Titreşim kısıtları altında gemi ana makine dairesi yapısal optimizasyonu
Ship main engine room structural optimization with vibration restrictions
Yazar: ABDULAZİZ MERT DOĞAN
Danışman: DR. ÖĞR. ÜYESİ SERDAR AYTEKİN KÖROĞLU
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Gemi ve Deniz Teknoloji Mühendisliği Ana Bilim Dalı / Gemi ve Deniz Teknolojisi Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Gemi Mühendisliği = Marine Engineering
Dizin: Serbest titreşim analizi = Free vibration analysis ; Serbest titreşimler = Free vibrations ; Tasarım optimizasyonu = Design optimization ; Yapı optimizasyonu = Structural optimization

Özet:
Gelişen dünyada artan gemi taşımacılığı talebi, gemi tasarımı için önemli bir rol oynamaktadır. Talepleri karşılamak için daha büyük gemiler daha hızlı seyir yapacak şekilde tasarlanmaya başlandı. Daha büyük ve daha hızlı gemiler daha fazla güce ihtiyaç duyar ve daha büyük makine ihtiyacı doğar. Gemilerde daha büyük ve daha hızlı sevk sistemlerinin kullanılması birçok sorunu da beraberinde getirmiştir. Bu makinelerin getirdiği sorunlardan birisi de titreşimdir. Gemilerdeki en büyük titreşim kaynakları geminin ana makinesi ve sevk sistemidir, ana makine ve sevk sistemi gemiler için hayati önem taşımaktadır. Gemilerin sevk sistemini kaybetmesi veya zarar görmesi durumunda gemi hareket kabiliyetini kaybeder. Bu yüzden ana makine dairesinde oluşacak olan problemler önem arz etmektedir. Geminin en büyük ve hayati önem taşıyan elemanları ana makine dairesinde bulunduğundan, titreşim problemi bu bölgenin tasarımında önemli bir yere sahiptir. Tasarım aşamasında tasarımcılar sorunu önceden görür ve çözüm üretirler. Tasarım aşmasında öngörülemeyen titreşim problemlerinin daha sonra çözümü hem maliyetli hem de zordur.
Bu tez için örnek olarak alınan 500 TEU taşıma kapasiteli konteyner gemisinin ana makine dairesi sonlu elemanlar yöntemi ile modellenmiş ve dizayn optimizasyonu yapılmıştır. Serbest titreşim analizleri sonucunda rezonans problemi olduğu ortaya çıkan konteyner gemisinin ana makine dairesinde dizayn optimizasyonu yapılmıştır. Serbest titreşim analizleri yapılan geminin analiz sonuçları optimizasyon kısıtı olarak kullanılmıştır. Ayrıca klas kurallarına göre güverte yükleri belirlenip statik analiz sonuçları da optimizasyon kısıtı olarak kullanılmıştır. Modellenen gemi için klas kurallarına göre rezonans problemi aralığı tanımlanmıştır. Analizler için parametrik bir sonlu eleman modeli (Ansys-APDL) oluşturulmuş ve harici bir optimizasyon koduna bağlanmıştır. Kod bağlantılı bir sonlu elemanlar çözücüsü kullanılarak analiz çözümleri elde edilmiştir. Optimizasyonda ağırlık (yapı maliyetinin bir göstergesi olarak) amaç fonksiyonu olarak seçilmiştir. Optimizasyon probleminin çözümü için COBYLA algoritması kullanılmıştır. Algoritma Python programı içinde bulunan NLOPT optimizasyon kütüphanesi içinde yer almaktadır. Algoritma, doğrusal olmayan eşitsizlik kısıtlamaları ile türevi olmayan problemleri çözmek için kullanılır. Sabit bir topoloji ile makine dairesindeki yapısal elemanların kalınlıkları tasarım probleminin dizayn değişkenleri olarak seçilmiştir. Dizayn değişkenleri olarak güverteler, güvertelerin enine ve boyuna elemanlar, ana makine yatağı ve perdeler alınmıştır. Kısıtlar, klas kurallarının yapısal gerekliliklerine ve sınırlamalarına göre her dizayn değişkeni için ayrı olarak belirlenmiştir. Algoritma, bu dizayn değişkenleri üzerinde ağırlık fonksiyonunun minimum yapmak için kullanılmaktadır. Algoritma her iterasyon için bir serbest titreşim analizi ve statik analiz çözmektedir. Analiz sonucu olarak alınan doğal frekans değeri belirlenen frekans değerinden düşük olup olmadığı kontrol edilir, benzer şekilde okunan gerilme değeri belirlenen güvenli
gerilme değerinden düşük olmalıdır. Her iki kısıt belirlenen aralıkta değilse bir sonraki iterasyon için döngü tekrar eder. Optimizasyon sonucunda, belirlenen rezonans probleminin çözümü gerçekleşmiştir. Rezonans problemi çözülen yapının toplam ağırlığında azalış görülmüştür.

Abstract:
The increasing demand for shipping in the developing world plays an important role in ship design. To meet the increasing demand for shipping in the developing world, larger ships were designed to sail faster. Larger and faster ships need more power and larger machinery. The use of larger and faster transportation systems on ships has brought about many problems. One of the problems these machines bring is vibration. There are many machines and equipment on ships, many of which contribute to vibration. In addition, the dynamic movements of the ship in the sea are also a source of vibration. The biggest sources of vibration in ships are the ship's main engine and propulsion system. Main machinery and propulsion systems are essential for ships. If a ship loses its propulsion system or is damaged, the ship loses its navigational ability. In this case, ships may encounter problems that may pose a risk to both themselves and their environment. For this reason, problems that may arise in the main engine room are of great importance. Since the largest and most vital elements of the ship are located in the main machinery compartment, the vibration problem has an important place in the design of this area. During the design phase, designers anticipate the problem and solve it. Solving unforeseen vibration problems at the design stage is both costly and challenging.
It is possible to predict vibration problems and produce solutions with mathematical approaches. There are many mathematical approaches to solving vibration problems. Finite element method is one of them. The purpose of the finite element method is to reduce the infinite number of points in the structure to a limited number of points. This creates a mathematical model for solving the problem. This model consists of a finite number of elements that is called mesh. During the design process, the ship is modeled using the finite element method to predict vibration problems. Vibration analyzes are performed on the ship model. These vibration analysis can be examined under two main headings: free and forced vibration. Ansys is the most preferred program as a finite element solver. So that this solver is choosen for vibration analysis.
In solving vibration problems, compliance with the minimum cost and established class rules is important. Optimization is the ideal solution to this situation. Optimization is the solution of the problem by using design variables in a specified range with the aim of minimizing or maximizing the problem that can be identified as a real function. The optimization application provides both time and cost gains for many structural problems, such as the vibration problem. For optimization, solutions can be made with different algorithms in many software languages. Python is one of these software. There are different libraries for optimization in Python software. These libraries not only provide mathematical solutions for the definition of the problem, but
also contain optimization algorithms. A library suitable for the optimization problem is selected and the appropriate optimization algorithm is used.
A container ship was modeled as an example for this thesis. The container ship was designed according to Türk Loydu class rules. The ship, sized according to class rules, was used in structural analysis. The engine room of a container ship with a carrying capacity of 500 TEU has been modeled using the finite element method and the design optimization has been performed. Resonance issues were identified through free vibration analyses in the engine room of the container ship, and design optimization was carried out accordingly. The results of the free vibration analyses were utilized as constraints for the optimization. Additionally, deck loads were determined according to class rules, and the results of static analyses were also used as constraints for optimization. According to the class rules, the operating frequency of the main engine is in resonance with the natural frequency of the ship. This situation creates problems according to the class rules. A resonance problem range was defined for the modeled ship based on class rules.
A parametric finite element model, specifically designed through Ansys-APDL, was meticulously crafted to facilitate the extensive analysis requirements and seamlessly integrated with an external optimization code. The optimization code was implemented in the Python program. Analysis solutions were obtained by utilizing a finite element solver integrated into the code. In the optimization process, weight (as an indicator of structural cost) was chosen as the objective function. The COBYLA algorithm was used to solve the optimization problem by linear approximation. The algorithm is included in the NLOPT optimization library within a Python program. It is used to solve problems related to nonlinear inequality constraints and derivative-independent objectives.
The thicknesses of the structural elements in the engine room with a fixed topology were chosen as the design variables of the design problem. The thickness of the ship structural elements was chosen as the design variable. Design variables; It is defined as the thickness of decks, transverse and longitudinal members of decks, main engine bed and bulkheads.Design variables are defined separately for each deck and there are 9 in total. Constraints were determined individually for each design variable according to structural requirements and limitations of class rules. The weight function is defined through design variables. The algorithm is used to minimize the weight function on these design variables. The optimization algorithm tries to reach the optimum result for the finite element model. The finite element solver(Ansys-APDL) solves a free vibration analysis and a static analysis for each iteration. The results obtained here are evaluated by the optimization program. It is checked whether the natural frequency value obtained from the analysis is lower than the determined frequency value. Similarly, the observed stress value must also be lower than the defined safe stress value. If no constraints are met within the specified range, the loop repeats for the next iteration. The cycle continues until the constraints are met. As a result of optimization, model variables with optimum weights are found under the determined constraints. The algorithm reaches optimum results by mathematically approximating the result in each iteration.
In solving the optimization problem, local minimum values were checked from three different starting points. These starting points allowed us to reach local minimum. The local minimum values found in the solution of the problem were compared with each other. As a result of optimization, both the resonance problem was solved and the weight was reduced. As a result of the optimization made to solve the problem that occurred in the ship designed for this thesis, there was a 1.12% weight reduction. The final results show that the optimization was successful.