Mechanical Engineering / Makina Mühendisliği
Permanent URI for this collectionhttps://hdl.handle.net/11147/4129
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Research Project Çapraz-kama haddeleme prosesinin teknik özelliklerinin Türk ve Belarus endüstrileri için detaylandırılması(2010) Güden, Mustafa; Yardımoğlu, Bülent; Çakırcalı, Metin; Kılıçaslan, CenkÇapraz kama haddeleme (ÇKH) üzerine son yıllarda yoğun deneysel ve modelleme çalışmaları yapılmaktadır. Çalışılan bu proje, ÇKH üzerine yapılan çalışmaların ötesinde daha detaylı deneysel ve modelleme çalışmalarını kapsamasının yanında, modellemede kullanılan malzeme özelliklerinin yüksek deformasyon hızlarında ve yüksek sıcaklıklarda belirlenmesini ve dolayısıyla daha hassas modelleme sonuçlarının elde edilmesini hedeflemiştir. Proje kapsamında, AISI 1045 çeliği ve Ti6Al4V alaşımı iş parçalarının ÇKH işlemi üzerindeki şekillendirme açısı, genişletme açısı, alan indirgemesi ve sürtünme katsayısı parametrelerinin etkileri ısıl-mekanik model analiziyle nümerik olarak araştırılmıştır. Yapılan nümerik analizler deneysel olarak ölçülen kalıp kuvvetleri ile doğrulanmıştır. Oda sıcaklığında gerçekleştirilen ÇKH işleminde, başlangıçta sürtünme katsayısı düşük olsa bile deformasyon esnasında oluşan ısınmadan dolayı yükselmektedir. Simülasyonlarda sürtünme katsayısı deneysel olarak belirlenen ortalama değer olan 0,5 alınmıştır. Ti6Al4V için belirlenen malzeme ve hasar modelleri Split Hopkinson Basınç Bar test sisteminde çentikli numunelere yapılan testlerle doğrulanmıştır. İş parçasının düşük ve yüksek sıcaklıklarda ÇKH işleminde, sıcaklığın, efektif gerinimin, efektif gerilmenin, maksimum asal gerilmenin, ortalama gerilmenin, üç eksenli gerilme parametresinin ve efektif gerinim hızının zamanla değişimi ısıl-mekanik analizlerle belirlenmiştir. Analizler, iş parçası üzerindeki sıcaklığın işlem sırasında homojen dağılmadığı göstermiştir. Düşük sıcaklıkta yapılan ÇKH işleminde iş parçası sıcaklığı artarken yüksek sıcaklıkta yapılan işlemde iş parçası sıcaklığı düşmektedir. Analizler, çalışılan proses parametre aralığında alan indirgemesinin ve genişletme açısının kalıp kuvvetleri, gerinim ve gerilmeler üzerinde en etkin işlem parametreleri olduğunu göstermiştir. Her iki parametrenin artışı ile kalıp kuvvetleri artmaktadır. Daha önce deneysel olarak gözlenen iş parçasının orta kesitinde oluşan çapraz kırılma simülasyonlarla doğrulanmıştır. İş parçası mikro yapısının ilk işlem sıcaklığı tarafından etkilendiği gösterilmiştir. İlk kez ÇKH prosesi uygulanan Ti6Al4V alaşımı için seçilen bir sıcaklıkta alan indirgemesi ve genişletme açılarına bağlı kırılma indeksi çıkartılmıştır.Article Citation - WoS: 15Citation - Scopus: 19Exact Longitudinal Vibration Characteristics of Rods With Variable Cross-Sections(Hindawi Publishing Corporation, 2011) Yardımoğlu, Bülent; Aydın, LeventLongitudinal natural vibration frequencies of rods (or bars) with variable cross-sections are obtained from the exact solutions of differential equation of motion based on transformation method. For the rods having cross-section variations as power of the sinusoidal functions of ax+b, the differential equation is reduced to associated Legendre equation by using the appropriate transformations. Frequency equations of rods with certain cross-section area variations are found from the general solution of this equation for different boundary conditions. The present solutions are benchmarked by the solutions available in the literature for the special case of present cross-sectional variations. Moreover, the effects of cross-sectional area variations of rods on natural characteristics are studied with numerical examples.Other Citation - WoS: 4Citation - Scopus: 4Exact Solutions for the Longitudinal Vibration of Non-Uniform Rods [j. Sound Vib. 207 (1997) 721-729](Academic Press Inc., 2010) Yardımoğlu, BülentThe aims of this communication are to correct the frequency equation for a free–free rod with area variation A(x)=A0 s in2(ax+b) in a published article [1] and present the corrected non-dimensional natural frequencies.Article Citation - WoS: 16Citation - Scopus: 19A Novel Finite Element Model for Vibration Analysis of Rotating Tapered Timoshenko Beam of Equal Strength(Elsevier Ltd., 2010) Yardımoğlu, BülentA new finite element model based on the coupled displacement field and the tapering functions of the beam is formulated for transverse vibrations of rotating Timoshenko beams of equal strength. In the coupled displacement field, the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium. The tapering functions of breadth and depth of the beam are obtained from the principle of equal strength in the longitudinal direction of the beam. After finding the displacement functions using the tapering functions, the stiffness and mass matrices are expressed by using the strain and kinetic energy equations. A semi-symbolic computer program in Mathematica is developed and subsequently used to evaluate the new model. The results of the illustrative example regarding the problem indicated in the title of this paper are obtained and compared with the results found from the models created in ABAQUS. Very good agreement is found between the results of new model and the other results. © 2010 Elsevier B.V.Article Citation - WoS: 30Citation - Scopus: 33Coupled Out of Plane Vibrations of Spiral Beams for Micro-Scale Applications(Academic Press Inc., 2010) Karami, M. A.; Yardımoğlu, Bülent; Inman, Daniel J.An analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.Conference Object Citation - Scopus: 6Coupled Out of Plane Vibrations of Spiral Beams(American Institute of Aeronautics and Astronautics Inc. (AIAA), 2009) Karami, M. A.; Yardımoğlu, Bülent; Inman, Daniel J.An analytical method is proposed to calculate the natural frequencies and corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equation and the boundary conditions are derived using Hamilton's principle. The vibration problem of a constant radius curved beam is solved using a general exponential solution with complex coefficients. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the R′ terms have negligible effect on the structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joint together to consider the slow change of radius along the spiral. The natural frequencies and mode shapes of two spiral structures have been calculated for illustration.Article Citation - WoS: 17Citation - Scopus: 22Vibration Analysis of Rotating Tapered Timoshenko Beams by a New Finite Element Model(Hindawi Publishing Corporation, 2006) Yardımoğlu, BülentA new finite element model is developed and subsequently used for transverse vibrations of tapered Timoshenko beams with rectangular cross-section. The displacement functions of the finite element are derived from the coupled displacement field (the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium) approach by considering the tapering functions of breadth and depth of the beam. This procedure reduces the number of nodal variables. The new model can also be used for uniform beams. The stiffness and mass matrices of the finite element model are expressed by using the energy equations. To confirm the accuracy, efficiency, and versatility of the new model, a semi-symbolic computer program in MATLAB® is developed. As illustrative examples, the bending natural frequencies of non-rotating/rotating uniform and tapered Timoshenko beams are obtained and compared with previously published results and the results obtained from the finite element models of solids created in ABAQUS. Excellent agreement is found between the results of new finite element model and the other results.Article Citation - WoS: 39Citation - Scopus: 46Finite Element Model for Vibration Analysis of Pre-Twisted Timoshenko Beam(Academic Press Inc., 2004) Yardımoğlu, Bülent; Yıldırım, TolgaA new linearly pre-twisted Timoshenko beam finite element, which has two nodes and four-degrees-of-freedom per node, is developed and subsequently used for coupled bending-bending vibration analysis of pre-twisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pre-twisted beams whose flexural displacements are coupled in two planes. This approach helps to reduce the number of nodal variables. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pre-twisted Timoshenko beams are obtained and compared with previously published theoretical and experimental results to confirm the accuracy and efficiency of the present model. Excellent agreement is found with the previous studies. Also, the new pre-twisted Timoshenko beam element has good convergence characteristics.Article Citation - WoS: 11Citation - Scopus: 14Coupled Bending-Bending Vibration of a Rotating Pre-Twisted Beam With Aerofoil Cross-Section and Flexible Root by Finite Element Method(Hindawi Publishing Corporation, 2004) Yardımoğlu, Bülent; Inman, Daniel J.The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.Article Citation - WoS: 8Citation - Scopus: 6Coupled Bending-Bending Vibration of a Pre-Twisted Beam With Aerofoil Cross-Section by the Finite Element Method(Hindawi Publishing Corporation, 2003) Yardımoğlu, Bülent; Inman, Daniel J.The present study deals with a finite element model for coupled bending-bending-torsion vibration analysis of a pretwisted Timoshenko beam with varying aerofoil cross-section. The element derived in this paper has two nodes, with seven degrees of freedom at each node. The nodal variables are transverse displacements, cross-section rotations and the shear angles in two planes and torsional displacement. The advantage of the present element is the exclusion of unnecessary derivatives of fundamental nodal variables, which were included to obtain invertable square matrix by other researchers, by choosing proper displacement functions and using relationship between cross-sectional rotation and the shear deformation. Element stiffness and mass matrices are developed from strain and kinetic energy expressions by assigning proper order polynomial expressions for cross-section properties and considering higher order coupling coefficients. The correctness of the present model is confirmed by the experimental results available in the literature. Comparison of the proposed model results with those in the literature indicates that a faster convergence is obtained. The results presented also provide some insights in the formulation by clearly indicating that higher order coupling terms have considerable influence on the natural frequencies.