Toz yatağında katmanlı imalat prosesinin sonlu elemanlarla modellenmesi
Process modeling of powder bed fusion additive manufacturing  with finite element method
Yazar: FATİH YARDIMCI
Danışman: PROF. DR. ZAHİT MECİTOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Uçak ve Uzay Mühendisliği Ana Bilim Dalı / Uçak ve Uzay Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Mühendislik Bilimleri = Engineering Sciences

Özet:
Konvansiyonel imal yöntemlerine göre sağladığı geometrik serbestlik, üretim esnekliği ve imal süresi avantajlarıyla katmanlı imalat günümüzde bir çok mühendislik alanında kullanılmakta ve giderek yaygınlık kazanmaktadır. Döküm ve dövme gibi imal yöntemlerinin aksine kalıp ihtiyacı olmadığı için üretim adetindeki artış birim maliyeti değiştirmemektedir. Bu sebeple üretim adetinin sınırlı ve hammadde değerinin yüksek olduğu havacılık sektörü için maliyet açısında da etkin bir yöntem olarak karşımıza çıkmakta ve geleneksel üretimin yerine kullanılabilmektedir. Katmanlı imalat teknolojisinin nihai ürünlerindeki fonksiyonel parçaların imalatında kullanılması ve kullanıldığı ürünlerin tasarımının geliştirilmesi için araştırılması gereken birçok kontrol parametresi mevcuttur. Yüksek soğutma ve ısıtma oranları nedeniyle parça içerisinde artık gerilmeler oluşması ve çarpılmaya sebebiyet vermesi tipik bir problemdir. Tasarım imal edildikten sonra bu problemlerin tespiti ve deneme yanılma yöntemi ile iterasyona gidilmesi süre ve maliyeti arttırmaktadır. 
Katmanlı imalat ile metal parçaların üretilmesi sırasında meydanda gelen faz değişimi, eriyik havuzundaki ısı iletimi, alaşım elementlerinin buharlaşması ve katılaşma gibi fiziksel süreçler prosesin modellenmesini zorlaştırmaktadır. Bu tez kapsamında toz yatağında ergitme prosesinin sonlu elemanlar analiziyle makro boyutta modellenmesine imkan veren toplu katman (ing. lumped layer) yönteminin incelenmesi ve örnek çalışma üzerinde uygulanması amaçlanmıştır. Bu sayede FEM ile katmanlı imalat modellenmesinin endüstriyel boyutlarda uygulanabilirliği ve sağlayacağı fayda görülecektir. Tez içerisinde toz yatağında gerçekleştirilen katmanlı imalat prosesinin sonlu elemanlar yöntemiyle modellenmiş ve proses sonucunda oluşan deformasyon ve gerilmeler elde edilerek test ölçümleri ile kıyaslanmıştır. İmal koşullarının simüle edilebilmesi için süreksiz (zamana bağlı) ve tek yönlü zayıf bağlı termo-mekanik modeller ANSYS 19.2 yazılımı ile çözdürülmüştür. 'T' kiriş geometrisindeki destek yapılarının asimetrik olarak kaldırılması sonucu oluşan çarpılma değerleri elde edilerek test verileriyle karşılaştırılmıştır. Çözüm ağı eleman boyutunun sonuçlara etkisi de incelenmiş ve çoklu katman yöntemiyle yapının genel çarpılma davranışının elde edilebildiği görülmüştür.
 Girdi olarak kullanılan malzeme verilerinin sonuçlarda yarattığı değişiklik incelenerek hassasiyet çalışması yapılmış ve sonucunda kritik malzeme parametreleri belirlenmiştir. Belirlenen girdi parametreleri için test verileri ile farkı azaltacak şekilde optimizasyon çalışması yapılmıştır. Optimizasyon cevap yüzeyi kullanılarak çok amaçlı genetik algoritma aracılığı ile gerçekleştirilmiştir ve yeni malzeme verileri ile tekrarlanan analizler ilk durumdaki hata değerleri ile karşılaştırılmıştır.

Abstract:
With the advantages of geometric freedom, production flexibility and manufacturing time compared to conventional manufacturing methods, additive manufacturing is being used in many engineering fields and is becoming increasingly widespread. Unlike manufacturing methods such as casting and forging, there is no need for molds, so the increase in the number of production does not change the unit cost. For this reason, it is a cost effective and preferable method for aviation sector where production quantity is limited and raw material value is high. While the use of layered manufacturing for prototype production is a common practice in aviation, additive manufacturing has also started to be used for the end product. Some examples are shared in this study; nickel alloy boroscope hubs of PW1100G GTF engines used in Airbus A320 Neo aircraft, fuel nozzles for GE9X engine, sensor housing measuring compressor inlet temperatures and so on.
Selective laser melting (SLM) and electron beam melting (EBM) are fusion-based layered manufacturing processes commonly used in the manufacture of metal parts Selective laser melting, modeled within the scope of the thesis, is a technique that uses a high power density laser to melt metal powders. Due to the high temperature it contains, thermal distortion as well as shrinkage of parts may also occur. A typical problem is  residual stresses occur in the part and distortion due to high cooling and heating rates. There are many control parameters that needs to be investigated in order to use additive manufacturing in functional parts and improve the design. In the additive manufacturing process, some of the process parameters that regulate the quality and reproducibility of parts are; support structures, build direction, layer thickness, scanning pattern and laser parameters (laser power, focal diameter, scanning speed are the main ones). When the effects of different process parameters are examined, it is seen that the most open to potential development are the build direction, support structures and scanning strategy.
Detection of aforementioned problems after the design is manufactured and solution iteration by trial and error method increases the time and cost. In recent years, computer aided simulations have been used frequently to resolve this problem. A common way to simulate the additive manufacturing process is to use the finite element method (FEM). The geometry is divided into elements which contain the nodes points where the calculations are made and the differential equations are solved separately. Time is divided into intervals to model the actual physical phenomenon, making it possible to solve time-varying complex problems. Nevertheless, physical processes such as phase change during the production of metal parts by layered manufacturing, heat conduction in the melt pool, evaporation of alloying elements and solidification make the process modeling difficult. Physics-based modeling has the potential to shed light on how the parameters underlying the process optimization interact. Length and time scale assessments require that models be divided into micro, meso and macro scale models. Micro models aim to investigate physical phenomena such as powder interaction with heat source, heat absorption and phase change in the dimensions of melt pool or heat affected zone (HAZ). Models of this size provide information about the melt pool size, thermal cycling, and solidification quality and could be used to determine the optimal laser parameters. However, these parameters have limitations due to material properties and commercial product suppliers. Meso models are used to calculate and provide the composition and temperature-dependent metallurgical properties that explain the thermomechanical behavior of the material. This information can be used as input in micro and macro models as required during its calculations. Macro models generally calculate residual stresses in models comparable in size to the workpiece produced using thermal cycling information. Raw material details and thermodynamic phase changes are not analyzed in this scale. The metallurgical phases and associated material properties are evaluated according to the thermal history of the workpiece and are taken into account using the values defined before the analysis. The source of the distortion and stresses that occur during the layered manufacturing process are the time-dependent thermal gradients and the resulting mechanical loads caused by the expansion. In this context, macro-scale process simulation can be divided into two main stages: heat transfer analysis and mechanical analysis.
In this thesis, it is aimed to examine the lumped layer method which enables the modeling of the melting process in the powder bed by finite element analysis in macro dimension and to apply it on the case study. In this way, the applicability and benefits of layered manufacturing modeling with FEM will be seen in industrial dimensions. Within this scope, the finite element method of the additive manufacturing process carried out in the powder bed was modeled and compared with the test measurements by obtaining the deformations and stresses that occurred as a result of the process. Discontinuous (time dependent) and one-way weakly connected thermo-mechanical models were solved with ANSYS 19.2 software to simulate manufacturing conditions. Distortion values resulting from asymmetric removal of support structures in T-beam geometry were obtained and compared with test data. The effect of the mesh element size on the results was also examined. When the test measurement and numerical measurement difference were examined, it was seen that minimum RMS error values were obtained with 0.7 mm and 0.9 mm element size for measurements taken along the beam (0.097 and 0.092, respectively). In the model with 0.7 mm element size, the maximum distortion values at the beam ends were closer with the test, while the model with 0.9 mm elements had a lower RMS error value. For the examined element size range, from 0.5 mm to 1 mm, it was found that the general distortion behavior of the structure could be obtained by the lumped-layer method and element size that has lowest RMS error was used as validation model. The analysis and test measurement difference at the left and right ends of the structure were read as 0.04 mm and 0.01 mm, respectively. In order to evaluate the error in all measurement points, the RMS difference of the two data was calculated as it was used when examining the effect of element size on the results. For this purpose, polynomial trend functions were assigned to both test and analysis data and the differences in the data were taken at 1 mm intervals and RMS was calculated. The RMS error value for the 127 points evaluated was found to be 0.092 mm.
The values of parameters used as analysis inputs can vary even depending on the part geometry, powder supplier and the manufacturing machine. In addition, analysis assumptions and simplifications reveal the need to examine the effect of input parameters on the results of the analysis and to align the numerical model with the test results. Sensitivity study was carried out by examining the change in the results of the material data used as input and critical material parameters were determined as a result. It was found that yield stress and thermal expansion coefficient were the most influential parameters. It is aimed to make an optimization study for yield strength and thermal expansion coefficients which are determined as the dominant input parameter as a result of parameter correlation. In order to serve the response surface, a sufficient number of sampling points must be obtained by the finite element method. Experimental Design (DOE) is a technique used to determine the location of sampling points in such a way that the field of random input parameters can be investigated in the most efficient manner and with the minimum number of sampling points necessary information is obtained. Central composite design, one of the most widely used experimental design methods, was used to create genetic aggregation response surface. This method uses a genetic algorithm that produces populations of different response surfaces that are resolved in parallel to select the best response surface. The suitability function of each response surface is used to determine which gives the best approach. Considers both the accuracy of the response surface at the design points and the stability (cross-validation) of the response surface. As a final step, the deflection values at endpoints which are output parameters are defined as the objective function and optimum values of yield strength and thermal expansion coefficients defined as input parameters are searched in order to obtain the values measured by test. In order to achieve the desired values by genetic algorithm, 2000 candidate points were created and 3755 candidates were evaluated for 7 iterations for the final values. The new yield strength and thermal expansion coefficient values obtained by optimization were solved by finite element analysis and the results were compared with the test and non-optimized values. Initially, it was seen that the error rate decreased from 2.3% to 0.2% for the amount of distortion at the left end, while the error value for the right end point decreased from 10.3% to 1.66%. The effect of the changed material properties on other measuring points was also checked and it was determined that the average square root error in the entire measuring region decreased by 2.28%. In conclusion, it is seen that the distortion behavior of a part produced by additive manufacturing method in powder bed can be obtained by finite element analysis and numerical models could be improved by using test results.