Dinamik titreşim absorberlerinin konum kontrollu olarak kullanılması
Başlık çevirisi mevcut değil.
- Tez No: 46544
- Danışmanlar: PROF.DR. MUSTAFA SAVCI
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 39
Özet
ÖZET Titreşim kontrolunda kullanılan çeşitli metodlar arasında, dinamik titreşim absorberlerinin özel bir yeri vardır. Basit bir kütle yay sistemi olarak düşünülen ilk dinamik absorberler, araştırmacılar tarafından geliştirilerek, kütle yay sistemlerinden başka, kiriş, plak ve kabuk titreşimlerinin sönümlemesinde başarıyla kullanılmıştır. Modern teknolojinin günümüzde, bilhassa uzay çalışmalarında ulaştığı hız, titreşim kontrolünün önemini artırmıştır. Bu çalışma; klasik kütle-yay dinamik titreşim absorberinin titreşimlerinin aktif kontrolunda kullanılabilecek şekilde, aktif dinamik absorberine dönüştürülmesini sunmaktadır. Çalışmada bir sönümsüz aktif dinamik absorber dizayn edilmiştir. Dinamik absorberin çubuk uzunluğunu kontrol eden bir otomatik kontrol devresi mevcuttur. Otomatik kontrol devresi yardımı ile titreşimlerin aktif olarak kontrol edilebileceği gösterilmiştir. V
Özet (Çeviri)
SUMMARY Of the possible ways to reduce undesirable vibrations in mechanical systems, dynamic absorbers have been used when internal modifications to the main system are difficult to carry out. The dynamic absorber it itself a passive vibrating system, consisting of a mass, a spring, and perhaps a damper, which is attached to a vibrating main system so as to modify its steady state response. The earliest design is the one proposed, Where in both the main system and the dynamic absorber possess little or no damping. It is intended for use when the primary system is excited mass and spring tuned to the main system resonance, is attached to the primary system. The resulting response is very nearly zero at the exciting frequency. However, the device will not be effective if a wide frequency range of excitation ispresent since the combined system will exhibit large resonant response at other frequencies. The optimization was carried out so as to minimize the maximum displacement response of the main system in the frequency domain. This natural phenomenon can be explained in engineering terms by first considering the response of a single-degree-of-freedom mechanical system subjected to a rectilinear vibrator force operating at a frequency which is the same as the resonant frequency of the system. The response can be reduced by adding a secondary mass which has motion relative to the system. This secondary mass and its support is commonly called a dynamic vibration absorber. The secondary mass does not, in fact, absorb energy. The effect of adding the secondary mass is to move the resonant frequency of the mechanical system away from the operating frequency of the vibrator force. The single-degree-of-freedom system becomes a two-degree-of freedom system with two resonant frequencies, neither of which will coincide with the operating frequency. By careful tuning of the absorber, the response of the system to the vibrator force acting at the operating frequency can be reduced to negligible proportions. The undimmed dynamic vibration absorber is effective therefore only for constant speed machinery. By fitting a damper in series with the secondary mass and in parallel with its support the frequency bandwidth over which the response is reduced can be considerably increased, although not such large reductions can be achieved as for the umdamped absorber. When a damper is used in the secondary system energy is dissipated in the damper and the system becomes a true dynamic vibration absorber. VIThis exciting force could force could be due to rotating out-of-balance, or unbalanced inertia forces, or windindduced forces, or, due to joints in railway lines. The assumption usually made is that the exciting force is harmonic, off magnitude F and frequency co.1 C -0 m:.> x Fig.l. The equation of motion of the mass m, shown in Fig.l, acted upon by a horizontal force F sincot.is. mx+cx+kx=Fsincot. (1) or x+(c/m)x+(k/m)x=(F/m) sincot. After substitution, equation 1 can be expressed diagrammatically as shown in Fig. 2. It can be seen that the spring force lags the exciting force by the phase angle r\ which can vary between 0 and % and that the spring force is always opposite in direction to the inertia force. Inertia force Exciting force F Damping force cuX Spring force kX Displacement Transmitted force Fig.2. Vector diagram describing equation 1 VIIThe passive dynamic vibration absorber is particularly suitable for attachment to systems where it is not possible to move an undesirable resonance by connecting to earth, for instance, in vehicles, tall structures, bridges and machine tools. The dynamic vibration absorber offers an alternative to what could possibly be an uneconomic redesign of an entire machine or structur. However, such absorbers are only effective if the excitation is nearly periodic and confined to a narrow frequency range. The addition of the absorber also causes two resonant conditions to arise in place of the original single resonant condition. Many real systems can be represented by a single degree of freedom model. However, most actual systems have several bodies and several restraints and therefore several degrees of freedom. The number of degrees of freedom that a system possesses is equal to the number of independent coordinates necessary to describe the motion of the system. Since nobody is completely rigid, and no spring is without mass, every real system has more than one degree of freedom, and sometimes it is not sufficiently realistic to approximate a system by a single degree of freedom model. Thus, it is necessary to study the vibration of systems with more than one degree of freedom. Each flexibly connected body in a multi-degree of freedom system can move independently of the other bodies, and only under certain conditions will all bodies undergo an harmonicmotion at the same frequency. Since all bodies move with the same frequency, they all attain their amplitudes at the sometime, even if they do not all move in the same direction. When suchmotion occurs the frequency is called a natural frequency of the system, and the motion is a principal mode of vibration the number of natural frequency and principal modes that a system possesses is equal to the number of degrees of freedom of that system. The deployment of the system at its lowest or first natural frequency is called its first mode, at the next highest or second natural frequency it is called the second mode, an so on. A two degrees of freedom system will be considered initially. This is because the addition of more degrees of freedom increases the labor of the solution procedure but does not introduce any new analytical principles. If a single degree of freedom system or made of a multi degree of freedom system is excited into resonance, large amplitudes of vibration result with accompanying high dynamic stresses and anise and fatigue problems. In most mechanical systems this is not acceptable. VIII} Vibration absorber x =x\, unwt Fig. 3. System with undamped vibration absorber. If neither the excitation frequency nor the natural frequency can conveniently be altered, this resonance condition can often be successfully controlled by adding a future single degree of freedom system. Consider the model of the system shown in Fig. 3, where K and M are the effective stiffness and mass of the system when vibrating in the trouble some mode. The absorber is represented by the system with parameters k and m. Fig.4. shows the primary system with a viscous damped absorber added. A design criteria that has to be carefully considered is the possible fatigue and failure of the absorber spring this could have severe consequences. In view of this, some damped absorber systems dispense with the absorber spring and sacrifice some of the absorber effectiveness. This has praticularly wide application in tarsional systems, where the device is known as a Lancaster Damper. Not all damped absorbers rely on viscous damping; dry friction damping is often used, and the replacement of the spring and damper elements by a single rubber black possessing both properties is fairly common. IX
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