Deployable Solar Array Structures with High Stowed Volume Efficiencies

The goal of this research is to develop new technologies which fulfill NASA Technology Roadmaps Technology Area Breakdown Structure (TABS) [1] goals of high-power generation of space solar arrays with low mass, high stiffness, and high strength (see specific TABS elements 3.1.3.1-4, 12.2.1.4, 12.3.1.4, and 12.3.1.6).

Approach
The research approach to achieve the objective was to:
1. Generate origami-based concepts that exhibit mass and volume-saving characteristics
2. Design, fabricate, and test concept prototype
3. Develop models to predict performance metrics for stiffness, strength, and power generation 
4. Perform systems-level analyses using validated models to explore the design space of the origami-based deployable systems

Results
The concept generation efforts resulted in a solar array concept that is Self-Deployable, Self-Stiffening, and Retractable (SDSR arrays). SDSR arrays are origami-based, fabricated using planar materials, fold up to stow into small volumes, self-deploy via release of stored strain energy, maintain stiffness via preload in a desired large-area 3D shape, and are retractable via reeled tension cables. The prototype in Figure 1 depicts several SDSR characteristics. Figure 1 (b) and (c) show a physical model of an SDSR array in its stowed configuration, which is 0.2 m tall and 0.4 m in diameter. Figure 1 (d) shows the array in a deployed state, 1 m in diameter. A primary gore and a secondary gore are indicated, eight pairs of which are patterned radially around the central hub. Eight cables are seen extending from the reel to the panels in Figure 1 (d). Figure 1 (a) shows the array in a slightly retracted state highlighting details of the cables routed through the panels and revolute joints with torsion springs.

Figure 1. Description of SDSR architecture.
Stored strain energy in joints releases to self-deploy once in space to perform the intended function (e.g. collect solar energy). Stiffness of deployed structures in space is required to maintain control of the spacecraft system; SDSR arrays obtain stiffness via the corrugations of the folds and the preloading of the cables routed through panels of the array. The routed cables can be wound on a central reel which controls deployment and retraction. SDSR arrays can be controlled such that they never obtain their fully flat state to maintain stiffness (as can be seen in Figure 1 (a) and (d), similar to corrugations) to ensure predictable behavior and to enable retraction. SDSR arrays can be controlled in-flight to tune stiffness or fully retract to mitigate effects of spacecraft maneuvers or to avoid micrometeoroid impacts.
Several models were used to predict SDSR array performance, including a multi-body dynamics model. The model can predict such metrics as stiffness, shape, reaction forces and moments, dynamic response, etc., and can animate the results. Figure 2 shows a prototype SDSR array transitioning from stowed to deployed on the top row and images of the model predicting the same motion on the bottom row.

Figure 2. SDSR array shown throughout deployment.
Another model was used to predict modal response, a way to measure system stiffness. This model used a simplified analytical approach that describes the vibration of annular plates. The model accurately predicted the mode shapes (see Figure 3) but required an empirical correction factor for the mode frequencies. The similarities of this array and the modeled plate indicate that this type of analytical approximation (with very low computational cost) can be used for SDSR arrays in parameter studies and systems analysis. However, it should be noted that if more predicable modeling is desired (i.e. in the design of flight hardware), higher-fidelity finite element models are recommended (at higher computational cost).

Figure 3. First four modeled and measured mode shapes.
Using the these and other prediction models, a system model was constructed to evaluate SDSR array performance in terms of critical mission metrics. These metrics are specific power and power density, measured in W/kg and kW/m3, respectively. NASA TABS goals suggest architectures with specific power over 100 W/kg and power density over 40 kW/m3 represent mission-enabling levels. Using the system model, SDSR arrays were demonstrated to achieve upwards of 200 W/kg and 60 kW/m3. Figure 4 shows the design space of an SDSR array architecture which is based off a constant-height origami flasher pattern. The figure indicates system trends as a function of design variables through the feasible and infeasible regions.

Figure 4. Specific power versus power density with constraint violations indicated.
Higher-performing designs tend to have fewer number of sides (N) and greater number of panels per side (n). According to the findings of this model, still higher-performing designs can be achieved by overcoming challenges of strength and stiffness as can be seen by the design trend lines in the figure. 
These research efforts produced a novel space array architecture achieving theoretically mission-enabling performance that does not require external booms to deploy, retract, or maintain stiffness. The concept was demonstrated using prototypes and low and high-level prediction models. This SDSR architecture presented a strong case to continue development of origami-based engineering for space applications.

Contributions
The following contributions to the literature were made over the course of the fellowship:

Fundamental research:
1. Design of compliant joints used for origami-based mechanisms [2], [3]
2. Folding thick origami techniques [4]–[7]

Space array research:
1. SDSR publications [8]–[13]