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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

Design of an experimental set-up to analyse compliant mechanisms used for the deployment of a panel

Florence Dewalque, Olivier Brüls

Department of Aerospace and Mechanical Engineering University of Liège, Belgium 14th European Conference on Spacecraft Structures, Materials and Environmental Testing Toulouse, France 30th September 2015

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

OUTLINE

INTRODUCTION EXPERIMENTAL SET-UP FINITE ELEMENT MODEL IDENTIFICATION OF THE PARAMETERS VALIDATION OF THE FE MODEL CONCLUSIONS

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

INTRODUCTION - TAPE SPRINGS

Definition: Thin strips curved along their width used as compliant mechanisms in replacement of common kinematic joints. Space applications: deployment of solar panels, reflectors, antennas, masts...

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

INTRODUCTION - TAPE SPRINGS

Assets:

◮ Storage of elastic energy ◮ Passive and self-actuated

deployment

◮ No lubricant ◮ Self-locking in deployed

configuration

◮ Possibilities of failure

limited

◮ Versatility

Complexity:

A B C D E F O G H M+

max

M_

max

M+

*

M_*

Bending angle Bending moment M +

heel

Opposite sense bending Equal sense bending

θ

θ

+ max

θ

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

INTRODUCTION - OBJECTIVES

◮ To design an experimental set-up ◮ To collect experimental data on tape springs ◮ To perform a large variety of tests (quasi-static, dynamic,

small amplitude, large amplitude, ...)

◮ To evaluate the parameters required to develop a finite

element model

◮ To correlate finite element models with the experimental

results

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

EXPERIMENTAL SET-UP

Constraints: Despite the presence of the gravity field,

◮ No buckling under its own

weight

◮ Passive deployment

starting from a downwards folded configuration

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

EXPERIMENTAL SET-UP

Acquisition equipment:

◮ 3D motion analysis system

(CODAMOTION)

◮ Acquisition frequency: 800 Hz ◮ Triangulation of active

markers (precision ∼ 0.3 mm)

◮ Force plate under the support

(KISTLER)

Codamotion CX1 unit

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

EXPERIMENTAL SET-UP

Deployment tests: Initial downwards folding in opposite sense

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

EXPERIMENTAL SET-UP

Positions: (superposition of 50 curves)

0.5 1 1.5 2 2.5 −80 −70 −60 −50 −40 −30 −20 −10

Time [s] Displacement along the x-axis [mm]

0.5 1 1.5 2 2.5 −120 −100 −80 −60 −40 −20 20 40 60 80

Time [s] Displacement along the z-axis [mm]

Vertical force:

0.5 1 1.5 2 2.5 −15 −10 −5 5 10 15 20

Time [s] Force along the z-axis [N]

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

DEPLOYMENT TESTS

Reproducibility of the experimental results: for 170 tests with 4 pairs of tape springs On the positions:

◮ Relative SD. < 1 % for

the peak amplitudes

◮ Relative SD. ր for the

peak times

1 2 3 4 5 6 7 8 9 10 0.2 0.4 0.6 0.8 1

Variation amplitude [%]

Peak max. x Peak min. x Peak max. z Peak min. z

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

Peak number [−] Variation time [%]

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

FINITE ELEMENT MODEL

Big interfaces T a p e s p r i n g s Small interfaces Rod

◮ Shells for tape springs and rod ◮ Rigid interfaces ◮ Big interfaces clamped

(fixation support not represented)

◮ Structural damping in the

tape springs

◮ Nonlinear dynamic analyses ◮ Generalised-α method ◮ Low numerical damping ◮ Automatic time stepping

procedure

◮ SAMCEF software

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

FINITE ELEMENT MODEL

Unknown parameters:

◮ Thickness t and Young’s modulus E of the tape springs

Why?

Small thickness (∼ 0.14 mm) Tape springs cut out from a common measuring

tape

Composite (metallic layer + coating + plastic) Non uniformity

Strategy of identification: Quasi-static three points bending tests

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

FINITE ELEMENT MODEL

Unknown parameters:

◮ Structural damping ε

Why?

Various sources (material, connections,

air resistance, acoustic effects, ...)

Important parameter to capture the physical

behaviour Strategy of identification: Small amplitude vibration tests

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

IDENTIFICATION OF t AND E

Three points bending tests:

S p a n Tape spring sample Load cell Loading head Support Support

• Exp. relative SD. < 5 %

Use of an optimisation algorithm coupled to a FE model to determine t and E fitting the experimental results

−10 −8 −6 −4 −2 2 4 6 8 10 −5 5 10 15 20

Displacement [mm] Load [N]

Experimental Numerical

∆(exp − num) < 14 %

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

IDENTIFICATION OF THE STRUCTURAL DAMPING

Small amplitude vibration tests:

5 10 15 20 25 30 −8 −6 −4 −2 2 4 6 8

Time [s] Displacement along the z-axis [mm]

Experimental curve Maximum peaks Minimum peaks

Hypothesis: Exponential decay of the oscillations Z exp(−εωt) ⇒ Can be represented by a Kelvin-Voigt model in the FE model

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

IDENTIFICATION OF ε

Small amplitude vibration tests: (510 tests in 11 sessions) Mean

• Max. diff.

Relative SD. ε 0.509 % 0.288 % 20.67 % ∆t 0.100 s 0.003 s 0.919 % Challenging measurements:

◮ Sensitivity to the assembly

procedure

◮ Non-uniformity of the

samples cut out from the same measuring tape

◮ Thermal effects within a

session of tests

5 10 15 20 25 30 35 40 45 50 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72

Test number [−] Structural damping [%]

Experimental results Mean 16 / 22

INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

VALIDATION OF THE FE MODEL

Deployment tests: comparison with the experimental results

0.5 1 1.5 2 2.5 −20 −10 10 20 30 40 50 60 70 80

Time [s] Displacement along the x-axis [mm]

FE model

0.5 1 1.5 2 2.5 20 40 60 80 100 120 140 160 180

Time [s] Displacement along the z-axis [mm]

FE model

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

VALIDATION OF THE FE MODEL

Deployment tests: comparison with the experimental results

0.5 1 1.5 2 2.5 −20 −10 10 20 30 40 50 60 70 80

Time [s] Displacement along the x-axis [mm]

FE model

0.5 1 1.5 2 2.5 20 40 60 80 100 120 140 160 180

Time [s] Displacement along the z-axis [mm]

FE model

1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30

|Aexp−Anum| max(Aexp) [%]

Peak max. x Peak min. x Peak max. z Peak min. z

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

Peak number [−]

|texp−tnum| max(texp) [%]

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

VALIDATION OF THE FE MODEL

Experimental Numerical

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

CONCLUSIONS

◮ Design of an experimental set-up ◮ Acquisition of experimental data by the means of a 3D

motion analysis system

◮ Good reproducibility of the deployment tests ◮ Identification of the FE parameters based on 3PBT and

small vibrations (no use of the deployment tests)

◮ Fair correlation of the FE model (∆ < 15 %) ◮ Good basis for a prediction of the behaviour in space

environment

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INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

CONCLUSIONS

Perspectives:

◮ Perform experimental tests in equal sense ◮ Add markers on the set-up ◮ Improve the numerical model

◮ Investigate other damping models ◮ Represent the fixation support in the FE model 21 / 22

INTRODUCTION SET-UP FE MODEL IDENTIFICATION VALIDATION CONCLUSIONS

THANK YOU FOR YOUR ATTENTION

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