Magnetorheological Fluid for Levitation Migration Technology

66 The Open Materials Science Journal, 2011, 5, 66-71 Magnetorheological Fluid for Levitation Migration Technology Guang Yang * and ZhuPing Chen * Open Access Faculty of Mechanical Engineering, Jiei University, Xiaen 361021, China Abstract: The dispersed particles of agnetorheological fluid for stable chain-like clusters under the agnetic field, and show an effect of controllable flowability and shape. Based on this characteristic, using igration agnetic acted on the agnetorheological fluid, the object directional igration can be realized, and then the agnetorheological fluid fors levitation at the sae tie, which has like fluctuation behavior. The principle of agnetorheological fluid levitation igration, the levitation agnetic circuit design, the agnetic field strength and the agnetic force were separately discussed in this paper. In this study, the finite eleent ethod was used to nuerically siulate the influence wedge-like of agnetic force applied on the agnetic particles in agnetorheological fluid. The relationships were given between flux and air gap width, agnetic field intensity and air gap width, flux and air gap angle, agnetic field intensity and air gap angle. The agnetic force applied on the agnetic particles in agnetorheological fluid has been calculated with virtual work ethod and Maxwell stress tensor ethod. The agnetorheological fluid levitation height was deterined by using the MSL icroeter and aerosol igration feasibility was confired experientally. Keywords: Levitation igration, agnetic circuit, agnetorheological fluid (MRF), finite eleent analysis, agnetic force. 1. INTRODUCTION MRF is a new type of function aterial. MRF is fored by cobining a non-agnetorheological fluid with uniforly dispersed sall particles, which have high pereability and low hysteresis. The behaviour of MRF reversibly changes fro the linear viscous fluid to non-linear high viscoplasticsolid in illiseconds when a agnetic field is applied. MRF has been widely applied in various engineering fields. MRF has any potential applications in areas of echanical engineering including seals, electric achines, vibration dapers, sensors, and lubrications [1-6]. Of particular concern is that this reasonable structure of agnetic field can for the different shape of MRF. Takioto J et al. [7], studied shear stress and cluster structure of MRF levitations under tilted agnetic field, the results were shown the fluids are easier to flow in one direction than reverse direction and dispersed particles for stable chain-like clusters even under the tilted agnetic field condition. In order to rapidly anufacture high-precision aspherical irrors ade fro RB-SiC, Cheng H.B. et al. [8], described a novel aspheric anufacturing syste equipped with MRF technology, an electroagnet located directly under the polishing wheel uses specially designed pole pieces to induce a strong local agnetic field gradient across the top section of the wheel. The finite eleent ethod was used to nuerically siulate agnetic force acting on the agnetic particles in MRF under wedge-like agnetic field. The agnetic force acting on the agnetic particles in MRF was calculated with virtual work ethod and Maxwell stress tensor ethod. This paper develops an effective structure of agnetic field for the MRF can be partially raised plastic solids. Using igration agnetic pole acted on the MRF, the object directional igration can be realized, and then the levitation of MRF was fored at the sae tie, which has like fluctuation behavior. Discussions were presented in this paper on the principle of MRF levitation igration, the levitation agnetic circuit design, the agnetic field strength and the agnetic force. The MRF levitation height was deterined by using the MSL icroeter and aerosol igration feasibility was confired experientally. 2. MIGRATION THEORY OF MRF LEVITATION Migration theory of MRF levitation is shown in Fig. (1). Two pairs of agnetic poles placed in the horizontal plane, respectively, MR fluid, in the tray, placed on the top of the agnetic poles. The agnetic poles were ade levitation of MRF and then the levitation has a height. MRF phase was transfored fro liquid into solid, while strong shear stress was coe into being. The left pole was oved to the right by certain velocity and wave was coe into being on top of the MRF. This solid wave was can pushed object ove. The object was oved to the levitation, which corresponding to right fixed agnetic pole, the object was stopped, to achieve the positioning of object. This ove was can greatly reduced the friction of levitation and noise, and iproved response tie. This way was had any advantages, copared with the traditional echanical transission. *Address correspondence to these authors at the Faculty of Mechanical Engineering, Jiei University, Xiaen 361021, China; Tel: +86-13859921923; E-ails: yangg999@126.co, zooparkchen@126.co Fig. (1). Migration theory of MRF levitation. 1. levatation of MRF, 2. Object, 3. Fixed agnetic poles, 4. Migration agnetic poles. 1874-088X/11 2011 Bentha Open

Magnetorheological Fluid for Levitation Migration Technology The Open Materials Science Journal, 2011, Volue 5 67 to it was provided. In the interval y 0, a x a, the siplified two-diensional Laplace equation is: 2 u x + 2 u 2 y = 0. (2) 2 General solution of equation (2) was derived using separation of variables, and into exponential for: u(x, y) = (K 1n cos x + K 2n sin x)(k 3n e y + K 4n e y ). (3) Fig. (2). Magnetic circuit structure. 1. Upper agnetic yoke, 2. Aluiniu plate, 3. Peranent agnets, 4. Nether agnetic yoke. 2.1. Magnetic Circuit Structure The design of agnetic circuit structure was becoe very iportant, in order to the MRF was fored wave and the wave was can pushed object ove. Magnetic circuit structure of levitation of MRF was used as shown in Fig. (2). The two upper agnetic yokes were above the poles. The poles and upper agnetic yokes were separated by an insulator. Nether agnetic pole yoke was placed on the two poles below, as a whole. U-shaped agnetic loop and wedge-shaped agnetic head were fored a high gradient agnetic field in the vertical direction of interspace of two upper agnetic yokes. 2.2. Magnetic Leakage Coefficient Two above agnetic yoke were separated by aluinu slice. The aluinu is not agnetic conductor and air gap was fored between the two agnetic yoke, which thickness was equivalent the size of aluinu. In this agnetic circuit structure, agnetic leakage coefficient was given as follows: K f = 1 + 2 f [1.7l 1 ( a f S g a + f ) + 1.4h + 0.94b l 2 + 0.25]. (1) where l 1 is the unilateral vertical cross-section perieter of agnetic pole, l 1 = 2(h + c) ; l 2 is the level of unilateral cross-section perieter of agnetic pole, l 2 = 2(d + c) ; S g is the air-gap area, S g = c r. 2.3. Scalar Magnetic Potential Magnetic field strength in a point is equal to negative gradient of this point s scalar agnetic potential. First, the equations of scalar agnetic potential were derived in the agnetic field, and then spatial distribution of agnetic field strength was derived. Peranent agnet provides a constant agnetic field. The above idpoint agnetic field of the agnetic poles was inspected and two-diensional analysis where K 1n, K 2n, K 3n, K 4n, are undeterined coefficients. The boundary conditions of agnetic field are as follows: 1. Infinity is the zero agnetic potential, that is, y =,u = 0. 2. y axis is equipotent line to the infinite distance, that is, x = 0, u = 0. 3. In points x = ±a, agnetic field lines parallel to the y axis and point to infinity, that is, x = ±a, u x = 0. 4. In the x axis, in the interspace, agnetic field is approxiate unifor distribution: y = 0, a x a, u = B g x. Where, B g is flux density of 5. interspace, B g = B S, B K f S is the agnetic g induction intensity of peranent agnet working gap, S is working area, S = c d ; is the vacuu agnetic pereability. For the upper and nether agnetic yoke, each agnetic bit is a constant. Fro the continuity, in point y = 0, we have u = B g B g f, f x a f, a x f. (4) Using the boundary conditions 1, 2 and equation (3), we have K 1n = 0, K 3n = 0, and equation (3) becoes u(x, y) = K n sin(x)e y. (5) Then the boundary conditions were introduced into the equation (5), the expression of is 2n 1 = n = 1, 2, 3 (6) In value y = 0, the agnetic potential equation is obtained by the boundary conditions 4 and 5:

68 The Open Materials Science Journal, 2011, Volue 5 Yang and Chen u = B g f, f x a B g x, f x f B g f, a x f. (7) 2n 1 u(x,0)= K n sin( x). (8) K n is solved using sine function's orthogonality. The equation (8) was ultiplied by expression sin[(2 1) x /], and integrated in the scope [,], we have 2 1 u(x,0)sin( x) dx f B g x 2 1 = 2[ sin( x) dx 0 a B g x 2 1. (9) + sin( x) dx] f 2 1 8a 2 B g sin( f ) = 2 (2 1) 2 Right side function of equation (8) is integrated, we have 2n 1 2 1 K n sin( x) sin( x)dx 2n 1 2 1 = K n sin( x) dx sin( x)dx. (10) = 0 2K n a n = n = 0 Therefore, the coefficient K n is 2n 1 4a B g sin( f ) K n =. (11) 2 (2n 1) 2 and particular solution of scalar agnetic potential is as follows: u(x, y) = 2n 1 sin( 4a B g sin( (2n 1) 2 x)e 2n1 y 2n 1 f ). (12) 2.4. Calculation of Magnetic Field Strength Magnetic field strength is equal to negative scalar agnetic gradient, for the above entioned agnetic field, we have H = ( u i + u j ). (13) x y The partial differential of particular solution of scalar agnetic potential is coputed by equation (13), and we have H = A n cos( x) e y i + A n sin( x) e y j. (14) where A n = K n = 2B g sin( f ). (15) (2n 1) The required agnetic field strength is obtained, which can ade levitation of MFR. Withstanding agnetic force of agnetic particles is calculated. Reaining agnetic induction intensity of spherical particles in agnetic field is B = 3μ H. (16) μ + 2 where μ is agnetic pereability of agnetic particle; H is the agnetic field strength in position of agnetic particle. Magnetic particles are very sall, therefore, in the agnetic filed, each particle is regarded as a agnetic dipole and its agnetic dipole oent is B = V M = V X μ. (17) where V is the volue of agnetic particle; X is the agnetic susceptibility of agnetic particle; M is agnetization strength of agnetic particle. In agnetic field, withstanding agnetic force of agnetic particles is F = ( ) B. (18) Fro equation (16), (17) and (18), we have 2 3μ F = V X 0 ( H ) H. (19) μ + 2 where ( H ) H H = A n cos( x) e y x + A H n sin( x) e y y. (20) H x = A n sin( x) e y i + A n cos( x) e y j. (21) H y = A n cos( x) e y i + A n sin( x) e y j. (22) Therefore, the expression of agnetic force is F = F xi + Fy j. (23) where 2 3μ F x = V X 0 ( A n sin( x) e y A n cos( x) μ + 2 A n cos( x) e y A n sin( x) e y ) e y. (24)

Magnetorheological Fluid for Levitation Migration Technology The Open Materials Science Journal, 2011, Volue 5 69 2 3μ F y = V X 0 ( A n sin( x) e y A n cos( x) μ + 2 + A n cos( x) e y A n sin( x) e y ) e y. (25) The levitation height of MRF increases as the agnetic force increase. In order to ove object with certain thickness, levitation height of MRF at least is higher than the object thickness. Fro the previous expressions we can see that the volue of agnetic particles and the agnetic susceptibility are proportionable to the agnetic field strength. In addition, the agnetic pereability of agnetic particles, the agnetic induction intensity of peranent agnet working gap, work area, agnetic leakage coefficient and area of air gap were affected the agnetic force. Fro equation (25) shows that the agnetic force acting on the agnetic particles in MRF was expanded by total of infinite ites and calculated by liited ites, but the error will change with the reservation nuber of liited ites, and then the finite eleent ethod was used to nuerically siulate the influence wedge-like of agnetic force applied on the agnetic particles in MRF. 3. FINITE ELEMENTANALYSIS OF MAGNETIC FIELD 3.1. Material Properties and Modeling The finite eleent analysis of agnetic field was calculated by electroagnetic field odule of ANSYS progra. The peranent agnet is N40H, coercive force is 900kA/, reanence is 1.28T and the deagnetization curve is reduced to as a straight line. Materials of agnetic yoke were used electric iron yoke, and the relative pereability is 1800. The experiental MRF aterials were used water-based aterial, with spherical carbonyl iron as the agnetic particles. The MRF initial viscosity is 0.5Pas, radius of agnetic particles is 2.510-6 and relative pereability is 2000. Relative pereability of air is 1. Values given above were assued at 20 C. As the air gap length is uch greater than its width, so the finite eleent analysis is reduced to two-diensional electroagnetic field analysis. The points, lines, planes geoetry creation of the peranent agnet and the agnetic yoke were copleted using botto-up odeling ethod. In order to calculate the agnetic force, air odel was created, which was between agnetic particles and the upper agnetic yoke. The scalar agnetic potential to satisfy the standards of the Laplace equation, and its parallel boundary conditions are autoatically satisfied in the progra, in the agnetic field of the plane stability in Cartesian coordinate syste. 3.2. Mesh Paraeters of the calculations are as follows: a=50, b=60, c=70, d=45, r=10, f=4, h=15. Therefore, the agnetic leakage coefficient is K f = 5.08 by calculation. PLANE53 is 4 polygon and 8 node eleent, witch is based on agnetic vector potential equation and is applicable to low frequency electroagnetic field analysis. PLANE53 eleent was used in this two-diensional electroagnetic field analysis. The agnetic field structure was odeled as 2272 PLANE53 eleents and 7172 nodes. The finite eleent odel of wedge-shaped agnetic field is shown in Fig (3). The eshes at air gap were subdivided in order to get accurate results of agnetic field strength. Fig. (3). Finite eleent odel. 3.3. Results and Discussion 3.3.1. Magnetic Flux and Magnetic Field Strength The agnetic field is siply connected iron area and the DSP ethod was selected to calculate. The Frontal solver was used for two-diensional analysis of static agnetic field. The agnetic flux density vector distribution and agnetic field intensity vector distribution are shown in Figs. (4, 5). As can be seen fro Figs. (4, 5), the agnetic flux density of upper air gap is denser, agnetic field intensity is stronger, and here MRF levitation can created. Fig. (4). Magnetic flux density vector.

70 The Open Materials Science Journal, 2011, Volue 5 Yang and Chen atrix ethod, and virtual work ethod is calculated by the energy of the whole syste. Fig. (8). Magnetic flux density for MRF working gap. Fig. (5). Magnetic field intensity vector. In order to optiize the agnetic field, the relationships were given between flux and air gap width, agnetic field intensity and air gap width, flux and air gap angle, agnetic field intensity and air gap angle. As can be seen fro Figs. (4, 5), the flux and agnetic field intensity can be changed with air gap size. The flux and agnetic field intensity increases as the air gap width decreases. The flux and agnetic field intensity increases as the air gap angle increases. However when the angle reached at 0.61rad, they began to decrease. The reason is that the larger agnetic field gradient increases as the air gap angle increases, but then the volue size of the peranent agnet becoes saller, and agnetic field strength reduces. Fig. (9). Magnetic field strength for MRF working gap. Curves of agnetic force for MRF working gap are shown in Figs. (10, 11). Study results show that the agnetic force can be changed with change of air gap size. Magnetic force increases as the air gap width decreases. The agnetic force was 1.5210-8 N, which was calculated by virtual work ethod as the air gap width was 10. The agnetic force was 4.0210-8 N and increase 164%, which was calculated by virtual work ethod as the air gap width is 2. The agnetic force increases as the air gap angle increases. However, when the angle reached at 0.61rad, agnetic force began to decrease. The reason is that the larger agnetic field gradient increases as the air gap angle increases, but then the volue size of the peranent agnet becoes saller, and agnetic field strength reduces. In addition, fro Figs. (10, 11) can be seen that the results obtained by Maxwell stress tensor ethod are generally higher than the results obtained by virtual work ethod. Fig. (6). Magnetic flux density in MRF working gap. Fig. (7). Magnetic field strength in MRF working gap. 3.3.2. Analysis of the Magnetic Force In this section, the agnetic force applied on the agnetic particles in MRF has been calculated with virtual work ethod and Maxwell stress tensor ethod. Maxwell stress tensor ethod and the virtual work ethod are two ethods for calculate electroagnetic force. The Maxwell stress tensor ethod is calculated by surface stress tensor Fig. (10). Curves of agnetic force for MRF working gap. 1. Virtual work ethod, 2. Maxwell stress tensor ethod. 4. EXPERMRNTAL VERIFICATION In order to validate the above theory is correct, the MRF levitation height and the levitation force were experiented using MSL icroeter and counter poise. Levitation igration was needed that the good flowability of MRF is good and has initial low viscosity and good rheological properties. The experiental MRF aterials were used water-based aterial, with spherical carbonyl iron as the

Magnetorheological Fluid for Levitation Migration Technology The Open Materials Science Journal, 2011, Volue 5 71 agnetic particles. The MRF initial viscosity is 0.5Pas, radius of agnetic particles is 2.510-6 and relative pereability is 2000. Yield stress is 20kPa, when agnetic field strength is 320kA/. Fig. (11). Curves of agnetic force for MRF working gap. 1. Virtual work ethod, 2. Maxwell stress tensor ethod. In the experient, two poles at the sae tie were acted on the MRF and the tray was holded up by two ribbons. Scheatic diagra of experiental verification is shown in Fig. (12). The whole device was placed on anti-vibration table, in order to avoid the interference of external lowfrequency vibration. In order to reduce the error, icroeter probe always contacts with the center of counter poise. The icroeter readings were read with agnetic field and the levitation height was obtained. Weight of the counter poise is equal to the double value of load. The test relationship between MRF levitation height and load is shown in Fig. (13). As can be seen fro Fig. (13), the MRF levitation effect was good, in certain load scope. Levitation height gradually decreased as the load increases until both achieve dynaic equilibration. Velocity V = 0.1/s was iposed on the left agnetic poles, the oving speed is 0.096/s of counter poise tray by speed sensor. The tray was soon stopped, when it touched the ribbon, which corresponding to right fixed agnetic poles. Fig. (13). Relationship between MRF levitation height and load. 5. CONCLUSIONS A new technique for foring the levitation igration of MRF was presented. The present technique is based on the igration of wedge-like agnetic field. The finite eleent analysis was given, which is about agnetic force acting on the agnetic particles under wedge-like agnetic field. The relationships between flux, agnetic field intensity and agnetic force with air gap width and air gap angle were also discussed. The MRF levitation height and the levitation force were experiented using MSL icroeter and counter poise. The results obtained in this paper indicate that the present procedure is valid and effective. ACKNOWLEDGEMENTS Project supported by the Science Foundation of Fujian Province (No:2010J01007) and Foundation of Jiei University Pan Jin-long(No:ZC2010018), China. REFERENCES [1] Bica D, Vecas L, Rasa L. Preparation and agnetic properties of concentrated agnetic fluids on alcohol and water carrier liquids. Magn Magn Mater 2002; 252: 10-2. [2] Vekas L, Potencz I, Bica D. The Behavior of Magnetic Fluids under Strong Nonunifor Magnetic Field in Rotating Seal. Magn Magn Mater 1987; 65: 223-6. [3] Evsing SI, Sokolov NA. Developent of agnetic fluid reciprocating otion seals. Magn Magn Mater 1990; 85: 253-6. [4] Anton I, Desata I, Vekas L. Magnetic fluid seals soe design probles and application. Magn Magn Mater 1987; 65: 379-81. [5] Choi SB, Lee SK. A hydro-echanical odel for hysteretic daping force prediction of ER daper: experiental verification. Sound Vibration 2001; 245:375-83. [6] Coulob JL, Meunier G. Finite eleent lpleentantion of virtual work principle for agnetic of electric force and torque coputation. IEEE Trans Magn 1984; 2: 1894-6. [7] Takioto J, Takeda H, Masubuchi Y, Koyaa K. Stress rectification in MR fluid under tilted agnetic field International. Modern Phys B 1999;13:2028-35. [8] Cheng HB, Feng ZJ, Wang YW. Magnetorheological Finishing of Sic Aspheric Mirrors. Mater Manuf Processes 2005; 20:917-31. Fig. (12). Experiental equipent. 1. Worktable, 2. Object, 3. Levitation equipent, 4. MSL. Received: August 26, 2010 Revised: Noveber 26, 2010 Accepted: Deceber 22, 2010 Yang and Chen; Licensee Bentha Open. This is an open access article licensed under the ters of the Creative Coons Attribution Non-Coercial License (http://creativecoons.org/licenses/ bync/3.0/) which perits unrestricted, non-coercial use, distribution and reproduction in any ediu, provided the work is properly cited.