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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

Experimental Validation of Structural Damping Models for Tape Springs

Florence Dewalque, Olivier Brüls

Department of Aerospace and Mechanical Engineering University of Liège, Belgium 6th European Conference for Aerospace and Space Sciences Krakow, 1st July 2015

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

OUTLINE

GPM Core Observatory satellite (Credit: NASA)

INTRODUCTION OBJECTIVES EXPERIMENTAL SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

TAPE SPRINGS - DEFINITION

Definition: Thin strip curved along its width used as a compliant mechanism. Known in the everyday life as Carpenter or measured tapes. Geometry:

L R α t

Credit: 01dB-Metravib & CNES 3 / 21

INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

TAPE SPRINGS - ASSETS

◮ Storage of elastic energy ◮ Passive and self-actuated

deployment

◮ No lubricant ◮ Self-locking in deployed

configuration

◮ Possibilities of failure limited

⇒ Valuable components for space applications.

• S. Hoffait et al.

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

TAPE SPRINGS - MECHANICAL BEHAVIOUR

◮ Highly nonlinear ◮ Different senses of bending ◮ Buckling ◮ Hysteresis phenomenon

M+

max

M_

max

M+

*

M

+

heel

θ

+ max

θ Loading Unloading Loading Unloading

Equal sense bending Opposite sense bending

Bending moment M Bending angle θ

_ *

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

TAPE SPRINGS - PREVIOUS RESULTS

Context: Impact of the structural and numerical dampings in FEM analyses (Dewalque, Rochus, Brüls, Importance of structural damping in the dynamic analysis of

compliant deployable structures, Acta Astronautica 2015)

20 40 60 80 100 120 140 160 −400 −200 200 400 600 800

Time [s] Bending moment [N mm] M M m ax

+

M m ax

−

Folding Deployment Peak moment Residual moment Buckling

20 40 60 80 100 120 140 160 −300 −200 −100 100 200 300 400 500

Time [s] Bending moment [N mm] M M m ax

+

M m ax

−

Folding Deployment Peak moment Residual moment Buckling

Without structural damping With structural damping

Conclusions:

◮ Numerical damping for the convergence of the solver ◮ Structural damping to capture the physical behaviour

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

OBJECTIVES

Based on an experimental set-up:

◮ Quantify the characteristics of the tape springs

(quasi-static tests)

◮ Perform deployments

(dynamic tests - large amplitudes)

◮ Characterise the structural damping

(dynamic tests - small amplitudes)

◮ Correlate the finite element model

in an environment affected by gravity.

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

EXPERIMENTAL SET-UP

Horizontal configuration: Vertical configuration:

Tape spring I n t e r f a c e

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

EXPERIMENTAL SET-UP

Measuring equipment:

◮ Force plate (Kistler) ◮ Motion sensors (Codamotion)

In the laboratory of human motion analysis (LAMH, ULg, Belgium).

Sensors Force plate

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

EXPERIMENTAL SET-UP

Geometry and material of the tape springs: Length Thickness Subtended angle Radius 100 mm 0.13 mm 1.219 rad 15.545 mm Young’s modulus Poisson’s ratio Density 210, 000 MPa 0.3 7, 850 kg/m3 Uncertainties on the dimensions and the material properties.

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

QUASI-STATIC TESTS

On the horizontal configuration, a vertical force is applied on the dummy panel:

2 4 6 8 10 12 14 16 18 5000 4000 3000 2000 1000 1000 2000 3000 4000

Time [s] M max

y

[N mm]

Loading Buckling Unloading

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

QUASI-STATIC TESTS

Quasi-static finite element model:

g x y z

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

QUASI-STATIC TESTS

Results: Mean exp. value FEM results

• Diff. wrt. FEM

Fmax

z

3.33 N 4.13 N 19.52 % θmax

+

11.54◦ 11.84◦ 2.51 % Mmax

y

1141.8 Nmm 980.6 Nmm 16.44 % Reasonable results for such nonlinear tests performed manually on our first set-up. Update of the FEM:

◮ Thickness: 0.15 mm ◮ Young’s modulus: 205, 000 MPa

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

DYNAMIC TESTS

On the vertical configuration, folding up to an angle of ∼ 50◦, then deployment: Limited lateral displacements

0.5 1 1.5 2 2.5 3 3.5 4 −200 −150 −100 −50 50 100 150

Time [s] X-position [mm]

Peak in equal sense Peak in opposite sense Limit for peaks in equal sense Limit for peaks in opposite sense

0.5 1 1.5 2 2.5 3 3.5 4 160 170 180 190 200 210 220 230

Time [s] Z-position [mm]

Peak in equal sense Peak in opposite sense

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

DYNAMIC TESTS

Complexity of the experimental tests:

◮ Vibration of the plate ◮ Repeatability

0.5 1 1.5 2 2.5 3 3.5 4 −200 −150 −100 −50 50 100 150 200

Time [s] X-position [mm] Test 1 Test 2 Test 3

◮ Plastic deformations in the tape springs

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

DYNAMIC TESTS

Identification of the structural damping:

◮ Sources of damping: tape springs, connexions, other

flexible parts, air resistance, acoustic effects

◮ Small amplitude vibration tests ⇒ linear dynamic response

1 2 3 4 5 6 7 8 9 10 396 398 400 402 404 406 408 410 412 414

Time [s] Z-position [mm] Experimental result Y exp(−εω0t) −Y exp(−εω0t)

y t

.5 1 .5 .5 1 .5

Δt

◮ Hypothesis: motion dominated by the first bending mode

⇒ exponential decay

◮ Mean experimental structural damping: ε = 0.65 %

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

DYNAMIC TESTS

Correlation of the FEM: (On the horizontal configuration)

◮ Structural damping represented by a Kelvin-Voigt model

based on a single viscosity coefficient

1 2 3 4 5 6 7 8 9 10 −5 −4 −3 −2 −1 1 2 3 4 5

Time [s] Z-displacement [mm] Numerical result [Y exp(−εω0t)]mean [−Y exp(−εω0t)]mean

Results ε Frequency Exp. 0.65 % 9.73 Hz Num. 0.645 % 9.59 Hz

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

DYNAMIC TESTS

Dynamic finite element model:

g x y z

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

DYNAMIC TESTS

Correlation of the FEM:

◮ Large amplitude motion

0.5 1 1.5 2 2.5 3 3.5 4 −200 −150 −100 −50 50 100 150 200 250

Time [s] X-position [mm] Numerical result Test 1 Test 2 Test 3

0.5 1 1.5 2 2.5 3 3.5 4 140 160 180 200 220 240 260 280

Time [s] Z-position [mm] Numerical result Test 1 Test 2 Test 3

Fair correlation for the oscillation frequency, but poor on the amplitudes.

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

CONCLUSIONS

◮ Building of an experimental set-up ◮ Limited lateral displacements ◮ Validation of the measuring equipment ◮ Proposition of a first measurement methodology ◮ Good correlation of the quasi-static behaviour ◮ Fair correlation on the frequency for dynamic tests ◮ Damping of the dynamic behaviour too complex to be

captured by a single viscosity coefficient model Perspectives:

◮ Implementation of more complex models in the FEM ◮ Improvement of the experimental set-up

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INTRODUCTION OBJECTIVES SET-UP QUASI-STATIC TESTS DYNAMIC TESTS CONCLUSIONS

THANK YOU FOR YOUR ATTENTION

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