an overview of dynamics modeling of inflatable solar array

doi:10.1016/j.egypro.2011.12.887 Energy Procedia Energy Procedia 00 2011 000–000 www.elsevier.com/locate/procedia Conference Title An Overview of Dynamics Modeling of Inflatable Sola

Energy Procedia 14 (2012) 1967 – 1972

1876-6102 © 2011 Published by Elsevier Ltd Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE).

doi:10.1016/j.egypro.2011.12.887

Energy Procedia

Energy Procedia 00 (2011) 000–000

www.elsevier.com/locate/procedia

Conference Title

An Overview of Dynamics Modeling of Inflatable Solar Array

Delin Cuia,b,, Shaoze Yana*, Xiaosong Guob, Fulei Chua

a The State Key Laboratory of Tribology, Department of Precision Instruments and Mechanology, Tsinghua University Haidian

District, Beijing 100084 P.R China

b Xi’an Research Institute of High Technology, Xi’an, Shanxi Province 710025 P.R China

Abstract

The inflatable solar array (ISA) is a new kind of solar array It has many advantages over the traditional ones, because

it can be packaged into small volumes during launch, then sent into a pre-selected orbit, and finally deployed by its inflatable booms This paper gives a brief overview of development of inflatable space structure dynamics during the last two decades, and covers the highlights of the work that has been done during this time interval Some of the dynamic model of space inflatable booms and current development efforts are introduced, and future outlook for this promising structures technology is indicated

Keywords: Inflatable solar array; spacecraft; dynamics; deployable structure

1 Introduction

In order to meet the requirements of energy supply in deep space exploration and reduce the launching costs, the inflatable solar array (ISA) technology is developed The inflatable deployment structure has many advantages over the traditional ones, because it can be packaged into small volumes during launch, then sent into a pre-selected orbit, and deployed by its inflatable booms Finally, the booms are hardened when the ISA is in full deployment and forms space structures [1] Therefore, knowledge of all states of inflation is essential for subsequent assessment of conditions of stability and controllability of the deployment process [2]

Two companies, ILC Dover [3] and L’Garde [4], have early researched the inflatable solar array Both of the companies have been devoted to the related programs since 1990 and obtained fruitful achievements For instance, L’Garde developed a new type of inflatable solar array in the Inflatable Torus Solar Array Technology program [5] shown in Fig.1(a); ILC[3] successfully developed Mars Rover Inflatable Solar Array and Teledesic Inflatable Solar Array, shown in Fig.1(b) and Fig.1(c) respectively Many scholars

* Shaoze Yan Tel.: 8610-18911300976; fax: +8610-62796046

E-mail address: yansz@tsinghua.edu.cn

have performed to study design and dynamics of inflatable structures [1] However, it has been widely noticed that the dynamic characteristics of the supporting tubes determine mainly the performance of solar array, because the deployment of inflatable solar array is remarkably influenced by the inflation of the tubes This is an important reason why researchers focus more on the deployment dynamic characteristics of inflatable structures nowadays than the other performances of this kind of solar array

(a)ITSAT Solar Array (b)Mars Rover Solar Array (c)Teledesic Solar Array

Fig 1 Application Examples of Inflatable Solar Arrays The inflatable solar arrays can be classified into Z-folded, rolled and some other types according to the different folding patterns of the supporting tubes The first two types are frequently used nowadays and deeply studied, so the related research developments of deployment dynamics for these two structures will be introduced in this paper

2 Theoretical Models of Inflatable Structures

Many scholars have pointed out that the practical and precise dynamic models of inflatable structures are extremely important in the space exploration [6] Several models suitable to different structures are presented as follows

2.1 Dynamic Model of Rolled Boom

Fay and Steel [6] studied the deployment dynamics of the rolled tubes for the first time, and Smith introduced a dynamic model of the rolled boom [7] The basic equation of motion for the deployment of an inflated strut rigidly mounted at the base and initially wrapped around a hub from tip to base is[6,7]

dt I s dt p s R r s

α

⎩ ⎭ (1) whereI is the moment of inertia about the lower edge of the unrolling portion of the strut, s is the arc

length along the midline of the portion of the strut wrapped around the hub, α is the rigid body rotation

of the roll, pis the internal pressure, Ris the radius of the tube cross section when inflated, and ris the distance from the hub centre to the bottom of the rolled strut

The assumed geometry of the deploying rolled strut is shown in Figure 2

Fig.2 Geometry of the Deploying Rolled Strut [7]

The moment of inertia of the unrolling tube is given by

( ) ( ) ( ) 2( )

I s =I s −I s +r s ρ Rhs (2) whereI0is the moment of inertia of the unrolling tube about the center of the hub and is given by

π

⎛ ⎞

= ⎜ ⎟ ⎣⎝ ⎠ ⎡ + − ⎤⎦ (3) where ρ is the tube material density, h is the thickness of the tube material, and

( ) 1 1{ ( 2) (1 2 2 3) log (1 2)1 2 }

8

G ϕ = +ϕ ϕ+ ϕ − ⎡⎢ϕ+ +ϕ ⎤⎥

⎣ ⎦ (4) TheI1term in Eq (2) is caused by the fact that the centre of rotation of the unrolling strut is not the

centre of mass and is defined by

0

3

1 2 2

π

+

⎛ ⎞

The wrapped arc length and wrap angle are related by [7]

( ) π ( 0) ( )0

h

s θ = ⎡⎣F θ θ+ −F θ ⎤⎦ (6) where

( ) 1{ (1 2)1 2 log (1 2)1 2 } 2

F ϕ = ϕ +ϕ + ⎡⎢ϕ+ +ϕ ⎤⎥

⎣ ⎦ (7) Steele and Fay [6] applied above method to analyze dynamics behavior of the rolled boom, and research

results shows thatthe reduction in pressure is greater, the average velocity is less, and the time required

for the tube to unroll is longer Smith performed experimental studies to find out thatthe inertia of

deployment gas caused a shock to the system when it struck the end of the tube at the conclusion of the

unrolling process [7] This shock is directly related to the magnitude of the final unrolling velocity

2.2 Dynamic Model of Z-Folded Tube

Several models have been applied in the dynamic studies of Z-folded tubes, including nonlinear hinge

model [7,9,10], conservation model of energy and momentum[8,13], fluid-structure interaction model[14] and

control volume model[11,12] The proper assignment of rotational spring stiffness to each hinge in the

application of nonlinear hinge model only depends on the experimental results [7] And the conservation

model of energy and momentum is only suitable for the case in which the injected gas flow is relatively

slow [13] Besides, the fluid-structure interaction model is in its infancy, further work is still needed [8]

Therefore, control volume model, which is used by many scholars, is introduced in this section In the

control volume model, the continuum of enclosed volume is discretized in its stowed state into a set of

connected smaller enclosures or finite volumes, or compartments [11], as shown in Figure 3

Fig.3 Discretization of Inflatable Enclosure Into Connected Finite Volumes [11]

Consider an ideal gas flowing between two finite volumes i and j , across orifice A Depending on the ij

ratio of pressures downstream and upstream from the orifice, the gas flow may be subsonic or sonic For

sub sonic flow, the rate of flow dm of mass of gas across the orifice can be approximated by a one- ij

dimensional quasi-steady flow, expressed by [11]

1

0

1

ij d

kA p

γ γ

−

(8)

where p , 0 p and u p are the initial pressure, upstream pressure, respectively, and downstream pressure, d

γ is the specific heat ratio, G is the gas constant, T is the gas temperature, and k is the orifice coefficient

Similarly, when the flow is sonic, it can be approximated in one dimension by [11]

1 1

1

ij d

d

kA p

γ γ

γ γ

γ γ

+ +

−

+

(9)

Wang [12] neglected the inertia of the inflation gas, assumed all variables are known at timet− Δ In t

their research paper, equation of motion of the inflatable structure has the form [12]

[ ]M D{ } +[ ]C D{ } +[ ]K D{ }={ }R e (10)

where[ ]M , [ ]C and[ ]K are the global mass, damping, and stiffness matrices computed with respect to the current configuration, { }D , { }D and { }D are displacement, velocity and acceleration vectors with respect to the current configuration at time t, { }R e is the external load vector

2.3 Simulation Analysis

Simulation is of great importance for analyzing and forecasting the ISA deployment dynamics Software LS-DYNA3D is applied by Salama [11], Wang [12], Wei [1] and some other researchers to analyze dynamic behaviour of inflation deployment process, and Salama’s simulation results [11] show that the LS-DYNA is much more suitable for inflation analysis than software ADAMS However, the deployment mechanism of the inflatable structures cannot be revealed completely only by finite element simulation [8]

3 Experimental Methods of Inflatable Structures

Three experimental methods, space-based experimentation, zero-gravity flight experimentation and Earth-based experimentation, have been adopted in analyzing dynamic characteristic of inflatable structures

3.1 Space-Based Experimentation

The mechanical performances of ISA or inflatable structures can be fully and profoundly understood

by space-based experiments NASA [15] successfully carried out the deployment of an inflatable antenna structure on May 20, 1996 This experiment clearly demonstrated the robustness of the inflatable space structures, and more important, it validated the potential of this new technology However, space-based experimentation is not an option for every new design for the expense of launching a test payload just to evaluate a design cannot be justified [16]

3.2 Zero-Gravity Flight Experimentation

This kind of experimentation is carried out on a specially modified plane Reference [17] applied this

method in a NASA-modified KC-135, which flied in a series of parabolic trajectories, causing

25-to-30-second periods of alternating zero-g and two-g conditions Campbell [18] also conducted the experiment of

inflating the scale-model solar concentrators aboard NASA’s KC-135 in 2002, and their results enabled

better understanding of controlled deployment for design A defect of this experimentation has to be

mentioned that the test space is usually small, so the size of test articles is limited [16]

3.3 Earth-Based Experimentation

The environmental condition experienced on earth, which includes gravity and atmospheric pressure,

has a dramatic effect of the deployment behaviour [16] Therefore, the air track shown in Figure 4 is

introduced into the experiments to simulate a type of microgravity environment

Fig.4 Earth-Based Experiment Schematic [16]

Clem [16] and Welch [19] conducted the experiments on an air table to predict the characteristics of the

inflating beam deployment Xiao [20] and Liu [21] also applied this method to analyze the deployment

velocity of the rolled booms at different times Although the earth-based experimentation can solve the

problem to some extent, it only provides limited insight into the performance of the inflatable

structures[16]

4 Conclusions

This paper mainly summarizes deployment dynamics of inflatable solar array This paper gives a brief

overview of the development of dynamics of inflatable space structures during the last three decades, and

covers the highlights of the work that has been done during this time interval This includes some of the

dynamic characteristics of space inflatable booms, current development efforts, and future outlook for this

promising structures technology

The inflatable solar array technology has improved a lot during these years, the research achievements

are fruitful However, there are many dynamics problems of the inflatable solar array to be solved, for

instance, Modelling dynamic model of inflatable solar array system are intensely built in details, and the

earth-based experimental equipments, which are much closer to the outer space environment, should be

developed in the future

Acknowledgements

This work was supported by the National Science Foundation of China under Contract No 50875149,

High Technology Project under Contract No 2009AA04Z401

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