Potentials of Numerical Methods for Increasing the Productivity of Additive Manufacturing Processes
Abstract
1. Introduction
2. Manufacturing Costs for AM Components
2.1. General Considerations
2.2. Cost Structure for Indirect and Direct AM Technologies
2.3. State-of-the-Art concerning the Component Arrangement
3. Optimization of Component Arrangement
3.1. Relations to Existing Packing Problems
3.2. Three Different Arrangement Cases
- Case 1. Individual packing: a small number of components with the same or different geometries are needed, arrangement in one building space, manufacturing in one printing job possible.
- Case 2. Packing for small-scale (small batch) production: many components with the same geometries (hundreds or thousands of each type of geometry) are needed, manufacturing in more than one printing job.
- Case 3. Packing for bulk (mass) production: with an almost unlimited number of elements of each type, considering the specified percentage for different types of components.
3.3. Boundary Conditions and an Exemplary Task for Demonstration
- non-overlapping of components taking into account minimal allowable distances between each pair of components;
- containment of components in the cuboidal container.
4. New Approach: Regular-Sectional Arrangement
4.1. Main Scenario and Techniques
4.2. Solution Algorithm
5. Results and Discussion
6. Conclusions
- Preparation-analysis and abstraction of the component geometry:
- an assessment of the manufacturability of the component as a function of the orientation on the build platform (manufacturability/probability of defect/…) is made in order to limit the number of possibilities for positioning the components during optimization of the feasible variants;
- an abstraction of the outer geometry of the components by simple three-dimensional geometries (sphere, cylinder, cuboid, tetrahedron, …) is carried out in order to reduce the computational effort.
- Optimization of the component arrangement:
- the arrangement of the (abstracted) components is optimized, whereby the (abstracted) components can be rotated around all three spatial axes;
- the specification of boundary conditions for the optimization takes place (e.g., (minimum) distance of the components to each other, desired number (interval), desired construction height/production time, …);
- a weighting of the boundary conditions can be carried out;
- optimization can be carried out according to several target variables/(weighted) boundary conditions.
- Generation of the CAM data:
- reconversion of the abstracted geometries into the original geometries;
- machine data are generated.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Modeling of Basis Geometric Constraints in Packing Problems
- non-overlapping condition: and do not intersect, but can touch each other, i.e., ;
- containment condition: is arranged fully inside the container , i.e., ;
- distance condition: the distance between objects and is grater than or equal to , i.e.,
Appendix A.2. Basic Definitions of the phi-Function Technique
Appendix A.3. Adjusted phi-Function
Appendix A.4. Phi-Function for Irregular Objects Composed by a Union of Basic Shapes
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Cylinder Geometry (CGx) | CG1 | CG2 | CG3 | |
---|---|---|---|---|
length | [mm] | 12.5 | 12.5 | 12.5 |
diameter | [mm] | 3 | 3 | 4.5 |
inclination | [°] | 0 | 15 | 15 |
numbers needed (approx.) | [1] | 1000 | 1000 | 1000 |
Numbers of CGx per Building Platform | Number of Building Platforms Needed for approx. 1000 Components per Type | |||
---|---|---|---|---|
Kind of Building Platform | CG1 | CG2 | CG3 | |
Max_CG1 (Figure E1) | 375 | 3|1125 | ||
Max_CG2 (Figure E2) | 196 | 5|980 | ||
Max_CG3 (Figure E3) | 110 | 9|990 | ||
sum | 17|1125 + 980 + 990 | |||
Equal_CGx (Figure E4) | 64 | 64 | 64 | 16|1024 |
Number of Building Platforms | Numbers of CGx per Building Platform | Total Number of CGx | |||||
---|---|---|---|---|---|---|---|
Kind of Building Platform | CG1 | CG2 | CG3 | CG1 | CG2 | CG3 | |
BP_1_1-1 | 9 | 109 | 109 | 109 | 981 | 981 | 981 |
10 | 109 | 109 | 109 | 1090 | 1090 | 1090 |
Number of Building Platforms | Numbers of CGx per Building Platform | Total Number of CGx | |||||
---|---|---|---|---|---|---|---|
Kind of Building Platform | CG1 | CG2 | CG3 | CG1 | CG2 | CG3 | |
BP_1_2-1 | 2 | 450 | 0 | 0 | 900 | 0 | 0 |
BP_1_2-2 | 2 | 0 | 400 | 17 | 0 | 800 | 34 |
BP_1_2-3 | 4 | 0 | 0 | 221 | 0 | 0 | 884 |
BP_1_2-4 | 1 | 88 | 188 | 70 | 88 | 188 | 70 |
sum | 9 | 988 | 988 | 988 |
Number of Building Platforms | Numbers of CGx per Building Platform | Total Number of CGx | |||||
---|---|---|---|---|---|---|---|
Kind of Building Platform | CG1 | CG2 | CG3 | CG1 | CG2 | CG3 | |
BP_1_3-1 | 2 | 450 | 0 | 0 | 900 | 0 | 0 |
BP_1_3-2 | 2 | 0 | 400 | 17 | 0 | 800 | 34 |
BP_1_3-3 | 4 | 0 | 0 | 221 | 0 | 0 | 884 |
BP_1_3-4 | 1 | 200 | 234 | 0 | 200 | 234 | 0 |
BP_1_3-5 | 1 | 0 | 66 | 182 | 0 | 66 | 182 |
sum | 10 | 1100 | 1100 | 1100 |
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Scheithauer, U.; Romanova, T.; Pankratov, O.; Schwarzer-Fischer, E.; Schwentenwein, M.; Ertl, F.; Fischer, A. Potentials of Numerical Methods for Increasing the Productivity of Additive Manufacturing Processes. Ceramics 2023, 6, 630-650. https://doi.org/10.3390/ceramics6010038
Scheithauer U, Romanova T, Pankratov O, Schwarzer-Fischer E, Schwentenwein M, Ertl F, Fischer A. Potentials of Numerical Methods for Increasing the Productivity of Additive Manufacturing Processes. Ceramics. 2023; 6(1):630-650. https://doi.org/10.3390/ceramics6010038
Chicago/Turabian StyleScheithauer, Uwe, Tetyana Romanova, Oleksandr Pankratov, Eric Schwarzer-Fischer, Martin Schwentenwein, Florian Ertl, and Andreas Fischer. 2023. "Potentials of Numerical Methods for Increasing the Productivity of Additive Manufacturing Processes" Ceramics 6, no. 1: 630-650. https://doi.org/10.3390/ceramics6010038
APA StyleScheithauer, U., Romanova, T., Pankratov, O., Schwarzer-Fischer, E., Schwentenwein, M., Ertl, F., & Fischer, A. (2023). Potentials of Numerical Methods for Increasing the Productivity of Additive Manufacturing Processes. Ceramics, 6(1), 630-650. https://doi.org/10.3390/ceramics6010038