Application of Eddy Current Damping Effect to Design a Novel Magnetic Damper

Transcription

1 2nd International Foru on Electrical Engineering and Autoation (IFEEA 2015) Application of Eddy Current Daping Effect to Design a Novel Magnetic Daper Xiao Denghong*1 Zhou Xiaohong1 Gao yong1 Quan Dongliang1 He Tian2 1 Beijing Electro-Mechanical Engineering Institute, Beijing 10074, P. R. China 2 School of transportation Science and Engineering, Beihang university, Beijing 10074, P. R. China xiaodenghong@buaa.edu.cn Keywords: Eddy current daper, FEM, daping characteristics Abstract. With advantages of no echanical contact, vacuu copatibility, oil-free, and high reliability, an eddy current daper (ECD) is designed for use in space. To obtain perfect daping characteristics, a conductor as an outer copper tube and two stationary plates, and an array of axially agnetized ring-shaped peranent agnets separated by iron pole pieces as a over are used in the proposed ECD. Aong the outer conductor tube, a steel tube is used to prevent the electroagnetic leakage. Since the generated eddy currents create are pulsive force that is proportional to the velocity of the conductor, the oving agnet and conductor behave like a viscous daper. An accurate analytical odel based on the electroagnetic theory for this type of eddy current daper is proposed, and a finite-eleent ethod (FEM) is carried out to predict the agnetic field and current density. 1. Introduction Eddy currents are generated in a conductor in a tie-varying agnetic field. They are induced either by the oveent of the conductor in the static field or by changing the strength of the agnetic field, initiating otional and transforer electrootive forces, respectively. Since the generated eddy currents create are pulsive force that is proportional to the velocity of the conductor, the oving agnet and conductor behave like a viscous daper. Copared with other types of dapers, such as viscous, viscoelastic, or piezoelectric dapers, the eddy current daper has advantages of no echanical contact, high reliability, high theral stability, and vacuu copatibility[1-3]. Although there are those locations that are particularly well suited for eddy current dapers, but perhaps the ost proising is in space. Because it did not require any liquid that could leak during operation, had low friction, and provided sall variation in daping over a fairly wide range of teperatures. When a device is placed into orbit, the syste ust function for its entire lifespan without requiring any type of aintenance[4-6]. This can place liitations on the type of daper used, leaving few systes left. The extreely cold teperatures that are present in space actually iprove the daping perforance of the eddy current daper, due to the decrease in resistivity of the conductor. This paper proposed a new configuration of eddy current dapers. Figure 2 depicts a scheatic configuration of the proposed eddy current daper. The proposed daper consists of a conductor as an outer tube and an array of axially agnetized, ring-shaped peranent agnets separated by iron poles as a over. Aong the outer conductor tube, there is another etal tube of steel aterial, which is used to prevent the electroagnetic leakage causing daages to coponents assebled in the spacecraft. This is extreely iportant for the daper designers. The relative oveent of the agnets and the conductor causes the conductor to undergo otional eddy currents. An analytical odel for this eddy current daper is derived based on electroagnetic theory, and the eddy current density is coputed using finite eleent analysis FEA. The results show that the new configuration of eddy current daper is effective The authors - Published by Atlantis Press 335

2 Fig. 1. Scheatic view of the proposed ECD. 2. Description of the prototype and analytical odeling The scheatic cross-section configuration of the proposed eddy current daper is depicted in Figure 2. Bold arrows indicate the direction of the agnetization for each Peranent agnet (PM). It consists of a ring-shaped conducting aluinu plate and two cylindrical peranent agnets, whose like-poles are in close proxiity. The lower peranent agnet and the two eddy current plates are stationary, while the upper agnet array has a reciprocating otion. The copper is chosen as the 7 conductor aterial because of its high electrical conductively ( / ). The relative oveent of the agnets causes the conducting plate to undergo a tie-varying agnetic field such that a transforer eddy current is generated. Since there is a relative oveent between agnets and the two conducting plates, a otional eddy current is generated as well. Fig. 2. Configuration of the proposed eddy current daper. Axially agnetized peranent agnets in the over result in a higher specific force capability than that of radially agnetized ones. Instead of disc-shaped agnets, annularly shaped agnets supported by a non-ferroagnetic rod are selected; they are fastened on a non-agnetic rod, reducing the effective air gap. Its diensions are listed in table 1. Table 1. ECD prototype diensions Ite/ sybol Value/ unit Magnet aterial NdFeB alloy (Br=1.17T) Plate and conductor aterial copper Magnet diaeter (Dout) 30 Magnet thickness (τ) 10 Magnet inner diaeter (Din) 10 Iron pole thickness (τ-τ) 5 Plate thickness (Lp) 4 Air gap (LAG) 0.5 ECD diaeter (DD) 61 Copper tube outer diaeter (Dc)

3 3 Magnetic flux density calculation There are a nuber of approaches for calculating the agnetic flux density of a peranent agnet. The siplest approach is the dipole oent odel, which is ore appropriate for the flux density calculation for long distances, copared with the agnets diaeter. For a peranent agnet with length τ and radius R, the agnetic flux density at a distance (r, z) fro the agnet geoetric centre is obtained [7] by coputing ' 2 0I ( zz) Br(, r z) R, 2 2 ' r[( Rr) ( zz) ] 2 2 ' 2 2 d R r ( zz) [ ' ' 2 14 Rr[( Rr) ( z z ) ] sin ( Rr) ( zz) 2 14 Rr[( Rr) ( z z ) ] sin d ] dz 2 ' ' 0 (1) where M is the constant agnetization of the agnet. For the proposed agnets configuration in figure 2, the total radial coponent of the agnetic flux density expelling fro each iron pole piece is the su of the agnetic flux density produced by each adjacent agnets as B (, r z) 2( B (, r z) B (, r z) ) r r D, r D, out in (2) The distribution of agnetic flux density of eddy current daper is further studied using the FEA ethod. Both the two-diensional odel and three-diensional odel of the daper are siulated, using ANSYS 13.0, for further analysis of the proposed ECD and to estiate the agnetic flux density [8]. Figure 3 shows the agnetic flux density analysis results of the proposed over configuration. Magnetic flux density strealines and the induced agnetic field are plotted in these two figures. (a) (b) Fig. 3. FE siulation results of the prototype ECD. (a) 2D Flux lines plot of the agnetic flux density; (b) 3D vector plot of the agnetic flux density. It is observed that the radial agnetic flux density is concentrated and enhanced at the iron pole pieces, causing ore eddy current induction such that the ECD is ore effective. And the agnetic flux density in areas beyond the ECD is exceedingly weak. That s to say the influence of electroagnetic leakage can be ignored. Since the 3D finite-eleent analysis ethod is uch ore precise than 2D analysis, the 3D finite-eleent analysis ethod is adopted to predict the eddy current density and daping coefficient for conductors oving inside the agnetic field. To add conductor velocity, a 3D transient analysis ethod is used to siulate a oving conductor under a static agnetic field excitation as oving conductor analysis can be done directly in a 2D static agnetic analysis, but not in 3D in ANSYS. 337

4 And the specific velocity can be assigned to the conductor. The Eddy current distribution of the proposed eddy current daper is depicted in Figure 4. Fig. 4. Eddy current plot of the prototype ECD. 4 Conclusion In this paper, a passive eddy current daper was developed that is capable of effectively suppressing vibrations. The structure of the new passive eddy current daper is straight forward, requiring no external power supply or any other electronic devices. A theoretical odel of the proposed syste is constructed by using the transforer eddy current contribution for the otional eddy current estiation. The agnetic flux and eddy current daping force are analytically calculated by finite eleent. The perforance of the proposed eddy current daper can be further iproved by using high-quality, low-weight peranent agnets, as well as conductors with higher conductivity. References [1] Fung, R-F., Sun, J-H., and Hsu, S-M., 2002, Vibration Control of the Rotating Flexible-Shaft/Multi-Flexible-Disk Syste with the Eddy Current Daper, ASME Journal of Vibration and Acoustics, Vol. 124, [2] Matsuzaki, T., Ikeda, T., Nae, A., and Sasaki, T., 2000, Electroagnetic Forces for a New Vibration Control Syste: Experiental Verification, Sart Materials and Structures, Vol. 9, No. 2, [3] Bae, J. S., Kwak, M. K., and Inan, D. J., 2004, Vibration Suppression of Cantilever Bea Using Eddy Current Daper, Journal of Sound and Vibration, in press. [4] J.S. Bae, M.K. Kwak, D.J. Inan, Vibration suppression of cantilever bea using eddy current daper, Journal of Sound and Vibration 284 (2005) [5] H. Sodano, J.S. Bae, D.J. Inan, W.K. Belvin, Concept and odel of eddy current daper for vibration suppression of a bea, Journal of Sound and Vibration 288 (2005) [6] Kienholtz, D. A., Sith, C. A., and Haile, W. B., 1996, A Magnetically Daped Vibration Isolation Syste for a Space Shuttle Payload, in Proceeding of the SPIE International Syposiu on Sart Structures and Materials, San Diego, CA, Vol. 2720, [7] Babak Ebrahiia, Mir Behrad Khaeseea, M. Farid Golnaraghib, Design and odeling of a agnetic shock absorber based on eddy current daping effect, Journal of Sound and Vibration 315 (2008)

5 [8] He T, Xiao D, Liu X, et al Design and analysis of a novel eddy current daper based on three-diensional transient analysis[j]. Journal of Vibroengineering, 2013, 15(1). 339