Design of an experimental set-up to analyse compliant mechanisms - PowerPoint PPT Presentation

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS 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 1 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS O UTLINE I NTRODUCTION E XPERIMENTAL SET - UP F INITE ELEMENT MODEL I DENTIFICATION OF THE PARAMETERS V ALIDATION OF THE FE MODEL C ONCLUSIONS 2 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS I NTRODUCTION - T APE 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... 3 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS I NTRODUCTION - T APE SPRINGS Complexity: Assets: ◮ Storage of elastic energy ◮ Passive and self-actuated Bending moment deployment M max M + A ◮ No lubricant ◮ Self-locking in deployed E configuration B D * M + C O max ◮ Possibilities of failure heel θ θ Bending angle H + + θ M _* G limited max M _ F ◮ Versatility Equal sense bending Opposite sense bending 4 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS I NTRODUCTION - O BJECTIVES ◮ 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 5 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS E XPERIMENTAL SET - UP Constraints: Despite the presence of the gravity field, ◮ No buckling under its own weight ◮ Passive deployment starting from a downwards folded configuration 6 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS E XPERIMENTAL SET - UP Acquisition equipment: ◮ 3D motion analysis system (C ODAMOTION ) ◮ Acquisition frequency: 800 Hz ◮ Triangulation of active markers (precision ∼ 0 . 3 mm ) ◮ Force plate under the support (K ISTLER ) Codamotion CX1 unit 7 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS E XPERIMENTAL SET - UP Deployment tests: Initial downwards folding in opposite sense 8 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS E XPERIMENTAL SET - UP Positions: (superposition of 50 curves) 80 Displacement along the x -axis [ mm ] 0 Displacement along the z -axis [ mm ] 60 −10 40 −20 20 −30 0 −40 −20 −40 −50 −60 −60 −80 −70 −100 −80 −120 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Time [ s ] Time [ s ] Vertical force: 20 15 Force along the z -axis [ N ] 10 5 0 −5 −10 −15 0 0.5 1 1.5 2 2.5 Time [ s ] 9 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS D EPLOYMENT TESTS Reproducibility of the experimental results: for 170 tests with 4 pairs of tape springs Variation amplitude [%] On the positions: 1 Peak max. x Peak min. x 0.8 Peak max. z Peak min. z 0.6 ◮ Relative SD. < 1 % for 0.4 the peak amplitudes 0.2 0 1 2 3 4 5 6 7 8 9 10 Variation time [%] 4 3 ◮ Relative SD. ր for the 2 peak times 1 0 1 2 3 4 5 6 7 8 9 10 Peak number [ − ] 10 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS F INITE ELEMENT MODEL ◮ Shells for tape springs and rod ◮ Rigid interfaces ◮ Big interfaces clamped (fixation support not represented) ◮ Structural damping in the Big interfaces tape springs s g n r i p ◮ Nonlinear dynamic analyses s e p Small interfaces a T ◮ Generalised- α method Rod ◮ Low numerical damping ◮ Automatic time stepping procedure ◮ S AMCEF software 11 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS F INITE 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 12 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS F INITE 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 13 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS I DENTIFICATION OF t AND E Three points bending tests: Use of an optimisation algorithm coupled to a FE model to determine t and E fitting the Load cell experimental results 20 Experimental Numerical Loading head Tape spring 15 sample Support Support 10 a n Load [ N ] p S 5 0 −5 −10 −8 −6 −4 −2 0 2 4 6 8 10 Displacement [ mm ] Exp. relative SD. < 5 % ∆( exp − num ) < 14 % 14 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS I DENTIFICATION OF THE STRUCTURAL DAMPING Small amplitude vibration tests: 8 Experimental curve Displacement along the z -axis [ mm ] Maximum peaks Minimum peaks 6 4 2 0 −2 −4 −6 −8 0 5 10 15 20 25 30 Time [ s ] Hypothesis: Exponential decay of the oscillations Z exp ( − εω t ) ⇒ Can be represented by a Kelvin-Voigt model in the FE model 15 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS I DENTIFICATION OF ε Small amplitude vibration tests: (510 tests in 11 sessions) Mean Max. diff. Relative SD. 0 . 509 % 0 . 288 % 20 . 67 % ε ∆ t 0 . 100 s 0 . 003 s 0 . 919 % 0.72 Challenging measurements: Experimental results Mean 0.7 ◮ Sensitivity to the assembly Structural damping [%] 0.68 procedure 0.66 ◮ Non-uniformity of the 0.64 samples cut out from the 0.62 0.6 same measuring tape 0.58 ◮ Thermal effects within a 0.56 session of tests 0.54 0 5 10 15 20 25 30 35 40 45 50 Test number [ − ] 16 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS V ALIDATION OF THE FE MODEL Deployment tests: comparison with the experimental results 80 180 FE model Displacement along the x -axis [ mm ] Displacement along the z -axis [ mm ] 70 160 60 140 50 120 40 100 30 80 20 60 10 0 40 −10 20 −20 FE model 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Time [ s ] Time [ s ] 17 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS V ALIDATION OF THE FE MODEL Deployment tests: comparison with the experimental results 80 180 FE model Displacement along the x -axis [ mm ] Displacement along the z -axis [ mm ] 70 160 60 140 50 120 40 100 30 30 Peak max. x max( A exp ) [%] 25 Peak min. x 80 20 Peak max. z | A exp − A num | 20 Peak min. z 10 60 15 0 40 10 −10 5 20 0 −20 FE model 1 2 3 4 5 6 7 8 9 10 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Time [ s ] Time [ s ] 10 max( t exp ) [%] 8 | t exp − t num | 6 4 2 0 1 2 3 4 5 6 7 8 9 10 Peak number [ − ] 18 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS V ALIDATION OF THE FE MODEL Experimental Numerical 19 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS C ONCLUSIONS ◮ 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 20 / 22

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS C ONCLUSIONS 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

I NTRODUCTION S ET - UP FE MODEL I DENTIFICATION V ALIDATION C ONCLUSIONS T HANK YOU FOR YOUR ATTENTION 22 / 22