A theoretical model for analyzing the dynamic behavior of a misaligned rotor with active magnetic bearings

Mechatronics ◽  
2011 ◽  
Vol 21 (6) ◽  
pp. 899-907 ◽  
Author(s):  
Slim Bouaziz ◽  
Najib Belhadj Messaoud ◽  
Mohamed Mataar ◽  
Taher Fakhfakh ◽  
Mohamed Haddar
Keyword(s):  
Theoretical Model ◽  
Dynamic Behavior ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings

Chaotic Vibration Analysis of a Coaxial Rotor System in Active Magnetic Bearings and Contact With Auxiliary Bearings

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Reza Ebrahimi ◽  
Mostafa Ghayour ◽  
Heshmatallah Mohammad Khanlo
Keyword(s):  
Dynamic Behavior ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Effective Control ◽  
Speed Ratio ◽  
Maximum Lyapunov Exponent ◽  
Active Magnetic Bearings ◽  
Coaxial Rotor ◽  
Speed Parameter ◽  
Amb System

In many cases of rotating systems, such as jet engines, two or more coaxial shafts are used for power transmission between a high/low-pressure turbine and a compressor. The major purpose of this study is to predict the nonlinear dynamic behavior of a coaxial rotor system supported by two active magnetic bearings (AMBs) and contact with two auxiliary bearings. The model of the system is formulated by ten degrees-of-freedom in two different planes. This model includes gyroscopic moments of disks and geometric coupling of the magnetic actuators. The nonlinear equations of motion are developed by the Lagrange's equations and solved using the Runge–Kutta method. The effects of speed parameter, speed ratio of shafts, and gravity parameter on the dynamic behavior of the coaxial rotor–AMB system are investigated by the dynamic trajectories, power spectra analysis, Poincaré maps, bifurcation diagrams, and the maximum Lyapunov exponent. Also, the contact forces between the inner shaft and auxiliary bearings are studied. The results indicate that the speed parameter, speed ratio of shafts, and gravity parameter have significant effects on the dynamic responses and can be used as effective control parameters for the coaxial rotor–AMB system. Also, the results of analysis reveal a variety of nonlinear dynamical behaviors such as periodic, quasi-periodic, period-4, and chaotic vibrations, as well as jump phenomena. The obtained results of this research can give some insight to engineers and researchers in designing and studying the coaxial rotor–AMB systems or some turbomachinery in the future.

DYNAMIC BEHAVIOR OF ACTIVE MAGNETIC BEARINGS IN PRESENCE OF ANGULAR MISALIGNMENT DEFECT

2011 ◽  
Vol 03 (03) ◽  
pp. 491-505 ◽  
Author(s):  
N. B. MESSAOUD ◽  
S. BOUAZIZ ◽  
T. FAKHFAKH ◽  
M. MAATAR ◽  
M. HADDAR
Keyword(s):  
Dynamic Behavior ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Mechanical Contact ◽  
Angular Misalignment ◽  
Electromagnetic Forces ◽  
Premature Failure ◽  
Shaft Misalignment ◽  
Speed Level ◽  
Stiffness And Damping

Active magnetic bearings (AMBs) is a device using controlled electromagnetic forces to support a shaft without mechanical contact. One of the primary techniques of condition monitoring of rotors is that of vibration control. Rotating machinery is facing some problems caused by shaft misalignment. This defect leads to a premature failure of the shaft, the coupling and the bearing because of the important vibrations and overloads generated. In this paper, the nonlinear dynamic behavior of a shaft supported by two identical AMBs with eight-pole legs is investigated in the presence of an angular misalignment defect. Thus, the electromagnetic forces, acting on the bearing in horizontal and vertical directions are computed. They are modeled by stiffness and damping matrices. The effects of air gap distance between the stator and the shaft, as well as rotor speed level on the electromagnetic forces are presented. To survey the vibratory response of a misaligned rotor, a numerical simulation of a theoretical model with an angular misalignment defect is studied. All results are presented and discussed in this work.

scholarly journals A Vibration Sensor-Based Method for Generating the Precise Rotor Orbit Shape with General Notch Filter Method for New Rotor Seal Design Testing and Diagnostics

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5249
Author(s):  
Karel Kalista ◽  
Jindrich Liska ◽  
Jan Jakl
Keyword(s):  
Notch Filter ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Harmonic Vibration ◽  
Filter Method ◽  
Vibration Exciter ◽  
Active Magnetic Bearings ◽  
Rotor Vibration ◽  
Seal Design ◽  
Exact Shape

Verification of the behaviour of new designs of rotor seals is a crucial phase necessary for their use in rotary machines. Therefore, experimental equipment for the verification of properties that have an effect on rotor dynamics is being developed in the test laboratories of the manufacturers of these components all over the world. In order to be able to compare the analytically derived and experimentally identified values of the seal parameters, specific requirements for the rotor vibration pattern during experiments are usually set. The rotor vibration signal must contain the specified dominant components, while the others, usually caused by unbalance, must be attenuated. Technological advances have made it possible to use magnetic bearings in test equipment to support the rotor and as a rotor vibration exciter. Active magnetic bearings allow control of the vibrations of the rotor and generate the desired shape of the rotor orbit. This article presents a solution developed for a real test rig equipped with active magnetic bearings and rotor vibration sensors, which is to be used for testing a new design of rotor seals. Generating the exact shape of the orbit is challenging. The exact shape of the rotor orbit is necessary to compare the experimentally and numerically identified properties of the seal. The generalized notch filter method is used to compensate for the undesired harmonic vibrations. In addition, a novel modified generalized notch filter is introduced, which is used for harmonic vibration generation. The excitation of harmonic vibration of the rotor in an AMB system is generally done by injecting the harmonic current into the control loop of each AMB axis. The motion of the rotor in the AMB axis is coupled, therefore adjustment of the amplitudes and phases of the injected signals may be tedious. The novel general notch filter algorithm achieves the desired harmonic vibration of the rotor automatically. At first, the general notch filter algorithm is simulated and the functionality is confirmed. Finally, an experimental test device with an active magnetic bearing is used for verification of the algorithm. The measured data are presented to demonstrate that this approach can be used for precise rotor orbit shape generation by active magnetic bearings.

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