Kompleks Koordinat Formülasyonuna Dayalı İzotropik ve Anizotropik Mesnetli Rotorların İç Sönümleme Kararsızlığı

Öz

Bu çalışma, rotordinamik sistemlerin iç sönümleme kararlılığı için kompleks koordinat formülasyonunun avantaj ve dezavantajlarını araştırmaktadır. Rotor yapısına özgü sönümleme mekanizmaları, sabit sönümleme kaynaklarına kıyasla titreşimler üzerinde farklı etkilere sahiptir. İç ve dış sönümleme kaynakları, sabit referans çerçevesine göre farklı titreşim frekanslarına sahiptir. Bu nedenle, harici sönümlemenin aksine, dahili sönümleme titreşimleri her zaman kararlı hale getirmez. Bu nedenle, titreşim özelliklerini doğru bir şekilde tahmin etmek için sönümleme kuvvetlerinin modele doğru bir şekilde dahil edilmesi araştırılmıştır. Rotor parçaları arasındaki sürtünme bağlantılarının ve yapısal sönümlemenin neden olduğu iç sönümleme nedeniyle rotordinamik kararlılığı incelemek için birleşik bir sonlu eleman modeli geliştirilmiştir. İç sürtünme bağlantılarını modellemek için döner yatak elemanları kullanılmış ve histerezis sönümlemeli dinamik denklemi, izotropik ve anizotropik bağlantılar üzerindeki rotorlar için karmaşık vektör gösterimi kullanılarak sağlanmıştır. Kompleks koordinat formülasyonu, dönen ve sabit referans çerçeveleri arasındaki vektörlerin dönüşümünde matematiksel avantajlar sağlamaktadır. İzotropik mesnetler söz konusu olduğunda, kompleks koordinat formülasyonunun kullanılması düşük boyutlu bir model ortaya çıkarmakta ve modelin verimliliğini artırmaktadır. Ancak, anizotropik mesnetler söz konusu olduğunda, modelin mertebesinin azaltılması mümkün olmamakta ve sistemin kinematiği nedeniyle hareket denklemi doğrusal değildir. Bu durum, özdeğer problemini çözmek için iteratif bir yöntem gerektirmektedir. Doğrulama için, geliştirilen modellerin sonuçları ticari bir sonlu elemanlar yazılımının sonuçları ile karşılaştırılmıştır. Sonuç olarak, farklı iç sönümleme kaynaklarının genel rotordinamik kararlılık üzerindeki etkisi gösterilmiştir.

Anahtar Kelimeler

• Rotordinamik
• iç sönüm kararlılığı
• kompleks koordinat formülasyonu
• sürtünmeli mafsallar
• yapısal sönümleme

Internal Damping Instability of Rotors with Isotropic and Anisotropic Supports based on Complex Coordinates Formulation

Öz

This study investigates the advantages and disadvantages of complex coordinates formulation for internal damping stability of rotordynamic systems. Damping mechanisms inherent to the rotor structure have different effects on vibrations when compared to stationary damping sources. The internal and external damping sources experience different vibration frequencies with respect to the stationary reference frame. Thus, in contrast to external damping, internal damping does not always stabilize vibrations. Therefore, the correct incorporation of damping forces into the model is investigated to predict vibration characteristics accurately. A unified finite element model is developed to study rotordynamic stability due to internal damping caused by frictional joints between rotor parts and structural damping. Rotating bearing elements are used to model internal frictional joints and the governing equation with hysteresis damping is provided using complex vector notation for rotors on isotropic and anisotropic mounts. Complex coordinates formulation provides mathematical advantages in transformation of vectors between rotating and stationary reference frames. In the case of isotropic supports, the use of complex coordinates formulation yields a low-dimensional model and increases the efficiency of the model. However, in the case of anisotropic supports, reduction in the order of the model is not possible and the equation of motion is nonlinear due to kinematics of the system. This requires an iterative method to solve the eigenvalue problem. For verifications, the results of the developed models are compared to those of a commercial finite element software. Consequently, the effect of different internal damping sources on the overall rotordynamic stability is demonstrated.

Anahtar Kelimeler

• Rotordynamics
• internal damping stability
• complex coordinates formulation
• frictional joints
• structural damping

Kaynakça

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