Abstract
Misalignment is one of the commonly encountered faults in rotor systems. The standard techniques that are used to detect misalignment are loopy orbits, multiple harmonics with predominant 2X and high axial vibration. In real rotor systems, it is caused due to improper seating of bearing housing on foundation or lack of concentricity between bearing and its housing. This chapter presents a numerical model of the coupling, which mimics the forces/moments produced due to parallel and angular misalignment. The coupling connects two rotor systems each with a centrally mounted disk and simply supported on two flexible bearings. The rotor train is modeled with two-node Timoshenko beam finite elements. An AMB is used as an auxiliary support on rotor-2. The coupling connecting the two rotor systems is modeled by a stiffness matrix, which has both static and additive components. While the static component is unchanging during operation, the additive component displays multi-harmonic behavior and exists only in the presence of misalignment. The multi-harmonic nature of coupling’s misalignment force/moment is mathematically modeled by an appropriate steering function. The development of mathematical model is followed by some response analysis, which shows lateral vibration of rotor, current signal of AMB and the orbit plots of rotor in the presence of misalignment and unbalance.
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Abbreviations
- \( {\varvec{\upeta}}_{0}^{c} \) :
-
Static deflection vector at coupling
- \( {\varvec{\upeta}}(t) \) :
-
Vibratory deflection vector in real coordinates
- \( {\mathbf{u}} \) :
-
Vibratory deflection vector in complex coordinates
- \( k_{s} \) :
-
AMB displacement stiffness
- \( k_{i} \) :
-
AMB current stiffness
- \( i_{c} \) :
-
AMB current in complex form
- \( {\mathbf{K}}_{\text{c}} \) :
-
Coupling static stiffness matrix
- \( {\mathbf{C}} \) :
-
Damping matrix
- \( {\mathbf{G}} \) :
-
Gyroscopic matrix
- \( {\mathbf{T}} \) :
-
Transformation matrix
- \( \Delta {\mathbf{k}}_{{\mathbf{c}}} (t) \) :
-
Coupling additive stiffness matrix
- \( {\mathbf{M}} \) :
-
Mass matrix
- \( {\mathbf{K}} \) :
-
Stiffness matrix
- ACS :
-
Additive coupling stiffness
- \( SCS \) :
-
Stiffness matrix
- rad :
-
Radial
- ang :
-
Angular
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The authors thank the reviewers for their valuable comments.
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Siva Srinivas, R., Tiwari, R., Kanna Babu, C. (2021). Finite Element Modeling and Analysis of Coupled Rotor System Integrated with AMB in the Presence of Parallel and Angular Misalignments. In: Rao, J.S., Arun Kumar, V., Jana, S. (eds) Proceedings of the 6th National Symposium on Rotor Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5701-9_34
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