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Research Papers

Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom

[+] Author and Article Information
Davide Piovesan

Biomedical Engineering Program,
Department of Mechanical Engineering,
Gannon University,
109 University Square,
Erie, PA 16541
e-mail: piovesan001@gannon.edu

Mirco Zaccariotto

Centre of Studies and Activities for Space,
CISAS—“G.Colombo,”
Via Venezia 15,
Padova 35131, Italy;
Department of Industrial Engineering,
University of Padua,
Via Venezia 1,
Padova 35131, Italy
e-mail: mirco.zaccariotto@unipd.it

Carlo Bettanini

Centre of Studies and Activities for Space,
CISAS—“G.Colombo,”
Via Venezia 15,
Padova 35131, Italy;
Department of Industrial Engineering,
University of Padua,
Via Venezia 1,
Padova 35131, Italy
e-mail: carlo.bettanini@unipd.it

Marco Pertile

Centre of Studies and Activities for Space,
CISAS—“G.Colombo,”
Via Venezia 15,
Padova 35131, Italy;
Department of Industrial Engineering,
University of Padua,
Via Venezia 1,
Padova 35131, Italy
e-mail: marco.pertile@unipd.it

Stefano Debei

Centre of Studies and Activities for Space,
CISAS—“G.Colombo,”
Via Venezia 15,
Padova 35131, Italy;
Department of Industrial Engineering,
University of Padua,
Via Venezia 1,
Padova 35131, Italy
e-mail: stefano.debei@unipd.it

1Corresponding author.

Manuscript received June 30, 2015; final manuscript received December 1, 2015; published online March 7, 2016. Assoc. Editor: Mary Frecker.

J. Mechanisms Robotics 8(3), 031007 (Mar 07, 2016) (11 pages) Paper No: JMR-15-1170; doi: 10.1115/1.4032271 History: Received June 30, 2015; Revised December 01, 2015

This work presents an analysis and validation of a foldable boom actuated by tape-spring foldable elastic hinges for space applications. The analytical equations of tape-springs are described, extending the classical equations for isotropic materials to orthotropic carbon-fiber composite materials. The analytical equations which describe the buckling of the hinge have been implemented in a multibody simulation software where the hinge was modeled as a nonlinear elastic bushing and the boom as a rigid body. In the experimental phase, the boom was fabricated using a thin layer carbon-fiber composite tube, and the residual vibrations after deployment were experimentally tested with a triaxial accelerometer. A direct comparison of the simulation with the physical prototype pointed out the dangerous effect of higher order vibrations which are difficult to capture in simulation. We observed that while the vibrational spectra of simulations and experiments were compatible at low frequencies during deployment, a marked difference was observed at frequencies beyond 30 Hz. While difficult to model, higher order frequencies should be carefully accounted for in the design of self-deployable space structures. Indeed, if tape-springs are used as a self-locking mechanism, the higher vibrational modes could have enough energy to unlock the structure during operation.

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References

Figures

Grahic Jump Location
Fig. 1

(a) Representation of two tape-springs in parallel with the concave side facing each other. L is the length of the spring, RT is the internal radius of the tube, and M is the bending moment of the forces. (b) Boom in its deployed configuration where the deployment angle is 2θ=0. (c) Configuration of the stowed boom of length Lb (2θ=90 deg). The variable ms g is the weight of the sensor, and mb g is the weight of the boom.

Grahic Jump Location
Fig. 2

(a) Reference frame of a single undeformed rib of a tape-spring. The x-axis points longitudinally, the y-axis transversally, and the z-axis points toward the center of the tube of radius RT. The thickness of the spring is h, and the subtended angle of the undeformed rib is 2α. (b) Deformation of the rib in opposite bending. Mx is the moment necessary to deform the spring. M− is the reaction moment generated by the spring under such deformation. Note that the centers of the longitudinal radius rL and transversal radius rT of the deformed spring are located at the opposite sides of the neutral plane of the rib and rL>0. (c) Deformed spring in equal bending.

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Fig. 5

(a) Prebuckling longitudinal configuration of the spring and (b) postbuckling longitudinal configuration of the spring

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Fig. 4

Simplified example of force control in a redundant system. (a) Force is generated along the horizontal axis on a viscoelastic system. The arm configuration is redundant since only a monodirectional force can be generated by either kinetic or kinematic inputs of both the wrist and elbow joints. In this example, only the elbow is directly commanded using either the torque M or the angle θ. (b) Example of torque–angle curve at steady state when either elbow torque (black) or elbow joint displacement (gray) is used as input to command the force at the point of contact with the environment. It is apparent that the torque input produces instability in the neighborhood of the system's kinematic singularity (hand and forearm are almost on the same line). The different phases of the experiment are described in Sec. 3.1.

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Fig. 3

(a) Orientation of force per unit measure on a spring sample and (b) orientation of moments per unit measure

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Fig. 6

Example of moment exerted by the spring as a function of the hinge rotation 2θ. All the solid lines are those followed by the real structure transitioning through flexural and torsional buckling. Dashed lines are theoretical conditions that are not achieved because of buckling transitions. Propagation moments during flexural buckling (a-b), flexural moment of nonbuckled structure (b-c and d-e-f), and torsional buckling caused by flexural moment in equal bending (a-c-d). The different transition phases are described in Sec. 4.

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Fig. 7

Buckling cycles of two springs in parallel where the gray spring is in equal bending and the black is in opposite bending. The diagram starts from the right and each step is described following the arrows counterclockwise.

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Fig. 11

Spectrum of the acceleration along the y-axis of the accelerometer. Solid line corresponds to the direct measurement obtained with the experimental setup. Dashed line is the spectrum estimated using the simulation performed with simwise 4D. The two black vertical dashed lines indicate the first two frequency of the deployed boom.

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Fig. 12

Spectrum of the acceleration along the z-axis of the accelerometer. Solid line corresponds to the direct measurement obtained with the experimental setup. Dashed line is the spectrum estimated using the simulation performed with simwise 4D. The two black vertical dashed lines indicate the first two frequency of the deployed boom.

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Fig. 9

(a) Simulated and experimental deployment angles. (b) Acceleration of the payload for the Z- and Y-axis of the payload as described in Fig. 8(a). The experimental measurements are calculated as the average of ten deployments. The shaded area represents one standard deviation. In both panels, the correspondence with the point in Fig. 7 is shown.

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Fig. 8

(a) The accelerometer is glued on the top flange of the tube and (b) upper part of the tube with the top flange mounted, rotation of the boom occurs around the x-axis

Grahic Jump Location
Fig. 10

Moment versus angle of deployment. The first part of the deployment from a′ to b′ is dashed. The oscillation from d′ to e′ is dashed–dotted.

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