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 Modeling and Analysis of Active Magnetic Bearings

2014 ◽  
Vol 494-495 ◽  
pp. 685-688
Author(s):  
Rong Gao ◽  
Gang Luo ◽  
Cong Xun Yan
Keyword(s):  
Dynamic Characteristic ◽  
Dynamic Modeling ◽  
Magnetic Bearing ◽  
Integrated System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Modeling And Analysis ◽  
Amb System ◽  
Mathematics Method

Active magnetic bearing (AMB) system is a complex integrated system including mechanics, electronic and magnetism. In order to research for the basic dynamic characteristic of rotor supported by AMB, it is necessary to present mathematics method. The dynamics formula of AMB is established using theory means of dynamics of rotator and mechanics of vibrations. At the same tine, the running stability of rotor is analyzed and the example is presented in detail.

Nonlinear Dynamic Study on Effects of Rub-Impact Caused by Oil-Rupture in a Multi-Shafts Turbine With a Squeeze Film Damper

2014 ◽  
Author(s):  
T. N. Shiau ◽  
C. R. Wang ◽  
D. S. Liu ◽  
W. C. Hsu ◽  
T. H. Young
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Rotor System ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Frequency Spectra ◽  
Squeeze Film Damper ◽  
Assumed Mode Method ◽  
Nonlinear Dynamic Behavior

An investigation is carried out the analysis of nonlinear dynamic behavior on effects of rub-impact caused by oil-rupture in a multi-shafts turbine system with a squeeze film damper. Main components of a multi-shafts turbine system includes an outer shaft, an inner shaft, an impeller shaft, ball bearings and a squeeze film damper. In the squeeze film damper, oil forces can be derived from the short bearing approximation and cavitated film assumption. The system equations of motion are formulated by the global assumed mode method (GAMM) and Lagrange’s approach. The nonlinear behavior of a multi-shafts turbine system which includes the trajectories in time domain, frequency spectra, Poincaré maps, and bifurcation diagrams are investigated. Numerical results show that large vibration amplitude is observed in steady state at rotating speed ratio adjacent to the first natural frequency when there is no squeeze film damper. The nonlinear dynamic behavior of a multi-shafts turbine system goes in its way into aperiodic motion due to oil-rupture and it is unlike the usual way (1T = >2T = >4T = >8T etc) as compared to one shaft rotor system. The typical routes of bifurcation to aperiodic motion are observed in a multi-shafts turbine rotor system and they suddenly turn into aperiodic motion from the periodic motion without any transition. Consequently, the increasing of geometric or oil parameters such as clearance or lubricant viscosity will improve the performance of SFD bearing.

Characteristic Parameters Estimation of Active Magnetic Bearings in a Coupled Rotor System

2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Sampath Kumar Kuppa ◽  
Mohit Lal
Keyword(s):  
Numerical Technique ◽  
Forced Response ◽  
Rotor System ◽  
Parameters Estimation ◽  
Magnetic Bearings ◽  
Fast Fourier Transformation ◽  
Active Magnetic Bearings ◽  
Least Squares Regression ◽  
Characteristic Parameters ◽  
Full Spectrum

Abstract Present research inspects the performance of rotor–bearing–coupling system in the presence of active magnetic bearings (AMBs). A methodology is suggested to quantify various fault characteristics along with AMB characteristic parameters of a coupled turbine generator system. A simplest possible turbogenerator system is modeled to analyze coupling misalignment. Conventional methodology to estimate dynamic system parameters based on forced response information is not enough for AMB-integrated rotor system because it requires current information along with displacement information. The controlling current of AMB is tuned and controlled with a controller of proportional–integral–derivative (PID) type. A numerical technique (Lagrange's equation) is applied to get equations of motion (EOM). Runge–Kutta technique is used to obtain EOM to acquire the time domain responses. The fast Fourier transformation (FFT) is applied on obtained responses to acquire responses in the frequency domain, and full spectrum technique is applied to propose the methodology. A methodology that depends on the least squares regression approach is proposed to evaluate the multifault parameters of AMB-integrated rotor system. The robustness of the algorithm is checked against various levels of noise and modeling error and observed efficient. An appreciable reduction in misalignment forces and moments is observed by using AMBs.

A Numerical Study on the Effect of Unbalance and Misalignment Fault Parameters in a Rigid Rotor Levitated by Active Magnetic Bearings

2019 ◽  
Author(s):  
Prabhat Kumar ◽  
Rajiv Tiwari
Keyword(s):  
Numerical Study ◽  
Equations Of Motion ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Inertia Force ◽  
Dimensional System ◽  
Rigid Rotor ◽  
Active Magnetic Bearings ◽  
Fault Parameters ◽  
Misalignment Fault

Abstract This paper focusses on analysing the vibration behaviour of a rigid rotor levitated by active magnetic bearings (AMB) under the influence of unbalance and misalignment parameters. Unbalance in rotor and misalignment between rotor and both supported AMBs are key fault parameters in the rotor system. To demonstrate this dynamic analysis, an unbalanced rigid rotor with a disc at the middle levitated by two misaligned active magnetic bearings has been mathematically modelled. One of the novel concepts is also described as how the force due to active magnetic bearings on the rigid rotor is modified when the rotor is parallel misaligned with AMBs. With inclusion of inertia force, unbalance force and force due to misaligned AMBs, the equations of motion of the rigid rotor system are derived and converted into dimensionless form in terms of various non-dimensional system and fault parameters. Numerical simulations have been performed to yield the dimensionless rotor displacement and controlling current responses at AMBs. The prime intention of the present paper is to study the effect on the displacement response of the rigid rotor system and the current consumption of AMBs for different ranges of disc eccentricities and rotor-AMB misalignments.

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
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