Experiments, analysis and an application of 3D-printed gyroid structures

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Örebro universitet Örebro University

Bachelor thesis, 15 ECTS

Experiments, analysis and an application

of 3D-printed gyroid structures

Experiment, analyser och en tillämpning av

3D-printade gyroidstrukturer

Jonatan Hussmo

Roman Schröder

Mechanical engineering, 180 ECTS

Örebro, spring semester 2020

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Abstract

The thesis investigates the mechanical properties of gyroid structures through various experiments and simulations. Gyroid structures consist of an intricate mesh of surfaces and can differ in density and cell size. The mechanical properties of the gyroid structure are inevitably dependent on the density. A convergence between density and the resulting mechanical stiffness of the lattice structure could be applied to a wide range of industrial components.

To test the mechanical properties of gyroid structures 3D-printed cubes are compressed in a test machine where stiffness is measured for a range of cubes with different density. The tests are confirmed by a finite element analysis (FEA) and all data is precisely analysed thereafter. A linear increase in density results in a non-linear increase in stiffness where the region between 30 % and 60 % density yields particularly good results.

After evaluating results from experiments and simulations, gyroid structure is implemented in one of ABB’s components for a circuit-breaker system to further display its advantages. Four different concepts are presented for the component where the most promising concept reached a weight reduction of 30 percent just by adding gyroid structures. No other design alterations have been made to the component. The results show great potential of being able to reduce the plunger’s weight whilst maintaining desired stiffness.

The results of the thesis can be applied widely to develop new methods of optimizing industrial components with additive manufacturing as the gyroid doesn’t need any supportive structure. It is possible to blend gyroid surfaces with other optimization tools such as topology optimization or grading to achieve even higher degrees of weight reduction.

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Abstract

Tesen undersöker de mekaniska egenskaperna av gyroidstrukturer genom olika experiment och simuleringar. Gyroidstrukturer består av ett komplext nätverk av ytor och kan variera i densitet och cellstorlek. Dess hållfasthetsegenskaper är givetvis beroende på densiteten. Konvergensen mellan densitet och den resulterande mekaniska styvheten av nätverksstrukturen skulle kunna tillämpas på ett brett spektrum av industriella komponenter. Det är möjligt att reducera vikt eller öka styvhet medan att kunna bibehålla hållfastheten.

För att testa hållfasthetsegenskaperna av gyroidstrukturer 3D-printade kuber komprimeras i en tryckmaskin där styvhet mäts för ett antal kuber med olika densitet. Testen bekräftas genom en analys med finita elementmetoden (FEM) och all data utvärderas noggrant därefter. En linjär ökning i densitet leder till en ickelinjär ökning i styvhet där området mellan 30% och 60% densitet ger ett särskilt bra förhållande mellan styvhet och vikt.

När resultatet från experimenten och analysen utvärderats, implementeras gyroidstruktur på en av ABB’s komponenter i en strömbrytare för att ytterligare visa dess fördelar. Fyra olika koncept presenteras där det mest lovande konceptet kunde viktoptimeras med 30 procent endast genom att tillägga gyroidstrukturer. Inga andra designändringar har gjorts på komponenten. Resultatet demonstrerar en stor potential när det gäller att viktreducera komponenten utan att tappa nödvändig styvhet.

Resultaten av tesen kan användas på många olika sätt för att ta fram nya metoder för optimering av industriella komponenter med additiv tillverkning då gyroiden inte behöver några stödstrukturer. Det är möjligt att blanda gyroidstrukturer med andra optimeringsverktyg såsom topologioptimering eller gradering för att åstadkomma ännu större viktminskningar.

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Acknowledgements

We wish to express our gratitude to the following people for their contribution to the thesis: Niclas Strömberg, for his supervision, ideas and valuable insight during this project;

Srikanth Purli and Benjamin Delignon, for their help and guidance with the project and report;

Erik Johansson, for all help with the application and technical background; Per Lindström and Joakim Larsson, for their support and practical help; Sören Hilmerby for the examination of the thesis.

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List of figures and tables

Figures:

1. Flowchart for completion of project in seven steps 9

2. Cubic lattice structures 15

3. Different lattice structures with additive manufacturing 15

4. TPMS described by Schwarz and Schoen 16

5. Assembly of gyroid structure 16

6. Mesh refinement in three steps (a) and adaptive meshing (b) 19

7. Gyroid cubes with density 20 %, 40 %, 60 % and 85 % 22

8. 3D-printed gyroid cubes with density 20%, 40%, 60%, 85% 23

9. Dimensions of test specimen (dog bone shape) 24

10. Tensile specimens with fracture and centreline 25

11. Stress/strain-curves, specimen 1-3 (a) and specimen 4-6 (b) 26

12. Example of load/displacement-chart with stiffness trendline 27

13. Plunger (a) and section view of the plunger (b). 29

14. Section view of the plunger with load distribution for opening and closing 30

15. Stress on original plunger at closing (a) and opening (b) 30

16. Deformation on original plunger at closing (a) and opening (b) 31 17. Gyroid plunger with partial section(a) and midplane section (b) 32

18. Section view of plunger concept A 33

19. Section view for stress at closing (a) and opening (b) 34

20. Section view of plunger concept B 34

22. Section view of plunger concept C 35

24. Section view of plunger concept D 36

26. High stress concentration in rounded edge 38

27. Mean stiffness of each density (a) and stiffness of specimens & mean (b) 40

28. Stiffness/density-curve for FEA 41

29. S/D-curve for FEA and compression test 42

30. Concept C original view (a), section view (b) 43

31. Bar chart for closing of original plunger and concept C 43

32. Bar chart for opening of original plunger and concept C 44

33. Test curve with different densities on the same build plate 45

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Tables:

1. Physical data of gyroid structures 23

2. Data from tensile test 25

3. Technical data Instron 4486 27

4. FEA results of original plunger 31

5. Properties of optimized plunger concepts 32

6. Results from FEA of concept A 33

7. Results from FEA of concept B 34

8. Results from FEA of concept C 36

9. Results from FEA of concept D 37

10. Evaluation of max stress and specific stiffness for plunger concepts 38

11. Data from compression tests 40

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Abbreviations

AM Additive Manufacturing

a.u. arbitrary unit

BCC Body Centred Cubic

CAD Computer Aided Design

FCC Face Centred Cubic

FDM Fused Deposition Modelling

FEA Finite Element Analysis

FEM Finite Element Method

pp percentage points

SC Spaceclaim

TO Topology Optimization

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1 Introduction

1.1 Project client

The thesis is written in cooperation with AMEXCI AB, a Karlskoga-based company that works as a research and development centre for additive manufacturing (AM), mainly with metals and polymers. AMEXCI’s team consists of 18 members working in all the aspects of AM; design, industrialisation, production, quality, supply-chain etc. AMEXCI was started by the initiative of Marcus Wallenberg with the purpose of accelerating the development and implementation of AM to the industrial sector in Sweden. They have several large industrial companies as shareholders and function as a hub in Scandinavia to help them develop their AM strategy, detect the best business cases, develop their applications from the initial designs to certified parts. They also help them to better understand the particularities of materials additively produced through trainings and research projects.

1.2 Project

The thesis project will consist of evaluating mechanical properties of Schoen’s gyroid structures (see 3.4) by analysing different volume fractions with FEA and testing 3D-printed prototypes in a compression test. The results are then compared and verified with regards to stiffness and relative density for the lattice structure.

The results will be used to investigate parts of Niclas Strömberg’s research about lattice structures in combination with topology optimization. This will be done by assessing whether the correlation between relative density and stiffness is accurate in FEA compared to the experimental analyses with physical parts.

Although this thesis project will mainly focus on physical tests and the comparison of gyroid structures in general, these results will also be used to create different concepts for optimizing a plunger that is used in a medium-voltage circuit breaker. The component is provided by one of AMEXCI’s shareholder companies ABB and is to be weight optimized. The presented concepts shall demonstrate the potential of weight reduction with gyroid structures and function as an initial design that can be developed for production of the component.

1.3 Procedure

In total, the project is planned to be finished within eight weeks and is organized into seven different stages as shown in figure 1. The different stages function as a guideline to check whether the project is on schedule or not.

Figure 1. Flowchart for completion of project in seven steps.

The project starts off with a literature study to acquire the necessary knowledge and theory. Previous modules contribute to understanding the project’s theory, but a few topics must be studied first before being able to start working on the actual problem of the project.

Study

1 week

TPMS

1 week

FEA

1 week 3D-printing1 week

Test 1 week Application 1 week Report 2 weeks

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Examples that are studied are TPMS, gyroid structures and how these are modelled using 3D-CAD. To ensure a minimal deviation in the 3D-printed parts, a study on how process parameters affect printed components’ properties is made.

This is followed up by determining what range of volume fractions that is to be used in the experiments. Initial modelling and printing test are carried out to ensure that all models are manufacturable. After clear constrains have been set for the project, the models have been produced, analysed and tested in a compression machine. The results from both physical tests and computational analysis have then been analysed and used to model a graph that describes the relationship between relative density and stiffness. The two graphs are compared and with the knowledge gained from this work, a number of concepts with different densities and cell size are presented to determine the performance on the circuit breaker plunger.

Although the stages were planned consecutively, some of them are done simultaneously. Upon finishing stage 1 (theoretical study) and stage 2 (modelling TPMS) it was possible to start stage 3 (FEA) and stage 4 (3D-printing) at the same time. Potential problems and unplanned tasks that evolve during the project were handled more reliably as several stages have been done simultaneously.

1.4 Outline

The thesis is composed after the university’s template and guideline for thesis in the engineering sciences. It is written in a way that makes it easy to follow and understand the different steps from introduction to conclusions.

To build a logical structure through the thesis the IMRad format (Introduction - Method - Results - and - Discussion) is used with the addition of an in-depth theoretical background of the problem.

The introduction provides an overview of the thesis while the background offers a more detailed perspective on the problem the thesis addresses. The extensive theoretical part delivers all the knowledge that is necessary to subsequently grasp the analysis and results of the project. A thorough discussion deals with different areas of improvement and the future work with the problem. To summarize the work all conclusions are extracted and concisely presented. References and appendices containing tables and figures are found in the very end of the report.

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2 Background

Designing lattice structures for additive manufacturing has in recent years become more and more popular. Modern technology opens new possibilities to alter/optimize the geometry of industrial components in order to reduce their weight whilst maintaining or even increasing stiffness. Especially the performance of components exposed to constant or sporadic motion can be enhanced when reducing the weight.

At Örebro university, Niclas Strömberg is researching within generative design, which means creating CAD models of lattice structures by combining topology optimization (TO) with support vector machines, morphing and other operations. This has shown to be highly effective when creating robust, lightweight components. It is also very advantageous to manufacture in AM since these lattice structures can often be produced without adding support structure. [1][2][3]

AMEXCI currently works with a project involving weight reduction of components in electrical circuit breakers. The implementation of lattice structures was seen as relevant for some of these components. Previously, a TO was performed on the mentioned circuit breaker system in order to reduce its weight and increase performance. Although the weight was able to be reduced with TO, a new study was started to see whether gyroid structures could be a more suitable option to improve the performance on at least the plunger.

2.1 Problem description

This thesis project is focused on evaluating results from FDM-experiments and analysis of gyroid structures, in order to display the great potential of such AM applications in the industry. The challenge was to determine the potential weight reduction for a component without neglecting the different constraints. This was expressed as the stiffness-to-weight ratio of a structure in combination with a specific material. Therefore, this project aimed to analyse whether the stiffness of the test samples increase in proportion to the increasing density. This is described as a mathematical function to model the scaling rate of the stiffness within a given interval of volume fractions. Furthermore, it was crucial to analyse whether the data from FEA and the compression tests converged in order to confirm the results for this industrial application.

The industrial plunger provided by AMEXCI and ABB had to be weight-optimized based on the outcomes of the stiffness-to-weight ratio analysis with different volume fractions for the gyroid structures. The optimized plunger has been tested with linear FEA where the implemented gyroid structure was put to the test.

Our main questions were: Is a reasonable weight optimization achievable for the component whilst meeting the necessary strength criteria? How large is the potential for weight reduction in this case?

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2.2 Previous work in the field

Most studies within the field investigate the gyroid and its mechanical properties in different volume fractions, manufacturing methods and materials [4][5][6][7][8][9]. There has been experiments done to determine the change of properties after certain structures yield and partially collapse [7].

At Örebro University, A. Jansson compared different periodic surface-based structures to truss-lattice structures, concluding that surface-based structures generally had the better performance [8]. A. Jansson and L. Pejryd also studied the behaviour and properties of the Schwarz diamond and BCC lattice structure both with and without induced fabrication errors during compression, using computational tomography. In this paper, it’s shown that the Schwarz diamond structure is more than 5 times better than the BCC lattice [10].

Some other studies also investigate how lattice structures can be combined with topology optimization in order to design stiff, lightweight components. [11]

The most relevant studies are those who investigate the relation between physical experiments and computational analysis. According to these, experiments and FEA results agree quite well but are tested in a smaller range of volume fractions. The studies also focus on comparing several mechanical properties and non-linear behaviour of the structures. It is also noted that surface roughness can have certain effect in stiffness, especially with thinner struts and cross-sectional area. [5][7]

2.3 Purpose

In order to solve the project’s problem accordingly it is mandatory to understand why the project is done in the first place and the goals that have been defined to achieve the project’s estimated results. Hence, the purpose of this project can be defined as “testing the stiffness of gyroid structures at different densities by conducting experiments and comparing these to results generated by computational simulation”.

The results from the experiments with the 3D-printed specimens are evaluated to understand how gyroid structures can be used on an industrial plunger. A marginal weight reduction can often be achieved by removing excess material in areas that are not exposed to stress and/or deformation. The potential weight reduction of a component by implementing gyroid structures, especially in combination with other methods can be far more effective and opens new ways of developing industrial components when produced with additive manufacturing.

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2.4 Constraints

The project scope consists of various constraints to define the limitations. The project is restricted by both the timeline and several other boundaries that are listed below. Compromising a project constraint may affect the project’s outcome and timeline. It is therefore important to define strong constraints that are observed throughout the project.

Project constraints:

1. All printed prototypes will be manufactured in plastic (PLA) in the same 3D-printer and without mixing filaments.

2. The geometry of the test objects will be cubical in shape. No advanced shapes (apart from the gyroid structure itself) will be analysed.

3. Twelve different volume fractions, varying from 20-85% with 5pp increments in the range of 20-65% and 10pp between 65-85% will be tested during the project. 4. To generate statistically representative results five samples of each volume fraction

of the gyroid structure will be tested.

5. Four concepts are presented that reduce the plunger’s weight with at least 10%. There are no requirements regarding strength and stiffness of the component, but a wish to preserve as much stiffness as possible.

6. Deviations in data from physical tests are carefully discussed but are not repeated, if not absolutely necessary.

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3 Theory

In order to successfully complete this project a relatively broad range of theory is needed. After revealing the field of technology below, this chapter presents the fundamental theory behind lattice structures in general and proceeds more in-depth with TPMS and gyroids.

Especially gyroid structures, their relevant mathematical equations and mechanical properties are presented since this could be considered the core of theory behind this project. A general explanation of linear FEA is also presented to provide the necessary understanding of calculations and analysis that are made. This is followed by an introduction to AM, 3D-printing gyroid structures using FDM and compression testing together with its standard methods.

3.1 Field of technology

The thesis’ field of technology is found within mechanical engineering and covers several different areas that need to be mastered in order to work with the project. The field of technology can be divided into five different branches that are assigned their respective fields in the list below.

1. Modelling of TPMS is part of 3D-CAD and construction technology. The mathematics behind minimal surfaces must be understood in order to understand the behaviour of minimal surfaces with different volume fractions when exposed to various load settings.

2. Compression tests are used within material technology to determine the mechanical properties of construction materials. Mechanics are essential to understanding both elastic and plastic properties of materials and how these can be translated to applying gyroid structures to a given component.

3. To perform various necessary calculations both mathematics, mechanics and the strength of materials must be grasped.

4. The analysis is performed with FEA which is a field within FEM (see 3.5). It is elementary to understand the meshing of objects and the different parameters that are needed to perform FEA. Furthermore, the software for performing FEA needs to be mastered in order to generate usable results.

5. Manufacturing the test objects requires knowledge of and experience with the respective 3D-printer and its software. Even the choice of the right materials requires some theoretical knowledge which can be found within production- and forming technology.

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3.2 Lattice structures

Lattice structures are crystal structures where nodes are connected in the form of a lattice to build a structure. One of the simplest lattice structures is the cubic lattice structure (figure 2, primitive) where a cube’s basic structure of eight nodes can be connected to four (BCC) or even six other nodes (FCC).

Figure 2. Cubic lattice structures with primitive, body-centred and face-centred (from left to right).

In the context of additive manufacturing lattice structures play a more and more important role due to their strong structure. Figure 3 below shows four different examples of lattice structures such as the 3D-lattice, the diamond lattice and the honeycomb.

Figure 3. Different lattice structures with additive manufacturing.

There are many more kinds of lattice structures due to the great freedom in both design and construction. By varying the number of the struts between the nodes and their geometry it is possible to develop other lattice structures.

3.3 Minimal surfaces & TPMS

A minimal surface can be described as a surface with minimal surface area where the mean curvature is equal to zero. The mean curvature of a surface is a measure for the curvature in any given point of a surface.

Soap films are a good example for minimal surfaces as they tend to minimize the surface area as much as possible between the given boundaries. When dipping a wireframe into a soap solution one can observe how the soap films spans between the wireframe (boundary) with minimal surface area.

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Triply Periodic Minimal Surfaces (TPMS) have a crystalline structure repeating themselves in three dimensions. Already in 1865, German mathematician Herman Schwarz described the first periodic minimal surfaces. In figure 4 below three common examples of TPMS are shown. [12]

Figure 4. TPMS described by Schwarz and Schoen. [12]

In 1970, NASA scientist Alan Schoen discovered twelve more TPMS including the gyroid surface which is explained in detail below.

3.4 Gyroid structures

The gyroid surface is a triply periodic minimal surface and is linked with copies of itself to assemble a gyroid cell as shown in figure 5. Only one surface structure is linked to another to form the desired structure of the gyroid. The gyroid is shaped after the six faces of a cube and it takes eight shapes to form a gyroid structure.

Figure 5. Assembly of gyroid cell with copies of the same gyroid surface. [12]

Every link of the structure is connected to only three other links in order to form the gyroid structure. It has a three-fold rotational symmetry and lacks mirror symmetry or straight lines.

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3.4.1 Mathematical equations of gyroid surfaces

A gyroid unit cell can be described with a trigonometrical equation and is approximated as follows in equation 1. sin(2𝜋𝑥 𝑎) cos(2𝜋 𝑦 𝑎) + sin(2𝜋 𝑦 𝑎) cos(2𝜋 𝑧 𝑎) + sin(2𝜋 𝑧 𝑎) cos(2𝜋 𝑥 𝑎) − 𝑡 = 0 (1)

where a is the unit cell size and t is a parameter for thickness/ relative density which varies between -1.5 (0% volume fraction) and 1.5 (100% volume fraction).

By changing the thickness of the gyroid structure the overall density of the cube is changed. The cube’s density can be expressed as relative density ρ in equation 2.

ρ =Vgyroid

Vcube (2)

where V_cube = cube’s volume and V_gyroid = volume for the gyroid structure.

To calculate the mechanical properties such as density and Young’s modulus of cellular materials, the following model from Gibson-Ashby is used. The model describes the relationship between a structure’s mechanical properties and its relative density with a simple formula. [13][14]

Equations 3 and 4 describe the elastic modulus, density of the gyroid, relative elastic modulus and relative density.

𝐸_{𝑔𝑦𝑟𝑜𝑖𝑑} 𝐸𝑐𝑢𝑏𝑒 = 𝐶1∗ ( 𝜌_{𝑔𝑦𝑟𝑜𝑖𝑑} 𝜌𝑐𝑢𝑏𝑒 ) 𝑛 (3) 𝐸_{𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒} = 𝐶₁∗ 𝜌_{𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒}𝑛 (4) where 𝐸_{𝑔𝑦𝑟𝑜𝑖𝑑}, 𝜌_{𝑔𝑦𝑟𝑜𝑖𝑑}, 𝐸_{𝑐𝑢𝑏𝑒} and 𝜌_{𝑐𝑢𝑏𝑒} are the elastic modulus and density of the gyroid structure and the solid material, respectively. 𝐶₁ and 𝑛 are constant parameters that are fitted from experimental measurements.

However, this equation is only reliable where the relative densities are low due to the model using thickness and cell length as measurements for density. At higher densities these approximations overestimate the density because of “double-counting”, meaning that the cell corners and edges are counted twice and in need of another order of approximation with more constants measured. [14]

3.4.2 Mechanical properties of gyroid structures

The gyroid structure has generally good mechanical properties in proportion to its weight. Because of the continuous geometry, the effect of stress concentrations on gyroid structures is minimal. Other mechanical properties (stiffness, strength and fracture toughness) also depend on material properties, cell size and relative density of the lattice. [4][5]

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When looking at the stress-strain curve for cellular materials in general, there are three regions of interest. Firstly, there is the linear-elastic response in which cell-bending or -stretching occurs, followed by a stress plateau where cellular layers collapse progressively.

The third region is what is called densification, when the collapsed layers reach contact and instead the cells within the material collapse. In this stage, the structures stiffness converges towards the stiffness of the solid material. [15]

D.W. Abueidda et al. investigated 3D-printed polymeric gyroid structures and concluded from the stress-strain curves that in the elastic region, deformation occurs uniformly. For structures with higher relative density, the uniform deformation continues beyond the elastic region when compared to lower relative density structures. [5]

3.4.3 Ansys Spaceclaim (CAD)

Different software is used to model TPMS in 3D-CAD and analyse these in FEA. Ansys is a well-known commercial solution for testing objects and simulating deformation with FEA. It is necessary to convert the 3D-models to different file formats (stl, stp, scdoc) to be able to model, analyse and print the structures. Therefore, Ansys’ inhouse 3D-CAD software Spaceclaim is used to create 3D-models of the different gyroid-structures. SpaceClaim offers a range of tools to model TPMS in 3D, including Schoen’s gyroid. The files can easily be exported from Spaceclaim to be analysed in Ansys mechanical and sliced in Ultimaker Cura for 3D-printing.

3.5 Linear FEM

Finite Element Method (FEM) or Finite Element Analysis (FEA) is a numerical analysis based on approximation which is embedded into software to calculate e.g. stress, strain and deformation of complex structures. FEA is used to simulate real-life scenarios and predict how a structure behaves when exposed to certain influences such as force, load, temperature and/or time.

3.5.1 Meshing

To calculate certain behaviours with FEA it is necessary to divide the geometry into smaller regular shapes (elements), usually noded triangles or quadrats. The elements are finite in nature because their size is highly relevant for the outcome of FEA. Smaller elements generate more precise calculations for the overall structure that is to be analysed. With the help of mesh refinement, it is possible to receive more precise calculations for either the whole geometry or a special region of interest. Figure 6 illustrates a mesh refinement done in three steps. The initial element size for the mesh is set to 35 mm, then reduced to 10 mm and finally to 3 mm to generate a fine mesh.

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Figure 6. Mesh refinement in three steps (a) and adaptive meshing (b).

Furthermore, an adaptive mesh can be used to create more elements in particular areas of interest and reduce mesh size in other areas, as shown in figure 6 b. This can cut down CPU time for complex models and reveals more precise measurements where it is desired.

3.5.2 Global stiffness matrix

The calculation of FEA uses a system of equations for every node of the finite elements. Partial differential equations are solved by approximation and need to be numerically stable so that small deviations can’t compromise the overall result of FEA. [16]

Once the system of equations is solved on a local basis it is necessary to solve the global system of equations with the help of the following relation shown in equation 5.

[𝐾] × {𝑄} = {𝐹} (5)

where K is the global stiffness matrix, Q is the displacement vector and F is the load vector. [16]

FEA is a widely used technique in the industry to explain how stress, strain and deformation act on complex structures.

3.6 Additive manufacturing (AM)

AM enables manufacturing of a broad range of components with a complex geometry, such as lattice structures, topology optimized parts or those generated from a CAD-fitting process. The basic process can be divided into six stages [17]:

1. Creating a three-dimensional model in CAD. 2. Converting CAD data to STL-format.

3. Slicing the part in thin cross-sectional layers.

4. If needed, create a support structure to hold the part in place during manufacturing. 5. Producing the desired part, layer-by-layer.

6. Postprocessing (removal of support structure, powder removal, finalizing shape etc.).

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3.6.1 Fused deposition modelling (FDM)

By adding the deposit layer after layer, the structure is slowly being moulded without neglecting hollow sections in between. It is possible to adjust the thickness and position of nodes and struts which offers great freedom in the design process to integrate desired functions into a component.

The printed component is also dependent on the chosen material. Soft materials require a somewhat thicker structure to reduce sag during the printing process. More rigid materials allow in general a greater design range and can produce thinner structures. [18]

3.6.2 3D-printing of lattice structures

Lattice structures have been difficult to manufacture due to their intricate geometry which conventional subtractive machines such as CNC-lathes or -mills can’t produce. Additive manufacturing (AM) has opened new possibilities to produce lattice structures allowing a great measure of control over the structure.

AM allows the designer to adjust the structure so it can reduce vibration and impact stress or for example increase shock-absorption. At the same time the technology can achieve reasonable weight reduction while maintaining strength and structural integrity. [18]

The 3D-printing of lattice structures offers great advantages since the structures are often self-supporting which mean they can be independent of support material during printing. [19]

3.6.3 Process parameters and mechanical properties

When printing PLA structures using FDM, there are plenty of parameters determining the mechanical properties. A few examples of these which need to be taken into consideration are layer thickness, build orientation, nozzle angle, nozzle diameter, air gap, infill density, infill pattern and feed rate. The combination of these parameters influences the mechanical properties in a complex way and can be difficult to understand.

Research by Y. Song et al. [10] shows that FDM-printed PLA is tougher in the build direction than the traverse direction (𝐾_𝐼𝐶 = 5 𝑀𝑃𝑎 √𝑚 compared to 𝐾𝐼𝐶 = 3 𝑀𝑃𝑎 √𝑚).

Gajdos et al. show in their research that alternating printing and platform temperature can improve structure homogeneity, which lead to improved mechanical properties. [20]

Tensile strength and flexural strength have been shown to increase as feed rate decreases. In regards of layer thickness, there are a couple of previous studies which presents quite controversial conclusions. [18]

3.6.4 PLA (Polylactic Acid)

The use of polymers like polyethylene (PE), polypropylene (PP), and related polymers is increasing as they replace conventional materials more and more. Polylactic acid (PLA) is a biodegradable type of polymer that is produced from renewable resources. It has shown to be a good alternative to petrochemically produced plastic filaments and has been extensively researched during the last decades, especially within biomedicine due to its good biocompatibility.

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Also, PLA has better thermal properties compared to other biopolymers in terms of processability, making it attractive for production in a variation of moulding, extrusion and AM processes.

While tensile strength and elastic modulus of PLA is comparable to polyethylene terephthalate (PET), it shows limitations in terms of toughness. It is a very brittle material, with a break at less than 10% elongation. [21]

3.7 Compression test

A compression test is used to test an object’s or a material’s strength and stiffness by applying a force that pushes inward on a sample. The purpose of a compression test is to determine a material’s strength and stiffness when exposed to an increasing force up until failure occurs. Thereby, conclusions can be drawn whether a material is suitable for a given application or not. To perform a compression-test a material sample is inserted into a test machine where it is being exposed to an increasing force at a pre-selected test speed (see 2.7.1). While the sample is slowly being compressed, sensors in the test machine measure the material’s displacement (mm) and the encountered stress level (Pa). With this data a stress/strain-curve (also S/N-curve) can be modelled to determine the material’s behaviour for elastic and plastic deformation. Of special interest are the material’s strain, yield strength, tensile strength and Young’s modulus. [22]

The following equations are used to calculate stress (6), strain (7), Young’s modulus (8). 𝜎 =𝐹 𝐴 (6) 𝜀 =Δ𝑙 𝑙0 (7) Hooke’s Law: 𝐸 = 𝜎 𝜀 (8)

where𝜎 = stress [Pa], F = force [N], A = cross section [m2], 𝜀 = strain, ∆𝑙 = change of length

[m], 𝑙₀ = initial length [m], 𝐸 = Young’s modulus [Pa].

3.7.1 ISO 604

ISO 604:2002(E) is an ISO standard for determining the compressive properties of plastics under defined conditions. It is used to set up the proper conditions for compression tests on rigid and semi-rigid thermoplastics.

The test speed (expressed in mm/min) is to be regulated according to test machine and the specimen that is to be tested. Any test machine that can keep a constant rate of cross-head-movement is eligible for performing the compression test. [23]

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4 Experiments & Analysis

This chapter focuses on the methodology describing the different physical tests and explaining the finite element analysis that is done for each volume fraction.

4.1 TPMS Modelling

The gyroid structures are modelled in Ansys’ CAD software Spaceclaim (SC). A cube with the dimensions 40x40x40 mm is modelled and Spaceclaim’s facets tool creates the gyroid. There are three parameters steering the structure. These are relative density (%), width (w) and thickness (t). It is possible to define two parameters at the same time. The third parameter is dependent on the value that was entered for the other two parameters. In this case relative density and cell width are defined to generate the desired gyroid cubes. Figure 7 below shows four different gyroid structures increasing in density from 20% to 85%.

Figure 7. Gyroid cubes with density 20%, 40%, 60% and 85% (from left to right).

Spaceclaim calculates the density of the gyroid in percent which can be varied between 0 and 100%. A density of 100% should theoretically generate a solid cube where the gyroid structure fills the whole volume of the cube and leaves no hollow space. This is not the case in SC when comparing the volume of each gyroid cube with that of a solid cube. Therefore, it is essential to calculate the true density for each cube with the help of a solid cube’s volume.

The solid cube has the same dimensions (40x40x40 mm) with a volume of 64x103 mm3. The discrepancy between density and true density proves to increase with

increasing density. Table 1 below shows the physical data of the different gyroid structures with density, width, thickness, volume and true density.

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Table 1. Physical data of gyroid structures.

density width thickness volume true density

% mm mm mm3 % 20 4 1,30 12757,07 19,93 25 4 1,62 15895,42 24,84 30 4 1,95 18999,78 29,69 35 4 2,27 22063,35 34,47 40 4 2,59 25097,43 39,21 45 4 2,92 28041,32 43,82 50 4 3,24 30942,16 48,35 55 4 3,57 33775,16 52,77 60 4 3,89 36533,77 57,10 65 4 4,21 39211,39 61,27 75 4 4,86 44299,33 69,17 85 4 5,51 48980,45 72,28

For 20% density the true density is only 0,07 percentage points (pp) lower, whereas for 85% density the deviation is 12,72 pp. This disparity originates most likely from SC using the Gibson-Ashby model, explained in chapter 3.4.1.

4.2 3D-printing

The structures used for the experiments are being 3D-printed via FDM onsite in the engineering laboratory at Örebro university, using desktop printers at room temperature. The printer of choice is an Ultimaker 2 with the associated software Cura used for slicing and controlling the process parameters. For every batch of relative density, a G-code is produced containing five parts each to be printed. Figure 8 shows four 3D-printed gyroid cubes, with a density of 20%, 40%, 60% and 85%.

Figure 8. 3D-printed gyroid cubes with density 20%, 40%, 60%, 85% (from left to right).

In regards of material, PLA is used for all specimens, samples and prototypes. The same batch is used to minimize the risk of deviation in material properties. Dimensions and properties of the material used is shown in appendix A.

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4.2.1 Printer settings

Studies show that the quality of printed PLA products using FDM can vary greatly in mechanical properties depending on several process parameters (see 3.6.3). In this project the mechanical properties of PLA are not investigated any further. It is very important for the outcome that the strength does not vary due to the change of external parameters since that may result in unreliable results. To avoid this, the same printer, material, settings and placement on the build plate are used for all parts produced during this project.

After initial research and testing, a few printer settings are changed before producing the parts to avoid defects. All parts are printed using an infill of 100%, a layer height of 0,15 mm and a printing speed of 55 mm/s. Apart from that, the recommended settings from Ultimaker Cura are used.

4.3 Tensile test

To determine the tensile properties of PLA, a tensile test is performed containing six specimens that were produced according to ISO-standard 527-2:2012, Plastics - Determination of tensile properties [24][25]. The specimens were designed in Creo and exported as stl-files to be prepared in Ultimaker Cura. The dimensions of the specimen in mm are shown in figure 9.

Figure 9. Dimensions of test specimen (dog bone shape) in mm.

The specimens are 3D-printed in the same printer, using the same settings and material as the gyroid structures lying flat on the printer’s base plate. Strain is measured by an extensometer and force is applied gradually by the test machine (Instron 4486).

4.3.1 Test results

The test specimens are elongated in the testing machine until failure occurs. Three of the six specimens are tested merely a few hours after printing whereas the remaining three are tested three days after printing. This is done to appreciate what effect material ageing has on the ductility of an otherwise relatively brittle material.

Figure 10 below shows all six specimens after testing. Specimens 1, 2 and 3 were tested shortly after printing, specimens 4, 5 and 6 three days after printing.

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Figure 10. Tensile specimens with fracture and centreline.

By looking at the specimens one can detect that 1, 2 and 3 are ductile fractures and necking occurs before the material fails. This behaviour is atypical for PLA and can most likely be traced back to the low material ageing before performing the test. The tensile test in specimen 3 was aborted prior to failure as the specimen continued to elongate without failing in a reasonable matter of time. Specimens 4, 5 and 6 show a brittle type of fracture where no necking occurs prior to the failure which is more typical for PLA.

It can also be observed that all fractures arose in one half of the specimen, but not exactly in the middle, as indicated by the orange centreline in figure 10 above. This occurs when the test specimen is slightly angled when inserted in the test machine. However, this deviation does not have any reasonable effect on calculating Young’s modulus for the specimens since the fractures occurred within the two sensors of the machine’s extensometer.

The measured parameters for determining the tensile properties of PLA are breaking displacement and breaking load. Table 2 shows the measured data from the tensile test.

Table 2. Data from tensile test.

specimen breaking displacement breaking load

mm kN 1 6,21 0,63 2 12,31 1,15 3 5,26 0,70 4 3,19 1,54 5 3,33 1,42 6 2,49 1,64

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Both breaking displacement and breaking load differ considerably in specimens 1, 2 and 3 compared to the remaining values for specimens 4, 5 and 6. It is therefore beneficial to evaluate the measured data with the stress-strain curve for all six specimens to generate a usable value for Young’s modulus. In figure 11 below, the stress/strain-curves are displayed for the six test specimens.

Figure 11. Stress/strain-curves, specimen 1-3 (a) and specimen 4-6 (b).

Specimens 1, 2 and 3 are very incoherent and the data will therefore not be considered for the Young’s modulus of 3D-printed PLA. Specimens 4, 5 and 6 on the other hand show high degree of consistency. Hence only those specimens will be used for computing Young’s modulus. The Young’s modulus for PLA is calculated by taking the slope of a defined interval in the linear, elastic part of the stress/strain-curve. The interval is defined by the specimen’s tensile strength and varies marginally between the different tests.

The individual modulus is 2,582 GPa for specimen 4, it is 2,555 GPa for specimen 5 and 2,707 GPa for specimen 6. The mean value of all three slopes as shown below in equation 9 yields the overall Young’s modulus for PLA that is used in FEA for all gyroid structures (see 4.5).

𝐸 =2,582+2,555+2,707

3 = 2,615 𝐺𝑃𝑎 (9)

The Young’s modulus of 2,615 GPa is only valid for this project and the specific 3D-printed PLA used during the project. Therefore, it is not applicable to other PLA specimens which might have various 3D-printing parameters.

4.4 Compression test of printed prototypes

The printed structures are tested in a compression test to compare whether their behaviour under compression is in line with FEA. Compression tests are performed using a machine of model Instron 4486. For technical specification of the machine, see table 3.

(b) (a)

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Table 3. Technical data Instron 4486. accessory depth 500 mm accessory height 85 mm accessory weight 184 kg accessory width 650 mm capacity 300 kN

All specimens are compressed in the build direction, one relative density at a time containing a batch of five test objects. Since this thesis focuses on the elastic deformation of the structures, plastic deformation is irrelevant and would generate a lot of unnecessary data. Therefore, all tests are terminated slightly after failure takes place, but before the structure collapses or reaches self-contact within its members.

During initial research and testing, it is found that ageing has a dramatic influence on the tensile properties of PLA. This is taken into consideration by letting the test objects linger for at least 48 hours in room temperature after printing before they are tested. Each specimen is also marked with a number indicating what position on the build plate it had while being produced, for possible back-tracking of deviations from the printer. For the compression test, a test speed of 1.3mm/min is used according to ISO 604:2002, Plastics - Determination of compressive properties (see 3.7.1).

Compression is achieved by a displacement of constant velocity where the machine’s cross head approaches the test specimen. It is mandatory to leave a small gap between cross head and specimen which results in a delay of the displacement, as seen in figure 12. When measuring stiffness this can be disregarded, as stiffness is measured from the difference of displacement rather than position.

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The data from the compression machine is imported into Matlab for processing and analysis. A code is written to plot a load-displacement graph for each set of data. As seen in figure 12, the stiffness of each specimen is calculated by generating a linear equation between two chosen points, as indicated by the two black markers on the curve. The program repeats this process for each specimen, storing the value of stiffness in an array, to later calculate the mean stiffness for each density batch. Figures of all compression tests can be found in appendix B.

4.5 Finite Element Analysis

The gyroid structures are analysed for their mechanical properties with linear FEM to validate the results of the compression test. The analysis simulates compression of the gyroids under the same conditions as the compression tests done in the test machine.

The gyroid structures vary in density between 20% and 85%. From 20%- to 65%-density a five-pp interval is afive-pplied whereas between 65% and 85% a ten-five-pp interval is afive-pplied. The accumulated force at 1 mm and 2 mm displacement is extracted and the stiffness is calculated in N/mm via the slope of the linear elastic deformation.

Conclusions regarding the stiffness of the different volume fractions can be drawn from FEA by taking out the load which is necessary to deform the geometry in a pre-defined manner. When analysing the mechanical properties in linear FEA it is not possible to determine the yield strength or tensile strength of the object since these aren’t detected when a force is increased leading to a linear displacement. This analysis focuses solely on the elastic deformation of the geometry and plastic deformation is therefore disregarded.

4.5.1 Settings

Prior to FEA the gyroid cubes are prepared for the analysis by adjusting the mesh size and removing potential defects in the geometry. The default mesh contains too many elements and mesh size is therefore increased to receive a reasonable number of elements for performing the analysis. Due to the software measuring the volume of gyroids by calculations that depend on the surface area, an increase of mesh size can affect the relative density by decreasing the volume. This is also taken into consideration when refining the mesh prior to analysis.

A structural, time independent analysis is used to perform a linear FEA in Ansys mechanical. The standard material data for PLA from ANSYS is inserted and the Young’s modulus from the tensile test (see 4.3.1) is applied. To simulate compression a vertical downward displacement is applied to the gyroid’s top surface with a maximum displacement of two millimetres. The object is fixed at the bottom. A force probe is added to measure the maximum force per displacement unit at predefined intervals. In total five points are defined to measure force at a displacement of 0 mm, -0.5 mm, -1.0 mm, -1.5 mm and -2 mm. The analysis is done individually for every volume fraction with the same settings and material data. The data is presented in the results in chapter 6.

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5 Application to industrial plunger

Upon verifying the results of both compression tests and FEA, the gyroid structure has been implemented on a component from the industry to emphasise its advantages in terms of weight reduction and/or stiffness increase. The component has been tested in FEA in both original- and optimized state to validate the strength of the structures applied on the component. A total of four different concepts have been developed in Spaceclaim with constant relative density varying from 30% to 40%. The concepts and their dimensions are presented in chapter 5.2.

5.1 Industrial plunger

The plunger is a component within a medium voltage circuit breaker that opens and closes a circuit with the help of a Thomson coil. Figure 13 below shows the plunger which is disc-like shaped and has a cylindrical extrusion in the middle. It is fixed in one constraint. The surfaces that are responsible for opening/closing the circuit are made of aluminium (top surface) and copper (bottom surface) due to electric conductivity. The plunger’s core is manufactured with AM and consists of AlSi10Mg (aluminium-alloy).

Figure 13. Plunger (a) and section view of the plunger (b).

The plunger’s mass is 0,151 kg with a volume of 47,944 cm3. Its surfaces are exposed to

different loads connected to the opening/closing mechanism of the circuit breaker. Figure 14 shows a section view of the plunger with the load setting for opening and closing and the respective materials.

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Figure 14. Section view of the plunger with load distribution for opening and closing.

When opening the plunger, a distributed load of 7875 N is acting on the copper surface of the plunger. When closing the plunger, a distributed load of 4000 N is acting on the aluminium surface of the plunger.

5.1.1 Analysis of original plunger

The plunger in its original state is analysed in Ansys, where a fixed support is placed in the constraint and the respective force is applied to the bottom- and top surface to simulate opening and closing. To be able to compare the stress levels of the original plunger and developed concepts the scale and colour scheme is adjusted in Ansys for each analysis. This way, stress levels are always indicated in the same colour. Dark blue indicates stress up to 15 MPa whereas red indicates high stresses between 130 MPa and 220 MPa. These values are derived from the material’s yield strength and the different stress levels in the plunger for opening and closing. The results of a stress analysis are shown below in figure 15.

Figure 15. Stress on original plunger at closing (a) and opening (b).

Distributed load: 7,875 kN Distributed load: 4 kN Aluminium Copper AM Aluminium (b) (a)

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The location of stress and deformation are also evaluated in order to understand where to apply a gyroid structure in the component to receive its best performance. Figure 16 shows the deformation on the plunger at closing and opening.

Figure 16. Deformation on plunger at closing (a) and opening (b).

In table 4 below, the parameters for opening and closing are presented. Max- and mean stress are measured in Ansys. A variable Κ (kappa) is introduced to describe stiffness where the applied force is divided by the maximum displacement resulting in N/mm.

The constraint in the geometry is used as a reference since it is defined as a fixed support which can’t encounter any displacement. Eventually, the specific stiffness is defined as stiffness K per mass for each concept and is expressed as an arbitrary unit (a.u.).

Table 4. FEA results of original plunger.

applied force max stress mean stress max disp. Κ specific stiffness

N MPa MPa mm N/mm a.u.

closing 4000 38,671 6,589 9,890e-3 4,045e5 2,6786

opening 7875 109,29 13,467 20,002e-3 3,937e5 2,6074

The values obtained for maximum stress and -displacement differ a lot for closing and opening where stress is nearly tripled when and deformation is doubled. When looking at the specific stiffness this difference isn’t noticeable anymore as they vary by only 2,7%. These values are important when analysing the different concepts as they function as a benchmark for determining whether a concept is eligible or not.

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5.2 Concepts and analysis

After the initial analysis of the plunger in its original state, four concepts with three different densities are developed. To achieve a reasonable weight reduction, densities between 30% and 40% are chosen and tested. Cell length and shell thickness are tested as well to investigate their effect on stress and stiffness.

The two example figures 17a and 17b below illustrate the concept of implementing a gyroid structure into the plunger. All concepts have the same outer dimensions and are created with a shell around the gyroid structure. In order to remove powder trapped inside the structure during printing at least one of the faces will be created without a shell, as seen in figure 17b.

Figure 17. Gyroid plunger with partial section(a) and midplane section (b).

In table 5 the four different concepts are presented with their respective parameters. Each concept is created with different cell lengths, shell thickness or open surfaces to investigate the spreading in stiffness and strength depending on these choices.

Table 5. Properties of optimized plunger concepts.

Concept A has a density of 40%, as well as concept B. Concept C has a density of 35% and concept D a density of 30%.

concept density cell length thickness shell thickness

% mm mm mm A 40 3,5 2,27 1 B 40 2 1,30 1 C 35 2 1,13 1,5 D 30 3 1,46 2 (a) (b)

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5.2.1 Concept A

The first concept as shown in figure 18 has a volume of 30,039 cm3 and a mass of 0,104 kg.

This translates to an overall weight reduction of 31,3% compared to the original plunger.

Figure 18. Section view of plunger concept A.

The concept plunger is tested in FEA for closing and opening with the same parameters as the analysis of the original plunger. Table 6 below shows the measured and calculated values for concept A.

Table 6. Results from FEA of concept A.

applied force max stress mean stress max disp. Κ specific stiffness

closing 4000 108,60 10,771 27,39e-3 1,46e5 1,4042

opening 7875 208,09 20,504 44,96e-3 1,75e5 1,6843

The plunger encounters the most stress in the cavity between the horizontal and the vertical surface indicated by the red area in figures 19a and 19b. How this can be reduced is thoroughly discussed later.

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Figure 19. Section view for stress at closing (a) and opening (b).

With a probe it is possible to measure the stress in different spots to gain an understanding how the stress is distributed within the component and especially the gyroid structure. The overall stress in the gyroid structure for closing (19a) is measures to be around 30-40 MPa. For opening (19b) the overall stress in the gyroid structure is between 50-90 MPa.

5.2.2 Concept B

The second concept as shown in figure 20 has a volume of 30,068 cm3 and a mass of 0,104 kg.

Figure 20. Section view of plunger concept B.

The concept is tested in FEA for closing and opening. Table 7 below shows the measured and calculated values for concept B.

Table 7. Results from FEA of concept B

closing 4000 135,46 11,371 22,1e-3 1,81e5 1,74

opening 7875 237,92 21,93 44,0e-3 1,79e5 1,72

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The plunger encounters the most stress in the cavity again between the horizontal and the vertical surface as seen in figures 21a and 21b.

The overall stress in the gyroid structure for closing (21a) is measures to be around 30-50 MPa. For opening (21b) the overall stress in the gyroid structure is between 60-80 MPa.

5.2.3 Concept C

The third concept as shown in figure 22 has a volume of 30,809 cm3 and a mass of 0,106 kg.

This translates to an overall weight reduction of 30% compared to the original plunger.

Figure 22. Section view of plunger concept C.

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The concept is tested in FEA for closing and opening. Table 8 below shows the measured and calculated values for concept C.

Table 8. Results from FEA for concept C.

closing 4000 93,752 10,75 19,9e-3 2,01e5 1,892

opening 7875 176,21 20,77 41,4e-3 1,90e5 1,793

Again, the plunger encounters the most stress in the cavity as seen in figures 23a and 23b.

The overall stress in the gyroid structure for closing (23a) is measures to be around 20-40 MPa. For opening (23b) the overall stress in the gyroid structure is between 40-60 MPa.

5.2.4 Concept D

The fourth concept as shown in figure 24 has a volume of 29,571 cm3 and a mass of 0,102 kg.

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The concept is tested in FEA for closing and opening. Table 9 below shows the measured and calculated values for concept D.

Table 9. Results from FEA for concept D.

closing 4000 183,27 12,341 25,4e-3 1,574e5 1,54

opening 7875 331,02 23,154 49,8e-3 1,582e5 1,55

The stress as shown in figures 25a and 25b is much higher compared to the other concepts which can be explained with the low density of only 30%. Most stress occurs again in the plunger’s cavity.

The overall stress in the gyroid structure is circa 50-70 MPa for closing (25a). For opening (25b) the overall stress in the gyroid structure is between 90-120 MPa.

5.3 Evaluation of concepts

All concepts are developed to optimize the original circuit breaker plunger in terms of weight reduction without compromising its stiffness. Implementing a gyroid structure into the component can be done in many ways since several different parameters can be defined such as density, cell length, included/excluded surfaces, build direction, grading and thickening of material.

In all concepts at least 30% weight can be saved in. Concept D could be optimized to only weigh 0,102 kg resulting in a reduction of 32,2%.

When comparing the equivalent stress of every concept for both closing and opening it is noticeable that the highest stress concentration is found in the rounded edge between the horizontal and the vertical surfaces as shown in figure 26.

(b) (a)

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Figure 26. High stress concentration in rounded edge.

This indicates that the gyroid structure itself can resist stress due to its intricate shape that distributes stress along its surfaces. The rounded edge on the other hand is much more prone to stress concentration which can possibly lead to failure after a number of cycles if the stress repeatedly exceeds the yield strength of the material (fatigue).

In general, areas with little material are more vulnerable to be exposed to high stresses. Due to the gyroid structure’s build direction which is either along the x-, y- or z-axis, it is difficult to avoid weak spots in the geometry. A possible solution could be to revolve the gyroid around an axis instead to create a more evenly distributed structure within the shell of the plunger. If stresses are exceeding predefined requirements it is also possible to place more material in certain areas called grading.

The concepts are evaluated by comparing their respective stresses and the specific stiffness for closing and opening of the plunger. Table 10 below summarizes maximum stress and specific stiffness for each concept.

Table 10. Evaluation of max stress and specific stiffness for plunger concepts.

concept max stress specific stiffness

MPa a.u. closing A 108,60 1,40 B 135,46 1,74 C 93,75 1,89 D 183,27 1,54 opening A 208,09 1,68 B 237,92 1,72 C 176,21 1,79 D 331,02 1,55

For closing it can be observed that stress peaks at 183,27 MPa in concept D which also provides the highest weight reduction. This can be traced back to the density of only 30%. The lowest maximum stress can be found in concept C with only 93,75 MPa.

In terms of specific stiffness, the peak is found in concept C, as well. Concept A showed a somewhat poor behaviour when comparing maximum stress and specific stiffness.

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For opening the maximum stress is found to be very high for concept D with 331,02 MPa. Concept C yield satisfying values with the lowest maximum stress at 176,21 MPa and a specific stiffness of 1,79 which is the peak.

An optimal concept for the industrial plunger would combine a narrow cell structure of around 30-35% density with a strong enough shell thickness between 1 and 2 mm. With an open cell structure, it would be possible to save weight without losing too much stiffness and strength properties. Grading in particularly weak areas would further strengthen the component to resist high stresses.

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6 Results

In this chapter the results are presented from the compression tests, the finite element analysis, the convergence between the two and finally the optimization of the plunger.

6.1 Compression test

Table 11 below shows a mean value of max applied force and stiffness, together with the respective standard deviation, for each density.

Table 11. Data from compression tests.

density true density force SD stiffness SD

% % N N/mm 20 18,72 6,22 0,71 5,15 0,77 25 21,59 6.16 0,60 5.11 0,66 30 29,40 11,01 0,45 9,76 0,58 35 34,57 14,17 0,34 12,47 0,43 40 39,03 17,57 0,32 16,17 0,25 45 42,55 20,14 0,35 17,92 0,58 50 45,68 21,49 0,89 19,08 0,69 55 51,65 26,98 0,27 24,55 0,35 60 55,17 29,28 0,37 26,89 0,59 65 59,67 34,12 0,34 30,57 0,84 75 66,25 40,69 0,92 36,23 0,73 85 72,28 47,2 1,53 40,56 1,55

In this table, another true density has been calculated by measuring the mass of each printed cube. As seen this density differentiates slightly from the previously calculated density, most likely due to printing inconsistency. For the full table containing data form all the specimen, see appendix A. Figure 27a displays the mean stiffness of each density and figure 27b shows the stiffness of each specimen in order to evaluate the deviation.

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6.2 Finite element analysis

The purpose of the FEA is to determine the stiffness of the gyroid structure for every volume fraction. Table 12 below shows the density of the tested geometry, the force and consequently the stiffness.

Table 12. FEA results for force and stiffness for the different densities.

density true density force at 1 mm force at 2 mm stiffness

% % N N N/mm 20 19,93 6189 12379 6,19 25 24,84 8310 16620 8,31 30 29,69 10647 21295 10,65 35 34,47 13264 26528 13,26 40 39,21 16125 32249 16,12 45 43,81 19257 38513 19,26 50 48,35 22647 45295 22,65 55 52,77 26299 52598 26,30 60 57,08 30205 60410 30,21 65 61,27 34409 68818 34,41 75 69,22 43523 87046 43,52 85 76,53 55381 110760 55,38 95 83,09 67372 134740 67,37

With increasing density force and stiffness are increasing as well. A Stiffness/Density-curve is modelled to visualize the growth rate of the geometry’s stiffness with increasing density. Stiffness is measured in kN/mm and relative density in percent. See figure 28 for the S/D-curve.

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To put the calculated values in perspective a minimum and maximum are added to the data at zero percent density (0, 0) and 100 percent density (1, 1). One hundred percent density yields a stiffness of 110,405 kN/mm.

6.3 Convergence between compression test and FEA

Another graph is constructed from experiment using the mean stiffness values and a fifth-degree polynomial curve from FEA values. This is used to evaluate how the scaling of stiffness at different relative densities is in convergence between physical tests and computational analysis. As seen in figure 29 the results from the experiments are close to or has a slightly lower stiffness than the simulation in most points and converge with the curve until around 0,65 density where stiffness is approximately 3-5 pp lower.

Figure 29. S/D-curve for FEA and compression test.

The stiffness and density are measured in relation to point (1,1) which is a solid cube (100% density) of the same dimensions as the other tests and a stiffness of 110,4 kN/mm.

Experiments, analysis and an application of 3D-printed gyroid structures

Bachelor thesis, 15 ECTS