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Mechatronic system design Mechatronic system design wb2414‐2012/2013 Course part 3 Electromagnetic actuators Prof.ir. R.H.Munnig Schmidt Mechatronic System Design Delft 1 University of Technology WB2414-Mechatronic System Design 2013-2014 Learning goals. The student: • Can select and calculate a single axis functional electromagnetic actuator for a given specification, working according to the Lorentz or reluctance force generation principle. Delft 2 University of Technology WB2414-Mechatronic System Design 2013-2014 1 Contents •Electricity and electromagnetism •Electromagnetic actuators •Lorentz actuator •Variable reluctance actuator •Hybrid actuator Delft 3 University of Technology WB2414-Mechatronic System Design 2013-2014 Ohm’s law, the definition of impedance Current (I) V VIRI R + Voltage (V) Power in Watt (W): Impedance V 2 (Z) PIVIR2 - Source R Complex impedance Z(f) Vf() Vf() IfZf ()() If() Z()f Delft 4 University of Technology WB2414-Mechatronic System Design 2013-2014 2 Rules of Kirchhoff (network theory) 1. At any node of an electronic circuit all currents add to zero. • No charge storage in a node 2. Following any loop in an electronic circuit all voltages add to zero. III123 0 VVV123 0 Delft 5 University of Technology WB2414-Mechatronic System Design 2013-2014 Combination of Impedances Serial •Current is shared, •Voltage is divided Vt VV1 2 Z V VV s Z t12 II s tt IItt IZ IZ I Z I Z t1 t2Z Z tt12 I 12 Z12 Z t It Parallel VV V 1 •Voltage is shared Z tt t p III VV 11 •current is divided t12 tt ZZ12Z12Z Delft 6 University of Technology WB2414-Mechatronic System Design 2013-2014 3 A voltage divider V I i ZZ12 VZi2 VIZo2 Z12 Z Delft 7 University of Technology WB2414-Mechatronic System Design 2013-2014 One of the oldest electromotors The Elias motor of 1842 An actuator is an electromotor for limited movements Delft 8 University of Technology WB2414-Mechatronic System Design 2013-2014 4 Definition of terms in Maxwell’s equations Delft 9 University of Technology WB2414-Mechatronic System Design 2013-2014 Maxwell equations for magnetics Delft 10 University of Technology WB2414-Mechatronic System Design 2013-2014 5 Gauss Law, magnetic fieldlines are closed loops • A magnetic field has its origin in a dipole, North and South pole • Density of fieldlines is proportional to flux density Delft 11 University of Technology WB2414-Mechatronic System Design 2013-2014 Faraday’s law, a changing magnetic field causes an electric field over a wire E, I dl nˆ L dS S The line‐integral of the electrical field over a closed loop L equals the change of the flux through the open surface S bounded by the loop L. This is a voltage source (EMF), B where the current is driven in the direction of the electric field. Delft 12 University of Technology WB2414-Mechatronic System Design 2013-2014 6 Ampere’s law, Current through a wire gives a magnetic field Not relevant for + electromagnetic actuators B x The line‐integral of the magnetic field I over a closed loop L is proportional _ to the current through the surface S I Bx() 0 enclosed by the loop L 2 x Bx() I (plus a surface‐integral term related Hx() to electric fields) 0 2 x 7 0 410 [Vs/Am] in vacuum/air Delft 13 University of Technology WB2414-Mechatronic System Design 2013-2014 The magnetic field of more current carrying wires Current directed towards observer The total magnetic field is a linear vectorial combination of the magnetic field from each separate winding. Delft 14 University of Technology WB2414-Mechatronic System Design 2013-2014 7 Average magnetic field from a coil 0nI Bw,av hc Bw nI H w,av 0ch 0.3 1 Infinitely long coil: 1 Delft 15 University of Technology WB2414-Mechatronic System Design 2013-2014 Hopkinson’s law of magnetics vs Ohm’s law on electricity Magnetomotive force ( m ) vs Electromotive force = Voltage ()e V Magnetic flux (Φ) vs electric current (I) Magnetic reluctance ( ) vs electrical resistance (R) • The Magnetomotive force is the amount of windings times the current • The reluctance is proportional to the nI average length of the flux‐path and m inversely proportional to cross‐section _ A times the magnetic permeability. • The magnetic flux follows Hopkinson’s law of magnetics nI m w Delft 16 University of Technology WB2414-Mechatronic System Design 2013-2014 8 The magnetic flux generated inside a coil w m nI Bwav, AAcc A c ii o io 0.3 1 AAi0 o0 A i0 This approximates to: 0nI BHw,av= 0 w,av i nI H w,av i Righthand rule: North and Southpole Delft 17 University of Technology WB2414-Mechatronic System Design 2013-2014 Magnetic energy The energy equals the integral of B*H , which are connected by 0 Bxyz EHBVJ d d[] m V 0 B BBVt xyz HEBVJ d d [ ] m 0000 Applying some relations like VA y and Hopkinson’s law: V yyB xyzw dVAH d d , d , d AdB d wm 00AA 0 0 0 Results in : B xyz ww11 2 EHBVd dd d2 mmw 22 V 000 Delft 18 University of Technology WB2414-Mechatronic System Design 2013-2014 9 Adding a ferromagnetic material reduces the reluctance m nI y ferromagnetic yoke 0ryA AnI I m y0r yw I V y _ + V + y nI B y 0r n windings w Ayy _ Ay Bw nI H w 0r y With a large μr the flux increases Delft 19 University of Technology WB2414-Mechatronic System Design 2013-2014 Magnetisation curve of ferromagnetic material (μr > 1) Saturation Bw BHw0rw BHw0w In vacuum or air H w ()I With ferromagnetic core Saturation Delft 20 University of Technology WB2414-Mechatronic System Design 2013-2014 10 A permanent magnet is a ferromagnetic material with a high hysteresis B Area of w B interest r Hc HIw () Virgin curve Delft 21 University of Technology WB2414-Mechatronic System Design 2013-2014 PM materials act like a current carrying coil Without an external field the magnet Br creates its own field as if it was a coil in air Brm B m nIequivalent H c m 0r,m H Modern PM μr,m= 1 c H B B = 1 T nI H rm r is equivalent to m equivalent c m 800000 Amp turns 0 per meter length of magnet Delft 22 University of Technology WB2414-Mechatronic System Design 2013-2014 11 Use a permanent magnet to create a magnetic field in an airgap. Ferromagnetic (iron) yokecore/yoke Ay The magnetic flux in A l m Ag g y the magnet equals: S N m B rm m t0 t m g yg BA m rm t AA A m AA m0 y0r g0 1my mg AAym r gm Delft 23 University of Technology WB2414-Mechatronic System Design 2013-2014 Practical approximation BArm m AAmy mg Ferromagnetic (iron) yokecore/yoke 1 AAym r gm Ay Am y A l m m Ag g y In practice r Ay m BA S N rm m A 1 mg A m g gm But the flux in the air gap is smaller because magnetic flux is lost outside the air gap by “fringe/stray flux”. Air is “conductive” for magnetic fields. Delft 24 University of Technology WB2414-Mechatronic System Design 2013-2014 12 The fringe flux takes in practice between 25 to 75% of the total flux! 17 0.33 1los s 50 gggBA m 0.25 0.57 If Ag=Am and gm= mmAB r B r Bg AA Br AAggmg g g B 1 g 2 AAgm m m Delft 25 University of Technology WB2414-Mechatronic System Design 2013-2014 Flat magnets have less fringe flux and pole pieces are not efficient! Delft 26 University of Technology WB2414-Mechatronic System Design 2013-2014 13 Concentration of flux by iron parts Am >> Ag Bg (~0,7T) > Br (~0,4T) Much fringe flux ! Delft 27 University of Technology WB2414-Mechatronic System Design 2013-2014 Contents •Basic electromagnetism •Electromagnetic actuators •Lorentz actuator •Variable reluctance actuator •Hybrid actuator Delft 28 University of Technology WB2414-Mechatronic System Design 2013-2014 14 With the field in the airgap an actuator can be made with a current wire inserted in the gap Lorentz Force on a charged particle F(E+v×B)= q where •F is the vectorial force (in Newton) •E is the electric field (in Volts per meter) •B is the magnetic field (in Tesla) •q is the electric charge of the particle (in coulombs) •v is the instantaneous velocity of the particle (in meters per second) •and ×is the cross product. Delft 29 University of Technology WB2414-Mechatronic System Design 2013-2014 For the magnetic force on a current this relation leads to The Lorentz Force with qI FBI w sin α = the angle between the current and the magnetic field w= length of the wire in the field lw Corkscrew rule due to cross product Delft 30 University of Technology WB2414-Mechatronic System Design 2013-2014 15 Formulate the Lorentz force differently to avoid mistakes lw The Lorentz Force FBI w sin Can also be written as : (α = π/2) d x FI w dx For multiple windings this becomes Because d FnI w dw B w dx dx n = number of windings Φw =flux per winding Delft 31 University of Technology WB2414-Mechatronic System Design 2013-2014 A first example, a flat Lorentz actuator Permanent Magnets Ferromagnetic yoke F Magnetic Field Flat wound coil A Delft 32 University of Technology WB2414-Mechatronic System Design 2013-2014 16 Efficiency of a flat Lorentz actuator Permanent Magnets Ferromagnetic yoke F Magnetic Field Flat wound coil F A Detail A Delft 33 University of Technology WB2414-Mechatronic System Design 2013-2014 Importance of dΦw/dx, risk of non functional actuator Permanent Magnets Ferromagnetic yoke F=0 Magnetic Field Flat wound coil There should be motion between coil and permanent magnetic field.
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