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I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS Mechanical Behaviour of Tape Springs Used in the Deployment of Reflectors Around a Solar Panel Florence Dewalque 1 , Jean-Paul Collette 2 , Olivier Brls 1 1 Department of

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

Mechanical Behaviour of Tape Springs Used in the Deployment of Reflectors Around a Solar Panel

Florence Dewalque1, Jean-Paul Collette2, Olivier Brüls1

1 Department of Aerospace and Mechanical Engineering

University of Liège, Belgium

2 Walopt, Embourg, Belgium

6th International Conference on Mechanics and Materials in Design Ponta Delgada, 27th July 2015

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

OUTLINE

INTRODUCTION DEFINITION OF THE PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

INTRODUCTION - REFLECTORS

Main objective: reduction of the mass for small satellites. However, slower power consumption decrease for the electronic equipment. Solution: deployment of solar panels with reflectors.

Credit: REIMEI, Jaxa

Reflector R e f l e c t

  • r

In this work: use of tape springs to deploy reflectors.

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

INTRODUCTION - TAPE SPRINGS

Definition: Thin strip curved along its width used as a compliant mechanism.

◮ Storage of elastic energy ◮ Passive and self-actuated

deployment

◮ No lubricant ◮ Self-locking in deployed

configuration

◮ Possibilities of failure

limited

  • S. Hoffait et al.

⇒ Valuable components for space applications.

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

INTRODUCTION - 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 PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

DEFINITION OF THE PROBLEM

Folded configuration: reflector folded on the top of the solar panel considered as clamped. Deployed configuration: 120◦. Fixed parameters:

◮ Reflector: 200 × 200 mm2,

m = 0.4 kg

◮ Two tape springs:

L = 50 mm

◮ Opposite sense

Design variables: t, R, α with w ≤ 30 mm, h ≤ 15 mm

L R

α t

Solar panel Tape spring Reflector 200 50 120°

w max 30 h max 15

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

DEFINITION OF THE PROBLEM

Material: beryllium copper E ν ρ σy 131000 MPa 0.3 8100 kg/m3 1175 MPa Objectives of this work: perform the deployment while

◮ minimising the maximum Von Mises stress σVM max ◮ minimising the maximum amplitude motion dmax

by the means of an optimisation procedure.

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

PARAMETRIC STUDIES - THICKNESS

With R = 20 mm and α = 90◦. If t ր :

◮ Mmax ր ◮ θmax ր ◮ M∗ ր ◮ ∆E ր ◮ σVM max ր

−30 −20 −10 10 20 30 −1500 −1000 −500 500 1000 1500 2000 2500 3000

Bending angle [deg] Bending moment [Nmm] 0.1 mm 0.15 mm 0.2 mm 0.25 mm

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

PARAMETRIC STUDIES - RADIUS

With t = 0.1 mm and w = 28.28 mm. If R ր and α ց :

◮ Mmax ց ◮ θmax ր ◮ M∗ ց ◮ ∆E ց ◮ σVM max ց

−10 −8 −6 −4 −2 2 4 6 8 10 −300 −200 −100 100 200 300 400 500 600

Bending angle [deg] Bending moment [Nmm] 20 mm 22.5 mm 25 mm 27.5 mm

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

OPTIMISATION - MODEL DESCRIPTION

Initial geometry F.E. analysis

  • Folding up to 120°
  • Deployment

Post-treatment of the results New geometry Optimisation routine Optimised geometry

min f ?

Optimisation procedure performed on one tape spring with half the reflector mass (symmetric system). Confirmation for the complete hinge (two tape springs) a posteriori.

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

OPTIMISATION - MODEL DESCRIPTION

Optimisation problem: min

x

f(x) such that c(x) ≤ 0 lb ≤ x ≤ ub Nonlinear inequality constraints: c1 = w(α, R) − wmax ≤ c2 = h(α, R) − hmax ≤ with wmax = 30 mm and hmax = 15 mm Lower and upper bounds: t[mm] R[mm] α[rad] lb 0.08 10 π/3 ub 0.25 32.5 3π/4

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

OPTIMISATION - MINIMISATION OF σVM

max

Results: t R α Initial geometry 0.08 mm 30 mm π/3 rad Optimised geometry 0.08 mm 19.07 mm π/3 rad

100 105 110 115 120 125 130 135 140 145 150 −60 −40 −20 20

X displacement [mm]

100 105 110 115 120 125 130 135 140 145 150 −40 −20 20 40

Time [s] Z displacement [mm]

−200 −150 −100 −50 50 100 150 200 250 −100 −50 50 100 150 200

X [mm] Z [mm] Solar panel Tape spring Reflector

σVM

max = 666.25 MPa < σy

dmax = 53.92 mm

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

OPTIMISATION - MINIMISATION OF dmax

Results: t R α Initial geometry 0.1 mm 15 mm π/2 rad Optimised geometry 0.244 mm 29.68 mm 1.0588 rad

100 105 110 115 120 125 130 135 140 145 150 −60 −40 −20 20

X displacement [mm]

100 105 110 115 120 125 130 135 140 145 150 −40 −20 20 40

Time [s] Z displacement [mm]

−150 −100 −50 50 100 150 200 250 −100 −50 50 100 150 200

X [mm] Z [mm] Solar panel Tape spring Reflector

σVM

max = 1856 MPa > σy

dmax = 51.26 mm

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

OPTIMISATION - MINIMISATION OF σVM

max AND dmax

Objective function: f(x) = w1σVM

max + w2dmax

Results: t R α Initial geometry 0.08 mm 10 mm π/3 rad Optimised geometry 0.0804 mm 30 mm π/3 rad σVM

max = 877.75 MPa < σy

dmax = 52.08 mm

100 105 110 115 120 125 130 135 140 145 150 −60 −40 −20 20

X displacement [mm]

100 105 110 115 120 125 130 135 140 145 150 −40 −20 20 40

Time [s] Z displacement [mm]

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

DEPLOYMENT OF THE REFLECTOR

Complete finite element model:

Solar panel Solar panel Lumped mass (reflector) 160 1 5

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

DEPLOYMENT OF THE REFLECTOR

Results: σVM

max,1TS = 877 MPa

σVM

max,2TS = 866 MPa

100 105 110 115 120 125 130 135 140 145 150 −60 −40 −20 20

X displacement [mm] Hinge 1 tape spring

100 105 110 115 120 125 130 135 140 145 150 −40 −20 20 40

Time [s] Z displacement [mm]

−150 −100 −50 50 100 150 200 250 −100 −50 50 100 150 200

X [mm] Z [mm] Solar panel Tape spring Reflector

Validation of the optimisation procedure performed on a single tape spring.

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

DEPLOYMENT OF THE REFLECTOR

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

CONCLUSIONS

◮ Exploitation of tape springs to deploy reflectors. ◮ Parametric studies on the impact of the geometry. ◮ Optimisation procedure to minimise σVM max and/or dmax on

a single tape spring.

◮ Validation of the procedure for the complete hinge.

Perspectives:

◮ Material properties as design variables. ◮ Other orientations of the tape springs. ◮ Relevance of minimising dmax?

min σVM

max

min dmax min(w1σVM

max + w2dmax)

dmax 53.92 mm 51.26 mm 52.08 mm

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INTRODUCTION PROBLEM PARAMETRIC STUDIES OPTIMISATION CONCLUSIONS

THANK YOU FOR YOUR ATTENTION

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