Nonlinear Vibration in a Vertical Rigid Rotor Supported by the Magnetic Bearing: Case Considering the Delays of Both Electric Current and Magnetic Flux

2007 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Motoki Sugiyama ◽  
Yasuhiko Sugawara ◽  
Yukio Ishida
Keyword(s):  
Magnetic Flux ◽  
Electric Current ◽  
Magnetic Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Control Force ◽  
Rigid Rotor ◽  
Rotating Speed ◽  
First Order

Active magnetic bearing (AMB) becomes to be widely used in various kinds of rotating machinery. However, as the magnetic force is nonlinear, nonlinear phenomena may occur when the rotating speed becomes higher and delay of control force increases. In this paper, the magnetic force is modeled by considering both the second order delay of the electric current and the first order delay of the magnetic flux, and the AMB force is represented by a power series function of the electric current and shaft displacement. The nonlinear theoretical analysis of the vertical rigid rotor supported by AMB is demonstrated. The effects of the delays and other AMB parameters on the nonlinear phenomena are clarified theoretically and experimentally.

Modeling and Nonlinear Vibration Analysis of a Rigid Rotor System Supported by the Magnetic Bearing (Effects of Delays of Both Electric Current and Magnetic Flux)

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Yasuhiko Sugawara ◽  
Motoki Sugiyama
Keyword(s):  
Magnetic Flux ◽  
Electric Current ◽  
Magnetic Force ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Rigid Rotor ◽  
Rotating Speed ◽  
First Order

Active magnetic bearing (AMB) becomes widely used in various kinds of rotating machinery. However, as the magnetic force is nonlinear, nonlinear phenomena may occur when the rotating speed becomes high and delays of electric current or magnetic flux in the AMB relatively increase. In this paper, the magnetic force in the AMB is modeled by considering both the second-order delay of the electric current and the first-order delay of the magnetic flux. The magnetic flux in the AMB is represented by a power series function of the electric current and shaft displacement, and its appropriate representation for AMB is discussed. Furthermore, by using them, the nonlinear theoretical analysis of the rigid rotor system supported by the AMB is demonstrated. The effects of the delays and other AMB parameters on the nonlinear phenomena are clarified theoretically, and they are confirmed experimentally.

Effects of eccentricity and vibration response on high-speed rigid rotor supported by hybrid foil-magnetic bearing

2015 ◽  
Vol 230 (6) ◽  
pp. 994-1006 ◽  
Author(s):  
Sena Jeong ◽  
Yong Bok Lee
Keyword(s):  
Load Distribution ◽  
High Speed ◽  
Control Algorithm ◽  
Initial Position ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Control Force ◽  
Rigid Rotor ◽  
Reliability Parameters ◽  
Derivative Control

A hybrid foil-magnetic bearing (HFMB) consists of an air foil bearing (AFB) and an active magnetic bearing (AMB). The HFMB, inherently proposed as a backup bearing for an AMB, has many advantages, such as good controllability and the ability to exhibit preload sharing with the two types of bearings (i.e., the AFB and AMB) in high-speed turbomachinery. However, because the bearing has a limited clearance, the eccentric position of the rotor affects its stability and the reliability parameters of the AFBs such as the initial preload rub. In this study, a rigid rotor supported by an HFMB was operated at speeds of up to 18 kr/min and was tested using a proportional-derivative control algorithm, in order to reduce the vibration amplitude. In addition, to elucidate the effect of the initial eccentric position of the rotor, the control algorithm was started from the initial position of the rotor (X: from –100 to 100 µm and Y: from –80 to 200 µm) using a constant gain value. When the HFMB was active, the magnetic control force was remarkably effective in reducing the subsynchronous vibration of the rotor supported by the HFMB. Eccentricities of 0.2–0.5 corresponded to appropriate rotor positions for the hybrid bearing, and the corresponding load distribution of the AFB was found to be the optimal one. In addition, the proportional-derivative control gain was not very high. The performance of the bearing could be improved further by controlling the eccentricity. An HFMB was tested experimentally, and it was verified that it is possible to determine the effective load carrying capacity for a specific load distribution of the AFB.

Calculation and Verification of Magnetic Field Parameters in Axial Active Magnetic Bearing

2014 ◽  
Vol 214 ◽  
pp. 143-150
Author(s):  
Piotr Graca
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Magnetic Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Magnetic Flux Density ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Magnetic Field Computation

The paper presents numerical modeling of an Axial Active Magnetic Bearing (AAMB) based on two-dimensional (2D) magnetic field computation. The calculations, assisted by the Finite Element Method (FEM), have focused on the determination of the magnetic flux density and the magnetic force. Obtained magnetic field parameters were then measured and verified on a physical model.

Some Nonlinear Effects of Magnetic Bearings

1999 ◽  
Author(s):  
Norbert Steinschaden ◽  
Helmut Springer
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Path Following ◽  
Nonlinear Effects ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Amb System ◽  
Large Rotor

Abstract In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used. The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.

scholarly journals Research on Automatic Balance Control of Active Magnetic Bearing-Rigid Rotor System

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yang Liu ◽  
Shuaishuai Ming ◽  
Siyao Zhao ◽  
Jiyuan Han ◽  
Yaxin Ma
Keyword(s):  
Vibration Control ◽  
Rotational Speed ◽  
Notch Filter ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Vibration Response ◽  
Active Magnetic Bearing ◽  
Rigid Rotor ◽  
Phase Compensation ◽  
Synchronous Control

In this paper, in order to solve the problem of unbalance vibration of rigid rotor system supported by the active magnetic bearing (AMB), automatic balancing method is applied to suppress the unbalance vibration of the rotor system. Firstly, considering the dynamic and static imbalance of the rotor, the detailed dynamic equations of the AMB-rigid rotor system are established according to Newton’s second law. Then, in order to rotate the rotor around the inertia axis, the notch filter with phase compensation is used to eliminate the synchronous control current. Finally, the variable-step fourth-order Runge–Kutta iteration method is used to solve the unbalanced vibration response of the rotor system in MATLAB simulation. The effects of the rotational speed and phase compensation angle on the unbalanced vibration control are analysed in detail. It is found that the synchronous control currents would increase rapidly with the increase of rotational speed if the unbalance vibration cannot be controlled. When the notch filter with phase shift is used to balance the rotor system automatically, the control current is reduced significantly. It avoids the saturation of the power amplifier and reduces the vibration response of the rotor system. The rotor system can be stabilized over the entire operating speed range by adjusting the compensation phase of the notch filter. The method in the paper is easy to implement, and the research result can provide theoretical support for the unbalance vibration control of AMB-rotor systems.

Comparison of three-pole AMB and HMB for magnetic suspended molecular pump

2018 ◽  
Vol 32 (34n36) ◽  
pp. 1840074
Author(s):  
Jintao Ju ◽  
Xiaobin Liu ◽  
Zegang Xu ◽  
Chao Gu ◽  
Yilin Liu
Keyword(s):  
Power Loss ◽  
High Vacuum ◽  
Three Dimensional ◽  
Radial Force ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Rotating Speed ◽  
Characteristics Analysis ◽  
Current Characteristics

Molecular pumps have been widely used in the vacuum metallurgy, coating, semiconductor manufacturing and many other fields in which the high vacuum, ultra-clean environment is needed. The application of magnetic bearings can bring many advantages for molecular pump, such as eliminating the friction, decreasing the power loss, lowering the maintenance costs, and increasing the rotating speed and service life. Besides, the magnetic bearings can fundamentally solve the vacuum chamber pollution problem which is caused by the backflow of lubrication oil steam. The three-pole magnetic bearings are the simplest structure of radial magnetic bearings and can be driven by three-phase converter which has the advantages of low costs, small volume and low power loss. In this paper, the performance of the three-pole active magnetic bearing (AMB) and hybrid magnetic bearing (HMB) are compared based on radial force–current characteristics analysis. Firstly, the mathematical model of three-pole AMB and HMB is built by equivalent magnetic circuit model, and the radial force–current characteristics are analyzed. Then, simulation by the three-dimensional (3D) finite element method (FEM) is performed. Finally, the experiment is conducted. The FEM results are consistent with the analytical results, showing that the nonlinearity and coupling of three-pole HMB are lower than three-pole AMB. The reason of causing nonlinearity and coupling is also discussed.

Controlling Journal Bearing Instability Using Active Magnetic Bearings

2007 ◽  
Author(s):  
A. El-Shafei ◽  
A. S. Dimitri
Keyword(s):  
Journal Bearing ◽  
Magnetic Bearing ◽  
Journal Bearings ◽  
Active Magnetic Bearing ◽  
Rotating Speed ◽  
Damping Characteristics ◽  
Oil Whip ◽  
Novel Approach ◽  
Oil Whirl ◽  
Load Carrying

Journal Bearings are excellent bearings due to their large load carrying capacity and favorable damping characteristics. However, Journal bearings are known to be prone to instabilities. The oil whirl and oil whip instabilities limit the rotor maximum rotating speed. In this paper, a novel approach is used to control the Journal bearing (JB) instability. An Active Magnetic Bearing (AMB) is used to overcome the JB instability and to increase its range of operation. The concept is quite simple: rather than using the AMB as a load carrying element, the AMB is used as a controller only, resulting in a much smaller and more efficient AMB. The load carrying is done by the Journal bearings, exploiting their excellent load carrying capabilities, and the JB instability is overcome with the AMB. This results in a combined AMB/JB that exploits the advantages of each device, and eliminates the deficiencies of each bearing. Different controllers for the AMB to control the JB instability are examined and compared theoretically and numerically. The possibility of collocating the JB and the AMB is also examined. The results illustrate the effectiveness of the concept.

Development of a Novel Linear Magnetic Actuator

2014 ◽  
Vol 8 (6) ◽  
pp. 864-873 ◽  
Author(s):  
Truong Quoc Thanh ◽  
◽  
Dinh Quang Truong ◽  
Nguyen Minh Tri ◽  
Kyoung Kwan Ahn ◽  
...  
Keyword(s):  
Magnetic Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Magnetic Actuator ◽  
Actual System ◽  
Fuzzy Pid Controller ◽  
Working Performance ◽  
Electro Magnetic ◽  
And Control ◽  
Online Tuning

The aim of this paper is to design, fabricate and control a novel Linear Magnetic Actuator (LMA) for applications such as active magnetic bearing systems to deal with vibration problems in rotating machines. This LMA actuator contains a moving body named ‘mover’ and three driving parts to drive the mover. Firstly, experiments have been conducted on the LMA to derive its mathematical model in order to investigate the generated electro-magnetic force as well as further research. The modeling result in a comparison with the actual system performance show that the electro-magnetic force varied symmetrically with the mover motion defined by the applied current. Secondly, an advanced trajectory controller named online tuning fuzzy PID controller has been designed for the LMA to improve the working performance. Finally, real-time experiments have been carried out to evaluate the tracking performance of the designed LMA control system. The results prove that the LMA driven by the proposed controller could track the desired trajectories with high accuracy.

A Numerical Study on Effect of Electromagnetic Actuator on Rigid Rotor Supported on Gas Foil Bearing

2017 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Numerical Study ◽  
Load Capacity ◽  
Current Trend ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Normal Operation ◽  
Electromagnetic Actuator ◽  
Rigid Rotor ◽  
Magnetic Actuator ◽  
The Stability

Generally, Gas Foil Bearings (GFBs) are used in high speed machineries which are quite prone to instability or wear and tear. The current trend is to develop hybrid bearings which has conventional bearing (GFB) along with active magnetic bearing as an electromagnetic actuator (EMA). The GFBs are used for normal operation and the magnetic actuator can be used for the improvement of the stability and the load capacity of the bearing. In the present work a numerical study has been carried out to study the effects of magnetic actuator on the stability of bump type GFB supported rigid rotor. A rigid rotor supported on two identical GFBs with and without EMA has been investigated. The electromagnetic forces are incorporated in the equation of motion to provide the active control. A PD controller has been used as a controller for the magnetic actuator. It has been observed that the incorporation of EMA to the GFB reduces the sub synchronous vibrations and hence increases the stability.

Vibration control of high-speed rotor supported by hybrid foil-magnetic bearing with sudden imbalance

2015 ◽  
Vol 23 (8) ◽  
pp. 1296-1308 ◽  
Author(s):  
Sena Jeong ◽  
Yong Bok Lee
Keyword(s):  
Mass Loss ◽  
Vibration Control ◽  
High Speed ◽  
Turbine Rotor ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Control Force ◽  
Transient Vibration ◽  
Stability Performance ◽  
Foil Bearing

A hybrid foil-magnetic bearing (HFMB) was successfully studied as a vibration isolator by introducing a sudden imbalance or an unexpected disturbance during turbine/rotor operation. This HFMB is used to achieve stability during transient vibration behavior. The HFMB consists of two oil-free bearing technologies: an active magnetic bearing (AMB) and air foil bearing (AFB). Using both technologies takes advantage of the strengths of each bearing while compensating for their inherent weaknesses. In addition, the HFMB has good dynamic characteristics, and the damping can be adjusted using the appropriate gain selection for the AMB controller. Based on these unique features, dynamic stability can be enhanced, even if a sudden imbalance occurs while the rotor is operating. In this study, a rigid rotor was operated at up to 12,000 rpm and tested using a control algorithm to reduce the sudden imbalance vibration amplitudes. The experiment was conducted under the situation that the mass dropped out at 6,000 rpm. In order to validate the stability performance of the HFMB with a sudden mass loss, the vibration response results for the AFB and HFMB were compared. When applying the HFMB, the asynchronous vibration was suppressed, and the 1x vibration results showed reductions of almost 30%. When the sudden mass loss occurred, the magnetic control force was remarkably effective at reducing the asynchronous vibration of the rotor supported by the HFMB. In conclusion, it was experimentally verified that using the HFMB made sudden imbalance vibration control possible during rotor operation with an air foil bearing. In this respect, the HFMB has the characteristics of high stiffness/damping, which prevent rubbing and suppress excessive vibration due to a sudden imbalance event.

Sign in / Sign up

Export Citation Format

Share Document