Oklu kren tasarımı ve sonlu elemanlar metoduyla analizi
Boom crane design and analysis with finite element method
Yazar: ONUR TAV
Danışman: DR. ÖĞR. ÜYESİ İSMAİL GERDEMELİ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Sistem Dinamiği ve Kontrol Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Yük kaldırma ve taşıma işlerini yerine getiren makinalardan olan krenler, ağır endüstride, limanlarda, tersanelerde, depolarda kullanım alanı bulmaktadırlar. Kren çeşitlerinden en çok karşılaşılanlar köprülü krenler, portal krenler, oklu krenler ve mobil krenlerdir.

Kren tasarımı yaparken, krene etkiyen çeşitli yükler dikkate alınmalıdır. Taşınacak yükün ağırlığı, krenin zati ağırlığı, haraketten doğan dinamik yükler ve rüzgar yükleri kren yükleri olarak sıralanabilir. Bu yüklerin tesirlerinden başka, yapının titreşim etkilerine göre analizinin yapılması da uygun bir tasarım açısından gereklidir. Analizler, kısa süreler zarfında en uygun sonuçlara ulaşmak amacıyla sonlu elemanlar metodu kullanılarak yapılabilmektedir. 

Tez çalışmasında, limanlar ve tersanelerde çeşitli malları kaldırmak ve taşımak amacıyla kullanılan oklu kren tasarımı yapılmıştır. Tasarımı yapılan 60 m. x 50 ton kapasiteli kren, raylar üzerinde hareket edebilmekte ve döner platforma bağlı ok parçası vasıtasıyla çeşitli malları istenen yere taşıyabilmektedir.

Çalışmada öncelikli olarak, kren ve kren çeşitleri hakkında genel bilgiler verilmiştir. Sonrasında, krenin çeşitli tasarım adımları ile nihai halini alan kren geometrik modeli oluşturulmuş, bu modeli oluşturan parçalar tanıtılmış ve tasarımla ilgili hususlar aktarılmıştır. Bu kısımları takiben, FEM ve DIN standartlarına göre kren sınıflandırılması yapılmış, kren tasarımı ile ilgili analitik hesaplamalar irdelenerek gerekli değişiklikler gerçekleştirilmiştir. Kren denge hesapları, kren parçalarının boyutlandırılması, gerekli seçili motor güçlerinin hesapları, halatların seçimi için yapılan hesaplar analitik hesaplamaları oluşturmaktadır.

S.E.M ile tasarımı yapılan kren, bu metodla elde edilen sonuçların doğrulamalarının yapılması gerekmektedir. Bu sebeple, kren sehim sonuçlarının, gerilme analizi sonuçlarıyla birlikte Rayleigh-Ritz metodu ve Euler-Bernoulli kiriş teorisi vasıtasıyla da eldeleri sağlanabilmektedir. Ayrıca, Rayleigh metodu sayesinde yapının ilk doğal frekansının eldesi karmaşık olmayan çalışmayla ortaya konabilmektedir. Beşinci bölümde, teorik açıdan yukarda bahsi geçen  konuların bilgileri  ve prosedür adımları aktarılmıştır. İlerleyen bölümde ise S.E.M yazılım paketi ANSY hakkında bilgiler verilmiş ve basit geometride bir kirişin S.E.M ile çözümü ve Euler-Bernoulli kiriş teorisi vasıtasıyla da doğrulama çalışması yapılmıştır.

Yedinci bölümde, değişken kesitli parçalardan oluşan ok parçasının, zati ağırlıktan ve yükler altındayken analizleri gerçekleştirilmiştir. Ok parçasının Rayleigh-Ritz metoduyla sehim ve Euler-Bernoulli kiriş teorisi yardımıyla sehim ve gerilmeleri elde edilmiştir. İlgili sınır koşullarında ve yüklerde S.E.M analizi yürütülmüş ve ok parçası için sonuçlar bulunmuştur. Sonrasında, taşıyıcı gövdenin S.E.M analizleri yine sınır koşulları ve yükler etkisinde gerçekleştirilerek bölüm tamamlanmıştır.

Sekizinci bölümde, titreşim analizleri irdelenmiştir. S.E.M ile yapılan ok parçasının modal analizinin doğrulaması ise Rayleigh metoduyla yapının ilk doğal frekansının eldesi ile sağlanmıştır. İlk doğal frekansa karşılık gelen titreşim modu eğilme modudur ve bu modun titreşim analizi açısından en önemli mod olduğu anlaşılmaktadır. S.E.M modal analiz ile ilk on iki modun doğal frekansları ve bu doğal frekanslardaki mod şekilleri elde edilmiştir. Modal analizi takiben harmonik analiz yapılarak, yapının frekans cevabı fonksiyonu bulunmuştur.

Son bölümde, sonuçlar yorumlanmış ve bazı önerilerde bulunulmuştur. Rayleigh-Ritz, Rayleigh metodlarıyla bulunana sonuçlar S.E.M sonuçlarıyla karşılaştırılmıştır. S.E.M sonuçlarından sapmalar verilmiş ve görülmüştür ki doğrulama amacıyla kullanılan metodlar iyi yaklaşımlıkla sonuç vermektedirler. Yapılan çalışmaların tasarım ile ilgili sonuçları aktarılmış ve tasarım için yapılan seçimlerden söz edilmiştir. Çalışma neticesinde elde edilen veriler göstermektedir ki; S.E.M  sonuçlarını doğrulamak amacıyla Rayleigh-Ritz ve Rayleigh metodlarının kullanılması uygundur. S.E.M analizleri ile tasarım yapılması, hem zaman kazanımı hem de bazı tasarım unsurlarının daha kolay tespit edilmesini sağlamaktadır. Bu sebeplerden ötürü, sonlu elemanlar metodunun pratik ve güvenilir bir tasarım aracı olduğu anlaşılmaktadır.

Abstract:
Cranes are the machines that have duties at heavy industry, ship ports, shipyards and warehouses, these machines can lift and carry goods. Most remarkable crane types are bridge crane, portal crane, boom crane and mobile crane and these crane types take important place in machine industry. From perspective of safety, importance of crane design arise. Under various loads and hard working conditions of crane must be considered firstly in design step.

When designing crane, various loads that effects crane should be considered. These loads are mainly, weight of goods that will be carried, crane self weight, dynamic loads that rised from motion, wind loads and these loads should be considered to make proper crane design. Force and moment effects are important at the design stage however these loads are not enough for satisfactory crane design. In addition to these loads, vibrational effects are also should be considered and analyses should be made.

Making analyses in short terms with optimal design result is the goal to  achieve with "Finite Element Method".  In this thesis work, boom crane design is made, designed crane will be capable of carry and lift loads, goods at ship ports and shipyards. Crane that is designed with the capacity of 60 m x 50 tonne, can move on the rails with aid of boom part that is connected to platform, can lift and carry various goods and loads.

Firstly,crane definition and crane types have explained and general informations have given in the thesis. Afterwards, crane geometric model has designed, model is reached to its last design condition after repeated design steps. Parts that form geometric model assembly has explained and concerns that are related to design has given. CATIA software used in forming geometric model of crane.  This CAD software is a good tool for CAD modelling and also output of design could easily imported by various simulation packages.

In the following sections, crane classification has made according to  FEM and DIN standarts and analytical calculations has made which are related with crane design. Analytical calculations in design of crane are consist of crane equilibrium calculation, crane parts sizing, choosen motor power calculations and lifting ropes selection calculations. FEM and DIN standarts give information about using coefficients in design step. Also, some design related graphics and schematics given in these standarts. These coefficients, graphics and schematics that are related with crane classification is explained and used especially in analytical calculations. By obtained results of analytical calculations, design of crane adjusted for optimal design.

"Finite Element Method" results are validated with Rayleigh-Ritz, Rayleigh methods and with Euler Bernoulli beam theory. Theoritically, these methods explained with derivations and principles they rely on. Rayleigh-Ritz  method procedures give deflection of beams, Rayleigh method gives first natural frequency of beam without complex mathematical operations. Euler-Bernoulli beam theory is helpful when finding stress values.

In the following chapter, some information about "Finite Element Method" software ANSYS has given.
ANSYS software application fields and modular structure of the software explained. Following section of this chapter is focused on simple beam solution with "Finite Element Method" and  solution validated with Euler-Bernoulli theory. Simple model solution steps showed in detail and results indicate validation of simulation with theory.

At chapter seven, boom which is made of different cross sectioned parts solved with Rayleigh-Ritz method for deflection. By using MATLAB software, matlab code for solving Rayleigh-Ritz beam problems have written. MATLAB software is good tool for computing mathematical problems. It is used for solving validation problems in short terms while it is a big advantage in design process. Also, using computing software is valuable for making calculations more easily. Codes are given in Appendix of the thesis. Two main loading condition has considered in Rayleigh-Ritz method analyses. These are self weight analysis of boom part and analysis of boom when effected with various loads. Boundary conditions and loading conditions are defined and solved with given procedures with help of MATLAB codes.

Following sections are crane finite element solutions of loading cases that are told previously. Also, boundary condition for vento rope is applied to the structure and results are found with small deviation to previous ones and this shows that both boundary conditions could be used for analysis. Last part of this chapter ends with portal assembly stress and total deformation analyses of the crane with  boundary conditions and loading case by using "Finite Element Method" software package. Good mesh structure formed for the assembly analyses and boundary conditions with loads carefully entered to software. Results are obtained and showed that parts designed are suitable for strength point of view.

Result are validated with Rayleigh-Ritz method , Rayleigh method and with help of Euler-Bernoulli beam theory. Safe and good optimization of structure achieved with using these analysis methods and "Finite Element Method". 

At chapter eight, vibration analyses took place and structural vibration effects are investigated. Modal analysis with "Finite Element Method" validation has made with Rayleigh method. First natural frequency of boom part is achieved without complex operations using Rayleigh method. First twelve mod shapes with natural frequencies solved with "Finite Element Method" modal analysis. Rayleigh method result didnt showed too much deviation from "Finite Element Method" modal analysis result.  After this section, harmonic analysis has made with ANSYS and "Frequency Response Function" results are obtained. 

"Frequency Response Function" results shows that first mode which is first bending mode is important and gives relatively bigger amplitude than other modes. In modal analysis mesh structure also formed and boundary conditions applied with setting maximum modes to find property and analysis solved. In harmonic analysis, modal analysis setup is used and with defining harmonic force and by setting frequency range, analysis prepared for solving. Following solutions of two analysis, results obtained for vibrational analysis of the structure.

At last chapter, results showed and discussed. Boom part solution plots which are Rayleigh-Ritz solution and "Finite Element Method" solution are given. From plots it is seen that deviation from Rayleigh-Ritz method solution to "Finite Element Solution" is at acceptable values.  All results are given in a table and also close deviation values from both loading condition shows the consistency of the analyses. It is seen that Self weight loading contion show better approximation. For vibration analyses, deviation from computed first natural frequency to "Finite Element Method"  is not a higher value. Natural frequency of other modes could be obtained in the future works with use of Rayleigh-Ritz method and also deviations from frequency results will be reduced. Harmonic analysis results show 0-20 Hz vibrational effects are also concluded and discussed in this chapter.  Mod shapes consist of bending modes, which are for horizontal and vertical bending, torsional mode and elongation mode. It is seen that most dominant modes are for bending.  As demonstrated,  "Finite Element Method" and other methods for validation of the simulation, result deviations are in expected range so we can say that "Finite Element Method" results are consistent. Methods for using validation of structure also gives inner understanding of the system. Also, good approximations of methods for validation shows that these methods are valuable for design steps. Changes and actions taken that made for optimal design results are discussed and works done about this subject explained.

Thesis results and datas showed that "Finite Element Method" is a efficient, reliable tool for structural analysis of systems such as crane systems. Also, making fast optimization of design steps is another advantage of using "Finite Element Method". However "Finite Element Method" results should be validated for consistency of analyses. In this thesis, Rayleigh-Ritz, Rayleigh and with help of Euler-Bernoulli theory explained and problems solved with these methods. Approximation of the solutions show that methods are good tools for validation and can be used with "Finite Element Method".

Crane design thesis work revealed that using simulation based design with validation gives good results. For safety of the design, some aspects should be considered. Standarts about system  regulations are also important should be carefully inspected. Use of simulations took important place however some analytical calculations also still remain important because of this aspect strength, materials knowledge, mechanical theories and other design related  knowledge is very valuable. In heavy industry these systems will be improved and optimum results will be obtained. In future works, crane design will be improved and valuable design informations will be demonstrated regarding to design and application.  Also, it is seen from literature that crane design related with mechatronics, control theory aspects are important and  will be investigated for future works.