İç sönümlü elastik kavrama ile bağlı iki kütleli bir sistemin dinamik davranışı
Simulation of the dynamic behavior of a system with two rotating masses qhich are connected an elastic coupling with internal damping
- Tez No: 14377
- Danışmanlar: DOÇ.DR. M. SAİT YÜCENUR
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Dinamik davranış, Elastik kavrama, İki kütleli sistem, Dynamic behavior, Elastic coupling, Two masses system
- Yıl: 1991
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Kavramalar milleri birbirine bağlayan makina ele manlarıdır. Elastik kavramalar, mil eksenleri arasındaki çeşitli düzgünsüzlükleri karşılamak, darbeleri azaltmak ve titreşimleri söndürmek için kullanılır. Bu vasıflar kavramanın rijit elemanlarını birbirine bağlayan elastik elemanlar tarafından sağlanmaktadır. Şekil ve tip bakı mından büyük çeşitlilik gösteren elastik elemanlar ma densel ve lastik yaylar şeklinde iki gruba ayrılabilir. Bünyesindeki bu elastik elemanların özelliklerinden dola yı, elastik kavramalar lineer ve lineer olmayan karakte ristiklere sahiptir. Ayrıca kavrama bünyesindeki elastik elemanların söndürme etkisi, yüksek hızlarda sistem ile hava arasında meydana gelen söndürme şeklinin bir sıvı söndürmesi hali olduğu var sayılabilir. Elastik kavramaya bağlı iki dönel kütleli bir sis temde, kütlelerden birinden etkiyen çeşitli ikaz momentle ri etkisiyle elastik kavramanın davranışını incelemek için ikaz momentleri idealize edilmiştir, periyodik ikaz mo menti, basamak ikaz momenti ve ımpuls ikaz momentinin et kimesi durumunda lineer karakteristikli elastik kavrama nın davranışını ve periyodik ikaz momentinin etkimesi duru munda lineer olmayan karakteristiğe sahip elastik kavra maların davranışını incelemek için sistem bilgisayarda si- müle edilmiştir. Ayrıca yükselen karakteristikli elastik kavramalarda ikaz momenti etki etmeden önce iş makinasının direncini yenmek için harcanan çeşitli motor momentleri (ön moment; üzerine sabit periyodik ikaz momentinin etki mesi durumunda, elastik kavramanın davranışı incelenmiştir. Kullanılan bilgisayar programlama dili basic' t ir. Elde edilen sonuçlar bilgisayarda çizilmiştir.
Özet (Çeviri)
SUMMARY SIMULATION ÖF THE DYNAMIC BEHAVIOR OF A SYSTEM WITH TWO ROTATING MASSES WHICH ARE CONNECTED AN ELASTIC COUPLING WITH INTERNAL DAMPING In this thesis, it has been studied on the subject“simulation of dynamic behavior of a system with two ro tating masses which are connected an elastic coupling with internal damping”. Couplings are machine members that they connect shafts with each other. Elastic couplings are used for eliminating varios irregularities between driving and driver parts of machine and decreasing shocks and damping vibrations. These features are obtained by elastic mem bers which connect rigid parts of elastic coupling with each other. Elastic members which show varieties in res pect type and shape can be seperated into two groups as metallic and rubber springs. To investigate dynamic behavior of an elastic coupling which produce an elastic connection between dri ver and driving parts of machine can be based following model. (Figure 1 ) Jl J2 Figure 1. The model of a system with two rotating masses which are connected an elastic coupling Equation of general motion of the system with Mi-Exciting torque which acts on from number one mass is as follows: 71da<f J j. + Mr + Mc = Mi at* ji In this equation ; J.tf is mass torque. Mr is damping torque. Mc is elastic torque. Jl and J2 are mass inertia torque, fl and ^ 2 are angular displacements. J is equivalence mass inertia torque. (Jl. J2/J1-kT2) Mi-Exciting Torque: Some kind of torques which act on from driving and driver parts of machine are ide alized and it is taken into consideration variations stated easily. These variations are as follows: - Exciting torque with periodic variation. Mi = Mo. Sin wit Wi: Exciting angular velocity Mo: The amplitude of exciting torque - Step exciting torque - Impulse exciting torque Mr-Damping Torque: Damping effect in Elastic coupling depends on Coulomb friction or viscose friction. Both of damping style at different ratio can be in the system at many state. The style of damping which is for med among system and air at high speed can be supposed the condition of viscose friction. Mr = R.Y E is damping factor Rigidity which designate elastic torque depends on the characteristics of system. The rigidity (C; of elastic coupling which has linear characteristics is constant. C = Mc/Y The rigidity (0) of elastic coupling which has no linear characteristics is changeable. C = dMc/dY The figure showing relation between Wi/Wo (the ratio of exciting frequency to natural frequency) and MKE/MKR (the ratio of torque transmitted by elastic coupling to the torque transmitted by rigid coupling) for some kind of damping ratio ( 7 ) at linear elastic coupling, because of periodic exciting torque is iigure 2. It is seen on figure 2 that when Wi/¥b is equal 1, it is the most dangerous operating zone for elastic VTTMKE/MKR O 0.5.6 2 2.5 3 a 5 Wi/W o îigure 2. The relation between Wi/Wo and MKE/MKR for some kind of damping ratio( 7 ) a* linear elastic coupling TTTTTcouplings. When Wi/Wo is greater than 1, it is the most appropriate operating zone for elastic couplings. When the step exciting torque acts on elastic coupling, Transmitted torque is greater than rigid coup ling's. Altough transmitted torques are equal in a de- finete time, especially at small damping ratios, the max imum torque transmitted by elastic coupling till regime state is fairly greater than rigid coupling's. When the impulse torque acts on an elastic coup ling, the transmitted max. moment is greater than rigid coupling's, especially at small damping ratios. Figure 3 shows the behavi©r of a nonlinea* elas tic coupling with progressive characteristics for“? = 0.2 damping ratio, According to Wi/Wo (the ratio of exciting frequency to natural frequency) The behavior of an elastic coupling with progres sive characteristics, according to figure 3, can be ex plained like that: When Wi increases, |f I angular displac- ment follows 1-2 part of curve and increases till num ber 2 point. Then |f I decreases till number 3 point sud denly and decreases as following 3 - 4 part of curve. When Wi decreases, If I angular displacement follows 4- - 5 part of curve and increases to number 5 point and sud denly jump to number 6 point. If it is continued to dec rease Wi, IYJ decreases as following 6-1 part of curve. It is seen on figure 3 that the hesitating zone occurs, when Wi/Wo is greater than 1. Figure 4- shows the behavior of a nonlinear elas tic coupling with degressive characteristics for ? =0.15 damping ratio, According to Wi/Wo (the ratio of exciting frequency to natural frequency) It is seen on figure 4 that when Wi increases. |¥ | angular displacement follows 1-2 part of curve and inc reases to number 2 point and suddenly jump to number 3 point. If it is continued to increase Wijjf | decreases as following 3 - 4- part of curve. When Wi decreases, |f | angular displacement increases as following 4-5 part of curve and reach to max. point at number 5 and then suddenly decreases to number 6 point and decreases as following 6-1 part of curve. It is seen that the hesitating zone occurs, when Wi/Wo is smaller than 1. Consequently, ¥o(natural angular velocity) can be under Wi (operating angular velocity) or upper Wi as it is chosen an appropriate elastic coupling as depen ding on operating conditions. If pretorque which is used for overcoming resis tance of force machine by motor machine increases, the nonlinear elastic coupling with progressive characteris tics behaviors like elastic coupling with degressive characteristics. IXffigure 3. Ehe behavior of a nonlinear elastic coupling with progressive characteristics for ? = 0.2, According to Wi/Wo ratio Q F.M 0.3 0.25 0.2 - 0.15 0.1 0.05 n 0 s?.2ı +-”^ 4- Mf U' 4- 4- yi -» - ? - * r "f- -p-..4.D.8 1JD 1.2 Wi/Wo Figure 4. îhe behavior of nonlinear elastic coupling with degressive characteristics for ? = 0.15, According to Wi/Wo ratio. 1.4 XI
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