3 boyutlu masa üstü yazıcı ile matematiksel bir modelden gerçek bir nesnenin dijital üretimi

Abstract

3 boyutlu yazıcı teknolojisi son yıllarda giderek yaygınlaştı ve bu da matematiksel modellerden, elle tutulabilir somut gerçek nesnelerin üretimini, şimdiye kadar hiç olmadığı kadar çok kolaylaştırdı. Bu çalışmanın amacı da eriterek üst üste yığma metodunu kullanan bir masa üstü 3 boyutlu yazıcı kullanarak, matematiksel denklemlerden yola çıkarak onların 3 boyutlu matematiksel modellerini oluşturmak ve oluşturulan bu modelleri de dijital olarak 3 boyutlu yazıcı ile üretmektir. Matematiksel denklemleri kullanarak 3 boyutlu matematiksel modellerin oluşturulması işlemi K3DSurf yazılımı kullanılarak gerçekleştirildi. 3 boyutlu matematiksel modeli oluşturan x, y, z koordinatlarına ait veriler daha sonra üretimi gerçekleştirecek 3 boyutlu yazıcının tanıdığı format olan “.obj” dosya formatına dönüştürüldü. MakerBot® firmasının MakerWare™ adlı katmanlara ayırma programı kullanılarak üretilecek model istenilen kalınlıktaki katmanlara ayrıldı, baskı kafasının x-y ekseni boyunca yapacağı hareketler hesaplattırıldı ve bu veriler “.gcode” formatına çevrilerek bir sd karta aktarıldı. Örnek çalışma olarak ise, Diamand denklemi, belirlenen sınır şartları arasında değerler verilerek 3 boyutlu matematiksel modeli oluşturuldu ve Flashforge Creator modeli masaüstü 3 boyutlu yazıcı ile dijital üretimi yapıldı.

Keywords

• 3 boyutlu yazıcı,matematiksel modelleme,katmanlı üretim

Digital fabrication of a real object from a mathematical model by using 3D desktop printer

Abstract

3-D printing technology is becoming widely available and can help to produce tangible solid physical objects from mathematical models much easier than ever before. The aim of this paper is to construct mathematical models from mathematical equations and to fabricate real solid objects digitally from mathematical models by using a 3-D Fused Deposition Modelling (FDM) printer. Formation of 3D mathematical models using mathematical equations was performed using K3DSurf software. The data for the x, y, z coordinates that form the 3-D mathematical model are then converted to the ".obj" file format, which is the format recognized by the 3-dimensional FDM printer that will realize the fabrication. Using MakerBot®'s slicing software MakerWare ™, the model to be fabricated is sliced into layers of desired thickness, movements of the printing head along the x-y axis are calculated, and this data is transferred to a secure digital (SD) card in “.gcode” format. As a case study, a 3D mathematical model was obtained by assigning values to the Diamand equation between the boundary conditions, and it is digitally fabricated by using a FlashForge Creator desktop FDM 3D printer.

Keywords

• 3D printing,mathematical modelling,additive manufacturing

References

1. Hull, C.W., Apparatus for production of three-dimensional objects by stereolithography. U.S.Patent 4,575,330 (Publication Date: 3/11/1986; Filing Date 8/8/1984). http://www.google.com/patents/US4575330. (10.06.2014).
2. Lim, C.S., Chua, C.K. ve Leong, K.F., Rapid prototyping, World Scientific, Second edition, (2003).
3. Cooper, K.G., Rapid prototyping pechnology, selection and application, Marcel Dekker Inc., (2001),
4. Crawford, S., How 3-D Printing Works, http://computer. howstuffworks.com/3-d-printing1.htm, (2013).
5. Rosen, D., Gibson, I. ve Stucker, B., Additive manufacturing technologies, Springer, (2010).
6. Knill, O. ve Slavkovsky, E., Illustrating Mathematics using 3D Printers, Cornel University Library, arXiv:1306.5599 [math.HO], (2013).
7. Rosen, D.E., MakerBot industries to print anything and everything at one metro tech. retrieved from commercial observer, http://commercialobserver.com/2012/05/makerbot-industries-to-print-anything-and-everything-at-one-metrotech/, (2014), (05.09.2014).
8. Rowan, D., 3D printing – An “Industrial Revolution in the Digital Age”? Retrieved from WIRED Business Future Shock http://www.wired.com/2011/05/3d-printing-an-industrial-revolution-in-the-digital-age/, (2011), (05.09.2011).

9. Berman B., 3-D printing: The new industrial revolution. Business Horizons, 55, 2, 155-162, (2012), DOI:10.1016/j.bushor.2011.11.003.
10. Segerman, H. 3D Printing for Mathematical Visualisation, The Mathematical Intelligencer, 34, 4, 56-62, (2012), DOI:10.1007/s00283-012-9319-7.
11. Chapela, V. M., Percino, M. J., Calvo, F. D., Calvo, F. ve Trinidad, L., Manufacture of 3D Möbius-Listing Models with a 3D Printer, Proceedings of the World Congress on Engineering Vol I, WCE 2013, July 3-5, London, U.K. (2013).
12. Slavkovsky, E.A., Feasibility study for teaching geometry and other topics using three-dimensional printers. M.L.A Thesis. Harvard University, (2012).
13. Gür, Y., Additive manufacturing of anatomical models from computed tomography scan data, MCB: Molecular & Cellular Biomechanics, 11, 4, 249-258, (2014), DOI:10.3970/mcb.2014.011.249.
14. Marcincin, J.N., Marcincinova,L.N., Barna,J. ve Janak,M., Application of FDM rapid prototyping technology in experimental gearbox development process, Tehnički Vjesnik-Technical Gazette, 19, 3, 689-694, (2012).
15. Taha, A., K3DSurf software package. URL:http://k3dsurf.sourceforge.net/. (04.01.2015).
16. Schoen, A.H., Infinite periodic minimal surfaces without self-intersections, NASA Technical Note TN D-5541, (1970).
17. Weber, M., Hoffmann, D. ve Hoffman J.T., Triply periodic level surfaces, http://www.msri.org/publications/sgp/jim/geom/level/library/triper/indexd.html (11.06.2017)
18. Knapp, M.E., Wolff, R. ve Lipson, H., Developing printable content: A repository for printable teaching models, Retrieved from http://utwired.engr.utexas.edu/lff/symposium/proceedingsArchive/ pubs/Manuscripts/2008/2008-52-Knapp.pdf, (2008).
19. MakerBot® MakerWare™ 3-D printing software, Retrieved from http://www.makerbot.com/support/makerware/ documentation/slicer/, (2014), (Retrieved 04.01.2015).