Proceedings of the International MultiConference of Engineers and Computer Scientists 2014 Vol II, IMECS 2014, March 12 - 14, 2014, Hong Kong The Electromagnetic Analysis and Design of a New Permanent Magnetic Eddy Current Damper XIE Hu, MA Shuyuan, LI Wenbin Abstract—The thesis suggests the design of a passive Depending on different primary excitation sources, the permanent magnetic eddy current damper. The damping force electromagnetic damper has three sub-types: electrical from the eddy currents which are generated by a conductor excitation magnetic damper, hybrid excitation plate cutting through magnetic lines of forces can help make a electromagnetic damper and permanent magnetic damper[2]. maglev positioning platform more stable. The formulas for Electrical excitation magnetic damper can regulate the calculating damping force are proposed by applying molecular braking force by adjusting the air gap magnetic flux density current methods. The feasibility of the design is proved by the amplitude. However, its braking force is lower in density finite element simulation of the proposed damper. and has more excitation magnetic loss. Hybrid excitation air gap magnetic field is under the effects of excitation winding Keywords—Maglev Positioning Platform, Permanent and permanent magnets, with the advantages of large air gap Magnetic Eddy Current Damper, Molecular Current, Finite magnetic amplitude, flexibility and high efficiency and the Element Analysis, Damping Coefficient disadvantages of complicated structure and large size. Permanent magnetic damper does not require extra I. INTRODUCTION power supply or excitation winding, so it is energy-saving, [3] hen a conductor moves in a magnetic field, it will be highly efficient and greater in braking density . Wforced on Ampere’s force by the induced current The design of a new permanent magnetic eddy current whose direction always hinders the movement of the damper is proposed in this thesis, which can provide planar conductor. This phenomenon is known as electromagnetic electromagnetic damping force on maglev positioning [4] damping. Eddy current is generated by a moving conductor platform and other accurate positioning systems and meet in a magnetic field, and it will be dissipated in the form of the needs of fast, accurate and stable positioning. Based on heat resistance. The main effects of an electromagnetic the structural design, the thesis suggests a three-dimensional damper are braking and damping. As a new device and with simulation model of permanent magnetic eddy current the advantages of non-contact, mechanical friction free, damper by using finite element analysis software. The thesis lubrication free, controllable and measurable stiffness and also discusses how the air gap magnetic fields change in damping properties, the electromagnetic damper has been both stationary and working dampers and their different paid growing attention since late 1970s[1]. damping effects on maglev positioning platform. Manuscript received December 08, 2013; revised January 13, 2014. This II. THE STRUCTURE AND WORKING PRINCIPLE work was supported in part by the National Natural Science Foundation of OF EDDY CURRENT DAMPER China under Grant 51375052. The movement of a non-magnetic conductor in a XIE Hu is a doctorate student from School of Mechanical Engineering, magnetic field will lead to the cutting of magnetic lines and Beijing Institute of Technology, Beijing,100081, P. R. China (phone: conductor. According to the law of electromagnetic 86-15010195742; e-mail: [email protected]). induction, the cutting will generate electromotive in the MA Shuyuan is a professor from School of Mechanical Engineering, conductor and then generate current. The distribution of the Beijing Institute of Technology, Beijing,100081, P. R. China (e-mail: current varies because of the different conductor shapes and [email protected]). the varied magnetic flux. The path of the current looks like LI Wenbin is a master-degree student from School of Mechanical eddies in water, thus it is called electric eddy current. Eddy [5] Engineering, Beijing Institute of Technology, Beijing,100081, P. R. China current has thermal effect and mechanical effect . (e-mail: [email protected]) According to the principle of energy conservation, when an ISBN: 978-988-19253-3-6 IMECS 2014 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) Proceedings of the International MultiConference of Engineers and Computer Scientists 2014 Vol II, IMECS 2014, March 12 - 14, 2014, Hong Kong object is under the effect of eddy current damping (in other by permanent magnet. The interaction between these two words damping force), the kinetic energy of the object magnetic fields leads to a force that hinders relative transforms to thermal energy. The vibration of the object is movement—the electromagnetic damping force which thus reduced and the stable positioning of the object is suppresses the vibration of maglev positioning platform and achieved. helps make a more stable positioning. The proposed damper can also provide damping forces in two directions, simplifying the mechanical system of the damper and meeting the requirements of stability as well. The parameters of the proposed damper are shown in Table I. Z Table I Parameters of Permanent Magnetic Eddy Current θz θy Damper X θx Y Parameter Value Fig. 1 The Overall Structure of the Maglev Positioning Radius of the Copper Plate(mm) 3.0 Platform Thickness of the Copper Plate(mm) 5 Remanence of the Permanent Magnet(T)1.35 Gap of Permanent Magnets(mm) 10 Width of the Permanent Magnet(mm) 20 (a) The Front View Length of the Permanent Magnet(mm) 20 Thickness of the Permanent Magnet(mm) 10 III. THE MATHEMATIC MODEL OF PERMANENT MAGNETIC EDDY CURRENT DAMPER (b) The Top View A. The Magnetic Fields Distribution of Permanent Magnetic Eddy Current Damper Fig. 2 Permanent Magnetic Eddy Current Damper Based on the relative movement between maglev Figure 1 is the overall structure of the maglev positioning platform and permanent magnetic eddy current positioning platform. The new design will meet the damper, the relative movement between permanent magnet requirement of different nano-manufacturing experiments, and non-magnetic copper conductor is shown in Figure 3. greatly improving the experimental condition of the research The permanent magnet used in the present study is on nano-manufacturing. The design can be used in the rectangular with a square cross-section. Take its movement research of micro-nano mechatronics, the research and in Y direction for example, the conductor plate moves application of micro-nano devices’ assembly and horizontally at the speed v above the magnet. From the measurement, and can serve as the platforms for fiber optic magnet to observe in the direction of the plate, the eddy alignment, semiconductor testing and CMM as well. Figure current distribution is as shown in Figure 4. 2 shows the permanent magnetic eddy current damper which is below the moving platform and without relative motion to the platform. The proposed damper in this thesis is a passive device, consisting of the magnetic source (a permanent magnet) and a conductor (a copper plate). Relative to the permanent magnetic array, the conductor plate moves horizontally at a certain speed; the magnetic field generated by the array changes as the plate moves through. The changing magnetic field will generate electromotive force in the plate and induce eddy current. According to Lenz’s law, Fig. 3 The Relative Movement of Rectangular Permanent the direction of the magnetic field generated by eddy current Magnet and Conductor is opposite to the direction of the magnetic field generated ISBN: 978-988-19253-3-6 IMECS 2014 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) Proceedings of the International MultiConference of Engineers and Computer Scientists 2014 Vol II, IMECS 2014, March 12 - 14, 2014, Hong Kong three-dimensional magnetic field intensity generated by each current is dB1, dB2, dB3, dB4. BZ, the component along Z direction in the spatial magnetic field around the permanent magnet, is as follows, h B ()dB dB dB dB k (1) Zzzzz0 1234 According to Biot-Savart law, the vertical magnetic field generated by the remanent three currents of A’B’C’D’A’ loop is Fig. 4 The Distribution of Generated Current in the b 0J 1 dz 0 a x dBz1 dy0 Conductor Plate 0 3 4 2 2 2 2 ()()()x a y y0 z z0 There are two magnetizing principles concerning a 0J 1 dz 0 b y magnetic medium, focusing on molecular current and dBz2 dx0 0 3 4 2 2 2 2 (2) magnetic charge respectively. The present study applies the ()()()x x0 y b z z0 b method of molecular current to analyze the spatial 0J 1 dz 0 x dBz3 dy0 0 3 three-dimensional magnetic field of the proposed damper. 4 2 2 2 2 x()() y y0 z z0 According to Ampere molecular circulation hypothesis, a 0J 1 dz 0 y dBz4 dx0 permanent magnet only has surface current but no volume 0 3 4 2 2 2 2 ()()x x0 y z z0 current. Thus, the magnetic field of any external point -7 outside the magnet can only be generated by the surface μ0=4π×10 is the permeability in the vacuum. current circulation ABCDA as shown in Figure 5. The length Using the above formula and integral in the thickness and the width of the magnet are a and the thickness is h. The direction of the permanent magnet, the component BZ along closed surface current element dI consists of the surface Z direction is current circulation A’B’C’D’A’ and dI=J1∙dz0. dz0 is the b ax 3 dy0 height of the circulation A’B’C’D’A’. 0 2222 ()()()xa yy00 zz P(x,y,z) a a by D C dx h 0 3 0 (3) C¡¯ 22 22 D¡¯ h ()()()xx00 yb zz a BKz dz O 0 b x dy 0 3 0 2222 (x0,y0,z0) dz0 xyyzz()()00 A B a y A¡¯ dx B¡¯ z0 0 3 0 ()xx22 y () zz 22 y0 dy0 00 Assume K=μ0 J1/4π=μ0 M/4π=Br/4π，K is a constant, Fig.