Experimental Validation of Structural Damping Models for Tape - PowerPoint PPT Presentation

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS 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 1 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS O UTLINE I NTRODUCTION O BJECTIVES E XPERIMENTAL SET - UP Q UASI - STATIC TESTS D YNAMIC TESTS GPM Core Observatory satellite (Credit: NASA) C ONCLUSIONS 2 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS T APE SPRINGS - D EFINITION Definition: Thin strip curved along its width used as a compliant mechanism. Known in the everyday life as Carpenter or measured tapes. Geometry: R L α t Credit: 01dB-Metravib & CNES 3 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS T APE SPRINGS - A SSETS ◮ 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. 4 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS T APE SPRINGS - M ECHANICAL BEHAVIOUR ◮ Highly nonlinear ◮ Different senses of bending ◮ Buckling ◮ Hysteresis phenomenon Bending moment M max M + Loading * M + Unloading max heel θ Bending angle θ θ + + Unloading * M _ Loading max M _ Equal sense bending Opposite sense bending 5 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS T APE SPRINGS - P REVIOUS 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) 800 500 M M M m ax Peak M m ax + + moment M m ax M m ax 400 − − 600 Peak 300 Bending moment [N mm] moment Bending moment [N mm] 400 Buckling 200 Buckling 200 100 Residual moment Residual moment 0 0 − 100 − 200 − 200 − 400 − 300 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Time [s] Time [s] Folding Deployment Folding Deployment Without structural damping With structural damping Conclusions: ◮ Numerical damping for the convergence of the solver ◮ Structural damping to capture the physical behaviour 6 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS O BJECTIVES 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. 7 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS E XPERIMENTAL SET - UP Horizontal configuration: Vertical configuration: Tape spring e c a f r e n t I 8 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS E XPERIMENTAL SET - UP Measuring equipment: ◮ Force plate ( Kistler ) ◮ Motion sensors ( Codamotion ) In the laboratory of human motion analysis (LAMH, ULg, Belgium). Sensors Force plate 9 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS E XPERIMENTAL 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 7 , 850 kg / m 3 210 , 000 MPa 0 . 3 Uncertainties on the dimensions and the material properties. 10 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS Q UASI - STATIC TESTS On the horizontal configuration, a vertical force is applied on the dummy panel: 4000 Buckling 3000 Loading 2000 [N mm] 1000 Unloading 0 M max 1000 y 2000 3000 4000 5000 0 2 4 6 8 10 12 14 16 18 Time [s] 11 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS Q UASI - STATIC TESTS Quasi-static finite element model: z y x g 12 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS Q UASI - STATIC TESTS Results: Mean exp. value FEM results Diff. wrt. FEM F max 3 . 33 N 4 . 13 N 19 . 52 % z θ max 11 . 54 ◦ 11 . 84 ◦ 2 . 51 % + M max 1141 . 8 Nmm 980 . 6 Nmm 16 . 44 % y 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 13 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS D YNAMIC TESTS On the vertical configuration, folding up to an angle of ∼ 50 ◦ , then deployment: 150 100 X-position [ mm ] 50 0 −50 −100 Peak in equal sense −150 Peak in opposite sense Limit for peaks in equal sense Limit for peaks in opposite sense −200 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [ s ] 230 Peak in equal sense Peak in opposite sense 220 210 Z-position [ mm ] 200 190 180 170 Limited lateral displacements 160 0 0.5 1 1.5 2 2.5 3 3.5 4 14 / 21 Time [ s ]

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS D YNAMIC TESTS Complexity of the experimental tests: ◮ Vibration of the plate ◮ Repeatability 200 Test 1 Test 2 Test 3 150 100 X-position [ mm ] 50 0 −50 −100 −150 −200 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [ s ] ◮ Plastic deformations in the tape springs 15 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS D YNAMIC 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 414 y 412 .5 410 Z-position [ mm ] 1 408 Δ t 406 .5 404 0 t 402 .5 400 Experimental result Y exp ( − εω 0 t ) 398 1 − Y exp ( − εω 0 t ) 396 0 1 2 3 4 5 6 7 8 9 10 Time [ s ] .5 ◮ Hypothesis: motion dominated by the first bending mode ⇒ exponential decay ◮ Mean experimental structural damping: ε = 0 . 65 % 16 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS D YNAMIC TESTS Correlation of the FEM: (On the horizontal configuration) ◮ Structural damping represented by a Kelvin-Voigt model based on a single viscosity coefficient 5 Numerical result [ Y exp ( − εω 0 t )] mean 4 [ − Y exp ( − εω 0 t )] mean 3 Z-displacement [ mm ] 2 1 Results ε Frequency 0 Exp. 0 . 65 % 9 . 73 Hz −1 0 . 645 % 9 . 59 Hz Num. −2 −3 −4 −5 0 1 2 3 4 5 6 7 8 9 10 Time [ s ] 17 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS D YNAMIC TESTS Dynamic finite element model: z y x g 18 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS D YNAMIC TESTS Correlation of the FEM: ◮ Large amplitude motion 250 280 Numerical result Numerical result Test 1 Test 1 200 Test 2 Test 2 260 Test 3 Test 3 150 240 X-position [ mm ] Z-position [ mm ] 100 220 50 0 200 −50 180 −100 160 −150 −200 140 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [ s ] Time [ s ] Fair correlation for the oscillation frequency, but poor on the amplitudes. 19 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS C ONCLUSIONS ◮ 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 20 / 21

I NTRODUCTION O BJECTIVES S ET - UP Q UASI - STATIC TESTS D YNAMIC TESTS C ONCLUSIONS T HANK YOU FOR YOUR ATTENTION 21 / 21