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

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.

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

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,

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