Hillyard - Joint Advanced Student School 2006 Jeff Hillyard...

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Unformatted text preview: Joint Advanced Student School 2006 Jeff Hillyard Technische Universitt Mnchen Magnetic Bearings Overview Magnetic Bearings Introduction Magnetism Review Active Magnetic Bearings Passive Magnetic Bearings Industry Applications Introduction Magnetic Bearing Types Active/passive magnetic bearings electrically controlled no control system Radial/axial magnetic bearings Introduction Motivations Advantages of magnetic bearings: contact-free no lubricant (no) maintenance tolerable against heat, cold, vacuum, chemicals low losses very high rotational speeds Disadvantages: complexity high initial cost Minimum Equipment for AMB Source: Betschon Introduction Survey of Magnetic Bearings Source: Schweitzer Magnetism Magnetic Field north pole south pole magnetic field line iron filings Pole Transition Magnetism Magnetic Field Magnetic field, H, is found around a magnet or a current carrying body. r i H 2 = i ds H = (for one current loop) H i Magnetism Magnetic Flux Density B = magnetic flux density = magnetic permeability H = magnetic field H B = r = = permeability of free space r = relative permeability 1 < 1 diamagnetic paramagnetic ferromagnetic r ni H 2 = multiple loops of wire, n 1 Meissner-Ochsenfeld Effect Magnetism B-H Diagram H B area within loop represents hysteresis loss magnetic saturation Ferromagnetic: a material that can be magnetized H B = Coercivity, H c Remanence, B r Magnetism Lorentz Force f = force Q = electric charge E = electric field V = velocity of charge Q B = magnetic flux density ( 29 B v E Q f + = Magnetism Lorentz Force Simplification: ( 29 B v Q f Source: MIT Physics Dept. website ( 29 B v E Q f + = ( 29 B v E < < Magnetism Lorentz Force Further simplification: B i f = B v Q f = v Q i = force perpendicular to flux! f i B Analogous Wire Magnetism Reluctance Force = V BHdV U 2 1 The energy in a magnetic field with linear materials is given by: Force resulting from a difference between magnetic permeabilities in the presence of a magnetic field. force perpendicular to surface! 2 2 A B f = U = energy V = volume l U f = A a s l Fe 2 + Magnetism Reluctance Force = V BHdV U 2 1 Basic equation: s A H B V H B U a a a a a a a 2 2 1 2 1 = = Energy contained within airgap: Magnetism Reluctance Force Evaluating the magnetic circuit for a simple system: ni sH H l Hds a Fe Fe = + = 2 NI ni B s B l r Fe = = + 2 + = s l NI B r Fe 2 a a Fe Fe A B A B = = B B B a Fe = = Assumption: A a s l Fe 2 + Magnetism Reluctance Force Principle of virtual displacement: B H a = a a a A BH l U f = = cos 2 2 a r Fe A s l ni f + = 2 2 s i k f = quadratic!...
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Hillyard - Joint Advanced Student School 2006 Jeff Hillyard...

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