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MODEL AND RESULT ANALYSIS OF DRAG SAIL

MODULE EARLY TESTING

ANSHUMAN SHUKLA,

C.P. Vidya Niketan, Kaimganj, UP 209502, India

PRANAV M. SAWANT,

Army Public School, Pune, MH 411041, India

PROF. R.P. SHIMPI,

Former Adjunct Professor, Dept. of Aerospace Engineering, IIT B., MH 400076, India

Abstract—An inverted stepper motor assembly was

previously proposed in a design of a satellite deorbiting

module incorporating the drag sail method by the authors.

Following it, tests were conducted on an embodiment of

the module over an adjusted version of a deployment

sequence. The results from these tests were compared and

reproduced using a numerical model of the stepper motor.

A need was identified to produce a model of the tension

varying throughout the deployment sequence.. Curve

fitting technique was employed to generate from the data

obtained during test runs. Moreover, additional results

from test runs are discussed in the paper.

Index terms: Curve-fitting, Analytical Model, Motor

Drives, Drag Sail, Control System

I. INTRODUCTION

The need and feasibility of a plug and play, scalable drag

sail module was overviewed in [1]. Since then, early tests

have been done on an early prototype of AirDragMod

(ADM) obtaining important data in the process. This

prototype had four degrees of freedom. It consists of an

embodiment of the deployment mechanism described in

[1] with adequate sensors to obtain necessary data needed

to iterate the mechanism and derive an analytical model of

tension force at the motor drive during the deployment

sequence.

The primary components of the system are the rotator, aid

masses, and the sail deployment drives. The rotator,

controlled by said mechanism, generates the necessary

rotation in sync with a pre-defined sequence. The aid

masses are released first; due to the sail being connected to

these masses at free end, the tension created causes

elongation of the sail. The motor units drive the sail,

essentially “spewing it out”, at a constant rate upto

complete extension.

In the setup, the deployment sequence was normalized

down to 184 seconds with 120 seconds of sail deployment.

The data obtained will be used to develop an active control

system for perturbations caused to the system during this

deployment. To perform accurate dynamic modeling of the

forces at the base of the sail extension (at motor drives), an

analytical model is needed. In the paper, the analytical

model of tension caused due to centripetal force acting on

sail petals is derived with the help of flex sensors at the

same in the experimental setup. Additionally, interpolation

of angular velocities is performed, the data for which was

obtained using IMUs. Additionally, vibration data from the

system derived is visualized on a surface plot with the

derived model. This helps identify the periods of amplified

vibration during the sequence.

II. BACKGROUND

Equation of motion (domain equation) for extended sail

petal is [2]

(1)

This equation along with its boundary values and initial

values forms the initial value boundary problem [2] and

can be used to model the motion in Simulink®. in

the equation is a function of tension varying with position

on the petal. The sail petal can be assumed to be a

continuous mass distribution; mass of sail spread over the

length of the petal. Figure 1 provides a representation of

the location where tension data is recorded. Using

Newton’s second law and definite integration over a small

mass element, can be found to be:

(2)

Here, is the linear mass density; for a sail the

linear mass density for a petal is if

material chosen were Aluminized Kapton® Polymer [3].

Here, position is a function of time; the rate at which

motor drive units release the petals. This rate is dependent

upon deployment time and sail petal length to be extended.

For a sail, this rate for the 120 second sail release

period (for the setup mentioned prior) is .

is the angular velocity of the rotator unit. The model of

the physical system i.e. the ADM module in Simulink® is

shown in Figure 2. This model forms the physical system

over which active control is to be achieved.

Figure 1: Location of flex sensor recording tension

Figure 2: SimScape Physical System Block Diagram

III. NUMERICAL MODEL SETUP

Owing to hardware limitations, the force models do not

account for lateral forces on sail petals during deployment,

nor are the disturbance models computed in the y-axis of

the system as setup was placed on a surface and not in a

simulated microgravity environment. The force and

acceleration profiles are two dimensional but consistent

with the expected three dimensional model. Hence, the

current modeling can be extended into three dimensions.

The general setup along with axes are shown in figure 3.

Sail placeholders were used in the setup. Testing using

actual sail material would yield the lateral force profile.

The configuration geometry is novel to the design,

however, the number of deployment motor drives can be

varied with a minimum of 4. The setup consisted of 4 such

motor drives. The release rate was kept as mentioned

earlier. The tension data recorded at prototype was at the

base of motor drive units during the sail petal release

period of the deployment sequence. Theoretically, tension

would increase initially, then decrease to attain a constant

value. The axes for the setup are shown in Figure 3. Roll

axis for the setup is the y-axis; angular velocity is

measured around it. Ideally, there should not be any

movement in other axes, however, perturbations would be

caused and thus need for an active control system.

Figure 3: Setup CAD model with local axes

IV. RESULTS

The curve-fit of tension force data was done in

MATLAB®.The best fit model equation obtained is given

below with the coefficient values given in Table 1.

(3)

Table 1: Curve-fit coefficient values

Figure 4 shows the curve-fit plot along with the residuals

plot for the given fit is shown in Figure 5.

The Tension values are normalized moving means of

values recorded over multiple test runs.

The interpolation of angular velocity recorded using IMU

in x-axis is displayed. The cubic spline interpolant in is

a piecewise polynomial over p, where is normalized by

mean 92.03 and standard deviation 53.02 and p is a

coefficient structure. From plot Figure 6, it can be inferred

that some periodic disturbance of oscillation nature is

caused in the x-axis. This disturbance needs to be

controlled by the control system under development.

Figure 6 shows a surface and contour plot of time, angular

velocity and tension values obtained from the numerical

model (3).

Figure 4: Curve-fit of Normalized Tension Values vs. Time

Figure 5: Residuals Plot of Curve-fit in Figure 4

Figure 6: Interpolant of Angular Velocity in X-axis vs. Time

Figure 7: Surface Plot with Time as X-axis, Angular Velocity as Y-axis, and Tension as Z-axis

V. FUTURE WORK

Future work towards refining the models of disturbance

and formulas of motion should follow. Development of an

active control system is the next milestone towards the

development of AirDragMod. More tests with accurate

hardware and sail material should be done to obtain the

model of lateral forces. The result of these tests would also

be improved and rectified formula (2) modified.

Eventually, the active control system would need to be

tested out on a full scale AirDragMod.

VI. CONCLUSIONS

The curve-fit model of tension varying on a sail release

motor drive is useful dynamic modeling of such

microgravity release systems. The model derived using

data and numerical model in two dimensions was

visualized using surface plot matching closely with the

scatter plot obtained further testifying the accuracy. The

vibration data interpolation obtained is needed to

understand the intervals of increased disturbance and thus

help in development of the active control system. The

models obtained can be further extended to create three

dimensional models with tests improvised according to

results of said models. Additional refinement in formulas

would help refine models.

Future work would involve further testing and extensions

of setup degree of freedom into 4 to help in three

dimension modeling.

REFERENCES

[1] Shukla, Anshuman & Sawant, Pranav & Mohite, KC.

(2022). Scalable PnP Drag Sail Module Deorbit System for

LEO Satellites. 10.13140/RG.2.2.17377.38244/1.

[2] Daniel. S. Stutts (2000),

https://web.mst.edu/~stutts/PRESENTATIONS/ModalAnal

ysisofaTightString.pdf

[3]

https://www.dupont.com/content/dam/dupont/amer/us/en/p

roducts/ei-transformation/documents/EI-10142-Kapton-Su

mmary-of-Properties.pdf