Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

1998 ◽  
Vol 120 (4) ◽  
pp. 848-853 ◽  
Author(s):  
Y. Kligerman ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Eddy Current ◽  
Eddy Currents ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
System Response ◽  
Rotating System ◽  
Restoring Force ◽  
Rotating Systems ◽  
Eddy Current Damper

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

1997 ◽  
Author(s):  
Yuri Kligerman ◽  
Oded Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Eddy Current ◽  
Eddy Currents ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
System Response ◽  
Rotating System ◽  
Restoring Force ◽  
Rotating Systems ◽  
Eddy Current Damper

Abstract The investigation of nonlinear dynamics and stability of a rotating system with an electromagnetic non-contact eddy-current damper is carried out. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the unbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

Modeling of Eddy Current Damper Composed of Spherical Magnet and Conducting Shell

2006 ◽  
Author(s):  
Yoshihisa Takayama ◽  
Atsuo Sueoka ◽  
Takahiro Kondou
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Magnetic Force ◽  
Eddy Currents ◽  
Reaction Force ◽  
Damping Force ◽  
Magnetic Damping ◽  
Conducting Plate ◽  
Direction Of Movement ◽  
Eddy Current Damper

If a conducting plate moves through a nonuniform magnetic field, eddy currents are induced in the conducting plate. The eddy currents produce a magnetic force of drag, known as Fleming's left-hand rule. This rule means that a magnetic field perpendicular to the direction of movement generates a magnetic damping force. We have fabricated the eddy current damper composed of the spherical magnet and the conducting shell. The spherical magnet produces the axisymmetric magnetic field, and the shape of the conducting shell appears to combine a semispherical shell conductor and a cylinder conductor. When the eddy current damper works, the conducting shell is fixed in space, and the spherical magnet moves under the conducting shell. In this case, since there are magnetic flux densities perpendicular to the direction of movement, eddy currents flow inside the conducting shell, and then a magnetic force is produced. The reaction force of this magnetic force acts on the spherical magnet. In our study, eddy current dampers composed of a magnet and a conducting plate have been modeled using infinitesimal loop coils. As a result, magnetic damping forces are obtained. Our modeling has three merits as follows: the equation of a magnetic damping force is simple in the equation, we can use the static magnetic field obtained using FEM, the Biot-Savart law or experiments and the equation automatically satisfies boundary conditions using infinitesimal loop coils. In this study, we explain simply the principle of this method, and model an eddy current damper composed of a spherical magnet and a conducting shell. The analytical results of the modeling agree well with the experimental results.

Eddy Current Damper for Turbine Blading: Electromagnetic Finite Element Analysis and Measurement Results

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Jacob Laborenz ◽  
Malte Krack ◽  
Lars Panning ◽  
Jörg Wallaschek ◽  
Markus Denk ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Eddy Current ◽  
Dynamic Performance ◽  
Forced Response ◽  
Element Analysis ◽  
Transient Electromagnetic ◽  
Eddy Current Damper ◽  
Mechanical Damping ◽  
Turbine Blading

In the dynamics of turbomachinery, the mechanical damping of the blading has been the focus of research for the last decades to improve the dynamic performance in terms of high cycle fatigue issues. In addition, an increased mechanical damping can produce a higher flutter safety margin such that stable operation conditions are achievable in a bigger range. Hence, novel damping techniques are considered besides the well known friction based damping devices. In this paper, an extended analysis of the eddy current based damping device for a last stage steam turbine blading presented in GT2009-59593 is conducted. A transient electromagnetic finite element analysis of the eddy current damper is performed, and the resulting damping forces are compared to their analytical solution. Parameter studies are carried out, and equivalent damping factors are calculated. Furthermore, for the validation of the finite element model, a test rig was built that allows for the direct measurement of damping forces when forcing a sinusoidal relative motion. Forced response measurements and simulations are used to demonstrate its dynamic performance and predictability.

Design of a vibration isolation system using eddy current damper

2013 ◽  
Vol 228 (4) ◽  
pp. 664-675 ◽  
Author(s):  
Partha Paul ◽  
Chetan Ingale ◽  
Bishakh Bhattacharya
Keyword(s):  
Eddy Current ◽  
Vibration Isolation ◽  
Eddy Currents ◽  
High Efficiency ◽  
Experimental Studies ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Analysis And Design ◽  
Passive Vibration Isolation ◽  
Eddy Current Damper

This article aims at modeling, analysis and design of a passive vibration isolation system using a magnetic damper with high efficiency and compactness. The experimental set-up was developed for a single degree-of-freedom vibration isolation system, where the damper consists of two elements: an outer stationary conducting tube made up of copper and a moving core made up of an array of three ring-shaped neodymium magnets of Nd–Fe–B alloy separated by four block cylinders made of mild steel that are fixed to a steel rod. The generation of eddy currents in the conductor and its resistance causes the mechanical vibration to dissipate heat energy. The vibration response of the system is obtained starting from a low-frequency range. The proposed magnetic damper achieves a maximum transmissibility value less than two for a natural frequency that is less than 10 Hz and the excitations at higher frequencies are successfully isolated. Numerical and experimental studies were carried out for a range of system parameters which show that isolators based on magnetic damping could be very effective for passive vibration isolation. Further, a theoretical model for an active isolation system is proposed in order to reduce the transmissibility at resonance. It is envisaged that the combined active–passive eddy current damper could be effectively used for vibration isolation.

Eddy Current Damper for Turbine Blading: Electromagnetic Finite Element Analysis and Measurement Results

2011 ◽  
Author(s):  
Jacob Laborenz ◽  
Malte Krack ◽  
Lars Panning ◽  
Jo¨rg Wallaschek ◽  
Markus Denk ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Eddy Current ◽  
Dynamic Performance ◽  
Forced Response ◽  
Element Analysis ◽  
Transient Electromagnetic ◽  
Eddy Current Damper ◽  
Mechanical Damping ◽  
Turbine Blading

In the dynamics of turbomachinery the mechanical damping of the blading is in the focus of research for the last decades to improve the dynamic performance in terms of high cycle fatigue issues. Besides that an increased mechanical damping can produce a higher flutter safety margin such that stable operation conditions are achievable in a bigger range. Hence, novel damping techniques are considered besides the well known friction based damping devices. In this paper an extended analysis of the eddy current based damping device for a last stage steam turbine blading presented in GT2009-59593 is conducted. A transient electromagnetic finite element analysis of the eddy current damper is performed and the resulting damping forces are compared to their analytical solution. Parameter studies are carried out and equivalent damping factors are calculated. Furthermore, for the validation of the finite element model a test rig was built which allows for the direct measurement of damping forces when forcing a sinusoidal relative motion. Forced response measurements and simulations are used to demonstrate its dynamic performance and predictability.

Precision Motion Control with Active Eddy Current Damper

2010 ◽  
Vol 447-448 ◽  
pp. 493-497
Author(s):  
Chek Sing Teo ◽  
Chea Jack Ong ◽  
C.J. Ho ◽  
S. Huang ◽  
K.K. Tan
Keyword(s):  
Eddy Current ◽  
Eddy Currents ◽  
Vibration Suppression ◽  
Linear Motor ◽  
Precision Motion Control ◽  
Damping Effect ◽  
Eddy Current Damper ◽  
Damper Design ◽  
Precision Motion ◽  
Conducting Sheet

This paper describes the design and proof of concept for an active eddy current damper which is integrated into a single-axis linear motor. Although developments on active eddy current damper are well documented, none has been implemented in a linear motor. The advantage of such a system is two-fold. Firstly, the relative motion between the magnets and the conducting sheet produces eddy currents resulting in an electromagnetic force opposing the direction of motion; which can be utilized to suppress vibrations. Secondly, it is possible to enhance the damping effect of the system; Due to environmental noise, it is normally not possible to increase the D coefficient in a PID controller as much as desirable. The damper is thus able to supplement this damping effect to improve settling time. Here, we will present the damper design as well as the preliminary experiment results for both vibration suppression and motion damping.

Improved Concept and Model of Eddy Current Damper

2005 ◽  
Vol 128 (3) ◽  
pp. 294-302 ◽  
Author(s):  
Henry A. Sodano ◽  
Jae-Sung Bae ◽  
Daniel J. Inman ◽  
W. Keith Belvin
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Eddy Current ◽  
Eddy Currents ◽  
Opposite Polarity ◽  
Image Method ◽  
Time Varying ◽  
Transverse Beam ◽  
Eddy Current Damper ◽  
Improved Model

When a conductive material experiences a time-varying magnetic field, eddy currents are generated in the conductor. These eddy currents circulate such that they generate a magnetic field of their own, however the field generated is of opposite polarity, causing a repulsive force. The time-varying magnetic field needed to produce such currents can be induced either by movement of the conductor in the field or by changing the strength or position of the source of the magnetic field. In the case of a dynamic system the conductor is moving relative to the magnetic source, thus generating eddy currents that will dissipate into heat due to the resistivity of the conductor. This process of the generation and dissipation of eddy current causes the system to function as a viscous damper. In a previous study, the concept and theoretical model was developed for one eddy current damping system that was shown to be effective in the suppression of transverse beam vibrations. The mathematical model developed to predict the amount of damping induced on the structure was shown to be accurate when the magnet was far from the beam but was less accurate for the case that the gap between the magnet and beam was small. In the present study, an improved theoretical model of the previously developed system will be formulated using the image method, thus allowing the eddy current density to be more accurately computed. In addition to the development of an improved model, an improved concept of the eddy current damper configuration is developed, modeled, and tested. The new damper configuration adds significantly more damping to the structure than the previously implemented design and has the capability to critically damp the beam’s first bending mode. The eddy current damper is a noncontacting system, thus allowing it to be easily applied and able to add significant damping to the structure without changing dynamic response. Furthermore, the previous model and the improved model will be applied to the new damper design and the enhanced accuracy of this new theoretical model will be proven.

Operation of an Electromagnetic Eddy-Current Damper with a Supercritical Shaft

1994 ◽  
Vol 116 (4) ◽  
pp. 578-580 ◽  
Author(s):  
J. R. Frederick ◽  
M. S. Darlow
Keyword(s):  
Eddy Current ◽  
High Speed ◽  
Eddy Currents ◽  
Squeeze Film ◽  
Future Research ◽  
Rotating Shaft ◽  
Small Disk ◽  
Eddy Current Damper ◽  
Speed Stability

A basic problem inherent with the operation of supercritical shafting is the application of appropriate external damping, which is generally necessary to suppress nonsynchronous instabilities and limit the synchronous response of even a well-balanced shaft. Typically, coulomb or squeeze film-type dampers are used, in which case the damping properties tend to change with temperature, and the necessary contact results in additional torque loading and wear. An alternative damping method currently under investigation is the application of a noncontact electromagnetic damper that dissipates energy through induced eddy-currents generated in a small disk mounted to, and rotating with the shaft (Frederick, 1990). Research is underway on the design and development of a damper of this type that could eventually lend itself to active control applications. The objectives of this investigation are the initial design of a magnetic circuit, an appropriate d-c power supply, and the characterization of preliminary performance experiments on a composite shaft. Damper operation was evaluated during rotating shaft tests and compared to prior tests which involved the use of a permanent magnet eddy-current damper. This Note concerns some interesting results obtained from these preliminary tests. The damper worked well at low speeds, but some high-speed stability problems were encountered. Potential solutions to these problems as well as areas of future research are discussed.

Determination of eddy current losses and hysteresis losses in magnetic circuits of electrical machines

2020 ◽  
pp. 54-58
Author(s):  
S. M. Plotnikov
Keyword(s):  
Eddy Current ◽  
Magnetization Reversal ◽  
Eddy Currents ◽  
Technical Problem ◽  
Electrical Machines ◽  
Eddy Current Losses ◽  
Hysteresis Losses ◽  
Magnetic Circuits ◽  
Core Losses ◽  
Reversal Frequency

The division of the total core losses in the electrical steel of the magnetic circuit into two components – losses dueto hysteresis and eddy currents – is a serious technical problem, the solution of which will effectively design and construct electrical machines with magnetic circuits having low magnetic losses. In this regard, an important parameter is the exponent α, with which the frequency of magnetization reversal is included in the total losses in steel. Theoretically, this indicator can take values from 1 to 2. Most authors take α equal to 1.3, which corresponds to the special case when the eddy current losses are three times higher than the hysteresis losses. In fact, for modern electrical steels, the opposite is true. To refine the index α, an attempt was made to separate the total core losses on the basis that the hysteresis component is proportional to the first degree of the magnetization reversal frequency, and the eddy current component is proportional to the second degree. In the article, the calculation formulas of these components are obtained, containing the values of the total losses measured in idling experiments at two different frequencies, and the ratio of these frequencies. It is shown that the rational frequency ratio is within 1.2. Presented the graphs and expressions to determine the exponent α depending on the measured no-load losses and the frequency of magnetization reversal.

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