Megan Ochalek - Module 8 - Part 1

Space applications are greatly limited by space allowances of payloads. As such, space structures have to be packaged down into the minimal volume possible; this often is realized in the form of deployable structures. One such deployable structure are coilable booms, which can buckle controllably into a tightly wound ‘coiled’ state for packaging, then be deployed into a structural boom (like a tape measure!).

These booms can be used as structural ribs for lightweight arrays, such as solar or RF arrays, which are often very thin and have little stiffness themselves. Shown below is one example of this, which uses coilable booms as the structure to deploy the antenna.

My tool aims to help users trying to make a cubeSat deployable array using booms make initial design decisions by generating possible options and weighing them against each other.

Intended users

CubeSats are a small type of satellite that has dimensions in multiples of 10cm cubes (so 10x10x10 cm is the smallest, but 20x10x10cm and 30x20x40cm are also possible). These satellites are much more accessible as an entry-point to smaller, less resource-abundant groups, such as college clubs. The intended users for my tool would be these groups, because it could be helpful to start your design with a better sense of the trade offs.

Need you’re trying to provide a solution or support for

I am trying to support the design of these coilable-boom-supported structures by helping narrow down the design space early on to inform decisions. The critical considerations of these structures are:

• avoiding buckling failure mode - if the booms buckle, it can be catastrophic to the mission. For most use cases, they would experience buckling from bending-imposed loads. Hence, my tool will have a simple measure of the maximum compressive force felt in the boom during this load case; by minimizing this, we can be more robust to these loads
• achieving mission requirements -
• minimizing weight, and staying below the mission’s weight limit
• achieving the mission requirement for surface area, or maximizing surface area
• avoiding plastic failure - when these booms are coiled, they can only be coiled so tightly before they experience plastic deformation, which can cause them to fail. We want to know what radius we can coil the booms to safely; this also dictates how large the packaged volume is
• minimizing spare volume - cubesats have a set volume allowance, and while we want to minimize overall volume and mass, ideally there isn’t much unused volume in the cubesat

Underlying logic of the model you’ll implement

I am going to be using generative design for this tool. It will let users control what inputs are varied/fixed/limited depending on what their specific needs are.

Assumptions:

• here, we are only going to consider the option where 4 booms are used in an ‘X’ configuration (similar to the image above). These 4 booms all coil into the same central spool, which is oriented along the z-axis
• assume the array is square for simplicity - $l \times l$
• for packaged volume, we are going to neglect the thickness of the array. These arrays are often membranes, and are much thinner than the booms. Calculating the thickness for the folding pattern that accompanies the ‘X’ boom configuration is difficult and not necessary for a first pass design tool.
• I’m just going to model the half moon and cylindrical shell options for boom cross sections

Logic:

As we are calculating these designs, we will also build a model of the deployed configuration.

1. booms are modeled as shells, depending on the user’s input for shape & cross section size :
• cylindrical
• half-moon
2. the second moment I of these cross sections, as well as their neutral axis for bending, can be calculated (using the associated formula and extracting the NA from solid.centroid, respectively)
3. based on the radius r of the uncoiled boom (dictated in a), calculate the minimum coiled radius R that will not cause plastic deformation during stowage
4. using R and r, calculate the Minimum Rolled Volume (MRV) of the structure. We can model the rolled structure as a cylinder with $height = \pi r$ (the flattened boom cross section) and $radius = l_b/(2 \pi R)*t + R$, where $l_b = l/\sqrt(2)$ is the length of the boom and t is a fixed boom thickness
5. calculate spare volume: $SV = CSV - MRV$, where CSV is cubesat volume
6. calculate mass of structure
7. calculate surface area of deployed array
8. calculate max compressive stress

Inputs

to vary:

• dimension of cubesat units - what cubesat volume are we working with? ie, are we limited to a single 10x10x10cm unit, or can we use up to 30x10x10cm?
• array dimension, $l$
• what type of boom cross section? (if this is too much, might just do one cross section type)
• boom cross section dimension - for simplicity, each boom cross section will be driven by just one dimension that scales the cross section uniformly

as requirements:

• maximum allowable mass
• minimum allowable array area

Outputs

The metrics that a user could care about are:

• surface area of deployed array - want to maximize or achieve mission requirement minimum
• total mass - want to minimize or stay below mission requirement maximum
• maximum compressive stress - want to minimize or stay below mission requirement maximum
• minimum coiling radius - this inherently minimizes the packaged volume, but is useful to have outputted for the designer
• packaged volume - if the designers are debating between say a 2U and a 1U payload, its useful to see what the actual packed volume is. In some cases, it might be better to reevaluate goals (ex, if you can only have 1U), while in others, you may decide it is better to go for a larger payload and adjust accordingly.
• spare volume - want to minimize

Depending on exactly what the user needed, different visualizations could be helpful, and with the generative design side of dynamo, they would be able to vary that. However, I think that having a visualization chart showing spare volume vs maximum compressive stress, with boom cross section as the size of the marker would be a quick and efficient way to digest design trade offs.