DEGREE PROJECT IN TECHNOLOGY, SECOND CYCLE, 30 CREDITS
STOCKHOLM, SWEDEN 2020
Design for Additive Manufacturing :
An Optimization driven design approach
Satabdee Dash
Master of Science Thesis TRITA-ITM-EX 2020 : 482 KTH Industrial Engineering and Management
Machine Design
iii
Examensarbete TRITA-ITM-EX 2020:482
Design för additiv tillverkning:
En optimeringsdriven designmetod
Satabdee Dash
Godkänt
2020-09-02
Examinator
Ulf Sellgren ulfs@md.kth.se
Handledare
Mårten Olsson mart@kth.se
Uppdragsgivare
Scania CV AB
Kontaktperson
Morgan Wallin
morgan.wallin@scania.com
Sammanfattning
Ökad användning av Additive Manufacturing (AM) i industriell produktion kräver ett nytänkade av produkter (enheter, delsystem) ur AM-synvinkel. Simuleringsdrivna designverktyg spelar en viktig roll för att nå detta med designoptimering med hänsyn taget till AM-teknikens möjligheter. Därför ville bussramavdelningen (RBRF) på Scania CV AB, Södertälje undersöka synergierna mellan topologioptimering och Design för AM (DfAM) i detta examensarbete.
I examensarbetet utvecklas en metodik för att skapa en DfAM-ramverk som involverar topologioptimering och åtföljs av ett tillverkningsanalyssteg. En fallstudieimplementering av denna utvecklade metodik utförs för validering och fortsatt utveckling. Fallstudien ersätter en befintlig lastbärande tvärbalk med en ny struktur optimerad med avseende på vikt och tillverkningsprocess. Det resulterade i en nästan självbärande AM-vänlig design med förbättrad styvhet tillsammans med en viktminskning på 9,5 %, vilket visar fördelen med att integrera topologioptimering och grundläggande AM-design tidigt i designfasen.
Nyckelord: Additiv tillverkning, Design för Additiv tillverkning, överhängsbegränsning, Topologioptimering.
v
Master of Science Thesis TRITA-ITM-EX 2020:482
Design for Additive Manufacturing : An Optimization driven design approach
Satabdee Dash
Approved
2020-09-02
Examiner
Ulf Sellgren ulfs@md.kth.se
Supervisor
Mårten Olsson mart@kth.se
Commissioner
Scania CV AB
Contact person
Morgan Wallin
morgan.wallin@scania.com
Abstract
Increasing application of Additive Manufacturing (AM) in industrial production demands product reimagination (assemblies, subsystems) from an AM standpoint. Simulation driven design tools play an important part in achieving this with design optimization subject to the capabilities of AM technologies. Therefore, the bus frames department (RBRF) in Scania CV AB, Södertälje wanted to examine the synergies between topology optimization and Design for AM (DfAM) in the context of this thesis.
In this thesis, a methodology is developed to establish a DfAM framework involving topology optimization and is accompanied by a manufacturability analysis stage. A case study implementation of this developed methodology is performed for validation and further development. The case study replaces an existing load bearing cross member with a new structure optimized with respect to weight and manufacturing process.
It resulted in a nearly self supporting AM friendly design with improved stiffness along with a 9.5% weight reduction, thereby proving the benefit of incorporating topology optimization and AM design fundamentals during the early design phase.
Keywords: Additive Manufacturing, Design for Additive Manufacturing, Overhang Constraint, Topology Optimization.
Foreword
This thesis was conducted at SCANIA CV AB, Södertälje, in the bus-frames and installation department, RBRF during spring 2020. I feel fortunate to successfully accomplish this work amidst the COVID-19 pandemic. First of all, I would like to thank my thesis supervisor Morgan Wallin for consistently directing me and presenting me with new perspectives for solving problems. I am thankful to my manager Piotr Bownik for providing me with all the requisite facilities to keep my thesis going.
My special thanks to Mikael Thellner who was in the support group for my thesis.
His expertise and spectacular insights into any problem were highly valuable to my thesis. I would also like to thank Andreas Wrang and Mats Lundstedt for providing me a helping hand with the structural analyses. My extended gratitude to Fredrik Idberg and Jaideep Bangal (Altair) as well as Srikant Purli (Amexci) for the insightful discussions and providing me with ample support and advice.
I would like to thank my KTH supervisor Prof. Mårten Olsson who has shared knowledge and academic guidance throughout the writing process.
I am grateful to Scania and all the team members of RBRF for providing me the opportunity to get a wonderful learning experience. Big thanks to Karin Sondell for being my confidante in this journey with Scania and RBRF. My heartfelt gratitude to all who have assisted me in some way or other in this challenging thesis period.
Finally, I would like to express my deepest gratitude to my family and friends for believing in me and continuously encouraging me throughout all these academic years.
Satabdee Dash Stockholm, Sweden
Nomenclature
List of Abbreviations
AM Additive Manufacturing CAD Computer Aided Design
DfAM Design for Additive Manufacturing DFX Design for X
FEA Finite Element Analysis
FE Finite Element
MFD Method of Feasible Directions MINDENS Minimum Member Density MINDIM Minimum Member Thickness MMA Method of Moving Asymptotes OC Optimality Criteria
OHA Overhang Angle
OH Overhang
RBRA Bus - Dynamics & Strength Analysis RBRF Bus - Frames & Installations
SDD Simulation Driven Design
SIMP Solid Isotropic Material with Penalisation SLM Selective Laser Melting
SLP Sequential Linear Programming
Table of Contents
Page
List of Figures xiii
List of Tables xv
1 Introduction 1
1.1 Background . . . . 1
1.2 Research Questions . . . . 2
1.3 Purpose . . . . 2
1.4 Deliverables . . . . 3
1.5 Delimitations and limitations . . . . 3
1.6 Research Approach . . . . 5
1.7 Outline . . . . 6
2 Theoretical background and Tools 7 2.1 Introduction to Structural Optimization . . . . 7
2.2 Topology Optimization . . . . 8
2.2.1 Introduction . . . . 8
2.2.2 Problem Definition and Design Parameterization . . . . 8
2.2.3 SIMP Interpolation Method . . . . 9
2.2.4 Checkerboard Solution . . . . 10
2.2.5 Optimization Problem Formulation . . . . 11
2.2.6 Solution Methods . . . . 12
2.3 Additive manufacturing . . . . 13
2.3.1 Introduction . . . . 13
2.3.2 Categories . . . . 13
2.3.3 Applications . . . . 18
2.3.4 Advantages . . . . 18
2.3.5 Challenges . . . . 19
2.3.6 Support structures . . . . 20
2.4 Topology Optimization with Manufacturing Constraints . . . . 21
2.5 Design for Additive Manufacturing - DFX Approach . . . . 22
2.6 Software Tools . . . . 23
2.6.1 Optimization Driven Design in Altair InspireTM . . . . 23
2.6.2 Additive Manufacturing simulations in Altair InspireTMPrint3D 26 3 Optimization Driven Design Methodology 29 3.1 Outline of the proposed methodology . . . . 29
3.2 Project Definition . . . . 30
3.2.1 Project scope definition . . . . 30
3.2.2 Design scope definition . . . . 30
3.2.3 Design problem formulation . . . . 31
3.2.4 Selection of material and appropriate AM process . . . . 31
3.3 Concept Development . . . . 32
3.3.1 Free topology optimization . . . . 32
3.3.2 Constrained topology optimization . . . . 34
3.3.3 Conceptualization/CAD modelling . . . . 35
3.4 Manufacturability analysis . . . . 36
3.4.1 Buildability . . . . 37
3.4.2 AM Simulations . . . . 37
4 Case study: Implementation of proposed methodology 39 4.1 Project Definition . . . . 39
4.1.1 Project scope definition . . . . 39
4.1.2 Design scope definition . . . . 39
4.1.3 Design problem formulation . . . . 41
4.1.4 Selection of material and AM process . . . . 41
4.1.5 Loading scenarios . . . . 42
4.2 Concept Development . . . . 42
4.2.1 Free topology optimization . . . . 42
4.2.2 Constrained topology optimization . . . . 50
4.2.3 Conceptualization/CAD modelling . . . . 55
4.3 Manufacturability analysis . . . . 65
4.3.1 Buildability . . . . 65
4.3.2 AM simulations . . . . 66
5 Discussion 71 5.1 Simplified Design Space . . . . 71
5.2 3D Modelling in Altair PolyNURBS . . . . 71
5.3 Overhang constraint . . . . 72
5.4 Mesh resolution . . . . 73
5.5 Materials . . . . 73
5.6 AM simulations . . . . 73
6 Conclusions 75 6.1 Research question 1 . . . . 75
6.2 Research question 2 . . . . 76
7 Future work 77
Bibliography 78
Appendix A: Methodology Flowchart 81
Appendix B: Project plan 82
Appendix C: Risk Register 83
List of Figures
Figure Page
1.1 Overview of thesis method . . . . 5
2.1 Categories of Structural optimization. a) Sizing optimization, Truss structure b) Shape optimization c) Topology optimization. Figure courtesy: [10]. . . . 7
2.2 A black and white minimum compliance design representing the binary approach for assigning materials using SIMP interpolation method. Figure courtesy: [21] . . . . 9
2.3 Problem of checkerboard solution with SIMP model . . . . 10
2.4 Process illustration for Fused Deposition Modeling. Figure courtesy:[12] . 14 2.5 Process illustration for Stereolithography. Figure courtesy:[12] . . . . 14
2.6 Process illustration for Material Jetting (3D Printing). Figure courtesy:[12] 15 2.7 Process illustration for Sheet Lamination. Figure courtesy:[12] . . . . 15
2.8 Process illustration for Selective Laser Melting. Figure courtesy:[12] . . . . 16
2.9 Process illustration for Selective Laser Sintering. Figure courtesy:[12] . . . 16
2.10 Process illustration for Direct Energy Deposition. Figure courtesy: [1] . . . 17
2.11 Process illustration for Binder Jetting. Figure courtesy:[8] . . . . 17
2.12 Illustration of AM part with indicated build direction, showing self- supporting members for OHA less than 45º (green) and overhanging areas with support for OHA greater than 45º (red). Figure courtesy: [17] . . . . 22
3.1 Optimization driven design methodology . . . . 29
3.2 Process and material selection for AM . . . . 31
4.1 Case study element represented in reddish brown . . . . 40
4.2 Design space modelling . . . . 43
4.3 Wheel swept volume and Design volume . . . . 43
4.4 DV represented in reddish brown, NDV represented in grey, fixed supports are highlighted in red . . . . 44
4.5 Contact constraints and load . . . . 45 4.6 Resulting topology with 40% volume (Outline of DV1 is shown for reference) 46
4.7 Free topology optimization results with variable Vf (DV1 is shown for
reference) . . . . 47
4.8 Modified design volume . . . . 48
4.9 Free topology optimized structure and the prelim stress analysis results (Non-linear scale, Red zones imply violation of constraints) . . . . 50
4.10 Orientation and support structures for free topology optimized structure (Print direction normal to the print bed, Z axis and Recoater direction parallel to print bed, X axis) . . . . 51
4.11 Multi-Dimensional 3 pillar comparison between support area, support volume and printing time corresponding to support structures per orientation 52 4.12 Constrained topology optimization for custom orientation . . . . 54
4.13 Constrained topology optimization for orientation with maximum build height . . . . 54
4.14 Constrained topology optimized structure and the prelim stress analysis results (Non-linear scale, Red zones imply violation of constraints) . . . . 55
4.15 Understanding constraints and performance. Figure courtesy: [6] . . . . . 57
4.16 3D modelling and positioning . . . . 57
4.17 Modelling of additional features in concept C for attachment to the mating components . . . . 58
4.18 Example of design modification performed for concept C . . . . 59
4.19 Design modification inspired by stress results . . . . 59
4.20 Part build volume compared to printer dimensions . . . . 60
4.21 ISO view showing support structures (highlighted in yellow) for orientations a,b and c . . . . 61
4.22 TOP view showing varying regions (highlighted in red) of the structure requiring support when oriented as per a,b and c . . . . 61
4.23 Structural member with OHA below 45◦ . . . . 62
4.24 Support structures (yellow) including the fillet region . . . . 62
4.25 Support structures (yellow) deteriorates the surface quality at the rounded corners . . . . 63
4.26 Final structural analysis results . . . . 64
4.27 Final optimized part designed for AM . . . . 65
4.28 TOP view showing the slicing operation in Print3D module . . . . 65
4.29 Simulation results for model displacement during printing . . . . 67
4.30 Simulation results for model displacement post printing . . . . 67 4.31 Simulation results for post spring back . . . . 68 4.32 Free body diagram explaining the spring back behaviour . . . . 68 4.33 Simulation results showing von Mises stress distribution (Red regions
depict maximum stress) . . . . 69 4.34 Simulation results showing temperature distribution (Red regions depict
maximum temperature) . . . . 69 5.1 Patch operation in Inspire to edit the 3D model (PolyNURBS) . . . . 72
List of Tables
Table Page
4.2.1 Optimization parameters and weight for 40% volume . . . . 45 4.2.2 Free topology optimization results for DV1, with Element size = 10 mm,
Min. member size =30 mm and Elemental density threshold = 0.50 . . . 46 4.2.3 Free Topology optimization results for modified design volumes DV1 to
DV5, with Vf = 0.3, Element size = 10 mm, Min. member size =30 mm and Elemental density threshold = 0.50 . . . . 48 4.2.4 Preliminary results for orientation setup in Print3D module presented in
terms of support structures requirement . . . . 51 4.2.5 Constrained topology optimization setup . . . . 53 4.2.6 Comparison results for conceptual designs A and B . . . . 56 4.2.7 Comparison results for initial design and resulting design after
implementation of the developed methodology . . . . 63 4.3.1 Process parameters for thermo-mechanical simulation with layerwise
scan strategy . . . . 66
1. Introduction
In this chapter, the background of the thesis project, its purpose, delimitations and limitations, research questions as well as the method used to reach the defined purpose are presented.
1.1 Background
This master thesis has been conducted at Scania CV AB, situated in Södertälje and is undertaken in cooperation with the Bus - Frames and Installations (RBRF) department. Scania is a global manufacturing company which deals with the production of heavy-duty vehicles (like trucks and buses) as well as engines for the industry and transportation sector. Scania has been constantly advancing towards the development of its products and methodologies with focus on innovation, modularization, customization and sustainability [29].
With this focus in mind, it is extremely beneficial for designers to validate their concepts during the early phases of product development. This can be easily facilitated by manufacturing prototypes. Challenges with these prototypes are that they are expensive, have complex geometries and may result in longer lead time if special tools are required. Sometimes these tools fail to represent the final product quality, leading to limited evaluation of the design. Thus, there is a scope to evaluate and optimize each conceptual prototype design with regard to its performance and manufacturability in the early design phases.
Simulation-Driven Design (SDD) refers to the design approach that relies on simulation strategies in order to guide a designer in conceptualization phase, by providing better and advanced solutions, instead of merely verifying an existing concept. Implementation of SDD, along with CAD software can reduce the number of manufactured prototypes for physical testing since the outcomes of SDD leads to fewer, refined and sophisticated prototypes, thereby resulting in significant quality improvement along with time and cost reduction. This in turn increases the product development efficiency [20].
Topology optimization is one among the several tools that are used in order to
implement SDD. The outcome is a complex and organic part structure, which can most efficiently be manufactured (after few refinements) using Additive Manufacturing (AM) technique. AM is used for manufacturing spare parts, tools and fixtures, prototypes as well as end use products. Aerospace is currently one of the leading industries harnessing maximum benefit out of AM.
Advances in the field of AM has made it a great alternative when it comes to parts with complex design and/or small volumes. The lead time for prototypes built using AM, in many cases is better than that by traditional methods. Often, the benefits from optimization is not utilized to its maximum potential due to the limitations of conventional machining. This is when AM can be of great advantage. Therefore, Scania in cooperation with other companies has started investigating on AM technologies and methodologies to ’design parts for AM’.
1.2 Research Questions
Before beginning the thesis work, two research questions are framed which are presented below:
1. How to formulate an optimization driven design process to Design (parts) for Additive manufacturing (DfAM), using Altair InspireTM?
2. What are the advantages, limitations and difficulties that are expected with the implementation of the proposed methodology in terms of practicality and capability for catering multitude of design requirements?
1.3 Purpose
The purpose of this thesis work is to formulate an optimization driven design methodology to design parts for AM. This proposed methodology is validated by its implementation onto a case study component. The aim is to incorporate topology optimization and AM design principles for conceptualizing structures, optimized for function as well as the manufacturing process (i.e. AM).
To achieve the aim of this thesis, the following objectives have been stated:
• To find a suitable design space for the structure.
• To perform topology optimization using Altair Inspire which can be used as inspiration for concept development.
• To DfAM aiming both performance and manufacturability by incorporating AM design principles during and post optimization using Altair Inspire Print3D.
• To perform FE analysis on the optimized part.
• To present design proposals for the case study component by analyzing the results from above optimizations and to perform CAD modelling.
• To perform manufacturability analyses/ AM simulation in Print3D.
• To validate the work done and establish a final design methodology.
1.4 Deliverables
In order to meet the thesis requirements, the following deliverables are established as outcome of this thesis work:
• Process flowchart for developed methodology.
• Thesis report and relevant project documentation.
• Case study results along with finally selected design concept(s) model.
• Prelim interpretation of manufacturability analysis/AM simulation results.
1.5 Delimitations and limitations
The thesis delimitations and limitations are stated as follows:
• Topology optimization, 3D modelling and AM simulation are bounded by the software limitations of Altair InspireTM and Altair InspireTM Print3D.
• The case study results are used to study the implementation of proposed methodology and they do not guarantee best performance or manufacturability.
This is due to the simplified design space, loading scenarios and boundary conditions.
• The methodology is developed with the aim of using AM for building prototypes.
However, its applicability can be assessed for the production of end use products,
once the challenges (Section 2.3.5) associated with it have been eradicated.
• The case study component selected for validating the optimization driven methodology is selected from a bus chassis of specific variant. Therefore, the final methodology will be developed with its own limitations.
• Suitable simplifications and assumptions are considered while constructing the design space, easing out the implementation of the proposed methodology.
Only critical load case with simplified boundary conditions are considered for optimization.
• Iterations on modification of the design space are done, in order to simplify the optimizations and to get closer towards the most optimized concept.
• New methods for generating flexible CAD compatible models from Inspire are not proposed. Manual modelling in .STL format is performed, by taking design inspiration from optimized Inspire model.
• The developed concepts are analyzed and validated using FEA. Physical testing is not involved as part of the thesis scope. Details on the method of FEA is not extensively covered in this thesis work.
• FEA can be time consuming and due to time limitation of the project, such tasks are sometimes outsourced from calculations department (RBRA) at Scania.
• Bus chassis parts are mainly made of metals, hence metal AM processes, specifically SLM (Selective Laser Melting) is considered for validation of the proposed methodology.
• DfAM is restricted to few parameters such as build orientation, support structures and build layers (layer slicing). Parameters such as residual stresses and porosity of micro-structures are not investigated. Post-processing for AM such as machining processes for enhancing the surface finish, etc. are not covered in the thesis scope.
• Only performance model with a suitable objective is considered and other models such as Cost model are not considered within the thesis scope.
1.6 Research Approach
An overview of the method chosen for conducting the thesis work is presented in Figure 1.1. Pre-study phase marks the beginning of the project, wherein literature study is performed in the form of published journals, research papers, books, including previously published thesis work in the relevant domains [11],[23],[26],[1] and knowledge gained therein is applied in this thesis work. It also involves bench marking, AM workshop at Amexci [7] and webinars [6]. Based on the foundation laid by the pre- study phase, a methodology is proposed. This proposed methodology is implemented on a case study component in Scania bus chassis. The results from conceptualisation, optimization and FE simulation are evaluated and validated against a pre-defined set of design requirements. This resulted in the development of optimization driven design methodology aimed as part of the thesis.
A fully developed methodology flowchart is presented in Appendix A. A schematic version of GANTT chart, created as part of project planning is shown in Appendix B and a risk register for the project is presented in Appendix C.
Figure 1.1: Overview of thesis method
Throughout this design process, care is taken to ensure that the design becomes more and more suitable for easy manufacturing with AM and at the same time meets the design objectives better than that in the baseline. Build/thermo-mechanical simulations are performed and manufacturability using AM is interpreted based on
these results. At every step of the proposed methodology, additional information is gathered in order to improve the process until a fully developed methodology is established. In this way, this project serves for continuous design and process improvement.
1.7 Outline
The thesis report comprises of seven chapters. In the first chapter, the thesis work is introduced and the theory and tools relating to topology optimization, additive manufacturing and other relevant subjects are presented in the second chapter. The optimization driven design methodology is explained in the third chapter and the case study implementation along with the results are captured in the fourth chapter.
Different aspects of the developed methodology and the implications of its limitations are discussed in chapter five. Important conclusions are drawn and potential future research are suggested in the two concluding chapters of this report.
2. Theoretical background and Tools
In this chapter, a detailed description of the background of the theoretical concepts and tools used in this thesis work are presented. The initial sections introduce structural optimization and summarize the theory of topology optimization. The following section explains the theory behind design and process related to additive manufacturing which is followed by an introduction to DfAM and the use of topology optimization in DfAM. The last section describes the software tools used in the optimization process.
2.1 Introduction to Structural Optimization
The subject of Engineering Design optimization often involves maximization or minimization of one or more structural performance parameters. This is referred to as Structural Optimization [21]. Material distribution method is one of the commonly used method for optimization in the design domain and is often used for finding the optimum layout of a linearly elastic structure. Based on this method, structural optimization can be categorized as: Size, shape and topology optimization as shown in Figure 2.1.
Figure 2.1: Categories of Structural optimization. a) Sizing optimization, Truss structure b) Shape optimization c) Topology optimization. Figure courtesy:
[10].
Sizing optimization, typically applied to truss structures aims at achieving optimal cross section or thickness of beams. Shape optimization aims to find optimal shape of the available design domain. Both of these optimizations are dependant on the initial structure. Topology optimization, on the other hand, involves finding structural features (e.g: number of holes, their optimal shape, positions, etc.) and connectivity of the structural domain [10].
2.2 Topology Optimization
2.2.1 Introduction
Topology optimization is a structural optimization method aimed at achieving pre- defined objective(s) by optimal distribution of material within a specified design volume under a given set of loads, boundary conditions and constraints. State function constraints and manufacturing constraints are applied in order to maximize or minimize the objective function for generation of optimal structures. Industrially, it is one of the most popular techniques adopted for designing lightweight components.
Several approaches are available for performing topology optimization from which density based method is the most widely one. Solid Isotropic Material with Penalization (SIMP) is one of the computational models which employs density based method and is widely used in industrial optimization software.
2.2.2 Problem Definition and Design Parameterization
Design parameterization for the topology of a structure is achieved by determining the optimal material distribution in space i.e. finding spatial points where the material is present and points where it is devoid of material (void). Mathematically, this can be interpreted as a search for an optimal subset of material distribution Ωmat within the available design space Ω.
The general setup for optimization problem deals with minimum compliance design.
The admissible stiffness tensors complying with the above approach have material points as their design variables and thus result in a discrete binary (0 − 1) design problem. Solution of this optimization problem using gradient based algorithm requires a continuous optimization problem. Hence, in order to cope with this 0 or 1 problem, the integer variable of elemental stiffness matrix E, is converted to
continuous variable E(ρ) by modifying it as a function of density vector ρ as per Equation (2.1), where ρ contains all the elemental densities, ρe. The design variable for this optimization problem is ρeand is expressed as shown in Equation (2.2).
E(ρ) = ρE0, (2.1)
ρe=
1 if e ∈ Ωmat
0 if e ∈ Ω\Ωmat
(2.2)
The volume constraint is ∫
Ω
ρdV = V ol(Ωmat)≤ V (2.3)
where V is the available design volume.
2.2.3 SIMP Interpolation Method
With the optimization approach mentioned in the previous section, it is expected to achieve designs consisting of complete material or no material. This in turn requires to penalise the intermediate values of density function to steer the solution towards a discrete form. SIMP method employing power law with penalisation as per Equation (2.4) is one of the efficient methods used to achieve this as represented in Figure 2.2.
E = ρpE0 (2.4)
where E0 is the stiffness tensor of given isotropic material, p is the penalising factor that penalises intermediate elemental densities ρebetween 0 and 1 [10].
Figure 2.2: A black and white minimum compliance design representing the binary approach for assigning materials using SIMP interpolation method. Figure courtesy: [21]
The SIMP model is a computational model which deals with material interpolation within the design space such that,
E(ρ = 0) = 0, E(ρ = 1) = E0 (2.5)
The contribution of intermediate densities towards the material stiffness is usually small compared to the material volume and hence, p > 1 render the intermediate densities ineffective towards their contribution to the material stiffness. SIMP model has been questioned for its physical relevance as it does not produce complete black- white designs. However, it has been proved in [9] that the SIMP model can be used as long as p > 3. This method is quite popular within industries due to the commercially available software packages such as Altair Inspire, TOSCA, and Ansys Mechanical, making use of SIMP as their FEA solver.
2.2.4 Checkerboard Solution
Implementation of the SIMP method for topology optimization usually results in structures exhibiting a checkerboard pattern. Discretized solid elements filled with material (1) or devoid of material (0) can be viewed as a checkerboard pattern in the optimized structure as shown in Figure 2.3a.
This pattern is undesirable as it is produced due to numerical instabilities caused by the numerical approximations employed in the finite element methods. Hence, they do not correspond to optimal material distribution [14].
(a) Checkerboard solution (b) Uncheckerboard solution Figure 2.3: Problem of checkerboard solution with SIMP model
Figure 2.3 is generated by running a 99-line topology optimization MATLAB code developed by O.Sigmund [31]. A checkerboard solution for a general 2D simply supported beam is presented in Figure 2.3a. Restriction methods in terms of filters are implemented to generate uncheckerboard solutions as shown in Figure 2.3b. Filtering techniques enforce geometrical constraints to ensure existence of solutions by FE
convergence. This results in reduction or removal of checkerboard patterns by allowing the formation of only realistic geometrical features and boundaries [10].
2.2.5 Optimization Problem Formulation
A simple topology optimization problem can be formulated as shown in Equation (2.6).
minx f (x)
Subject to
x (design variable) limits State variable constraints Manufacturing constraints
(2.6)
where f represents an objective function which is the quantity we seek to minimize and x represents the design variable which is the quantity that is varied in order to achieve the target objective function. This optimization problem is subjected to constraints that represent the conditions that the optimized solution must satisfy. State function constraints may include conditions on displacement, stress, etc. whereas Manufacturing constraints represent the conditions imposed due to manufacturing limitations such as the Overhang constraint applicable for the AM process (further explained in Section 2.4).
2.2.5.1 Compliance minimization with volume fraction constraint
The most common type of topology optimization involves compliance as the objective function [10] and the same has been used in this thesis work in order to achieve minimum compliance (maximum stiffness) for a given volume fraction of available design domain. The optimization problem is formulated as per Equation (2.7).
minρ c(ρ) = UTKU =∑N
e=1(ρe)puTekeue
Subject to
0 < f < 1 ; V (ρ)/Vo = f KU = F
0 < ρmin ≤ ρ ≤ 1
(2.7)
Where c(ρ) is the compliance, U and F are global displacement and force vectors, ue and keare the element displacement vector and stiffness matrix respectively and K is
the global stiffness matrix. ρ is elemental density vector and ρmin is the lower limit of density to avoid singularities, N is the number of discretized elements in design domain, p is penalization power, V (ρ) is material volume, V0is available design volume and f is volume fraction.
2.2.5.2 Volume minimization with stress constraint
The SIMP method can be used with a stress criterion to form a topology optimization problem with an objective of volume (or weight) minimization. It is expressed mathematically as stated in Equation (2.8).
minρ
∑N e=1
veρe
Subject to
Ku = f
(σe)V M ≤ ρeσl if ρ > 0,
0 < ρmin ≤ ρ ≤ 1, e = 1, 2, ...., N
(2.8)
Where the stress for example, is evaluated at the center node of individual FE elements.
The equivalent von-Mises stress is represented by (σe)V M and the maximum allowable stress is represented by σl[10].
2.2.6 Solution Methods
Mathematical methods such as Optimality Criteria (OC), Mathematical Programming such as Sequential Linear Programming (SLP), Method of Moving Asymptotes (MMA), etc. are adopted for solving the optimization problem [10]. The OC method for a compliance minimization problem iteratively defines an update scheme for the density, ρ, based on a pre-defined optimality condition employing Lagrange multipliers. The MMA method employs algorithm [32] that solves nonlinear problems using a sequence of approximate sub-problems of a given type (linear, quadratic) similar to that followed in mathematical programming algorithms like SLP.
Mathematical programming software involve well established methods but their implementation onto a problem involving several variables and constraints is deemed challenging. Thus, the MMA [32] algorithm is used when large scale optimization problems are involved. When compared with the OC method, the Mathematical programming tools provide more flexibility by avoiding the requirement to develop
new algorithm for each new problem and also handle geometric considerations where physical intuition is limited [10].
2.3 Additive manufacturing
2.3.1 Introduction
With technological advancements, we have the opportunity to make manufacturing processes digitally flexible and efficient. Additive Manufacturing, otherwise referred to as AM is one of the transformative technologies as compared to the conventional subtractive processes such as turning, milling, shaping, etc. To be precise, AM is a process of generating 3D objects by depositing material layer by layer from a digitalized 3Dmodel.
Object information is fed to the hardware, through data derived from CAD models or by using 3D scanners. Thin layers of objects are sliced digitally in the form of .STL files in order to support the layering operation for depositing material. Upon repetitive deposition of material on the preceding layer, a 3D object is produced [16].
Wide variety of materials such as metals, ceramics, polymers, composites or their hybrids are used for AM. However, material development, standardization and qualification are certain aspects which needs to be further improved.
Suitability of a part for AM is decided based on the selection criteria which includes integrated design, customization, lightweight design and efficient design. Details of these selection criteria along with instances of their implementation in practical scenarios are presented in [22].
2.3.2 Categories
According to ISO/ASTM 52900 : 2015 [18], there are 7 categories of AM processes.
Process specifications are mentioned in [12] and the associated pros/cons are mentioned in [34].
The 7 types of AM techniques are described as follows [27]:
• Material extrusion: Material is extruded through a nozzle in tracks and these are combined into multi-layer models. They can use heated thermoplastic extrusion or
syringe dispensing. E.g: Fused Deposition Modeling (FDM) and Fused Filament Fabrication (FFF).
Figure 2.4: Process illustration for Fused Deposition Modeling. Figure courtesy:[12]
• VAT polymerization: A vat of liquid photo polymer resin is cured through selective exposure to light (via a laser/projector), followed by initiation of polymerization, thus converting the exposed areas to a solid part. E.g: Stereolithography (SLA), Digital Light Processing (DLP), Continuous Liquid Interphase Production (CLIP) and Scan,Spin and Selectively photocure (3SP).
Figure 2.5: Process illustration for Stereolithography. Figure courtesy:[12]
• Material Jetting: This process is also sometimes called 3D printing. Droplets of material are deposited layer by layer to make 3D parts. This can be done by jetting a photo-curable resin and curing it with UV light or by jetting thermally molten
materials that then solidify at ambient temperature. E.g: Multi-Jet Modeling (MJM) and Drop on Demand (DOD).
Figure 2.6: Process illustration for Material Jetting (3D Printing). Figure courtesy:[12]
• Sheet Lamination: Sheets of material are stacked and laminated together to form an object. The lamination method can be adhesives, ultrasonic welding or brazing (of metals). The regions that are not required are cut out layer by layer and removed after the object is built. E.g: Selective Deposition Lamination (SDL), Laminated Object Manufacturing (LOM), Ultrasonic Additive Manufacturing (UAM).
Figure 2.7: Process illustration for Sheet Lamination. Figure courtesy:[12]
• Powder Bed Fusion: Powdered material are selectively consolidated by melting them together using a heat source such as a laser or electron beam. The powder surrounding the consolidated part acts as support material for the overhanging features. E.g: Selective Laser Melting (SLM), Electron Beam Melting (EBM), Selective Laser Sintering (SLS), Selective Heat Sintering (SHS) and Direct Metal Laser Sintering (DMLS).
Figure 2.8: Process illustration for Selective Laser Melting. Figure courtesy:[12]
Figure 2.9: Process illustration for Selective Laser Sintering. Figure courtesy:[12]
• Direct Energy Deposition: Metal powder or wire is fed into a melt pool which has been generated on the surface of the part where it adheres to the underlying part or layer. Laser or electron beam is usually used as the power source.
E.g: Laser Metal Deposition (LMD), Electron Beam Free-Form Fabrication (EBF3), Direct Metal Deposition (DMD) and Laser Engineered Net Shaping (LENS).
Figure 2.10: Process illustration for Direct Energy Deposition. Figure courtesy: [1]
• Binder Jetting: Liquid binding agents are selectively applied onto thin layers of powdered material to build up parts layer by layer. The binders include both organic and inorganic materials. Metal or ceramic powdered parts are typically cured in a furnace after they are printed. E.g: Drop on Powder (DOP) and Powder Bed printing.
Figure 2.11: Process illustration for Binder Jetting. Figure courtesy:[8]
2.3.3 Applications
AM is mostly used for manufacturing prototypes, spare parts, tools and fixtures and also for end use products. Below are some of the application areas [34]:
• Automobile industry: Part integration, Production of spare parts and accessories, Prototypes for tests.
• Aerospace/Aeronautics: Production of accessories of complex geometries, Lightweight structures.
• Medicine/Pharmaceutical industry: Orthopedic implants and prosthetics, Printing of biodegradable living tissues for medicinal testing.
• Sports industry: Adjusted protective equipment, Prototypes for product testing.
• Construction industry: Printing of concretes for conventional buildings, for cement free buildings and for low cost/energy buildings.
2.3.4 Advantages
AM benefits the most when it is used for consolidating more than two parts, manufacturing low volumes and complex shaped structures. Some of the advantages of AM [13] are listed below:
• Complexity and performance: AM enables manufacturing of highly complex shaped components with increased performance, which otherwise are not possible with conventional methods. For instance: NASA redesigned an engine fuel injector to consolidate 115 subcomponents into just 2 subcomponents.
The redesigned injector fuelled an engine which produced 20000 pounds thrust (3300°C) while withstanding 1400 pounds psi [13].
• Customization: Individually customized and unique products can be created with greater design freedom and without the need of special tools or additional post processing. For instance: Siemens created over 10 million hearing aid shells using AM and claims that these customized shells have better fitting and hence improved customer satisfaction [13].
• Cost reduction: Lower inventories, fewer machines and tools lead to lower total cost of ownership. Longer lead time due to requirement of special tools in
conventional machining is negated using AM. Less material requirement and less waste generation post production. For instance: A NASCAR race team was able to reduce testing cost of prototype parts for wind tunnel testing by 89% due to scrap elimination and lack of tooling creation [13].
• Time to market: AM increases design flexibility and enables faster product modifications, without the need for assembly, tool creation, shipping, etc. For instance: A manufacturer was able to print a one component turbine wax mold in 18 hours as opposed to 170 hours with traditional multi-tool process [13].
• Eco-friendliness: Lightweight structures with efficient resource usage and shorter supply chain enables AM to create a smaller environmental footprint than conventional methods. For instance: An aircraft manufacturer reduced mass of engine component by 4− 7% and saved 7200 GJ energy as well as 550 metric tons of CO2equivalent emissions per aircraft annually [13].
2.3.5 Challenges
Although AM benefits us in variety of ways, there are certain challenges [13] associated with it and its scaling towards production.
Some of these challenges are listed below:
• Technical challenges: Material challenges include lack of improved material properties, lack of globally accepted quality standards. Manufacturing challenges include lack of precisely timed production lines, lack in process stability, part quality and reproducability .
• Design challenges: Capabilities of AM cannot be fully harnessed if the part(s) is not designed for AM. Requirement of additional support structures for part printability, shape distortion due to heat accumulation, generation of residual stresses and post-processing tasks are some of the AM challenges.
• Capability challenges: Includes lack of skilled workforce who can combine the knowledge from interdisciplinary domains (mechanical, fluid, material engineering) to make the most of AM capabilities, Lack of norms for AM design principles. Full fledged development of AM compatible design and simulation software as well as 3D scanning technologies are still under progress.
• Financial challenges: Generation of a positive business case for serial production using AM as compared to more established conventional methods is difficult.
Manufacturing cost models may not reveal the full extent of financial and environmental potential of AM. Difficulty in analyzing the overall impact of adopting AM on the existing supply chain process.
2.3.6 Support structures
AM involves free-form fabrication of parts. However, this requires sacrificial structures referred to as support structures in order to aid part printability during manufacturing. AM parts are deemed favorable when they are designed to be as self supporting as possible, thus optimizing the requirement of support structures. A better understanding into these structures is required in order to reduce them or redesign them effectively.
2.3.6.1 Advantages
Support structures benefit the AM process by playing several advantageous roles as listed below [19]:
• They act as heat diffuser and rigidity enhancer.
• They ensure that material is deposited at the intended height and the expected output geometry is achieved.
• They act as fixture, else the part will collapse under its weight.
• They act as tethering elements in powder bed processes to stop any shift, especially layer shift during re-coating processes.
2.3.6.2 Challenges
There are certain disadvantages associated with the addition of these support structures as listed below [19]:
• Manual labor and extra time required for removal of support structures.
• Support structure removal can be detrimental to the surface finish of final product.
• Surface roughness differs with support structure types, thus affects post processing.
• Extra time spent in designing these structures. This also implies larger digital data size.
• Wastage of material in case they are not reusable.
• Longer print duration and thus increased energy usage.
2.4 Topology Optimization with Manufacturing Constraints
The advantage of increased design freedom in AM processes compared to the conventional manufacturing processes has increased our interest in manufacturing near optimal design which is facilitated by topology optimization. Many topologically optimized geometries present manufacturing problems derived from the lack of self-supporting capacities and require sacrificial support material for 3D printing as shown in Figure 2.12. Since application of manufacturing constraint enhances manufacturability, this thesis focuses on achieving a structure as self supporting as possible. Researches have been done previously to obtain such structures as presented in [25].
Optistruct solver in Altair Inspire applies an overhang (OH) constraint on the part geometry driving it towards a self supporting design. This involves prevention of any overhanging structures beyond a pre defined critical overhang angle (referred as OHA).
The proposed method utilizes a series of projection methods such that the overhang constraint may be imposed without adding explicit local geometrical constraints to the optimization problem. This projection based approach is followed to develop the overhang constraint, where the structure is constrained to grow from the base plate within the specified OHA [15].
In this method, an element would be considered as a solid element only if they are supported by sufficient elements in a cone underneath them in build direction. The shape of the cone is determined by the chosen OHA. If there is insufficient support, the design variable (element density) is reduced to zero. In this sense, the algorithm can only produce parts which are satisfying the constraint without exception [17].
The commonly used powder bed fusion process is SLM and the metal structures produced using this technique can only be printed from this critical OHA from the vertical. Common standard is 45◦ from the normal to the print bed, however it can vary depending upon printing machine parameters and material characteristics.
Figure 2.12: Illustration of AM part with indicated build direction, showing self- supporting members for OHA less than 45º (green) and overhanging areas with support for OHA greater than 45º (red). Figure courtesy: [17]
OptiStruct implements OH constraint using two methods [17]:
1. Strict: This method provides a full constraint on the geometry, avoiding all overhanging members.
2. Lenient: This method penalises some of the applied constraints in order to reach a structure with good compromise between structural performance and overhanging members.
2.5 Design for Additive Manufacturing - DFX Approach
Design for X (DFX) approach with X representing manufacturability, utilizes methods and tools by integrating different manufacturing considerations into design processes.
This approach when applied for AM is referred to as DfAM. Most of the existing design processes actually ’Adapt for AM’ and not ’Design for AM’ [28]. This necessitates a DfAM framework which integrates existing tools in order to harness AM potentials and generate AM conformal designs. Within DfAM framework, SDD tools such
as topology optimization can be used with AM manufacturing constraint to allow development of concepts with immense design freedom whilst optimizing them for improved performance.
The DfAM approach aims at incorporating AM design principles and fundamentals [7], focusing most importantly on optimizing build orientation, overhanging members in parts, support structures, surface and part quality and post processing requirements. It also aims to reduce stress concentrated areas arising due to design features or residual stresses produced due to temperature gradients during printing. An article [24]
summarizes several researches done for DfAM both in broader and stricter context.
In this thesis work, DfAM framework is created to successfully design parts for AM by only considering build orientation, support structure reduction and their dependencies as the focus areas.
2.6 Software Tools
2.6.1 Optimization Driven Design in AltairInspireTM
Altair Inspire is equipped with robust SDD tools like topology optimization, thus providing user-friendly solution to designers. It has been upgraded to include a Print3D module that enables design engineers to design parts for AM. Details have been summarized in the following sections:
2.6.1.1 Topology optimization algorithm in AltairInspireTM
Scania uses Altair Inspire as the software platform for topology optimization and the FE solver incorporated in Inspire is OptiStruct. The OptiStruct algorithm is based on Gradient-based optimization method which alters the material distribution to optimize the user-defined objective(s) under a given set of constraints. It calculates the material properties for each discretized element within the specified material domain.
Gradient-based optimization method employs Method of Feasible Directions (MFD) as its default optimization algorithm. Detailed information of MFD method is available in Optistruct User manual [2].
According to [2], OptiStruct uses an iterative procedure known as the local approximation method to determine the solution of the optimization problem using the following steps: