The Basics of Permanent Magnet Motor Operations

Transcription

1 COURSE# - 1 The Basics of Permanent Magnet Motor Operations By George Holling

2 COURSE# - 2 Introduction Introduction The physics of permanent magnets Basic PM motor operating principles Basic motor parameters Motor construction

3 The Physics of Permament Magnets COURSE# - 3

4 COURSE# - 4 The Physics of Permament Magnets a typical magnetization curve for a PM magnet is shown here

5 COURSE# - 5 The Physics of Permament Magnets the outmost outline of the magnetization curve is for a single cycle of a fully magnetized magnet as the operating point of the magnetic circuit s permeance P line intersects with the demagnetization curve the magnet weakens the magnetization is not a single curve, but a family of curves

6 The Physics of Permament Magnets the permeance P of the magnetic circuit determines the operating point of the permanent magnet P = F m R g F : magnetic flux leakage m : magnet thickness parallel the direction of flux in inches R : magnetic reluctance factor - typically g : air gap thickness parallel the direction of flux in inches COURSE# - 6

7 COURSE# - 7 The Physics of Permament Magnets plotting the permeance into the magnetization curve yields the operating point of the magnetic circuit idealistic assumption no saturated steel µ r >>1 ignores the effects of demagnatization internal field from windings demagnetization curve magnet temperature ignores the effect of the magnet s temperature

8 COURSE# - 8 The Physics of Permament Magnets the magnet s flux changes with temperature reversible irreversible

9 COURSE# - 9 The Physics of Permament Magnets the magnet s linear, reversible flux change as a function of temperature is: B( T ) = B( T 0 )[1 β ( T T 0 )] B( T ) : air gap flux density at temperature T B( T 0 ) : air gap flux density at temperature T β : linear coefficient of demagnetization T : magnet temperature ( C) 0

10 COURSE# - 10 The Physics of Permament Magnets irreversible changes can occur in the magnet well below its Curie temperature

11 COURSE# - 11 The Physics of Permament Magnets the motor s conductors can cause irreversible damage to its magnet the flux generated by an inductor in the magnet is: H Z i = 3 P ( m + g) Z : i : P : m : g : total number of conductors the winding current the permeance of the magnetic circuit magnet thickness parallel the direction of flux in inches air gap thickness parallel the direction of flux in inches

12 COURSE# - 12 The Physics of Permament Magnets each PM motor therefore has a thermal current rating due to wire constraints an absolute peak current rating due to magnet constraints

13 COURSE# - 13 The Physics of Permament Magnets most PM motors use one of the following PM magnet materials Alnico: Aluminum Nickel Cobalt Fe 3 O 4 : Ceramic/Ferrite SmCo: Samarium Cobalt NeFeBo: Neodymium Iron Boron none is generally better or worse

14 COURSE# - 14 The Physics of Permament Magnets a comparison of different magnet materials

15 Basic PM motor operating principles COURSE# - 15

16 COURSE# - 16 Basic PM motor operating principles PM motors operate on the principle that a force is generated when current flows in an inductor that is placed in a magnetic field

17 COURSE# - 17 Basic PM motor operating principles force generated in a conductor in a magnetic field F m = i l Β F m i : l : Β : : mechanical force vector current flowing in the conductor length of the conductor (perpendicular to magnetic flux) magnetic flux vector

18 COURSE# - 18 Basic PM motor operating principles this force generates torque in a rotary motor T = B r l Z i T : B : r : l : Z : i : rotor torque magnetic flux average winding radius effective conductor length (stack length) number of conductors current flowing in the conductor

19 COURSE# - 19 Basic PM motor operating principles a conductor that moves in a magnetic field generates a voltage V l = v 0 y B x dz = B l v V : v y B x : : induced voltage velocity of inductor perpendicular to the magnetic field magnetic flux vector

20 COURSE# - 20 Basic PM motor operating principles a rotary motor produces the back-emf (Lenz s Law) V = B r l Z ω V : induced voltage B : magnetic flux vector r : radius l : effective conductor length (stack length) Z : number of condutors ω : angular velocity

21 COURSE# - 21 Basic PM motor operating principles inductor loop in a magnetic field

22 COURSE# - 22 Basic PM motor operating principles adding a mechanical commutator yields a brush PMDC motor adding two or more mechanically offset windings yields a PM DLDC or PM BLAC motor

23 Basic motor parameters COURSE# - 23

24 COURSE# - 24 Basic motor parameters the torque constant K t T = K t ω (N m) K t = B r l Z (N m / A)

25 COURSE# - 25 Basic motor parameters the back-emf (voltage) constant K e V = K ω E (volt) K E = B r l Z (volt/rad/sec)

26 COURSE# - 26 Basic motor parameters armature resistance R (Ohm) a armature inductance L a (Henry) electrical time constant τ e (sec) rotor inertia J r (Kg m 2 ) damping constant D m (N m / rad / sec) mechanical time constant τ m (sec) thermal resistance R Θ ( C / Watt) thermal capacitance C Θ (Joules / C) thermal time constant τ therm (sec)

27 COURSE# - 27 Basic motor parameters example of a typical speed/torque curve of a PM motor

28 COURSE# - 28 Basic motor parameters the Safe Continuous Operating Area SCOA the motor can safely be operated continuously anywhere in this region the Safe Intermittent Operating Area SIOA the motor may be operated in this region for short periods of time (typically < 1 min)

29 COURSE# - 29 Basic motor parameters the electrical equation for the PM DC machine is: V di = La + Ra I + KE dt ω

30 COURSE# - 30 Basic motor parameters the electrical equation for a single phase of the PM BLDC/BLAC machine with sinusoidal phase current is: V ( ϑ) = L a 2 π cos( π ϑ ) R a I 2 π ϑ sin( ) K E 2 π 2 π ϑ sin( ) dϑ d

31 COURSE# - 31 Basic motor parameters the power balance for the PM DC machine is: ω ω ω ω = + + = ) ( ) ( ) 2 ( ) 2 ( ) 2 ( L m L M E T T D D J dt d I R I L dt d P I K I R I L dt d P

32 COURSE# - 32 Basic motor parameters the power analysis reveals that: d dt L I ( 2 2 ) : magnetization energy R I 2 : electrical copper losses in the windings - > heat d dt J ( 2 ω ) 2 : mechanical energy ( D M + D L 2 ) ω : damping losses ( T m + T L ) ω : friction losses

33 COURSE# - 33 Basic motor parameters the power supplied to the load is: P mech = K ω I D ω - T E M m 2 ω

34 COURSE# - 34 Basic motor parameters the maximum continuous current allowed is: I max cont = Trise R( T T25 ) R rise C Θ (A) the maximum continuous torque allowed is: T max cont = K t Trise T25 ( Trise) R( T ) R rise C Θ (N m)

35 Motor construction COURSE# - 35

36 COURSE# - 36 Motor construction the field in the stator poles changes continuously, thus we must use laminated steel to reduce eddy current losses the backiron to support the PM flux is relatively constant and solid steel can be used

37 Motor construction COURSE# - 37

38 COURSE# - 38 Motor construction the eddy current losses are: P eddy 2 π = f 2 τ 6ρ 2 2 Β V P f : τ : Β P V : ρ : : electrical frequency of the motor (Hz) thickness of the lamonations (m) peak AC flux density (T) lamination volume volume electrical resistivity (ohm / m 3 )

39 COURSE# - 39 Motor construction motor steel choices

40 COURSE# - 40 Motor construction motor windings are generally copper wire with insulation (magnet wire) magnet wire comes in different grades temperature B, F, H, C insulation double, triple voltage rating

41 COURSE# - 41 Motor construction the resistance of the magnet wire changes with (the wire s) temperature R(T) = R(T 0 ) [1 + α (T - T 0 )] R(T T : α : 0 ): resistance at reference temperature, typically 25 C (ohm) winding temperature ( C) thermal coefficient for copper wire the value is / C