3D Printing & Internal Geometry | An Often Overlooked Critical Design Detail

03/15/2016

Background

3D printing is revolutionizing design and manufacturing. Chances are if you checked the news today it will somehow have been recently applied and demonstrated in a new field as a viable, commercial available, and widely supported approach by all leading global brands across every social-media channel.

This article discusses one piece of the 3D printing puzzle: the importance of design using one of the unique properties to 3D printing. It is a first-order demonstration of 3D printing parts to yield optimized stiffness to weight ratio by adjusting internal geometry. It is more in-depth than a typical 3D printing post, but not to be considered as a formal proof or fully optimized design pattern. It is a call to action to better utilize the tools available for design and manufacture when building using this technology.

Theory

When you look at organic structures in plant and animal life you see specific shapes and internal structures. Take for example, the shape of this palm frond leaf. When you look at the cross-section, there is an evident triangular bowl shape where most of the material is concentrated at the top. This shape grew to become optimized for resisting bending loads under gravity, but still flexible under wind loads from the sides. Additionally, as you take a look at the distribution of matter within the cross-section you may notice patterns that place smaller more dense elements near the periphery of the outside cross-section geometry, with more non-solid matter distribution towards the center. This is a property you can clearly see in the detailed mare's tail cross-sections.

When you look at a sectioned or broken animal bones you may notice a porous distribution of matter, where the size of each of the porous sections is reduced as it approaches the walls of the bone. This structure is designed for both bending and axial compressive loads. The webbing of the interior within the outer shell of the bone provides a rigidity to reduce the potential for localized buckling load failure modes. This is important if you do any impact loads, like running, jumping, or dropping out of trees if you are a primate. On the issue of optimized stiffness/weight, the white pelican beak is designed in this manner to reduce the overall weight of the beak, while affording stability and size to aid in capture of prey. This allows the pelican to take flight while maintaining a massive gullet.

Concentrating matter near the peripheries of an object in nearly all cases produces an increase in bending, torsional, and axial load bearing capacity, but internal webbing is required to provide local support for the peripheries of the object. Nature figured it out long before scientists did. What we need to do now is build 3D printed structures in ways that are optimized, much like the internal structure of plant and animal life. Here are some fun equations that illustrate the importance of matter distribution in a structure under axial compression loads when considering the buckling failure mode for a long-slender beam using classical methods from continuum mechanics:

Improving the internal structure in a 3D printed model is essentially increasing the value of I, the area moment of inertia, while attempting to keep the effect on the mass of the part constant. L is constant reflecting beam length and end constraint conditions, and K covers the constraint type. Increasing I while maintaining the mass results in an increased stiffness to weight ratio, and arguably a more efficient part if you are designing based on a fixed geometric size but under imposed strength requirements.

This is just a simple illustration of the basic concept, and there are many other considerations that come into play that prohibit certain geometries that would theoretically prove optimimum. I will show that these considerations become apparent with 3D printed parts, most notably details that place limitations on optimizing the value of I relating to localized geometry instability or buckling (e.g. thin unsupported walls) under bending, axial, and torsional loading conditions.

Finite Element Analysis

Buckling is not the easiest to demonstrate accurately using FEA, as it requires an iterative non-linear solver to compute accurately. However, we can instead use modal analysis to illustrate what happens on the macro-scale for a shape that has a value for I that is less in one direction than in the other direction. This shows the importance of designing parts that maintain suitable values for I under all expected load and constraint conditions.

Notice that the beam has a primary mode shape in the direction of the lowest value for I (area moment of inertia). This is the weakest direction in bending, and it becomes the failure mode direction in buckling. A better design would have comparable internal webbing if it were subject to the loads as illustrated above, and that resultant webbing shape would be a +, #, or x. With the buckling failure mode, the higher the frequency for a particular mode shape the more stable the structure. A structure with significant internal webbing and cross-bracing should have higher modal frequencies when compared to one with minimal internal structures. This is where 3D printing comes into play.

Experiment & Results

I put the theory to the test by using the closest known manufacturing technique currently available to provide voxel based deposition capacity. Aside from biological growth of materials, 3D printing is the only viable way to build objects in this manner between 5mm and 500mm in longest dimension. I used a Type A Series 1 Pro for the build, and I began with one rectilinear pattern vs one 3D honeycomb pattern. I chose to use the Type A 3D printer because of its enormous build envelope of 12 x 12 x 12 inches, and a nozzle that maintains temperature well and that pushes out molten filament effortlessly and without skips or clogs. This means better interlayer adhesion, and a more realistic test result for either case.

I had a hunch that testing buckling failure mode would make for the most spectacular demonstration of failure using a high-speed camera, but it turns out that the parts were incredibly strong and I could not safely produce failure using the 80 pounds of metal weights I had available. For my first tests I 3D printed rigid supports for either side of the column to test, and I managed to arrange the system in a manner to keep the loads nearly axial on the test piece by using steel alignment rods as guide rails.

I used Slic3r 1.2.9 as a simple way to check whether or not this is a viable assertion. Slic3r recently added a 3D Honeycomb infill feature, which I argue is a first-order approximation of printing using an optimized interior infill pattern for a high stiffness to weight ratio while accounting for localized instability (unsupported walls). For my first tests I used a layer height 0.2mm, a single outer shell, a 10% infill ratio, and four solid bottom and top shells. I used PLA plastic, a 210C extrusion temperature, and 60C bed temperature with 3M "blue tape" to improve adhesion for the small 1 inch square base. I used a feed rate of 60 mm/s for perimeters, and 80mm/s for infill. I disabled retraction of filament to ensure there were no periodic weaknesses introduced into each layer.

Below is an example test result performed using bending load testing to induce failure of the sample since I couldn't achieve buckling failure using the equipment at my disposal.

I repeated this testing process for multiple different sample types (videos at 8x playback speed on vimeo here), and tabulated the results as shown below:

Test # Details Weight Buckling Bending
1 Infill: Rectilinear 0%, Layers:0.2mm 14.3 g N/A 25 lb
2 Infill: Rectilinear 10%, Layers: 0.2mm 40.5 g > 80 lb 50 lb
3 Infill: 3D Honeycomb 10%, Layers: 0.2mm 38.4 g N/A 49 lb
4 Infill: 3D Honeycomb 10%, Layers: 0.1mm 36.7 g N/A 50 lb

While there is a correlation between 0% and 10% infill, there was no correlation between the 3D honeycomb and rectilinear types. I anticipated that there would be some loss in signal due to the lack of rigid connection between subsequent infill layers, but did not expect it would fully wash out the signal. Here is a close up of the printed parts showing the interlayer bonding problem when using the 3D Hexagonal Infill slic3r provides, as well as a more design-loading condition driven approach that can be used with FEA solvers:

Should the software have afforded a few simple tweaks on the 3D honeycomb infill setting the test results could have produced a more meaningful result. Alternatives to fix this defect include crossing paths during each infill layer, adjusting the extrusion flow multiplier, or producing double-wall thickness paths. Reducing the layer height alone did not aid in improving fusion between layers as the root cause of the 3D honeycomb infill parts resides in the toolpath domain. This means that an alternate method need be devised to more conclusively produce comparable results for infill types of the 3D pattern variety.

Closing

Geometry, software, material, and additive fabrication process are all critical factors when building end-use 3D printed parts. Each decision in the design and manufacturing process affords a level of control unmatched to conventional manufacturing processes, and because of that there are numerous new challenges to resolve to take full advantage of the new capabilities while avoiding the risks.

Infill algorithms currently available for desktop 3D printing do not provide the level of detail and attention needed for mechanical optimization of overall part strength. The current state appears to be a race to the bottom in terms of perceived quality, exterior accuracy, print time, and and print completion reliability. Those are important considerations, but once this technology becomes more integrated into everyday objects, the needs of optimized internal geometry will become more apparent for the production of long-lasting durable parts. Until then we should continue to strive to design and build using 3D printing best-practices like using internal structures more like nature has discovered and engineering has confirmed. There are smart people and companies using optimized infill today, and soon this capacity will be extended to consumer-grade 3D printed parts too.

Credit: Edits by Christine Crockett, purveyor and expert of English Language and Writing.