Mechanical Behaviour of Tape Springs Used in the Deployment of - PowerPoint PPT Presentation

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 Brüls 1 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 1 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS O UTLINE I NTRODUCTION D EFINITION OF THE PROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS 2 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS I NTRODUCTION - R EFLECTORS Main objective: reduction of the Reflector mass for small satellites. However, slower power consumption decrease for the electronic equipment . Solution: deployment of solar r o t c panels with reflectors. e f l e Credit: REIMEI, Jaxa R In this work: use of tape springs to deploy reflectors. 3 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS I NTRODUCTION - T APE SPRINGS Definition: Thin strip curved along its width used as a compliant mechanism. ◮ Storage of elastic energy ◮ Self-locking in deployed ◮ Passive and self-actuated configuration deployment ◮ Possibilities of failure ◮ No lubricant limited S. Hoffait et al. ⇒ Valuable components for space applications . 4 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS I NTRODUCTION - T APE SPRINGS Mechanical behaviour: ◮ Highly nonlinear ◮ Different senses of bending ◮ Buckling ◮ Hysteresis phenomenon Bending moment M max M + Loading * M + Unloading max heel Bending angle θ θ θ + + Unloading * M _ Loading max M _ Equal sense bending Opposite sense bending 5 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS D EFINITION OF THE PROBLEM Folded configuration: reflector folded on the top of the solar R panel considered as clamped. L Deployed configuration: 120 ◦ . α Fixed parameters: t ◮ Reflector: 200 × 200 mm 2 , w max 30 m = 0 . 4 kg 200 h max 15 ◮ Two tape springs: L = 50 mm Reflector ◮ Opposite sense 50 120° Design variables: t , R , α with Tape spring w ≤ 30 mm , h ≤ 15 mm Solar panel 6 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS D EFINITION OF THE PROBLEM Material: beryllium copper ν ρ σ y E 8100 kg / m 3 131000 MPa 0 . 3 1175 MPa Objectives of this work: perform the deployment while ◮ minimising the maximum Von Mises stress σ VM max ◮ minimising the maximum amplitude motion d max by the means of an optimisation procedure. 7 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS P ARAMETRIC STUDIES - T HICKNESS With R = 20 mm and α = 90 ◦ . 3000 0 . 1 mm 0 . 15 mm 2500 0 . 2 mm 0 . 25 mm Bending moment [ Nmm ] If t ր : 2000 ◮ M max ր 1500 ◮ θ max ր 1000 ◮ M ∗ ր 500 ◮ ∆ E ր 0 ◮ σ VM max ր −500 −1000 −1500 −30 −20 −10 0 10 20 30 Bending angle [ deg ] 8 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS P ARAMETRIC STUDIES - R ADIUS With t = 0 . 1 mm and w = 28 . 28 mm . 600 20 mm 22 . 5 mm 500 25 mm 27 . 5 mm If R ր and α ց : Bending moment [ Nmm ] 400 300 ◮ M max ց ◮ θ max ր 200 ◮ M ∗ ց 100 0 ◮ ∆ E ց ◮ σ VM −100 max ց −200 −300 −10 −8 −6 −4 −2 0 2 4 6 8 10 Bending angle [ deg ] 9 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS O PTIMISATION - M ODEL DESCRIPTION min f ? F.E. analysis Initial Post-treatment of Optimisation Optimised -Folding up to 120° geometry the results routine geometry -Deployment New geometry Optimisation procedure performed on one tape spring with half the reflector mass (symmetric system). Confirmation for the complete hinge (two tape springs) a posteriori . 10 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS O PTIMISATION - M ODEL DESCRIPTION Optimisation problem: � c ( x ) ≤ 0 min f ( x ) such that lb ≤ x ≤ ub x Nonlinear inequality constraints: c 1 = w ( α, R ) − w max ≤ 0 c 2 = h ( α, R ) − h max 0 ≤ with w max = 30 mm and h max = 15 mm Lower and upper bounds: t [ mm ] R [ mm ] α [ rad ] lb 0 . 08 10 π/ 3 0 . 25 32 . 5 3 π/ 4 ub 11 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS O PTIMISATION - M INIMISATION OF σ VM max Results: α t R 0 . 08 mm π/ 3 rad Initial geometry 30 mm Optimised geometry 0 . 08 mm 19 . 07 mm π/ 3 rad X displacement [ mm ] 20 Solar panel 200 Tape spring 0 Reflector 150 −20 −40 100 Z [ mm ] −60 100 105 110 115 120 125 130 135 140 145 150 50 Z displacement [ mm ] 40 0 20 −50 0 −100 −20 −40 −200 −150 −100 −50 0 50 100 150 200 250 100 105 110 115 120 125 130 135 140 145 150 X [ mm ] Time [ s ] σ VM max = 666 . 25 MPa < σ y d max = 53 . 92 mm 12 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS O PTIMISATION - M INIMISATION OF d max Results: α t R 0 . 1 mm π/ 2 rad Initial geometry 15 mm Optimised geometry 0 . 244 mm 29 . 68 mm 1 . 0588 rad X displacement [ mm ] 20 Solar panel 200 Tape spring 0 Reflector 150 −20 −40 100 Z [ mm ] −60 100 105 110 115 120 125 130 135 140 145 150 50 Z displacement [ mm ] 40 0 20 −50 0 −100 −20 −40 −150 −100 −50 0 50 100 150 200 250 100 105 110 115 120 125 130 135 140 145 150 X [ mm ] Time [ s ] σ VM max = 1856 MPa > σ y d max = 51 . 26 mm 13 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS O PTIMISATION - M INIMISATION OF σ VM max AND d max f ( x ) = w 1 σ VM max + w 2 d max Objective function: Results: t R α Initial geometry 0 . 08 mm 10 mm π/ 3 rad Optimised geometry 0 . 0804 mm 30 mm π/ 3 rad X displacement [ mm ] 20 0 −20 −40 σ VM max = 877 . 75 MPa < σ y −60 100 105 110 115 120 125 130 135 140 145 150 Z displacement [ mm ] 40 d max = 52 . 08 mm 20 0 −20 −40 100 105 110 115 120 125 130 135 140 145 150 Time [ s ] 14 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS D EPLOYMENT OF THE REFLECTOR Complete finite element model: Solar panel 160 1 0 0 Lumped mass Solar panel (reflector) 5 0 15 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS D EPLOYMENT OF THE REFLECTOR Results: σ VM σ VM max , 1 TS = 877 MPa max , 2 TS = 866 MPa X displacement [ mm ] 20 Solar panel 200 Tape spring 0 Reflector −20 150 Hinge −40 100 1 tape spring −60 Z [ mm ] 100 105 110 115 120 125 130 135 140 145 150 50 Z displacement [ mm ] 40 0 20 −50 0 −20 −100 −40 100 105 110 115 120 125 130 135 140 145 150 −150 −100 −50 0 50 100 150 200 250 Time [ s ] X [ mm ] Validation of the optimisation procedure performed on a single tape spring. 16 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS D EPLOYMENT OF THE REFLECTOR 17 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS C ONCLUSIONS ◮ Exploitation of tape springs to deploy reflectors. ◮ Parametric studies on the impact of the geometry. ◮ Optimisation procedure to minimise σ VM max and/or d max 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 d max ? min σ VM min ( w 1 σ VM min d max max + w 2 d max ) max d max 53 . 92 mm 51 . 26 mm 52 . 08 mm 18 / 19

I NTRODUCTION P ROBLEM P ARAMETRIC STUDIES O PTIMISATION C ONCLUSIONS T HANK YOU FOR YOUR ATTENTION 19 / 19