DOC PREVIEW
MIT 6 013 - MAGNETIC FORCES ON FLAT SURFACES

This preview shows page 1-2-3 out of 9 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

L6-1MAGNETIC FORCES ON FLAT SURFACESLorentz Force Law:WI1I2sF [N/m]F [N/m] = Nqv11×μooH2=I1×μ H12v∫∫Hd•=sCAw∫J•da=I21≅ 2H2WF =μzˆo1I I2/ 2W [N/m]Currents exert no net force on themselvesTotal H method:v∫∫Hd•=s •aCAw∫Jd=Let I12 = I = I = HoWF1o [N/m] = I1×μ <H>H= zzˆˆI1oμo = μoI1I2/ 2W [N/m]21P = F/W = zˆμ H22oo [N/m ]2"Magnetic pressure"0 for C1I for C2zyxIWC1HC2s << Wconductor<H> = Ho/2magnetic pressureI1HoH0=zJyF1cfq m=×vμNoH []L6-2ROTARY WIRE MOTORSingle wire loop spinning in uniform H:Axial forces from wires at ends cancelF [Nm-1] =×I μoHT =×v∫r F ds = r2WIμoH zˆ [Nm]cT = IAμoH zˆ (A is loop area, N = 1 turn)T = NIAμoH zˆ for N-turn coil fNSWrθIT,HdsTorque = f(θ):T[Nm]With commutatorNIμoH(θ)A0π 2πθCommutators:Switch currents to maximize torqueCan have N coils and 2N brushesCθspring-loadedcarbon brusheszˆL6-3MOTOR BACK VOLTAGEForce on electron inside moving wire:Open-circuit wire:Open-circuit voltage:( )feee= −+Ev×μoH=0⇒=Eve−×μoH insideΦ=EW=eovμHW [V]Force balance−ev ×μoHH-ev−eEe+-ΦHWv,f,xˆfeMechanical power output, N turns:Pm= ωT = ωNIAμoH [W] I = (V - Φ)/RΦ = 2NvμoHW = 2NωrμoHW = NAμoHωPm= ωN(V - NAμoHω)AμoH/R = ωK1– ω2K2 RI+ +VΦ- -PpPm(ω)0ωpωωmaxmotorgeneratorωmax= V/NAμoH= 2ωpΦp= V/2L6-4RELUCTANCE MOTOR FIELDS2-Pole Reluctance Motor:()μμ≅o4∇•B0= ⇒ BμμBgap ⇒ H≅ Hgap<<Hgap [ > ~10]μμo∫∫J •=da NI =vvH•ds =∫Hgap+Hμ•ds ≅2bHAccgap (if Hμv∫ds << 2bHcgap)NITherefore H ≅gap [A /m]2bμμrotorstatorgap bθDIN turns+ V -TN turnsI+ V -μμrotorstatorDdsArea AL6-5RELUCTANCE MOTOR TORQUEμμrotorstatorgap bθDN turnsI+ V -TSet V = dΛ/dt = 0:We power coil until overlap is maximum, then coast until it is zeroΛ= N∫∫B•da = NμoHAgap gapA = N2μoIAgap/2b (Agap= RDθ)Λ⇒ = LI L = N2μoRDθ/2b112Λ2wm = LI = 22LFields:NIHgap=2bMagnetic Flux Linkage Λ:dwmΛΛ2-dL1 22bT = - = - = I222 [ ∝ ], Λμ=N Hd2θθd2N μ RDθogapRθDo1 = μoH2dVgap2bD R = Wolumegap [Nm] Torque2dθMagnetic pressure = Energy density [J/m3= N/m2]L6-6¾-POLE RELUCTANCE MOTORWinding Excitation Plan:First excite windings A and B, pulling pole 1 into pole B. Pole area A = constant, temporarily.When Δθ = π/3, excite B and C.When Δθ = 2π/3, excite C and A. Repeating this cycle results in nearly constant clockwise torque.To go counter-clockwise, excite BC, then AB, then CA.Torque:Only one pole is being pulled in here; the other excited winding has either one rotor pole fully in, or one entering and one leaving that cancel. Many pole combinations are used (more poles, more torque).AB1μ4θ2μCABCL6-7ELECTRIC AND MAGNETIC PRESSUREElectric and magnetic pressures equal the field energy densities, J/m3Both field types only pull along their length, and only push laterallyThe net pressure is the difference between two sides of any boundaryσ = ∞σ = ∞Area AArea BElectric pressure Pe= [N/m2] or [J/m2]1||2ε2oEForce fe= BPeForce fe= APeμ = ∞μ = ∞Area AArea BMagnetic pressure Pm= [N/m2] or [J/m2]1||2μ2oHForce fm= APmσ = ∞Force fm= BPmArea AForce fm= APmL6-8FORCES ON NEUTRAL MATTERKelvin polarization force density:Kelvin magnetization force density:xzy•+++++++ε > εo-------+-+-+V-fx/2fx/2dEIf ∇×E =0 = ∇•E, then:Field gradiants ⊥⇒E E is curvedCurved E pulls electric dipoles into stronger field regions for ε>εoIf H∇× =0 = ∇•B, then:Field gradiants ⊥⇒H H is curvedμ > μofx2fx1וμoμ > μoInduced current loopBB1B2ICurved H pulls current loops into stronger field regions for μ > μoB1> B2MIT OpenCourseWare http://ocw.mit.edu 6.013 Electromagnetics and Applications Spring 2009 For information about citing these materials or our Terms of Use, visit:


View Full Document

MIT 6 013 - MAGNETIC FORCES ON FLAT SURFACES

Documents in this Course
LASERS

LASERS

9 pages

Quiz 2

Quiz 2

7 pages

Quiz 1

Quiz 1

6 pages

Load more
Download MAGNETIC FORCES ON FLAT SURFACES
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view MAGNETIC FORCES ON FLAT SURFACES and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view MAGNETIC FORCES ON FLAT SURFACES 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?