itüdergisi (E-Journals - İstanbul Teknik Üniversitesi, Istanbul Teknik Uniersity., İTÜ)
itüdergisi (E-Journals - İstanbul Teknik Üniversitesi, Istanbul Teknik Uniersity., İTÜ)Not a member yet
1059 research outputs found
Sort by
A modeling and realization method for the control of Discrete Event Systems
Get PDFSonlu durum makineleri ya da otomatlar, Ayrık Olay Sistemlerinin (AOS) analiz, tasarım ve kontro-lüne yönelik formal yöntemlerin yer aldığı uygulamalarda yaygın olarak kullanılmaktadır. Ayrık olay sistemlerinin geribeslemeli kontrolü için kuramsal bir yapı tanımlayan Üstdenetim Kuramı ve bu kurama ilişkin uygulamalar buna örnek olarak verilebilir. Otomatın standart tanımının, tasarıma ilişkin ayrık olay sistem davranışını ifade edebilmesine rağmen, zamanlama ve sayma gibi bazı davranışları bu modelleme biçimi ile ifade etmek kolay değildir. Bu çalışmanın temel amacı, AOS davranışlarının, özel olarak kontrole yönelik davranış kurallarının tasarımını ve ifadesini mümkün kılan durum tabanlı bir modelleme biçiminin geliştirilmesi ve bu modele dayanarak tasarlanmış davranışın uygulanabilmesi için bir yöntemin elde edilmesidir. ZS-otomat olarak anılan yeni mo-delleme biçimi, uygulamada sıklıkla karşılaşılan zamanlama ve sayma davranışlarının durum gös-terimi ile ifade edilmesini mümkün kılan Zamanlama ve Sayma Yapısına sahiptir. Modelin önemli bir özelliği, gerçekleme aşamasında kullanılan teknolojik araçlarda doğrudan uygulanabilecek yapısal bileşenler içermesidir. Bu çalışmada, modelleme biçiminin yanı sıra, bir gerçekleme yöntemi de tanıtılmaktadır. Gerçekleme yöntemi, ele alınan bir AOS için tasarlanmış kontrolörün ya da üstdenetleyicinin Programlanabilir Lojik Kontrolörlerle (PLC) gerçeklenmesine yönelik adımları sistematik olarak tanımlamaktadır. Yöntemin, tasarım davranışını yanlış olarak gerçeklemeye neden olan “çığ etkisi” adlı bir problem için çözüm oluşturduğu da gösterilmiştir. Geliştirilen yöntemle, tasarımda öngörülen zamanlama ve sayma davranışları, PLC’lerde kullanılan Zamanlayıcı ve Sayıcı bloklarını doğrudan kullanılmasını mümkün kılmaktadır. Sistematik olarak tanımlanan bu yöntem, programlanarak otomatik kod üretimini mümkün kılan bir yapıdadır. Anahtar Kelimeler: Ayrık olay sistemleri, gerçekleme, Programlanabilir Lojik Kontrolör.When formal methods are applied in control design of Discrete Event Systems (DES), it becomes necessary to model the system behavior and specifications by a formalism such as automata or Petri nets. For example, the supervisory control theory (SCT) introduced by Ramadge and Wonham in 1987, uses formal languages to model system behavior and, specifications and formal languages are often expressed by automata. The synthesized controllers or supervisors are also represented by automata which are then needed to be realized by a programmable device. Standard definition of the automaton is capable of describing the DES behavior of a design; however some behaviors like timing and counting can not directly or easily be represented in the standard formalism.Implementing a timing mechanism is necessary for discrete event control systems when a certain amount of delay is required to make a decision after an event occurs. A green traffic light, turning on after a certain time period following the red light could be an example. Likewise, a counting mechanism is applied if it is necessary to count the occurrence of a particular event for a number of times before issuing a control signal. For the case of manufacturing systems, packaging the products when a certain number of products are reached could be an example for the requirement of counting mechanism. While it is possible to implement the timing and counting requirements easily with the technological elements, formal definition of the standard automaton does not include such kind of mechanisms. However, it is possible to realize a time delay when utilizing formal methods. It is straightforward to define a time delay by assigning an event to indicate that a predetermined time has elapsed. However, in this case, a timing mechanism is required in the realization stage which is not a part of the formal structure. For counting an event for n times, n successive states in the automaton representation of the supervisor could be used, but in the general case, this may necessitate using large number of states. Therefore, a structure that is capable of representing the timing and counting behavior without using external mechanisms and excessive number of states is required. Another requirement regarding the implementation of formal supervisors is an output mechanism that would issue control signals (enabling or disabling signals for the example of Supervisory Control Theory) or events to drive the DES system being controlled. This requirement is generally met by employing automata with outputs for the representation of the supervisor.When implementing a DES control strategy for discrete event systems, timing and counting behaviors are frequently applied by using predefined objects of the technological device which is used for the realization of control strategy. Programmable Logic Controllers (PLCs) have been used in industrial applications for more than 35 years, and in today's industrial control systems Programmable Logic Controllers (PLCs) are extensively used for realizing control strategies. PLCs make it possible to realize timing and counting behaviors easily by utilizing ready-made objects called timers and counters. In this study, a formalism that enables designing and expressing DES behavior is developed, and a methodology that implements the designed behavior based on the introduced formalism is obtained. The new formalism, named TC-automaton, has a so called Timing and Counting Structure that enables the designer to assign timing and counting behaviors to the state based representation. An output function structure which enables outputting events depending on the states and/or on Timing-Counting Structure of the TC-automaton is also defined. TC-automaton is defined in such a way that, in the realization stage, it is possible to make use of the tools provided by the physical realization platform, i.e. PLCs. The implementation methodology introduced for the new formalism systematically defines the steps for realizing the designed controller or supervisor via PLCs. This systematic setting makes it possible to program the methodology, which is a step toward automatic code generation. It is also shown that, the methodology resolves "avalanche effect" problem, which might be encountered due to a particular structure of the automaton representation of the control behavior. PLC programs obtained by utilizing the methodology are also modular in structure which enhances program readability. Keywords: Discrete Event Systems, realization, Programmable Logic Controllers
Stabilizing constant diagonal controllers for TITO systems
Get PDFProses kontrolün ilk ve en önemli amacı sistemi kararlı kılmaktır, performans üzerine yapılacak her eylem bu temel koşul sağlandığı müddetçe bir anlam taşır. Kontrolör tasarımında kullanılan yöntemlerden biri sistemi kararlı kılacak tüm kontrolörleri bulmak ve ardından, tasarımdaki diğer beklentileri sağlamak üzere, bu sınıf içinden uygun bir kontrolörde karar kılmaktır. Bu hedef doğrultusunda yapılanlar şu özellikleri de barındırmalıdır ki, iyi bir kontrolör tasarım sürecinden söz edilebilsin. Kontrolör kırılgan olmamalıdır, yani kontrolör de parametre değişimlerine karşı sistemin kararlılığını ve mümkünse performansını zedelememelidir. Kontrolörün düşük mertebeden olması, parametre ayarlama sürecinde büyük kolaylıklar sağlar, zira ne kadar az parametre o kadar basit bir tasarım süreci demektir. Öte yandan pratik anlamı dolayısıyla da az parametre, ya da düşük mertebe endüstride görev alan uygulamacılar için problemlerin daha hızlı çözülmesi anlamına gelir. Bu çalışmada çok değişkenli kontrol yapıları arasında önemli bir yer tutan karakteristik değerler ve karakteristik değer eğrileri ele alınmış, rasyonel polinomlar cisminde indirgenebilir olan karakteristik denklemler için karakteristik değerlerin reel ekseni kesim noktaları ve bu noktalar civarındaki davranışları üzerinde durulmuştur. Zira bu değerler çok girişli çok çıkışlı sistemleri kararlı kılan kontrolörlerin bulunmasında ya da verilen bir kazanç değeri için kararlılığın analiz edilmesinde hızlı hesaplanabilirlikleri yönünden önem arz etmektedirler. Bu çalışma kapsamında iki girişli iki çıkışlı (TITO) sistemleri kararlı kılan sabit köşegen kontrolörler üzerinde durulmuş, karakteristik değer eğrilerinin reel ekseni kestikleri yerler ve eğrilerin bu noktalardaki geçiş yönlerinden hareket ederek hızlı bir algoritma geliştirilmiş ve bu tür sistemleri kararlı kılan kontrolörler örnek sistem üzerinde sınanarak hesaplanmıştır. Anahtar Kelimeler: Bilgisayar cebri, blok diyagram indirgeme, PID kontrol, parametre uzayı yaklaşımı, karakteristik değer eğrileri.A control system is an interconnection of compo-nents to perform certain tasks and to generate desired output signal, when it is driven by the input signal. In contrast to an open-loop system, a closed-loop control system uses sensors to measure the actual output to adjust the input in order to achieve desired output. Most industrial control systems are no longer single-input and single-output (SISO) but multi-input and multi-output (MIMO) systems with a high coupling between the channels. In the design of all dynamical systems stability is the most important property. When a dynamic system is described by its input-output relationship such as a transfer function, the system is stable if it generates bounded outputs for any bounded inputs; bounded-input bounded-output (BIBO) stability. For a linear, time-invariant system modeled by a transfer function matrix, the BIBO stability is guaranteed if and only if all the poles of the transfer function matrix are in the open-left-half complex plane. A reasonable approach to controller design is to find the set of all stabilizing compensators and then using a member of this set to satisfy further design criteria. A complete parameterization of all stabilizing controllers for a given system was suggested by Youla. An important disadvantage of this parameterization is that the order of the controller cannot be fixed. As a result, the order of the controller tends to be quite high most of the time. Therefore, in the last few years computation of all stabilizing controllers of a given order is examined by several researchers. It is a common fact that it is more difficult to design controllers for MIMO systems because there are usually interactions between different control loops. To overcome this difficulty decentralized controllers are considered which have fewer tuning parameters compared to general multivariable controllers. For example, decentralized PID (P: proportional, I: integral, D: derivative) controllers are widely used in process control due their simplicity and facility in working in case of actuator and/or sensor failure because it is relatively easy to tune manually as only one loop is directly affected by the failure. If a MIMO system described by a transfer-function matrix G(s) is diagonal dominant over the bandwidth of interest, or there exists an input compensator matrix C(s) to achieve diagonal dominance, then the stability and time domain behavior of the system can be inferred from the diagonal elements of G(s)C(s). The relative gain array, the (inverse) Nyquist array approach, the block Nyquist array method, the Perron-Frobenius scaling procedure and the characteristic locus method are among the analysis and design methods to reduce the interaction in a multivariable system. However, these approaches do not provide the set of all stabilizing controllers. Generalizing the Nyquist stability criterion for MIMO case is particularly important because plotting the characteristic values of the open-loop transfer function enables us to check the stability of the closed-loop system for a gain parameter. A stable characteristic polynomial, becomes unstable if and only if at least one root crosses the imaginary axis. The parameter values of the root crossing form the stability boundaries in the parameter space, which can be classified into three cases: the real root boundary, where a root crosses the imaginary axis at the origin, the infinite root boundary, where a root leaves the left half plane at infinity and the complex root boundary, where a pair of conjugate complex roots crosses the imaginary axes. These stability boundaries separate regions in which the number of closed loop system unstable poles does not change in parameter space.The main objective of this work is to develop an efficient and fast algorithm that can be used in finding all stabilizing constant controllers of diag(k,k)-type for TITO processes. Recall that a TITO system has two characteristic values that are in the field of rational functions, if the characteristic equation is reducible in this field. Hence Nyquist stability criterion can be applied to both of the characteristic values in order to determine the conditions for stability. Recall that the generalized Nyquist theorem requires that the net sum of encirclements of the point -1 by the characteristic values equal to the number of open-loop unstable poles of the system. Hence, it is of special importance to determine where the characteristic locus intersects with the real axis, i.e. where the imaginary part of, is zero. The direction of these crossings is also important, because the net count of crossings at an intersection point will indicate whether there are closed-loop poles to cross the imaginary axis. Keywords: Computer Algebra, block diagram reduction, PID control, parameter space approach, characteristic value plots
Statistical analysis of noise exposure levels for mine workers in Turkish Hard Coal Enterprise
Get PDFDevelopment of modern mechanized operations in mining industry has been considerably decreasing the physical burden of work. But the most undesired and unavoidable by-product of these operations is the generation of high levels of noise. Occupational noise exposure of mine workers is a potentially serious health problem. High-level of noise not only hinders communication between workers, but, depending upon the level, quality, and exposure duration of the noise, it may also result in different type of physical, physiological and psychological effects on the workers, especially Noise Induced Hearing Loss (NIHL). Occupational exposure limits specify the maximum sound pressure levels and exposure times to which nearly all workers may be repeatedly exposed without adverse effect on their ability to hear and understand normal speech. The European Union has reached agreement on new directives dealing with noise in the working environment - Noise at Work Directive 2003/10/EC. The Member States and candidate countries like Turkey are to comply with this Directive before 15 February 2006. The limit and action values are given in this directive. The specific objectives of this study were to estimate occupational noise exposure levels of mine workers employed in Turkish Hard Coal Enterprise and compare them with the exposure limit values. The method of Homogeneous Exposure Groups (HEG) was used for the estimation of occupational noise exposure levels of mine workers. The noise survey consisted of measuring and noting two variables: the noise levels to which the worker was exposed and his exposure time to those levels per work shift. After completion the survey, the daily noise exposure levels of groups were calculated. The homogeneity of the groups was tested statistically using one way analysis of variance. The normality of noise levels obtained for HEG's was investigated using Skewness and Kurtosis Coefficient of distributions and One Sample Kolmogorov - Simirnov Test were used to determine the normality of the data. In this study, the zonal method was selected as measuring technique due to the most cost-effective method. Noise measurements were carried out using a Type 1 integrated sound level meter (model NL-31) manu-factured by RION Co. Ltd., Japan. The equipment was operated on the A-weighted network, slow response and was acoustically calibrated before, during, and after each shift. Calibration was done using the RION NC-74 sound level calibrator which emits a 94 dB, 1 kHz tone. It is necessary to define an average noise level characterizing the mean exposure of the person to check compliance of noise exposure with regulations or to estimate the individual risk of hearing loss of an exposed person. Two parameters are defined by the ISO 1999 (1990) standard. These are daily and weekly noise exposure levels. The daily noise exposure level (LEX,8h = LAeq,8h = LEP,d) is time weighted average of the noise exposure levels, in dBA, for a nominal eight-hour working day. It covers all noises present at work, including impulsive noise. This concept is used when the worker is exposed daily, for 5 days per week, to the same level. The daily noise exposure levels for underground workers varied from 73.9 to 103.3 dBA. The daily noise exposure level of face worker is 89.7 dBA. The daily noise exposure levels of workers employed in underground such as face, development stoping, transportation, cager, mechanization and press, drilling and pumping are out of compliance with the EU Noise Directive of 2003/10/EC. The calculated daily noise exposure levels for surface workers varied from 80.8 to 100.1 dBA. These noise levels were obtained for engineman and carpenter workers respectively. The daily noise exposure level of engineman is only compliance with the EU Noise Directive of 2003/10/EC. The calculated daily noise exposure levels of other worker groups are out of compliance with the EU Noise Directive of 2003/10/EC. The daily noise exposure levels for mining machine plant workers varied from 86.5 to 97.7 dBA. These noise levels were obtained for welding and mechanization and press workers respectively. The daily noise exposure level of machinist, casting and electrician were determined as 91.6 dBA, 97.6 dBA and 88.7 dBA respectively. The daily noise exposure levels calculated for all occupational groups are out of compliance with the EU Noise Directive of 2003/10/EC. Keywords: Noise exposure level, underground mining, homogeneous exposure groups, statistical analysis.Günümüzde endüstriyel kalkınmanın ve modern teknolojinin ulaştığı düzey, bünyesinde birçok olumlu gelişme barındırmakla birlikte; yaşamı kolaylaştırmaya yönelik bu girişimlerin insan sağlığını olumsuz yönde etkileyen yanları da vardır. Bu tür olumsuzlukların biri de gürültüdür. Gelişen teknoloji ile birlikte gürültü, bütün işyerlerinde olduğu gibi maden işletmeleri için de önemli bir sorundur. Bu çalışmada, Zonguldak Taşkömürü Havzası’ndaki ocaklarda çalışanların maruz kaldıkları gürültü seviyelerini tespit ederek, ulusal ve uluslararası standartlarla karşılaştırmak için uygun bir strateji geliştirmek amaçlanmıştır. Türkiye Taşkömürü Kurumu (TTK)’na bağlı Yeraltı Maden İşletmelerinde işçilerin gürültü etkilenim düzeylerinin belirlenmesi için çalışanlar homojen etkilenim gruplarına ayrılmış ve gürültü ölçümleri herbir grubun gürültü etkilenim düzeyinin belirlenmesine yönelik olarak yapılmıştır. Homojenlik testi için tek yönlü varyans analizi kullanılmıştır. Normal dağılım varsayımının sağlanıp sağlanamadığının istatistiksel olarak araştırılmasında parametrik testlerden Çarpıklık ve Basıklık Katsayıları ile non-parametrik testlerden Tek Örneklem Kolmogorov – Simirnov Testi kullanılmıştır. Yeraltı homojen etkilenim grupları arasında en küçük ve en büyük günlük gürültü etkilenim düzeyleri 73.9 dBA ve 103.3 dBA olarak sırasıyla Barutçu ve Sondaj işçisi için elde edilmiştir. Yerüstü homojen etkilenim grupları arasında en düşük ve en büyük günlük gürültü etkilenim düzeyleri 80.8 dBA ve 100.1 dBA olarak sırasıyla Kuyu Vinç ve Ağaç İşleri işçisi için elde edilmiştir. Maden Makinaları Fabrikası homojen etkilenim grupları arasında en düşük ve en büyük günlük gürültü etkilenim düzeyleri 86.5 dBA ve 97.7 dBA olarak sırasıyla Kaynak ve Mekanizasyon ve Pres işçisi için elde edilmiştir. Anahtar Kelimeler: Yeraltı madeni, gürültü etkilenim düzeyi, homojen etkilenim grubu, istatistiksel analiz
The usage of historical seismograms: The 1912 earthquake records
Get PDFModern sismolojik yöntemlerle gerçekleştirilen deprem kayıtları son 40 yıllık dönemi kapsamaktadır, ancak aletsel sismolojik gözlemlerin başlangıcı 1880’lere dayanmaktadır. 1960’larda dünya standart sismograf ağının (WWSSN) kurulumuna kadar geçen süre içinde depremler ilksel mekanik sismograflar tarafından kaydedilmiştir. Bu deprem kayıtlarının modern metotlarla yeniden incelenmesi sismolojinin aletsel dönemini belirgin bir oranda genişletecektir. Bu çalışmada Ganos Fayı üzerinde meydana gelen 9 Ağustos (Ms = 7.4), 10 Ağustos (Ms = 6.2 ve 5.3) ve 13 Eylül 1912 (Ms = 6.9) ve çalışılmıştır. O tarihte 143 deprem istasyonun faal olduğu tespit edilmiş ve araştırmalar sonucunda bu depremlere ait 73 adet tarihsel sismogram elde edilmiştir. Sismogramlardan Bergen, Ebro ve Taranto istasyonlarına ait kayıtlar TESEO2 yazılımıyla sayısallaştırılmış, geometrik düzeltmeye tabii tutulmuş ve SAC (sismik analiz kodu) formatına dönüştürülmüştür. Toplamda 15 adet deprem kaydı, cihaz parametrelerine ihtiyaç duymayan Green Fonksiyonu hesabı yöntemiyle incelenmiştir. Taranto istasyonu kaydından elde edilen göreceli kaynak-zaman fonksiyonu 9 Ağustos depremi için 40 saniyelik bir kaynak süresi vermiştir ki bu süre 3 km/sn’lik ortalama kırılma hızıyla yaklaşık 120 km’lik bir kırık uzunluğu ifade eder. Bununla birlikte, düşey bileşen kaydı yapan Göttingen Toledo Ebro Pulkovo ve Hongo istasyonlarının P dalgası ilk varışları incelenmiş ve saha gözlemleriyle birleştirilerek 9 Ağustos 1912 şoku için bir fay mekanizması çözümü verilmiştir. Bu çalışmada tarihsel deprem kayıtları ve saha gözlemlerinin birleştirilmesi sonucunda 1912 depremleri için toplamda 150 km’lik bir fay kırığı hesaplanmıştır. Bu kırık boyu Marmara denizindeki sismik boşluğun boyutunun belirlenmesinde önemli bir sınır teşkil etmektedir. 9 Ağustos 1912 ve Kuzey Anadolu fayı üzerinde meydana gelen tarihsel depremlere ait tarihsel sismogramların yeniden incelenmesi bu depremler hakkında yeni parametreler sağlayacak ve deprem olgusunun anlaşılmasına yardımcı olacaktır. Anahtar Kelimeler: Sismoloji, tarihsel sismogram, 1912 depremi, Ganos Fayı, Kuzey Anadolu Fayı. Large earthquakes (M>7) occur with intervals more than hundreds of years. Quantitative data of large earthquakes are available through recordings of modern (digital) seismographs since the last 40 years. However historical (analog) seismograms encompass nearly 100 years of seismicity and document significant large earthquakes of the world. Contemporary analyses of old seismograms predate fundamental developments in quantitative seismology, while present techniques and methods in modern seismology allow comprehensive analysis of the earthquake phenomena (Kanamori and Brodsky, 2004). A reanalysis of old seismograms, integrated with modern methods will expand considerably the instrumental period of earthquake seismology and may provide key information for regional tectonics, kinematics of faults, earthquake parameters, recurrence intervals and seismic hazard (Batllo et al., 2008). In this work, it is here provided a short guideline how to collect and process historical seismograms by presenting a case study of the 1912 earthquake sequence along the North Anatolian Fault. The 9 August 1912 Mürefte earthquake (Ms=7.4) occurred at an early stage of seismological research. At that time, at least one primitive seismograph was active at 143 stations. 73 seismic records have been collected for the 9 August, 10 August and 13 September 1912 shocks, which occurred along the Ganos Fault. The majority of the records are from European stations located northwest and west of the epicentre. However, other recordings from Japan, Australia and Russia were also obtained. The SISMOS online database was the major source of the collected seismograms. The TESEO software has been used to vectorize and correct the waveforms and to convert them to SAC files. Signals were processed using the Empirical Green Function approach proposed by Vallee (2004), which avoids complexities due to unknown instrument parameters. The method uses the signal of a smaller event to model the Green function of the main earthquake. Comparable signal pairs 9 August and 13 September shocks from the Bergen, Ebro, and Taranto stations were digitized and corrected. 15 digital seismic signals have been modelled with the related method. Due to limitations by the applied method and majorly because of inadequate signal corrections our modelling revealed reliable results only for the Taranto station. The modelling of the 9 August and 13 September shocks provide a relative source time function and indicate that the moment ratio between the two shocks is about 30 which corresponds to 1 degree difference in magnitude and infer 40 second source duration for the 9 August. In addition to the modelling, we use the P-wave polarities at 5 stations to construct a focal mechanism. The vertical component seismograms from Göttingen, Toledo, Ebro, Pulkovo and Hongo and field based N68°E fault strike allow us to construct the focal mechanism solution for the 9 August 1912. The pure strike slip solution we obtained is in agreement with the known fault kinematics and slip measurements. The 40 second source duration implies ~ 120 km coseismic rupture length if a unilateral rupture propagation at 3 km/sec is attributed to the 9 August earthquake. On the other hand, the size of the 9 August shock corresponds to 1.5 x 1027 dyn*cm seismic moment which also suggests a 120 ± 20 km rupture length, assuming an average slip of 2.5 m and a fault width of 15 km. The size of the 13 September shock (Ms=6.9) implies 30 ± 10 km of surface rupture with similar fault parameters. As a result, the combined analysis of seismology, field observation and historical data suggest that the 1912 sequence caused a 150 km of surface faulting. This length is equal to the distance of the two major geometrical complexities of the Ganos Fault on its east and west; the Central Marmara Basin and the Saros Trough respectively. Therefore, it may be concluded that the eastern rupture end of 9 August 1912 Mürefte earthquake is located in the Central Marmara Basin and defines the western limit of the seismic gap in the Sea of Marmara. The comprehensive reanalysis of historical seismograms for the large earthquakes along the North Anatolian Fault will considerably extend our knowledge of the characteristics each earthquake and will provide new constraints to understand the earthquake behaviour along this large continental strike slip fault. Keywords: Seismology, historical seismogram, 1912 earthquake, Ganos Fault, North Anatolian Fault
Development of a portable rock cutting rig to determine rock cuttability
Get PDFKollu galeri açma makineleri ve tam cepheli tünel açma makineleri gibi mekanize kazı makinelerinin günümüzde kullanımları hem maden hem de inşaat sektöründe hızla artmaktadır. Bu tip makineler kullanılmadan önce kayaçların kesilebilirlik özellikleri çok iyi tespit edilmelidir. Makine seçiminde yapılacak hata projenin bitim süresinin uzamasına ve çok büyük maddi kayıplara yol açabilir. Bu yüzden makine seçimi ve performans tahmini proje başlamadan önce yapılmalıdır. Bu çalışmada taşınabilir, kolay kullanılabilir ve pahalı olmayan ve sonuçları güvenilir olan küçük boyutlu bir kazı seti geliştirilmiştir. Geliştirilen taşınabilir test cihazı için 13 cm çapında 70º uç açılı mini diskler imal ettirilmiştir. Numune boyutları 20x20x10 cm olan kayaç numuneleri 5 mm kesme derinliğinde yardımsız kazı modu ile kesilerek, keskiye gelen FN, FR kuvvetleri geliştirilen dinamometre ile kayıt edilmiştir. Kesme sonucu çıkan pasa miktarı kullanılarak spesifik enerji hesaplanmıştır. TÜBİTAK Proje No: MİSAG-274 kapsamında birim deformasyon ölçer’lerle donatılmış bir dinamometre geliştirilmiş ve saniyede 1000 veri alabilecek bir veri iletişim sistemi seçilmiştir. Dinamometrenin güvenirliliğini denemek için 9o’lik açılı ve düşey yüklemelerle kalibrasyon yapılmıştır, sonuçların güvenilir olduğu ve okumaların tekrar edilebilir olduğu kanısına varılmıştır.13 farklı kayaç numunesi üzerinde tam boyutlu doğrusal kazı setinde mini disk ve sabit kesit alanlı disk ile deneyler yapılmış sonuçlar geliştirilen kazı seti sonuçları ile karşılaştırılmış ve daha önceki çalışmalarda konik keskilerle aynı kayaçlar üzerinde yapılan deney sonuçları da veri tabanına eklenince yeni geliştirilen küçük boyutlu ve taşınabilir kazı setinin mekanize kazı makineleri için performans tahmininde belirli bir istatistiksel doğrulukla kullanılabileceği anlaşılmıştır. Anahtar Kelimeler: Kayaç kazılabilirliği, mekanize kazı makinalarının performs tahminleri, Roadheader, TBM.Full face tunnel boring machines and partial face tunnel boring machines utilization for mining and civil project are increasing enormously. Tunnels for civil projects at highly populated cities dictate minimum ground disturbance while tunneling. Full face tunneling machines are able to excavate through hard rock to soft ground with small surface deformation and faster compared to drill and blast. Selection of correct mechanized excavator for a given rock media is very important for the success of the project. A great care must be taken for equipment selection and performance prediction in the project design phase. Researchers worked on a wide range of parameters to predict the performance of mechanical excavators. Besides the theoretical approaches, the ones who correlate the mechanical properties of intact rock to the field performance of the excavators are more reliable in their data range and tunneling conditions. Full scale linear rock cutting, small scale core cutting and University of Trondheim performance prediction model are widely accepted on the international tunneling society. Laboratory cutting tests are expensive, needs specialists, special equipments and may take long time to perform. Therefore, a portable, easy to use, reliable, costs less than 10000 $ small scale rock cutting rig is developed in the scope of this research. The table of the rig is moved by a hydraulic cylinder powered by a hydraulic accumulator. Rock samples in 20x20x10 cm of size attached to the table with a special mechanism to cut the rock with a mini-disc, diameter of 13 cm and tip angle of 70°, and the forces acting on the mini-disc and specific energy to cut a unit volume of rock is measured. A force dynamometer equipped with strain gauges are developed in the scope of Tübitak Project No: MİSAG-274, to measure the forces and a data acquisition system that can collect 1000 data in a second is chosen. Many calibrations are performed to test the reliability of the dynamometer and data acquisition system. Calibrations are done by a hydraulic cylinder whose cross section area is known. Hydraulic cylinder is pressurized to 10, 20, 30, 40, 50 bar with a 9º inclined surface to the mini disc. Output from the dynamometer strain gauges are compared to the applied force where it is seen that output is linear and has R2 equals to 0.99. It is proved that the results of the developed cutting rig are reliable and repeatable. While making a cutting on the developed cutting rig, there are two ways to fix the rock sample. One can use the manufactured case where rock sample can be cemented inside. The other is to use the screwed clamp on the moving table. It is hard to adjust the cutting depth while pouring the cement into the case. Another disadvantage is you can only use one face of the rock sample. In this study, screwed clamp is used to make the cutting test because it is easy, faster to fix the sample and gives the opportunity to make 4 cuttings per sample.. Rock cutting tests are carried out on 14 different rock samples with the full scale linear cutting rig and the developed portable rock cutting rig. A 13” constant cross section (CCS) disc cutter and mini disc is used for the cutting tests with full scale linear cutting rig. Results from the full scale cutting rig 13” CCS with mini disc equipped developed rig are compared for 8 different rock samples for an unrelieved 5 mm depth of cut. Normal and cutting forces are correlated and correlation coeffients are found to be 0.86 and 0.75 respectively. Disc cutting theories of Roxborough (for discs with an tip angle) and Rostami (for CCS discs) are applied for rock samples used in cutting tests. Trendlines of CCS and mini disk forces are identical to theoretical comparison of disc normal and cutting forces for CCS disc and V shaped disc. The conical cutter results from previous studies on the full scale linear cutting rig are compared with the developed rock cutting rig results. Optimum specific energy values from relieved cutting tests with Sandvik S35/80H cutter are plotted with the index specific energy values from developed cutting rig. A good correlation and 0.62 correlation coefficient is found between optimum SE of conical cutter and mini disc index SE values. Keywords: Rock cutting tests, performance prediction of tunneling machines, Roadheader, TBM. 
Gökova Körfezi depremlerinin kaynak parametreleri ve Rodos-Dalaman bölgesinde tsunami riski
Get PDFThe Gulf of Gökova locates in soutwestern Turkey near the Aegean Sea and surrounded by Datça Peninsula to the south, the island of Kos to the west and Bodrum Peninsula to the north. Active deformation in the region has been observed from widespread seismicity, active normal faulting and tectonically generated topography. In recent and historical times, many destructive earthquakes have occurred in southwestern Turkey. Most of the seismic activity is concentrated along the northern branch of Gökova Fault Zone and it is controlled by E-W trending normal fault system. Intense earthquake activity occurred in Gulf of Gökova in August 2004 and January 2005. Source mechanism solutions and rupture histories for 10 earthquakes, of magnitude Mw ³ 5.0 and shallow focal depth (h < 20 km), which occurred in the region during the period 1986-2005, are used to investigate the geometry of faulting in the region. To obtain source mechanisms and slip distributions on the fault plane, we compared the shapes and amplitudes of long period P- and SH- waveforms recorded in the distance range of 30-90 degrees. The seismograms are formed by the combination of direct (P or SH) and reflected (pP and sP, or sS) phases from a point source embedded in a given velocity structure. Receiver structures are assumed to be homogeneous half-spaces. Seismograms were weighted according to the azimuthal distribution of stations. The solutions were also constrained by P-wave first motion polarities of near-field stations. All the distribution of P-wave first-motion polarities on the equal-area projection of the lower focal hemispheres are consistent with the minimum misfit solutions within a few degrees, with the strikes and dips of the nodal planes. We have also obtained earthquake rupture histories and slip distribution on the fault plane using teleseismic broad-band P waveforms. The rupture process were presented as a spatio temporal slip distribution on a fault plane which was divided into M x N subfaults with length dx and width dy. Then, slip-rate function on each sub fault was described by a series of triangle functions with a rise time. Generally, earthquakes initiates with an earthquake cluster activity and continue for a long time in the gulf. This kind of earthquake generation pattern can carry on by weeks or months decreasing in frequency and in magnitude. The kinematics of the deformation is controlled by normal faults with small strike slip components trending E-W, NE-SW and NW-SE directions. Earthquake source mechanism solutions indicate that normal fault mechanism with a strike-slip component have been observed on the E-W oriented graben and normal fault systems in the Gulf of Gökova and they confirm that extension is in a north - south direction that is in a good agreement with the geology and tectonic structure of the region. T-axes directions obtained from source mechanism solutions demonstrate the NW-SE direction of extension as a result of the convergence between the African plate and the Eurasian plate and the westward movement of the Anatolian block. On the other hand, all earthquakes have generally short source duration and uniform rupture propagation along the dip direction and their focal depths are generally less than 15 km and thus we may suggest that seismogenic thickness in this region is about ~10 km. All these slip distribution results show a uniform circular rupture propagation along the dip direction with a short source duration for earthquakes in Gulf of Gökova . On the other hand, the Gulf of Gökova has a real and major tsunami hazard to the lives and population since it is near the Eastern Mediterranean coast. In this study we have also investigated the tsunami wave propagations to obtain time histories of water surface fluctuations and water particle velocities created by historical 1481 Rhodes earthquakes (M~7.0-7.5) in the Eastern Mediterranean sea using TUNAMI-N2 and AVI-NAMI mathematical models based on the method of Okada (1985). The related parameters for the earthquake are adapted by an analogy of current plate boundaries and earthquake source mechanisms obtained by inversion of teleseismic P- and SH- waveforms. The understanding the faulting geometry, tectonic evolutions and source rupture processes along the active fault zones have significant importance on the tsunami generation. The major and well-known seismic generated tsunamis have occurred in Aegean and Mediterranean Seas and these waves affected the coastal regions since historical times. Keywords: Anatolia, earthquakes, Gulf of Gökova, Rodos-Dalaman, seismotectonics, tsunami.Gökova Körfezi Türkiye’nin güneybatısında Ege Denizi kıyısında yer alan ve bölgedeki tektonik ve depremsellik açısından aktif graben sistemlerinden biridir. Son yıllarda özellikle 2004-2005 tarihleri arasında körfez içerisinde bir çok sayıda orta büyüklükte (Mw³5.0) deprem meydana gelmiştir. Bu çalışmada ters çözüm teknikleri ve telesismik uzaklıklarda kaydedilen P ve SH dalga şekilleri kullanılarak bölgede oluşan güncel depremlerin kaynak mekanizması parametreleri ve fay düzlemi üzerinde meydana getirdikleri kayma dağılımı ve yırtılma süreçleri modelleri elde edilmiştir. En küçük hatalı kaynak mekanizması çözümlerine göre depremler genel olarak D-B doğrultulu normal faylanma mekanizması ile sığ odak derinliklerinde meydana gelmektedirler. Kaynak mekanizması çözümlerinde çok küçük miktarlarda doğrultu atımlı faylanma bileşenleri bulunmaktadır. Telesismik cisim dalgalarının ve yakın alan istasyonların ters çözüm ile modellenmesi sonucu elde edilen kayma dağılımı modelleri ise depremlerin oldukça basit şekilli ve dalım yönünde ilerleyen dairesel kırılmalar ile meydana geldiklerini göstermektedir. Ayrıca, Hellenik Yayı’nın doğu uzanımı üzerinde yer alan Rodos adası ve çevresinde tarihsel dönem içerisinde meydana gelen ve tsunami (depreşim) dalgalarına neden olduğu rapor edilen birçok sayıda deprem bulunmaktadır. 1481 yılında meydana gelen tarihsel depremler için sığ su dalgası teorisine dayalı yöntemlerle ve GEBCO-BODC batimetri verisi ile tsunami dalga simülasyonları yapılmıştır. Simülasyon sonuçları bu bölgede meydana gelen bir depremin daha çok episantıra yakın bölgelerde örneğin Rodos adası ve çevresinde ve Gökova Körfezi - Fethiye kıyılarında etkili tsunami dalgalarına neden olduğunu göstermektedir. Anahtar Kelimeler: Anadolu, deprem, Gökova Körfezi, Rodos-Dalaman, sismotektonik, tsunami
Effect of surface characteristics of Istanbul and its outskirts on the local weather circulation
Get PDFBir bölgenin yerel hava akışını, kara-deniz meltemi, şehir ısı adası gibi farklı yüzeylerin termal özelliklerinin neden olduğu mezo-ölçek sirkulasyonlar etkilemektedir. Bu çalışmada, hem stratejik açıdan önemli olan hem de Türkiye’nin en kalabalık şehri olan İstanbul ve çevresi için yerel hava akışı incelenmiştir. Şehrin morfolojisinin ve şehirleşmenin yerel hava akışına yapmış olduğu katkıyı göreceli olarak incelemek için duyarlılık testleri, atmosferik-meteorolojik sayısal model yardımı ile gerçekleştirilmiştir. Dinamik modelleme, duyarlılık testlerinin gerçekleştirilmesi sırasında kullanılan yöntemdir. Bu çalışmada, üç boyutlu, hidrostatik olmayan mezo-ölçek model Operational Multi-scale Environment model with Grid Adaptivity (OMEGA) kullanılmıştır. İstanbul Boğazı’nın etkisi ve hafif yükseltilerden oluşan şehir topoğrafyasının meydana getireceği etki de bu çalışmada incelenmiştir. Duyarlılık testleri kurgulanırken, mümkün olabilecek en basit durumdan mevcut duruma kadar yapılan çeşitli değişikliklerle akış özellikleri incelenmiştir. Topoğrafyanın olmadığı ve tek bir arazi örtüsünün kullanıldığı bölge üzerindeki mevcut su yüzeylerinin etkisinin de izole edildiği test en basit durum olarak düşünülmüştür. Daha sonra İstanbul Boğazı ilave edilerek boğaz etkisi incelenmiştir. Büyük ölçek hava akışlarının etkisini anlamak için ise farklı jeostrofik rüzgâr yönü ile benzeşim yapılmıştır. Bu testlere topoğrafya ve mevcut arazi örtüsü de ilave edilerek simülasyonlar gerçekleştirilmiştir. Çalışmada, Boğaz’ın kanal etkisi yarattığı ve topoğrafyanın varolan akışı kuvvetlendirdiği gözlenmiştir. Boğaz boyunca yer alan yerleşimin ise deniz melteminin kıyıdan içeriye dogru ilerlemesini engellediği belirlenmiştir. Ayrıca sinoptik ölçekli rüzgârın yön değişiminin yerel akışı etkilediği de elde edilen önemli bir sonuçtur. Anahtar Kelimeler: Karadeniz meltemi, şehir ısı adası, dinamik modelleme.Atmospheric motion is affected by wide range of scales from a few milimeters to thousands of kilometers. Therefore, it is crucial to understand the behavior of the atmospheric flows on these scales. Although all of these scales play a role on the transport and dispersion of the pollutants, mesoscale atmospheric processes are significant over the traveling time and distance for short and long range transport and dispersion of pollutants. Thermally and terrain induced circulations contribute to the transport and dispersion pattern of the pollutants via terrain characteristics and the surface inhomogeneities. Besides, growing urbanization modifies the mesoscale circulation characteristics. The response of the local scale circulation to the other scales or its interaction with them influences the characteristics of pollutant transport by means of the modified mesoscale circulation. Therefore, understanding mechanism of the development and evolution of small scale flow features and their interaction with large scale flow features is one of the desires. Mesoscale circulations such as sea-land breeze, urban heat island are controls our local atmosphere. Theoretically, the mechanism behind the development of the sea-land breeze circulation has been known since 1800s. Thermally-induced circulations, sea-land breeze and urban heat island, occur depending on the difference on the heating and cooling of the underlying surface. Heat capacity difference between land and water triggers the onset of the sea-land breeze. Similar to the sea-land breeze circulation, urban heat island circulation occurs due to the heat capacity difference between the urban and rural areas. Although mechanisms of the thermally-induced circulations are known, the interaction between other mesoscale features (such as mountain-valley wind) or large scale circulations is important and it changes by the properties of the location. Since the shorelines are preferred as a residential area, it is unavoidable to encounter the interaction between the sea-land breeze and the urban heat island. In addition to these circulations, topography makes the contribution to the local flow. The present research is concentrated on the mesoscale circulations, sea-land breeze and urban heat island. Since the dynamic downscaling is very useful tool while studying sensitivity studies, the idealized numerical simulations are performed using a fully non-hydrostatic three-dimensional numerical model OMEGA with its unstructured grid. The unstructured grid enables us to resolve land and water boundaries better than the other mesoscale models which use structured grid. The more detailed information about the land cover benefits us to study mesoscale circulation. It should be kept in mind that it is not possible to solve any small properties of the domain even using unstructured grid. Uniform initial flow is utilized at horizontal and vertical directions. The study is focused on Istanbul since it is the longest and the most crowded city in Turkey and also the wide range of data availability for direct comparison. Since each feature of a region affects the local flow, relative effects of geographic features on the local circulation are exemplified by means of the idealized simulations. Simulations are conducted starting from very simple case to a complex one, which means that contribution of each feature is added one-by-one to the domain. For instance, as a simple case, surface is set to the flat, and a uniform land-use and land cover map is used. Then after, effect of the presence of a strait is investigated adding the Bosphorus strait to the domain. Topographic effect is also analyzed including model resolved topography. Finally, current land-use types and land-water properties are used with different large scale flow directions to investigate effect of the urbanization. Although studies in the literature have showed that smooth topography has no influence on the circulation, topography-induced effect is observed over the hilly topography of Istanbul. Results show that the Bosphorus strait channeled the air flow that is blowing from the north through the Bosphorus. This channeled flow is enhanced when the topography is added to the domain. Significant contribution to the local flow comes from urbanization by arranging the sea-land breeze existence or penetration over the domain. The presence of the urban area causes a convergence over the urbanized area by hindering the inland penetration of the sea breeze. Results indicate that the flow over Istanbul converges at a point depending on the surface properties which are utilized in the sensitivity simulation. The southwesterly flow direction prevents the existence of the land breeze that is observed under the northeasterly flow condition. Keywords: Sea-land breeze, urban heat island, dynamic modeling
Production of polyunsaturated fatty acids from rainbow trout oil: Optimization by responce surface methodology
Get PDFω-3 çoklu doymamış yağ asitleri (ÇDYA), özellikle eikosapentaenoik asit (EPA) ve dokosahekzaenoik asit (DHA) insan sağlığı açısından önemlerinden dolayı artan bir ilgi görmektedir. EPA ve DHA antiinflamatuar, antitrombotik, antiaritmik, antimitojenik, hipolipemik ve vazodilatör özellikler gösterirler. Bu özellikleri ile başta koroner kalp hastalıkları olmak üzere, hipertansiyon, tip 2 diyabet, ülseratif kolit, romatoid artrit, depresyon ve kanser gibi birçok hastalığın önlenmesinde ve tedavisinde potansiyel etkiye sahiptir. Bu çalışmada balık yağından gıda ve farmasötik kullanımlar için ÇDYA’ince zenginleştirilmiş ürünlerin eldesi amaçlanmıştır. Bu amaçla, alabalık (Oncorhynchus mykiss) yağından üre fraksiyonlama yöntemine göre ÇDYA (EPA, DHA, 18:3ω-3, 20:4 ω-3 ve 22:5 ω-3) içeriği yüksek konsantratlar üretilmiştir. Üre fraksiyonlama deneyleri 4 °C’ de üç değişkenli ve üç seviye değerli yüzey merkezli küp tasarım noktalarında yapılmıştır. Bağımsız değişkenler olan üre:yağ asitleri oranı (ağ/ağ), etanol:üre oranı (hac/ağ) ve kristalizasyon zamanının (saat) elde edilen ürünlerin ÇDYA içeriğine (tepki değerine) olan etkileri incelenmiş ve reaksiyon koşulları Tepki Yüzey Metodolojisi’ne göre optimize edilmiştir. Optimum reaksiyon koşulları 3.5 üre:yağ asitleri oranı (ağ/ağ), 5.6 etanol:üre oranı (hac/ağ) ve 4.8 saat kristalizasyon zamanı olarak bulunmuştur. Bu koşullarda, alabalık yağından % 88.1 ÇDYA içeren ürün elde edilmiştir. Ayrıca değişkenlerin tepki değerine olan etkisini gösteren kuadratik polinomiyal model denklem oluşturulmuştur. Elde edilen model denklemin regresyon katsayısı 0.99 olarak bulunmuştur. Bu da model denklemin güvenilir olduğunu göstermektedir. Anahtar Kelimeler: Çoklu doymamış yağ asidi, EPA, DHA, alabalık, üre fraksiyonlama, tepki yüzey metodolojisi.The -3 polyunsaturated fatty acids (PUFA), especially eicosapentaenoic acid (EPA), docosahexaenoic acid (DHA), alpha-linolenic acid (ALA) are attracting increasing attention because of their importance to human health. EPA is the precursor of prostaglandins, tromboxanes and leukotrienes, which are effective anti aggregatory substances. DHA is a main component of membrane phospholipids of brain and retina cells. Clinical studies show that DHA is essential for the growth and development of the brain in infants and for maintenance of normal brain functions in adults. Recently it has been shown that EPA and DHA supplementation has positive health effects including attenuation of coronary heart disease risk factors (hypertension, hyperlipidemia, platelet aggregation, glucose tolerance); modulation of eicosanoid synthesis (cellular immune system, dermal integrity) and tumoricidal activity. Some studies indicated that the PUFA concentrates, devoid of more saturated fatty acid, are much better than oils themselves since they allow the daily intake of total lipid to be kept as low as possible. The PUFA concentrates can be produced by several methods, including fractional crystallization, urea fractionation, molecular distillation, supercritical fluid extraction, silver ion complexation and enzymatic hydrolysis and esterification reactions. However, the simplest and the most efficient technique for obtaining PUFA concentrates in the form of free fatty acids is urea fractionation. Initially the triacylglycerols of the oil are split into their constituent fatty acids by using alcoholic KOH and these fatty acids are then mixed with an ethanol solution of urea for complex formation. The saturated and the monounsaturated fatty acids easily complex with urea and crystallize out on cooling. The liquid or non-urea complexed fraction (extract) is enriched with PUFA. In this study, urea fractionation of rainbow trout (Oncorhynchus mykiss) fatty acids was carried out to produce PUFA. Urea fractionation experiments were carried out at 4 °C according to a three-factor and three-level face-centered cube design points. The effects of independent variables such as urea-to-fatty acid ratio (w/w), ethanol-to-urea ratio (v/w) and crystallization time (h) on the PUFA content of the obtained products (responce) were investigated and reaction conditions were optimized by Responce Surface Methodology (RSM). Free fatty acids (4 g) were mixed with urea in 95 % aqueous ethanol and heated at 60°C with stirring until the mixture was turned into a clear homogenous solution. The ratio of urea-to-fatty acids was changed by using different amounts of urea, and the ratio of ethanol-to-urea was changed by using different amounts of ethanol. The homogenous solution was cooled to room temperature, placed in refrigerator kept at 4 °C for different periods for further crystallization. The crystals formed (urea-fatty acid adducts, also referred to as the urea complexing fraction) were separated from the liquid (non-urea complexing fraction) by fast filtration. The liquid was diluted with an equal volume of water and acidified to pH 2-3 with 6 N HCl; an equal volume of hexane and 10 mL of saturated salt solution were subsequently added and the mixture was stirred thoroughly for 1 h, and then transferred to a separatory funnel. The hexane layer containing the liberated extract fatty acids was separated from the aqueous layer.The solvent was removed using a rotary evaporator. The obtained fatty acids were weighted and designated as ?extract? throughout this study. The fatty acid composition of the extract was determined by GC. Before RSM was applied, an appropriate range (lower, middle, and upper points, levels) for each independent variable was determined by varying one independent variable at a time while keeping the others constant. A total of 17 experiments were carried out according to a three factor, three level face-centered cubic design points. In the urea fractionation of rainbow trout fatty acids, the range of each variable was selected as follows: urea-to-fatty acids ratio, 2-4; ethanol-to-urea ratio, 5-9; time, 1-15 h. Optimal conditions were determined to be a urea-to-fatty acids ratio of 3.5, ethanol-to-urea ratio of 5.6 and a time of 4.8 h. Experiments conducted under these optimized conditions will be yielded an product containing 88.1 % PUFA. A good quadratic model was obtained as highly significant with a satisfactory regression coefficient (R2) found as 0.99. In conclusion, the PUFA enriched product was obtained from rainbow trout fatty acids by urea fractionation in this study. This concentrate could be used as valuable supplement for food and pharmaceutical purposes. Keywords: PUFA, EPA, DHA, rainbow trout, urea fractionation, responce surface methodology
Finite element analysis of global ship vibrations
Get PDFGemi boyut ve hızlarındaki büyük artış nedeniyle gemi titreşimleri, gemi tasarımı ve yapımında büyük önem taşır hale gelmiştir. Gemi tasarımındaki son gelişmeler, daha büyük stroklu ve daha güçlü dizel motorların kullanıldığı, daha büyük boyutlarda, daha hafif, daha esnek teknelerin yapılmasına yol açmıştır. Deniz taşımacılığında artan talebi karşılamak için ihtiyaç duyulan bu yapıların daha esnek olması titreşim problemlerini de beraberinde getirmektedir. Aşırı gemi titreşimleri, yolcu konforunu ve mürettebat yaşamını önemli ölçüde etkilemektedir. İnsan üzerindeki istenmeyen etkilerinin yanında, aşırı gemi titreşimleri, makina ve cihazlarda bozulmalara neden olmakla birlikte yapısal elemanlarda da yorulma hasarına neden olmaktadır. Gemilerde titreşim problemlerinin çözüm kaynağının erken safhadaki tasarım aşamasında belirlenmesinin önemi ve sonradan yapılacak olan düzeltmelerin çok ağır maliyetler gerektirdiği bilinmektedir. Tasarım aşamasında yapılacak olan bir takım basit çalışmalarla ileride ortaya çıkacak büyük titreşim problemlerinin önlenmesi sağlanabilmektedir. Gemi titreşimleri bakımından, yerel titreşim problemlerinin yanı sıra geminin bütününde ortaya çıkan global titreşimler de gemi emniyeti açısından büyük önem taşımaktadır. Bu çalışma kapsamında tüm gemi, sonlu eleman analizi yöntemiyle global olarak serbest – serbest (susuz) ve su içinde olmak üzere serbest titreşim açısından incelenerek, tüm geminin doğal frekanslarının ve mod şekillerinin belirlenmesine çalışılmıştır. Bu şekilde geminin hangi frekanslarda rezonansa gireceği ve nasıl davranışlar sergileyeceği belirlenmiştir. Ayrıca sonlu eleman yöntemiyle hesaplanan doğal frekans değerleri, klas kuruluşları tarafından kullanılan ampirik formüllerle hesaplanan doğal frekans değerleri ile karşılaştırılarak, sonlu eleman analizinin gerekliliği üzerinde durulmuştur. Anahtar Kelimeler: Gemi titreşimi, sonlu eleman analizi, modal analiz.With the increase of ship size and speed, shipboard vibration becomes a great concern in the design and construction of the vessels. The flexibility of vessels which are needed to meet the demand in sea transportation, causes ship vibrations. In addition to undesired effects on passenger comfort and crew habitability, excessive ship vibration may result in the fatigue failure of local structural members or malfunction of machinery and equipment. The importance of the solutions of vibration problems which are addressed at the earliest design stage and the great cost in later correction efforts are clear. It is possible to avoid great vibration problems by means of simple studies in the early design stage. Besides local vibrations, global vibrations are of great importance to ship safety. In this study, global ship hull free vibration problems are studied under two conditions which are free - free (dry) and in water (wet) using finite element analysis. Excessive ship vibration is of great importance to the performance of precious navigation equipments and usually cause them to malfunction. In the condition of resonance which the propulsion frequency collides with the global natural frequency of the ship and during manoeuvres, the amplitude of oscillations on local structures exceeds certain limits. Concept design is where the vibration avoidance process must begin. It is clear that if the vibration problems, repeatedly identified by experience as the most important, are addressed at the earliest design stage, ultimately serious problems, involving great cost in correction efforts, may be avoided. The focus is on planning for vibration early at the concept design stage, where there has been no development of details. If as much as possible can be done in concept design with the simple tools and rules of thumb available at that level, it will help to avoid major vibration problems. The major potential problems may often be present in the crude concept design definition. Just identifying and addressing those potential problems in terms of the minimal technology available at the concept design stage is considered very important to the success of ship design. The design and construction of a ship free of excessive vibration continues to be a major concern and, as such, it is prudent to investigate, through analysis, the likelihood of vibration problems early in the design stage. Vibration analysis is aimed at the confirmation of the many design considerations associated with stern configuration, main propulsion machinery, propeller/shafting system and location and configuration of major structural assemblies. The ship hull structure includes the outer shell plating and all internal members, which collectively provide the necessary strength to satisfactorily perform the design functions in the expected sea environment. The hull structure responds as a free - free beam (both ends free) when subjected to dynamic loads. The vibration induced by the propulsion system is a common source of ship vibration. The vibration from this source manifests itself in several ways. Dynamic forces from the shafting system are transmitted to the hull through shaft bearings. The propeller induces fluctuating pressures on the surface of the hull, which induces vibration in the hull structure. The main and auxiliary engines can directly cause vibrations through dynamic forces transmitted through their supports and foundations. The response to this forcing can cause the vibration of the hull girder, deckhouse, deck and other structures, local structures and equipment. When attempting to determine the source of vibration, it is necessary to establish the frequency of excitation and to relate the frequency of excitation to the shaft rotational frequency by determining the number of oscillations per shaft revolution. Ship structures are complex and may be analyzed after idealization of the structure. Several simplifying assumptions are made in the finite element idealization of the hull structure. The modeling requirements are that all significant structural sections are to be captured and deflection/ velocity/acceleration are to be sufficiently predicted. A three-dimensional finite element model representing the entire ship hull, including the deckhouse and machinery propulsion system, needs to be developed for vibration analysis. If a global model exists from any previous tasks such as stress analysis, it needs to be conditioned for vibration analysis. In the section which the global vibrations are studied, a three dimensional ship model is prepared using a solid modelling software and the natural frequencies and mode shapes are determined using finite element analysis. In this way, the resonance frequencies and behaviour of the ship are determined. Keywords: Ship vibration, finite element analysis, modal analysis
A time-symmetric individual block time step algorithm in n-body integration
Get PDFAyrık blok zaman adımlı integrasyon algoritmaları, çok-cisim problemlerinde sıklıkla kullanılan algoritmalardandır. Farklı zaman ölçeklerine sahip cisimlerin aynı problemin parçaları olduğu durumlarda, kullanımları kaçınılmazdır. Ancak kullanılan integrasyon şeması zaman-simetrik bile olsa, blok zaman adımları kullanıldığında zaman simetrisi bozulmaktadır. Zaman simetrisinin bozulmasının doğal sonucu, toplam enerji üzerindeki hata birikiminin doğrusal olarak artmasıdır. Bu çalışmada, zaman-simetrik blok zaman adımlı bir algoritma geliştirilmiştir. Geliştirilen algoritma, sabit zaman adımları kullanıldığında zaman-simetrik yapısını koruyan integrasyon şemalarının, değişken ayrık blok adımlı bir algoritma içerisinde de zaman simetrik yapısını korumasını sağlamaktadır. Hatta integrasyon şeması tam olarak zaman simetrik olmasa bile, geliştirilen algoritma ile yüksek enerji korunumu sağlandığı gözlenmiştir. Özellikle uzun süreli integrasyonlarda algoritmanın yüksek başarımı belirgindir. Zaman-simetrik ayrık blok zaman adımlı algoritma, bir yineleme yapısı içermektedir. Bu yinelemenin ayrık zaman adımlı integrasyon şemasıyla uygulanabilmesi için, çağ aralıkları (era) belirlenmiş, yineleme işlemleri bu çağ aralıkları üzerinden sağlanmıştır. Yapılan testlerde bu çağ aralıklarının büyüklüğünün hem yineleme sayısı, hem de bellek tüketimi açısından önemli olduğu gözlenmiştir. Çalışmanın bu safhasında, algoritma çağ aralıklarının değişken tutulabildiği bir yapıya kavuşturulmuştur. Algoritma Leapfrog integrasyon şeması kullanılarak geliştirilmiş, etkinliği daha yüksek dereceden integrasyon şemalarıyla da sınanmıştır. İçerdiği yineleme yapısı yüzünden ayrık zaman adımlı önceki algoritmalardan daha yüksek zaman ve bellek tüketimine sahiptir. Ancak toplam enerji üzerindeki hata birikimlerini büyük ölçüde azaltmaktadır. Anahtar Kelimeler: Çok-cisim problemi, sayısal integrasyon, ayrık blok-zaman adımları.The gravitational N-body problem can not be solved analytically except for two-body cases. While there are various approximate methods, such as Monte Carlo or Fokker-Planck method, the most accurate way to solve the N-body problem is by direct integration of the orbits of the N bodies. Direct integration of the N-body problem is a necessity for many cases such as star cluster simulations. During the last fifteen years, two approaches have been put forward to improve numerical conservation of energy and other theoretically conserved quantities: symplectic integration schemes, where the simulated system is guaranteed to follow a slightly perturbed Hamiltonian system, and time-symmetric integration schemes, where the simulated system follows the same trajectory in phase space, when run backward or forward. Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of symplecticity. In contrast, time symmetry can be easily maintained, at least for a continuous choice of time step size. An iterative scheme must be combined with individual block time step scheme to apply the new algorithm to the n-body problem effectively. However, straightforward implementation of time-symmetry, translated to block time steps, faces significant hurdles for N-body problem. For example, iteration can lead to oscillatory behavior, and even when such behavior is suppressed, energy errors show a linear drift in time. In this work it is aimed to construct a time symmetric block time step integration scheme. We first consider to analyze block time step scheme with time symmetrization procedure for the gravitational two-body problem. It is hard to generate an efficient algorithm for N -body problem without deep and clear understanding of this fundamental problem. However it is easy to correct the algorithm in Kepler problem. Besides, it is known that contributions to the energy error are largely generated by close encounters between two particles. For these reasons, two-body problem is preferred to develop the algorithm in the first instance. The algorithm is developed and tested in two-body problem for accuracy and energy conservations in many different Kepler problem with different iteration numbers. In the process of the development work, leapfrog integration scheme which is the second order time-symmetry scheme is preferred. Also fourth, sixth, and eighth order Hermite integration schemes are used for test runs. The major conceptual difficulty in designing a time-symmetric block time step scheme is the global context information that is needed, with extensions toward the future as well as the past. We present an approach that circumvents these problems. We divide and conquer: we split the total history of our simulation into a number of smaller periods, which we call every one as era. Each era extends a period in time equal to the largest allowed time step tmax, or to an integer multiple of tmax, whatever turns out to be the most convenient. For such reasons, we have analyzed the era concept in more detail for time symmetrized block time steps. Our test results show that size of era must be chosen carefully for stable and robust integrations. This is important especially for long term simulations with highly desirable energy conservations. Era size is also important to avoid extra data storage and uselessly high number of iterations which require too much running times. As a second gain of the work, we re-designed the previous scheme, and suggested dynamically changing size for era. With this scheme, iteration process of the integration can follow needs of the simulation adaptively. And, era size will be well-adjusted with physics of the problem with proper criterion. Our basic integrator in the work is leapfrog scheme. It is a well known, second order, time symmetric integration scheme for fixed time steps. We also used fourth, sixth, and eighth order Hermite schemes to see the ability of the algorithm with higher order integration methods. We used different Kepler problems in two-body tests, and used Plummer model initial conditions for N-body tests. The algorithm does not show linear growing error with time symmetric integrations. It also shows high energy conservations with other integration schemes especially for long integration times. Keywords: N-Body integration, time symmetry, individual block - time step, Hermite integration
Data sources:
Access Repository Dashboard
Do you manage itüdergisi (E-Journals - İstanbul Teknik Üniversitesi, Istanbul Teknik Uniersity., İTÜ)? Access insider analytics, issue reports and manage access to outputs from your repository in the CORE Repository Dashboard!