LAD: LOW ALTITUDE DEMONSTRATOR Theory, Implementation
BACKGROUND
This page serves as an attempt to quantify some of the thought processes that my friend Andrew Chen and I went through in the development process of LAD. This is an ongoing project that has brought my prior 3D printed rocket endeavors to the high-powered class, and has proved the practicality of utilizing large 3D printed structures for intense load bearing purposes.
Through our experience developing this program, it is our firm belief that the possibilities afforded by direct, large-scale printing vastly expand the design space for high-powered rocketry and will continue to redefine what SEB as a club is capable of. These are some of the details regarding how we are able to produce, fly, and improve on the world’s first and (at time of writing) only fully MJF-printed high powered launch vehicles.
High-power rocketry is a class of hobby rocketry that, according to the National Association of Rocketry, describes vehicles with motors exceeding 160 newton-seconds of total impulse (corresponding to the “H” impulse class). The rockets flown by SEB exceed this minimum amount by an order of magnitude, ranging from 3000-5000 newton-seconds of total impulse (corresponding to the “L” impulse class) and typically exceeding 1000 newtons of average thrust. The airframes designed and flown by SEB have ranged between two and three meters in length, and 100 and 300 millimeters in diameter. The design and material selection of these airframes is governed primarily by the thrust-induced compressive forces on the rocket body. In our first-order estimate, total compressive forces consist of a sum of motor thrust and aerodynamic drag, the latter of which consists of pressure drag and skin friction. We arrived at our rough values for total stress on the airframe through a combination of a manufacturer-provided thrust curve and our own aerodynamic simulation utilizing a conservative estimation for coefficient of drag. Compressive forces contribute towards elastic buckling, which is a primary failure mode of slender airframe structures.
With the goal of weight optimization in mind, airframe structures used in high-power rocketry are commonly made from fiber-reinforced composite materials like glass fibers or carbon fibers with an epoxy resin matrix phase. To reduce the cost and complexity associated with the production of these fibrous composites, we have typically manufactured them using a “wet layup” technique, whereby dry fibers are saturated with a thermosetting matrix material in the liquid phase. Curing via. crosslinking of the thermoset occurs at ambient temperatures and pressures without the use of vacuum infrastructure or an autoclave. Nonetheless, the resulting structure is a high-stiffness, high-strength airframe capable of withstanding several kilonewtons of compressive force without yielding or buckling. Although the wet layup technique requires minimal infrastructure, it is often difficult to control for consistency in the produced part. Non-uniform matrix distribution, air pockets or voids, and misalignment of fibers are common issues encountered in our room-temperature wet layups. Furthermore, the post-processing of cured composite airframes is often labor-intensive, requiring intense personal protective equipment (PPE) to protect against airborne fibers during cutting and sanding. If internal mounting features, e.g. for fin structures, are desired, they must account for process deviations in nominal dimension and in cylindricity of a manually-produced airframe. Holes, hatches, and access panels are typically added after the structure is complete; even with appropriate tooling and jigging, these features can suffer from tolerance issues associated with process deviations. Cutting into a composite structure also greatly increases the chance of layer delamination.
Due to all of these factors, a solution that permits the direct fabrication of internal airframe features is incredibly attractive. Large-scale 3D-printing offers many promising avenues to tackle these challenges- specifically, the use of multi-jet fusion (MJF) technology permits the direct printing of airframe components without the need for support material (cf. filament extrusion methods) and chemical post-processing (cf. stereolithography). Furthermore, HP’s Jet Fusion 5200 printer has a build volume of 380mm by 284mm by 380mm, large enough to accommodate full-size airframe sections. The simultaneous printing of each XY layer in conjunction with the lack of overhang constraint also allows many parts to be stacked in one build volume, enabling incredible timelines. The most common materials used with the MJF process, polyamide (PA)-11 and PA-12, are lightweight thermoplastic materials with well-characterized properties, enabling more complete analysis of the structures we produced.
To a certain extent, the material properties of MJF-produced PA-12 are dependent on packing parameters (part-to-part spacing, printing location, and printing orientation) and part geometry. In particular, for coupon samples in the 1.0mm-4.0mm range, stiffness and strength was found to vary with specimen size. To a lesser extent, the failure characteristics (e.g. elongation at break) varied with printing orientation, particularly for samples printed at an angle greater than 45 degrees from the vertical.
TECHNICAL
To a certain extent, the material properties of MJF-produced PA-12 are dependent on packing parameters (part-to-part spacing, printing location, and printing orientation) and part geometry. In particular, for coupon samples in the 1.0mm-4.0mm range, stiffness and strength was found to vary with specimen size. To a lesser extent, the failure characteristics (e.g. elongation at break) varied with printing orientation, particularly for samples printed at an angle greater than 45 degrees from the vertical.
Figure 1: Empirically-determined material properties of MJF-printed polyamides.
With the goal of evaluating the use of a 3D-printed inner airframe structure with a composite overwrap layer, in January 2022 SEB designed the LAD-5 vehicle. Standing at 2.2 meters in height and having an outer diameter of 120mm, LAD-5 was designed to fly to 11,000 feet above ground level (AGL) in the transonic regime on an L-1300 solid motor with 4,567 newton-seconds of total impulse. To test the concept of producing a glass-fiber reinforced polymer (GFRP) on top of a printed structure, mechanical testing was performed using coupon samples of thermoplastic-GFRP composites. ASTM D638 Type-I “dogbone” samples were pulled in tension until failure to obtain the tensile strength and elastic modulus. The figure below shows the tensile stress-strain curve of seven such samples. A roughly bi-linear trend is evident, with a “knee” around 30-40 MPa tensile stress corresponding to the tensile strength of the thermoplastic phase alone. In the first linear region before the knee, both phases of the composite are sustaining load with an effective stiffness that accounts for contributions from the thermoplastic and the glass fibers. However, after the thermoplastic reaches its tensile strength, it enters the plastic regime where further elongation fails to produce an increase in stress-carrying capacity. Consequently, the GFRP phase of the composite bears the remaining load until ultimate failure begins to occur around 7% strain. The failure of the GFRP is characterized by a combination of layer delamination and fiber pull-out, the former of which is evidenced in the stress-strain characteristic of some samples just before failure. From a design perspective, low strains are anticipated under service loading. However, as a conservative estimate, the elastic modulus of the second linear region, which is lower than the elastic modulus of the first linear region, is used in design calculations involving thermoplastic-GFRP structures. This essentially corresponds to assuming that the thermoplastic phase makes a negligible contribution to the stiffness of the composite.
Figure 2: Tensile stress-strain behavior of a thermoplastic-GFRP composite structure.
Repeating this experiment with carbon-fiber reinforced polymer (CFRP) materials and cross-checking with existing literature characterizing the behavior of hand-layup samples allows us to establish a foundation for material selection in this unique structure. Synthesis of the testing data led to a final design choice of a three-layer laminate structure having a CFRP-GFRP-CFRP structure laid up on a PA-12 “substrate” airframe having the requisite internal and external mounting features, hatches, and holes. A first-order design calculation suggests that with this configuration and a fixed inner radius of 58.5mm, a minimum 2mm-thick composite layer (i.e. an outer radius of 60.5mm) is sufficient against buckling under the calculated service loading from thrust and drag forces.
Figure 3: Euler critical buckling load as a function of outer airframe radius for a given vehicle length and fixed inner radius. The total compressive design load on the airframe is marked with a dashed line.
The airframe substrate was printed out of PA-12 using the Jet Fusion 5200 printer over a total of three builds with approximately 10-15% utilization per build. As-printed, the airframe structure contained all of the requisite internal locating features, bulkheads, and hatches necessary for integration. The aforementioned three-layer laminate was laid up directly onto the PA-12 surface and allowed to cure at ambient conditions. From a process perspective, the procedure directly replicated that of traditional airframe construction, with the exception that the “mandrel” (i.e. the PA-12 substrate) was now left in place after curing, serving as a non-structural component. Producing the airframe of LAD-5 in this manner permitted a high degree of modularity and reconfigurability on a section-by-section basis. Integration was dramatically more efficient compared to a traditional, annular composite airframe through the use of threaded heat-set inserts which could be installed directly into the thermoplastic, allowing standard threaded fasteners to be used for coupling sections together and mounting auxiliary components like a standalone avionics bay.
Despite clear process advantages compared to full-scale traditional airframe manufacturing, especially in the integration stages, the production of a composite LAD airframe nevertheless suffered from several difficulties. In particular, through-holes needed to be drilled out after the composite skin cured; although the location of holes was determined by the printed part, the holes had to be drilled from the outside in, making it a non-trivial challenge to attain the positioning tolerance required for hole patterns. Furthermore, the composite layer had to be sanded and smoothed. Surface imperfections (nicks, pockmarks, and deep scratches) were addressed using the application of body-filling compound, which created additional sanding and polishing steps. On top of this higher than expected degree of manual labor, the uniformity issues of ambient-cure composites remained. The vehicle, fully assembled, weighed 14.2 kg dry.
Figure 4: Drilling holes for fasteners cutting away excess composite, and sanding body-filling compound during the post processing phase of LAD-5 development.
In March 2022, LAD-5 flew to approximately 10,800 feet over the Mojave Desert, its altitude and top speed slightly limited by high transverse winds. The airframe survived the dynamic pressure loading without buckling, validating the design parameters used for the structural component. However, a few seconds after parachute deployment at apogee, the shroud lines of the drogue parachute itself failed via. tearing, separating the parachute from the airframe. The airframe did not survive the subsequent ballistic fall and shattered on impact with terrain. Notably, several large sections of the composite remained intact, particularly those reinforced by strong internal structures like the motor casing.
Figure 5: Flight of LAD-5 at the Mojave Friends of Amateur Rocketry test site.
For the next flight-vehicle iteration of the rocket, LAD-7, which had the same basic design parameters, a fast turnaround time was desired. With existing manufacturing methods, the composite-overwrap production contributed the greatest time and had the highest degree of variability due to manual factors. Therefore, an analysis was conducted to determine whether it was possible to design an entirely-printable airframe structure that was capable of withstanding the design loads in compression. The structure would consist entirely of PA-12 and be directly printed in three builds, with the remaining integration step dominated by the installation of threaded heat-set inserts and the integration of adjoining airframe sections to form the full stack.
As a basis for the structural analysis, a baseline elastic modulus of 1.7 GPa was taken from the empirical data, given that the airframe thickness was to exceed 3.0mm everywhere. Using an identical design inner radius of 58.5mm, the same first-order buckling calculation was carried out to determine a sufficient minimum outer radius of PA-12.
Figure 6: Euler critical buckling load recalculated for PA-12 alone (orange), compared to the original composite-overwrap design (blue). Without the fiber-reinforced polymers, a thicker airframe is required.
Based on this calculation, a minimum outer radius of 62mm was required everywhere along the airframe to meet the design requirement against buckling. Using this value, a 30% increase in mass was predicted for the entire structure compared to the composite airframe. To further validate the design criteria, a series of static structural analyses were carried out using a finite-element model in nTopology. The service load was approximately doubled to 3500N for the simulation and applied to one end of the assembled airframe while the other end was given a fixed boundary condition. For simplicity, the material was modeled isotropically with a uniform stiffness, although empirical evidence suggests a degree of anisotropy in real, printed PA-12 parts. To address this discrepancy, the uniform stiffness used in the simulation (1.7GPa) corresponded to the minimum measured value for any printing orientation, thereby representing the worst-case scenario.
Figure 7: Finite-element simulation results for an applied static load of approximately twice the service load. Top: detail of the static stresses on an airframe component, demonstrating stress concentrations near mounting holes. Bottom: the simulated buckling deformation, if 1.15 times the simulation load were applied to the airframe.
Results of a static force analysis with these boundary conditions demonstrated that no mesh element exceeded 3 MPa von Mises stress, well under the measured yield stress of PA-12. As expected, stresses were higher around corners of hatches and around holes in the airframe, which act as stress risers compared to the bulk. To further protect against crack propagation, the features with the highest hole density (viz., the interstage couplers between adjoining airframe sections) were thickened to decrease the tendency for crack growth. Not considered in the simulation was the effect of threaded fasteners coupling parts together, which serves to add fixity to the structure. A buckling analysis demonstrated a 1.15 safety factor against first order buckling, which is the lowest-energy solution to the slender beam model. According to the simulation result, the buckling was predicted to propagate from large airframe hatches; these were also thickened for added stiffness.
Figure 8: Model of the LAD-7 full stack, demonstrating the interstage couplers used to join sections. For added stiffness and protection against crack propagation, the interstage couplers are thickened compared to the median airframe profile.
As a result of simulation results and iteration until convergence, a median airframe thickness of 5mm was chosen for the production vehicle. Like its predecessor, LAD-7 was printed over three builds using the Jet Fusion 5200 printer on the “Balanced” print profile. Parts were cooled naturally and cleaned using an automated bead-blaster, followed by compressed air. As designed, integration consisted primarily of installing threaded heat-set inserts followed by assembly, without the need for further processing steps. Compared to the composite-wrapped LAD-5, the production time of the fully-printed rocket system was shortened by a factor of two.
Figure 9: Representative build volumes of the Jet Fusion 5200
printer filled with airframe components.
I plan to write a separate page about the extensive ground testing campaign for the sub-modules of these rockets at some point in the future.
The flight of LAD-7, our first high powered entirely 3D-printed airframe, was a complete failure as far as rocket flights are concerned, but a resounding success for the strength of our airframe. Long story short, we flew a rocket possessing a static margin with a lower factor of safety than one would hope for in full-windsock conditions. This ended predictably. There may have been some inertia involved in the decision making on that day- the result was nonetheless incredibly entertaining. The textbook epic failure.
It seemed normal at first...
Problem...
Big problem... (Perturbation turns flat spin)
My current phone lock screen
Fate sealed
& a low quality video (NSFW sound warning)
So, this was disheartening of course, but as you can see, despite all the excitement, the airframe didn't buckle in the air, and thus me and Andrew narrowly avoided shaving our heads. This launch was more of a procedures failure than a technical one, although it did lead to the implementation of larger fins producing a larger static margin. It was also an opportunity to introduce a lot of quality of life improvements to LAD-8 that were ideated during assembly and integration of LAD-7, such as avbay reset interfaces accessible via. side hatch instead of the prior arrangement that required taking an entire body section off (something that, when connected to a launch rail, is very awkward and not conducive to tight launch windows).
Due to the pesky positioning of finals week in the calendars, we had to wait all the way until early June to launch LAD-8, but that came soon enough, and it was spectacular. Derek Honkowa, one of the FAR site staff members, put together a video that covers launch day operations & the flight itself on his excellent YouTube channel. Although we only hit about 8k ft, all of the recovery subsystems worked together in harmony (mostly, the main chute deployed but a couple lines got somewhat tangled), and there's immense room for improvement in the airframe itself. The simulations we've been doing for these airframe sections have been using static loads instead of dynamic inertia relief models, and have been using upper bounds for said static loads. This is something we've been well aware of, but a low apogee is better than getting clowned on when a radically different airframe buckles & then never being able to build back the team enthusiasm to fund more attempts. Currently, I've got an airframe design (same ish aerodynamics & form factor, different internal thickness and layout) in the works that utilizes an inertia relief FEA method to generate an entire airframe stress map, and uses topology optimization techniques to conform a structural lattice dynamically around hot points. This will deserve its own writeup.
Derek's video
Featured on the Berkeley Mechanical Engineering website! Front page as of early September 2022
As this is an ongoing project, I intend to eventually update this page and talk about the current simulation methodology & how this feeds back into the design loop. I also want to go back and dive into the in depth ground testing campaign.
Fun times.