parameters and working conditions for calculation In this section, using a sample parachute canopy system, we analyze influences of various factors on temperature rise and damage to the parachute canopy caused by frictional heating. The influencing factors include pressure, velocity, friction coefficient, specific heat capacity and thermal conductivity. Table 1 lists essential parameters with representative values and working conditions for the calculation. The target material is K59225 nylon fabric, which is one of typical materials for parachute canopy. Table 1 - Parameters for calculation Order number
Typical working Physical quantities
Symbols & units
Range of variety
condition and material’s properties
1
Contact pressure
p(Pa )
50~5×10
5×106
2
Velocity of friction
v( m / s )
0.1~80
50
3
coefficient of friction
0.1~1
0.3 [7,8]
Thermal conductivity of under-
_ B 2 （W/m
friction material
K）
0~1000
0.3 [12]
Specific heat of under-friction
CP-B1 （J/g K）
1.0~4.0
2.0 [12]
4 5
7
8
Order number
Typical working Physical quantities
Symbols & units
Range of variety
condition and material’s properties
material 6 7 8
Sliding distance (or the distance with friction action) Density of under-friction material Thickness of under-friction material
S （mm）
30~300
100
pB1 （g/cm3）
0.5~2.0
1.2 [12]
B1 （mm）
0.1~1.0
0.3[12]
9
Contact length of friction
L （mm）
30
30
10
Contact width of friction
W （mm）
30
30
A2 （W/m K）
0.3
0.3[12]
11
Thermal conductivity of frictional material
12
Density of frictional material
p_ A1 （g/cm3）
1.2
1.2[12]
13
Thickness of frictional material
_ A1 （mm）
0.3
0.3[12]
CP _ A1 （J/g K）
2.0
2.0[12]
hA2 _ C 、 hB 2 _ C
5.0
5.0
14 15
Specific heat of frictional material Convection heat transfer coefficient
4. Results and analysis The objective of the calculation is to investigate how the various factors affect the increase in temperature caused by friction. The factors are classified into three groups: 1) parameters that influence the heat generation such as contact pressure, sliding distance and coefficient of friction; 2) parameters that are related to heat absorption such as heat capacity, density and object dimensions; and 3) parameters that are influence the heat dismissing, including the sliding velocity and thermal conductivity. Although various parameters or factors may synergistically influence the final consequence, it is helpful to analyze effects of individual factors on heat generation and damage first, followed by looking into some synergistic effects. When investigate the effect of a specific parameter on frictional heating and temperature, other parameters are kept constant with typical values given in Table 1.
9
4.1 Effects of pressure, frictional coefficient, and sliding distance on temperature Effects of pressure, coefficient of friction, and sliding distance on temperature were analyzed using the proposed model. Results are illustrated in Figs 5, 6 and 7.
350
Rise of Temperature (℃)
100
0 0
2000
4000
6000
8000
300 250 200 150 100 50 0 0.0
10000
0.5
1.0
Pressure (kPa)
Frictional Coefficient
Fig.5 Rise of temperature vs. pressure.
Fig. 6 Rise of temperature vs. friction coefficient.
350
Rise of Temperature (℃)
Rise of Temperature (℃)
200
300 250 200 150 100 50 0 0
50
100
150
200
250
300
Distance of Friction (cm)
Fig.7 Rise of temperature vs sliding distance As shown, temperature increases linearly with pressure, coefficient of friction and sliding distance, respectively. The melting temperature of textile materials used to make parachute is usually above 200C. If set 200C as a critical point (as an input parameter rather than a fixed
10
constant in the model) above which the parachute would be melt or damaged, one may estimate critical pressure, frictional coefficient or sliding distance, beyond which the parachute is damaged (other parameters are constant). For instance, according to Fig.5, one may see that the textile would be melted as the pressure reaches 10MPa when friction coefficient (=0.3) and sliding distance (=100mm) have typical values as listed in Table 1. 4.2 Effects of material’s specific heat, density, and thickness Effects of specific heat, density, and thickness of parachute canopy on temperature rise were analyzed using the proposed model. Results of the analysis are presented in Figs. 8, 9 and 10, respectively. Again, in order to determine how a specific parameter affected the rise of temperature, other parameters were kept constant with typical values given in Table 1.
Rise of Temperature (℃)
200 180 160 140 120 100 80 60
200
100
40 0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.4
4.5
Specific Heat (J/g.℃)
0.6
0.8
1.0
1.2
1.6
1.8
Density of Material (g/cm )
Fig.9 Rise of temperature vs material density 700 600 500 400 300 200 100 0 0.0
1.4
3
Fig.8 Rise of temperature vs specific heat
Rise of Temperature (℃)
Rise of Temperature (℃)
220
0.2
0.4
0.6
0.8
Thickness of Material (mm)
1.0
2.0
2.2
11
Rise of Temperature (℃)
Fig.10 Rise of temperature vs thickness of material
100
80
60 0
200
400
600
800
1000
Thermal Conductivity (W/m. C) o
Fig.11 Rise of temperature vs thermal conductivity
As illustrated, these parameters are inversely related to the rise of temperature. These are attributed to the fact that the larger the parameters, the more the absorbed heat. As a result, the rise of temperature is smaller. Thus, increasing the specific heat, density and thickness of the canopy reduces the temperature rise, thus increasing its durability. 4.3 Effects of sliding velocity and material’s thermal conductivity The sliding velocity and material thermal conductivity are of importance to the heat generation and accumulation, respectively. Figs.11 and 12 show how these two factors influence the rise of temperature. As illustrated, temperature increases rapidly as the velocity of sliding between the bag and canopy increases. However, after reaching a certain level around 1 m/s, further increasing the velocity does not further raise temperature. This happens because the fabric material’s thermal conductivity is generally small (usually smaller than 1.0 W/m ℃), so that the heat-generation is much more than heat-dismiss at a high sliding velocity (> 5 m/s). As a result, the friction process could be approximately considered as an adiabatic process. A saturated state is reached as the velocity continuously increases.
Regarding the influence of material’s thermal conductivity on temperature rise, a larger thermal conductivity helps conduct heat away more quickly, thus reducing the temperature rise. As indicated earlier, different parameters may affect the temperature rise synergistically.
12
Since the thermal conductivity affects the heat dissipation while the sliding velocity affects the heat generation, it is of interest to have a look at how these two parameters synergistically affect the temperature rise. Fig.12 illustrates temperature rise with respect to the sliding velocity for two different thermal conductivities ( ), 0.3 and 300 W/m oC. As demonstrated, for =300 W/m oC, a sliding velocity of 200m/s is needed in order to raise temperature by 40oC, while this temperature rise can be achieved at a velocity not higher than 10m/s when the thermal conductivity is equal to 0.3 W/m oC. A lower thermal conductivity results in quick accumulation of heat and consequently a quick rise of temperature. 120
Rise of Temperature (℃)
100
80
λ=0.3 λ=300
60
40
20
0 0
50
100
150
200
Velocity of Friction (m/s)
Figure 12 Rise of temperature with respect to sliding velocity, influenced by the thermal conductivity: 0.3W / m C and 300W / m C .
4.4 Additional effect of the sliding velocity According to above-mentioned data analysis, the burn-damage to canopy occurs under high pressures (see Fig.5). Under the normal condition, such high pressures may not be reached. However, when the canopy is pulled out at a high velocity, the impact between the moving canopy and the canopy bag may generate a large dynamic contact pressure, which may result in large frictional force and rapid increase in temperature, thus damaging the canopy. 5. Testing and model verification In order to verify the model, a series of burn-prevention tests were performed using a testing system shown in Fig.13.
13
Fig.13 A system for burn-prevention tests
In this testing system，one side of the sample (canopy cloth) is fixed, and another side is pulled with a bob-weigh. The sample is in contact with a wheel (friction wheel) which is wrapped with a base cloth (material of canopy bag). During test, the wheel rotates for a certain period of testing time, driven by a motor, to cause friction between the sample cloth and the base cloth. With this apparatus, a number of tests were performed, results of which were compared with results of calculations using the proposed model. During tests, the burning damage was easily viewed. Images of two typical burning situations are illustrated in Fig.14. Results of both testing and calculation are given in Table 2 for comparison. In these tests, the linear velocity is 50 m/s, the contact area is 10mm×10mm. From Table 2, one may see that results of the experimental and computational analyses are consistent, demonstrating the effectiveness of the proposed model, although the comparison is qualitative in the present stage Table 2 Comparison between experimental observation and theoretical analysis Name of Testing Sample A sort of Nylon Ribbon A sort of Nylon Ribbon A sort of Nylon Fabric
Pressure （Pa） 1500 2000 3500 2000 3500 5000 1000 1500 2000 2500
Friction Time （s） 20 20 20 30 30 30 10 10 10 10
Experimental observation No burn No burn Burned No burn No burn Burned No burn No burn No burn 60% No burn，
Predicted temperature rise ( C )
Compliance of Test and Computation
124.15，No burn 158.83，No burn 262.98，Burned 110.11，No burn 177.71，No burn 245.32，Burned 89.45， No burn 124.13，No burn 158.81，No burn 193.59，Close to Burn
Accordance Accordance Accordance Accordance Accordance Accordance Accordance Accordance Accordance Accordance
14
3500 4500 5000
10 10 10
40% Slight burn Burned Burned Burned
262.94，Burned 332.40，Burned 367.07，Burned
Accordance Accordance Accordance
Notice: The material’s melting point is approximately 200 C .
Fig.14 Materials after prevent-burn testing
. A Remark Parachutes are required to be highly reliable. The parachute canopy may fail, triggered by local burn-damage caused by frictional heat. Thus, there is a demand for theoretical tools or models, which can provide useful clues for parachute design and material selection. However, to the authors’ knowledge, research in this specific area is rather limited and there is no such a theoretical tool/model which can be effectively used for parachute design. This article reports an attempt to develop such a theoretical tool. Although in the present stage the proposed model is validated by relevant experiments in a qualitative manner, it provides an approach or methodology for further development. 6. Conclusions Parachute has the risk of being damaged by local burn from frictional heating during its
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opening process. Such damage has not been well investigated in order to identify effective approaches with quantitative information to prevent or minimize it. In this study, we propose a mathematical model to evaluate effects of a number of factors on temperature rise involving heat generation, accumulation and dismissing. These factors include pressure, coefficient of friction, sliding distance with friction, and canopy textile’s properties, including specific heat, density and thickness of involved material components. Although the proposed is a first-stage model, it helps estimate and understand effects of these factors on temperature rise, which is beneficial to parachute design and material selection. Since these factors affect the temperature rise synergistically, there is no an order regarding which factor is more important than another. All these factors need to take account when design parachute systems. The model is verified by performed burn damage tests, results of which are consistent with predictions made using the model. Acknowledgment The authors are grateful for financial support from the National Study Fund Committee (China) and Natural Science and Engineering Research Council of Canada.
References 1. Li, J.,Tang, M.Z.: Improvement and tests of the Shenzhou-8 main parachute. Spacecraft Rec. Rem. Sens. 32(6), 26-32 (2011). 2. G. Watts, George C.: Space shuttle solid rocket booster main parachute damage reduction team report [ R]. NASA TM-4437(1993) 3. Xia, G., Cheng W.K., Qin, Z.Z.: Case study of main parachute malfunction in aerospace recovery，Spacecraft Rec. Rem. Sens. 23(4), 4-8(2002) 4. E. G. Ewing, H. W. Bixby, T. W. Knacke: Recovery systems design guide, Technical Report, FFDL-TR-78-151 (1978) 5. M.A. Bueno, R.Bocquet, M.Tourlonias, R.M. Rossi, S.Derier, Study of friction mechanisms of hairy textile fabrics, J. Wear 303, 343-353(2013) 6. R.Bocquet, M.A. Bueno, M.Tourlonias, R.M. Rossi, S.Derier, Brush model to predict the friction of hairy textile fabrics from indentation measurements, J. Wear 296, 519-527(2012) 7. V. K. Kothari, M. K. Ganga: Assessment of frictional properties of some woven fabrics, Ind.
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J. Fibre Tex. Res. 19, 151-155(1994) 8. V. Sülara, E. Öner, A. Okur: Roughness and frictional properties of cotton and polyester woven fabrics,Ind. J. Fibre Tex. Res. 38, 349-356(2013). 9. Wang, H.T., Qin, Z.Z., Song, X.M., Guo, P., Tao,W.S.: Analysis of the phenomenon of bull whipping in the deployment process of large parachute，J. Natl. Univ. Def. Tech. 32(5), 34-38(2010) 10. Song, X.M., Fan, L., Qin, Z.Z.: “Vent whip” during large parachute deployment, Spacecraft Rec. Rem. Sens. 30(3), 16-21(2009) 11. V. Lavrakas: Frictional forces and lubrication of textile fabrics at high sliding velocities, WADC TR 54-49, 192-208(1954) 12. Yao, M., Zhou, J.F., Huang, S.Z., Shao, L.H.:,An, R.F., Fan, D.Q.: Textile materials science, ISBN 7-5064-0083-9/TS.0083 (1980)
Highlights
A mathematic model is proposed to analyze local burn damage to parachute canopy caused by frictional heat
Evaluate effects of a number of factors, e.g., pressure, friction coefficient, sliding distance with friction, and canopy textile’s properties on temperature rise caused by friction
The theoretical model may provide useful information for parachute design and material selection