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Design, Analysis, and Build Preparation of a Bi-stable, Deployable, Lattice Structure

Evan Heatherington

Logan Sharp

Ryan Stebbins

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Problem 

Literature 

 Design

Material & Process 

FEA

Build Prep 

 Future Work

[www.3d-profi.de]

[1]

[nustar.caltech.edu]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Deployable structures have shown to be beneficial for many space, military, and defense applications.

[evajermyn.com]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Initial research was conducted as to the current, but limited, state of bi-stable lattice configurations.

[1]

[2]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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The team generated and evaluated many potential solutions to the problem defined.

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Iterative prototypes led to a functional final unit cell design and subsequent volume lattice.

Rapid prototyping done with NinjaTek Cheetah Filament

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Materials for SLA, SLS, and MJF were considered because of their ability to print in polymers with high precision.

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Due to the deployable, bi-stable nature of the lattice unit cell, the following materials were found to be suitable due to their hyper-elastic properties.

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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In order to develop both rapid and end-use prototypes in one of these materials, the following AM printers were determined to be  suitable options, but choices will alter the design and process parameters.

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Due to the complexity and required flexibility of the bi-stable lattice, SLS was chosen as the preferred AM technology.

[www.3dsystems.com]

DuraForm Flex

TPU 1301

PA 11

[www.3d-profi.de]

[www.bing.com]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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EOS TPU 1301 was chosen because of its high elongation and superior mechanical properties compared to DuraForm Flex.

•Great resilience after deformation

•Very good shock absorption

•Very high process stability

•Highly suited to footwear, lifestyle and automotive

•Cushioning elements, protective gears, and shoe soles

Benefits

•Difficult to remove powder from holes

•Not as accurate as PA2200

•Flexibility can vary slightly

•Not good for high stretch applications

Weaknesses

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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EOS P 396 was selected as the desired printer. 

EOS P 396

Average price: $303,000

Build Volume: 340 x 340 x 600 mm

Dimensional Accuracy: 120 micron

Minimum Layer Resolution: 60 micron

Minimum Detail Thickness: 0.7mm

Post-Processing: Yes

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Due to the large deformations in this component, non-linear FEA was required. This was performed in SolidWorks using the Blatz-Ko material model.

Where: 

µ is the initial shear modulus

and I1,2,3 are invariants of the strain tensor

Blatz-Ko requires minimal input parameter : Elastic Modulus and Tensile Strength

For TPU 3031

E = 60E6 Pa

T.S. = 7Ee6 Pa

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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A prescribed displacement was implemented as the input motion and the bottom of the unit cell was fixed. Simulations mimic prototyped response.

GIF of deformation simulation

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Stresses observed in part are highest in the flexure right before beam buckling demonstrating bi-stability of strain energy.

GIF of stress simulation

Prior to buckling: 1.938E7 Pa

Post- buckling: 1.711E7 Pa

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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A volume lattice was simulated in Fusion 360's cloud finite element solver with a single downward, central force

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Utilizing FEA in nTopology with the unit cell homogenization technique, the stability and stiffness of the unit cell was determined. The upper image shows the deformed unit cell, this validates the desired deflection. ��The image in the lower right visualizes the unit cell's stiffness matrix. This can be used in the future for volume lattice simulation that is not as computationally taxing.

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Autodesk Netfabb was used to verify the designed lattices stl files.

[www.3dprint-uk.co.uk]

Good

Bad

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Analysis of the lattices wall thickness was done to ensure the limitations of the EOS P 396 printer was not violated.

Thicker than 0.7mm

Thinner than 0.7mm

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Various part orientations were compared using Netfabb.

Preferred Orientation

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Print time for a 3x3 volume lattice was calculated using Netfabb to be 8hrs 41min.

Scan Speed: 3000 mm/s

Power: 15W

Hatch Spacing: 0.1mm

Layer Height: 0.1 mm

[14]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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The cost to print was calculated to be $68.43 (87.5 mm cube) 8% the cost of a solid comparable volume.

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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The team's project Gantt Chart is complete justifying the completion of the project

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Future work would involve designing an experiment to validate the optimal process parameters for production. The following L9 Taguchi experiment would test 3 levels of laser power, scan speed, and scan pitch, similar to researchers at Wuhan Polytechnic University [10].

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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Compression testing for plastics would be performed using ASTM D695-15 standard [11]. However, ASTM WK76163 is currently under development for compression testing of lattice structures manufactured through AM [12].

[13]

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

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In conclusion, the designed bi-stable lattice structure shows promise for use in deployable structures to increase transportability and reduce costs.

Future Work

Build Prep

FEA

Material & Process

Design

Literature

Problem Description

[nustar.caltech.edu]

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References

[1] Alqasimi, A., Lusk, C., & Chimento, J. (2016). Design of a linear bistable compliant crank–slider mechanism. Journal of Mechanisms and Robotics8(5). https://doi.org/10.1115/1.4032509 

[2] H. Yang and L. Ma, “1D to 3D multi-stable architected materials with zero Poisson's ratio and controllable thermal expansion,” Materials & Design, vol. 188, p. 108430, 2020. 

[3] Duraform Flex (SLS),” 3D Systems, 23-Sep-2021. [Online]. Available: https://www.3dsystems.com/materials/duraform-flex. [Accessed: 15-Sept-2021]. 

[4] “3D printing elastomers: TPE material for 3D Printers,” 3D Printing Elastomers | TPE Material for 3D Printers. [Online]. Available: https://www.eos.info/en/additive-manufacturing/3d-printing-plastic/sls-polymer-materials/tpe. [Accessed: 15-Sept-2021].

[5] “PA 11 (polyamide 11) for Industrial 3D printing: EOS GmbH,” PA 11 (Polyamide 11) for Industrial 3D Printing | EOS GmbH. [Online]. Available: https://www.eos.info/en/additive-manufacturing/3d-printing-plastic/sls-polymer-materials/pa-11-nylon-abs-pa6. [Accessed: 15-Sept-2021]. 

[6] “Flexible 80A resin 1 L,” Formlabs. [Online]. Available: https://formlabs.com/store/flexible-80a-resin/. [Accessed: 15-Sept-2021]. 

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References

[7] “F39 white flexible rubber-like 3D printer resin,” RESIONE. [Online]. Available: https://www.resione.com/products/f39-white-flexible-rubber-like-3d-printer-resin-1kg-1. [Accessed: 16-Sept-2021].

[8] “Cheetah 3D printer filament (95A),” NinjaTek, 12-Apr-2021. [Online]. Available: https://ninjatek.com/shop/cheetah/. [Accessed: 16-Sept-2021].

[9] “HP 3D Printing materials portfolio - expand your capabilities,” HP 3D Printing Materials Portfolio - Expand your capabilities | HP® Official Site. [Online]. Available: https://www.hp.com/us-en/printers/3d-printers/materials.html#section=3d-materials-properties. [Accessed: 16-Sept-2021].

[10] G. Hou, H. Zhu, and D. Xie, “The influence of SLS process parameters on the tensile strength of pa2200 powder,” IOP Conference Series: Earth and Environmental Science, vol. 571, no. 1, p. 012111, 2020. 

[11] “Standard test method for compressive properties of rigid plastics,” ASTM International - Standards Worldwide. [Online]. Available: https://www.astm.org/d0695-15.html. [Accessed: 29-Nov-2021]. 

[12] “WK76163 new test method for additive manufacturing -- test artifacts -- compression validation coupons for lattice designs,” ASTM International - Standards Worldwide. [Online]. Available: https://www.astm.org/workitem-wk76163#. [Accessed: 03-Dec-2021]. 

[13] A. Kumar, S. Verma, and J.-Y. Jeng, “Supportless lattice structures for energy absorption fabricated by fused deposition modeling,” 3D Printing and Additive Manufacturing, vol. 7, no. 2, pp. 85–96, 2020. 

[14] S. Yuan, “Development and optimization of selective laser sintered ‑ composites and structures for functional applications,” Nanyang Technological University, 2018.