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研究生： Ahmed
Gohar
論文名稱： 研究使用增材製造設計和製造的均勻和功能漸變的晶格結構懸臂樑的機械性能
Investigating the mechanical performance of uniform and functionally graded lattice structured cantilever beams designed and manufactured using additive manufacturing
指導教授： 鄭正元
Jeng Ywan Jeng
口試委員: 艾米爾
Aamer Nazir
許啟彬
Chi Pin Hsu
學位類別： 碩士
Master
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 111
中文關鍵詞： 增材製造 、懸臂梁 、功能分級結構 、轉動慣量 、彎曲
外文關鍵詞： Additive manufacturing, Cantilever beam, Functionally graded structures, Moment of inertia, Bending
相關次數： 點閱：155  下載：6 
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    • 受到大自然的啟發，晶格結構是一種輕型結構，更常應用於工程系統，作為減少質量和提高剛度的一種方式。這種結構的機械性能取決於結構的拓撲結構、相對密度和構成材料。對於懸臂梁，在研究最佳分佈質量的響應時，拓撲優化的使用是同義詞，但控制尺寸、質量和具有高應力集中的區域的問題使它們變得不可行，並且使用晶格結構成為一種有益的選擇。
    憑藉增材製造的力量，這種蜂窩晶格結構可以定制為具有不同的拓撲結構、相對密度和單元尺寸分佈，以獲得局部和全局機械性能。在這項研究中，研究了晶格結構懸臂梁在均勻和變化的相對密度下的響應。對於均勻密度梁，三種基於表面的結構，即 Schwarz-Diamond、Schwarz-Primitive 和 Gyroid 結構與結合在懸臂梁中的基於桁架的 Octet-truss 結構一起研究，而對於不同的相對密度，基於表面的晶格結構通過改變參數進行優化例如周期和相對密度，以創建功能漸變的基於表面的結構，優化材料分佈，同時保持質量與以恆定密度製成的結構相似。樣品使用 HP Multi-Jet Fusion 4200 製造，並在設計為與萬能試驗機兼容的懸臂梁測試夾具上進行測試。通過彎曲試驗獲得的實驗結果是使用平均面積慣性矩和它們所在的邊界框的值來評估的。 這些值的差異導致了 200% - 250% 的差異，同時計算均勻密度結構的彎曲應力，並強調了對功能梯度結構進行此類評估的必要性。總體而言，響應表明 Schwarz-D 結構在均勻密度下和在所有結構中進行功能分級時都具有最佳彎曲響應。關於功能梯度結構，變化之間的比較表明，對基於表面的結構的數學參數所做的改變改變了從韌性到脆性的響應，並表明周期性變化會導致高應力集中區域，從而導致較早的失效與其他變化。

    Inspired by nature, lattice structures are type of light-weight structures that are more commonly being applied to engineering systems as a way to reduce mass and enhance stiffness. The mechanical properties of such structures are dependent upon the topology of the structure, its relative density and the material it’s made up from. For cantilever beams the use of topology optimization has been synonymous while studying the response at optimally distributing mass but issues to control the dimensions, mass and regions with high stress concentration render them as unfeasible and the use of lattice structure becomes a beneficial alternative.
    With the power of additive manufacturing such cellular lattice structures can be customized with varying topologies, relative density and cell size distributions to obtain both localized and global mechanical properties. In this research the response of lattice structured cantilever beams was investigated both at uniform and varying relative densities. For uniform density beams three surface based structures namely, Schwarz-Diamond, Schwarz-Primitive and Gyroid structure were studied alongside truss-based Octet-truss structure incorporated in a cantilever beam whereas for varying relative density the surface based lattice structures were optimized by varying parameters such as period and relative density to create functionally graded surface based structures optimizing material distribution while keeping the mass similar to the structures made at constant density. The samples were fabricated using HP Multi-Jet Fusion 4200 and tested on a cantilever beam testing fixture that was designed to be compatible with the Universal Testing Machine. The experimental results obtained by bending test on them were evaluated both using the values of average area moment of inertia and that of the bounding box they are made in. The difference in these values leads to a difference of 200% - 250% while computing for flexural stress for uniform density structures and highlights the need of such evaluation for functionally graded structures. Overall, the response reveals that the Schwarz-D structure has the best bending response both at uniform density and when made functionally graded amongst all the structures. With regards to functionally graded structures a comparison in between the variations shows that changes done to the mathematical parameters of surface based structures alters the response from ductile to brittle and indicates that the periodic variation causes regions of high stress concentrations that lead to earlier failure in comparison with other variations.

    FRONT PAGE i MASTER'S THESIS RECOMMENDATION FORM ii QUALIFICATION FORM BY MASTER'S DEGREE EXAMINATION iii ACKNOWLEDGEMENT iv ABSTRACT v ABSTRACT (CHINESE) 摘要 vii TABLE OF CONTENTS viii LIST OF FIGURES xii LIST OF TABLES xvii CHAPTER 1 INTRODUCTION 1 1.1 Introduction to lattice structures 1 1.2 Problem Statement 3 1.3 Objectives 4 1.4 Thesis Organization 4 CHAPTER 2 LITERATURE REVIEW 6 2.1 Need for lattice structures 6 2.2 Introduction to cellular lattice structures 8 2.2.1 Types 8 2.2.2 Functionally Graded Structures 10 2.2.3 Mechanical Properties 12 2.3 Additive Manufacturing of lattice structures: 17 2.3.1 Limitation of conventional manufacturing methods: 18 2.3.2 Process flow in additive manufacturing 18 2.3.3 Additive Manufacturing Processes 20 2.4 Existing literature on flexure testing 25 CHAPTER 3 DESIGN AND MANUFACTURING 27 3.1 Design of lattice structured beams 27 3.1.1 Design of non-graded lattice structured beams 27 3.2 Design of functionally graded structures: 30 3.2.1 Linearly varying thickness variation: 31 3.2.2 Periodic variation in one direction: 32 3.2.3 Periodic variation in two dimensions 36 3.3 Conversion of STL 38 3.4 Manufacturing of samples 42 3.4.1 HP MJF 4200 43 3.4.2 Placement of parts in the Powder bed 46 3.4.3 Post Processing 47 3.4.4 Printed samples 49 CHAPTER 4 MATERIALS AND METHODS 51 4.1 Material 51 4.1.1 Material properties 51 4.1.1.1 Material Composition 52 4.1.2.2 Tensile Strength 52 4.2 Finite Element Analysis 53 4.2.1 FEA Solver 53 4.2.1.1 Material Properties 54 4.2.1.2 Geometry 54 4.2.1.3 Material Assignment 55 4.2.1.4 Contact Definition 55 4.2.1.5 Mesh Generation 57 4.2.1.6 Boundary Conditions 58 4.2.1.7 FEA Results Calculation 61 4.3 Experimental Methods 61 4.3.1 Fixture design 62 4.3.2 Weight and Volume Measurements 63 4.3.3 Bending test 63 4.4 Theoretical Calculations: 65 4.4.1 Moment of inertia 65 4.4.2 Flexural stress 66 4.4.3 Flexural strain 68 4.4.4 Flexural Modulus 69 CHAPTER 5 RESULTS AND DISCUSSION 70 5.1 Response of constant density lattice structured cantilever beam 70 5.1.1 Area Moment of inertia 70 5.1.2 Flexural deformation 74 5.1.3 Flexural Stress 76 5.1.4 Energy absorption of structures 77 5.1.5 FEA Analysis 78 5.1.6 Failure of structures 80 5.2 Response of functionally graded lattice structured cantilever beam 83 5.2.1 Area Moment of inertia 83 5.2.2 Flexural deformation 87 5.2.3 Bending stress in structures 90 5.2.4 Flexural Modulus and Energy absorption of structures 93 5.2.5 Failure of structures 94 5.3 Significance of research 96 5.4 Limitation of this study 97 CHAPTER 6 CONCLUSION: 98 REFERENCES 101 APPENDIX A: Data and additional graphical interpretation 106

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