2023_Launch_Vibration_Damping

Launch Vibration Damping Using Slip in Pretensioned Coils

Alexander Wen

∗

and Sergio Pellegrino

†

California Institute of Technology, Pasadena, CA, 91125

Vibration management is important for the survivability of structures during launch, and is

particularly challenging for large deployable space structures. Adding damping to a structure

reduces the overall level of response excitation, which increases survivability. Structural

damping occurs through the dissipation of energy during vibration. One such energy dissipation

mechanism that can be utilized to increase damping is friction, such as the friction between

slipping layers of a wound roll. In this paper, we study the vibration response of a structure,

which has a pre-tensioned coil wound around it. Here, the damping is provided by friction

between slipping layers in the pre-tensioned coil. An experiment is performed on a small-scale

setup to evaluate the feasibility of this approach by measuring the frequency response and

damping under different winding tensions. The same setup is used to measure layer slip during

vibration, using a high speed camera and tracking targets to identify the regions with the

largest slip, indicating higher contribution to energy dissipation. To confirm understanding

of the damping mechanism, a 3D finite-element simulation is created in an attempt to capture

the variation in frequency response and locations of slip with winding tension measured

experimentally.

I. Introduction

Vibration management is important for the survivability of structures during launch. There are two primary

approaches for vibration mitigation: increasing stiffness or adding damping. In this paper, we study the damping

approach, which utilizes energy dissipation to reduce amplitudes of excitation. There have been a variety of passive,

mechanical dampers proposed including: tuned mass dampers, liquid sloshing dampers, particle dampers, as well as

friction-based dampers [

–

]. However, the concept of

adding

damping, underscores that these types of dampers are

not intrinsic to the original structure, and thus their addition results in an increase in mass and complexity of the system.

Motivation for this work looks to state of the art deployable structures for space, where coiling as a packaging

architecture has seen increased usage for structures such as IKAROS, ROSA, and Starshade [

–

]. Here, looking at

these structures in the stowed, coiled configuration, we ask whether it is possible to make use of the existing mass and

re-purpose it as multi-functional, by having the coil itself provide an energy dissipation mechanism for damping. Prior

studies indicated that both the stiffness and interlayer slip of a wound roll undergoing vibration can be adjusted by

varying the winding tension [

]. Thus, we propose a variant of friction damping using a pre-tensioned, wound roll.

In this scheme, the roll is wound around a base structure with a tension that allows some degree of interlayer slip during

vibration. The friction between slipping layers provides the energy dissipation mechanism, which provides damping to

the system undergoing vibration, thereby reducing the overall level of excitation.

The objective of this research is to investigate how a coiled roll may be used as a passive, vibration damping device,

which utilizes friction as the energy dissipation mechanism. To do this, we first experimentally evaluate the effectiveness

of this scheme by measuring how the winding tension of the roll during coiling affects the vibration response on a

small-scale structural model. This is done by performing modal characterization of a wound roll assembly using a low

level sine sweep test. Damping is extracted from the experimental frequency response spectrum by using the half-power

bandwidth method on the first peak acceleration response.

Next, we want to identify the locations in the coil that are responsible for the damping energy dissipation mechanism

by experimentally measuring layer slip during vibration. This will provide understanding of how the vibration dynamics

dictate the active regions within the coil for the wound roll damper concept. The slip measurement experiment is

conducted using the same test sample used in the frequency response characterization. To measure slip, reference

tracking targets are placed at several locations along the length of the base structure. As a single, continuous membrane

is wound around the structure, additional tracking targets are placed on alternating layers, concentric to the base reference

∗

PhD Candidate, Graduate Aerospace Laboratories, 1200 E. California Blvd, MC105-50, Pasadena. email: awwen@caltech.edu.

†

Joyce and Kent Kresa Professor of Aerospace and Professor of Civil Engineering, Graduate Aerospace Laboratories, 1200 E. California Blvd,

MC105-50, Pasadena. AIAA Fellow. email: sergiop@caltech.edu.

targets. The wound roll is then excited using a sine dwell test at the natural frequency of the assembly, and a high speed

camera captures the position of the tracking targets. Measurements are performed both axially and transverse to the

axis of vibration. The high speed camera images are processed by identifying the centroids of the targets, where the

difference between the layer target and the reference indicates slip relative to the base structure, and the difference

between layer targets indicates interlayer slip.

Following these experiments, a finite-element analysis (FEA) is performed in order to build a model that correlates

with the variations in damping and locations of slip observed in the experiments. The simulation is conducted on a

simplified, 3D representation of a wound roll, which consists of several concentric, cylindrical shells, which approximate

coiled layers around a mandrel. For this simulation, we use geometry and properties derived from the experimental setup.

The coil layers are preloaded against the elastic mandrel using a range of pressures, and a friction interaction is defined

between all adjacent contact surfaces. Base excitation is then applied, both in the form of sine sweep and sine dwell.

The simulation is integrated in time, and the tip and base accelerations are recorded for the sweep excitation, while the

contact status of all elements is recorded for the dwell excitation. The simulated frequency response, corresponding

damping values, and slip locations are then compared against the experimentally measured values.

II. Vibration Experiment Setup and Procedure

A. Experiment setup

The vibration experiment consists of shaking 25 layers of 2 mil thick Kapton

HN membrane, consisting of one

continuous sheet wound around a polycarbonate mandrel via a winding machine. The configuration here is derived from

a previous experiment, where the materials and geometry were chosen so that a relatively small amount of layers would

have a sizeable impact on the structural response of the system [

]. We note that the stiffness and mass of the constituent

materials of the mandrel and membrane are approximately equal. Before the first winding, circular reference tracking

targets are applied to the mandrel surface at several locations near the base of the mandrel, Fig. 1a. One end of the

membrane is attached to the mandrel using tape, and the membrane is then wound over the initial reference targets.

During winding, circular ring targets are placed on subsequent alternating layers, concentric to the reference targets.

The tracking targets are placed only along one longitudinal line of the cylindrical sample. After coiling is complete, the

free end of the membrane is fixed to the outer surface of the roll with tape, Fig. 1b.

An internal illumination source allows the tracking targets to be visible through the transparent mandrel and

membrane layers, Fig. 1c. The internal surface of the mandrel was covered with aluminized Mylar, which creates a

mirrored surface that focuses the internal illumination onto a narrow section of the test sample containing the line of

targets in order to increase signal strength during high speed camera measurements. The coiled roll was assembled

using a range of different winding tensions, and parameterized by the interlayer stress measured at the innermost layer

using a pressure sensor. The preloaded, coiled assembly was then placed on a vibration table, and a retro-reflective

tracking marker was placed near the tip of the assembled roll on the outer layer as well as on the shaker head as depicted

in Fig. 2. The retroreflective tracking markers were used in concert with a Polytec PSV-500 Laser Scanning Vibrometer.

B. Vibration response experiment procedure

The vibrometer was used to control the vibration table in order to first perform a low-level sine sweep for each

winding tension case for the damping response characterization experiment. The sweep is run from 5 to 300 Hz for

duration. The acceleration spectrum of the tip tracking marker and the vibration table shaker head marker are

recorded in order to provide an acceleration transmissibility response curve. Damping is estimated from the experimental

transmissibility spectrum by using the half-power bandwidth method on the first peak acceleration response, which

corresponds to the natural frequency of the wound configuration.

C. Layer slip measurement procedure

Next, a sine dwell at the identified natural frequency is performed for the layer slip measurement experiment. The

internal illumination source is turned on, allowing a high speed camera to record the tracking targets during the vibration

experiment at 2000 fps. The experiment was performed both for a ‘loosely wound‘ case and a ‘tightly wound‘ case. The

slip measurement for each of the two tension levels tested is performed twice: once with the camera viewing direction

aligned axially to the excitation direction and once in the transverse direction, Fig. 2. Because the tracking targets are

placed only along one longitudinal line along the test sample, the wound roll and the high speed camera position must

(a) Polycarbonate mandrel with three

reference tracking targets and inter-

nal illumination source

(b) Wound Roll Assembly

by internal light source

Fig. 1 Wound roll damper test sample.

Fig. 2 Vibration experiment on a wound roll.

be rotated for each viewing direction.

Images from the high speed camera were exported onto a personal computer and processed using MATLAB. Each

frame was thresholded to create a grayscale image of binary values. The targets in the processed image are identified by

the number of connected pixels, as well as their circularity and diameter. Once successfully identified, the centroids

of each target, measured in the image coordinate frame,

(

푥, 푦

)

, were stored. A centroid based tracking scheme was

found to be more robust compared to an edge detection scheme, which was highly sensitive to imaging noise resulting

from high frame rate imaging that measured low signal-to-noise due to lower exposure time. Fig. 3 shows an example

processed image that indicates the accuracy of the centroid tracking scheme for one particular image. The targets at

a given longitudinal position are denoted as Group

푖

. The targets on a given layer are denoted with Layer

푗

. For a

given target Group

푖

, subtracting the position of the reference target,

(

푥

푟

, 푦

푟

)

푖

from the position of the layer targets,

(

푥, 푦

)

푗

푖

, eliminates the contribution of the mandrel movement. The resultant is the slip of layer

푗

(

푠

푥

, 푠

푦

)

푗

푖

, relative to

the mandrel:

(

푠

푥

, 푠

푦

)

푗

푖

=

(

푥

푟

, 푦

푟

)

푖

−(

푥, 푦

)

푗

푖

(1)

Interlayer slip can then be computed by taking the difference between layers:

(

푠

푥

, 푠

푦

)

푗

−

푗

푖

=

(

푠

푥

, 푠

푦

)

푗

푖

−(

푠

푥

, 푠

푦

)

푗

푖

(2)

Note that the slip calculations in Eq. (1) and Eq. (2) are performed in the time domain and the units are in pixels.

Fig. 3 Example processed image showing centroid tracking scheme. Here, layer targets were placed every five

layers starting from Layer 1 (Layers 1, 6, 11, 16).

The noise floor of the measurement and processing chain was evaluated by applying the entire procedure to the

sample measured at rest. High frequency noise present in the statically measured centroids in the time domain, Fig. 4a,

motivated performing analysis in the frequency domain and only considering the frequency range of interest that was

tested experimentally, Fig. 4b. This was done by taking the Fourier Transform of the time domain signals, which was a

preferred method over directly filtering or smoothing the time domain data to avoid impacting the slip measurement.

From this, the maximum uncertainty in the position of the targets measured statically in the frequency band of interest

was found to be

휎

=

푚푎푥

(

휎

푥

)

=

푚푎푥

(

휎

푦

) ≈

px. Since we calculate the slip from the difference of two uncertain

measurements, the propagation of uncertainty results in a total slip noise floor of

휎

푠

=

√

휎

≈

px. Slip magnitudes

at least

휎

푠

above the noise floor would be considered as a real signal, whereas values below this threshold would be

considered indistinguishable from the static, no slip condition. As a result, after first performing slip calculations in the

time domain, the results are converted into the frequency domain for evaluation.

III. Vibration Experiment Results

A. Vibration response of wound roll damper with winding tension

The frequency responses of the wound roll with different winding tensions were measured and are shown in Fig. 5a.

From these curves, we extract the natural frequency,

푓

푛

and estimate the damping,

휉

푒푠푡

. The damping of the wound

roll, plotted against the measured natural frequency of the wound roll normalized against the natural frequency of the

mandrel measured by itself, is shown in Fig. 5b. The response and damping of the mandrel by itself is also shown in

these figures.

From these plots, we observe an apparent bimodal response between ‘loosely wound‘ and ‘tightly wound‘ cases for

the range of winding tensions studied. We note there is some variability in distinguishing responses by the winding

pressures, likely due to the single point measurement of winding stress being of insufficient repeatability. This can be

mitigated in future experiments by taking the average of multiple measurements using multiple flexible pressure sensors

simultaneously. Despite this limitation, the difference in stiffness, amplitude of response, and damping are large enough

that there is a clear delineation between ‘loosely wound‘ and ‘tightly wound‘.