PHENOMENOLOGY OF MAGNETIC LOSSES Any variation of the flux density - - PowerPoint PPT Presentation

▶
phenomenology of magnetic losses any variation of the
SMART_READER_LITE
LIVE PREVIEW

PHENOMENOLOGY OF MAGNETIC LOSSES Any variation of the flux density - - PowerPoint PPT Presentation

Jun 21, 2023 359 likes •496 views

PHENOMENOLOGY OF MAGNETIC LOSSES Any variation of the flux density in a magnetic material is associated with dissipation of energy. The main physical mechanisms for dissipation are: 1) Eddy currents and the related Joule effect, associated with

slide-1
SLIDE 1

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

1

PHENOMENOLOGY OF MAGNETIC LOSSES Any variation of the flux density in a magnetic material is associated with dissipation of energy. The main physical mechanisms for dissipation are: 1) Eddy currents and the related Joule effect, associated with the scattering of moving charges with phonons and various lattice defects. The Joule effect is dominant in conducting and semiconducting materials. 2) Spin damping, related to the transfer of energy from the precessing spins to the lattice, either directly

  • r via magnon-phonon interaction. This is the favorite mechanism in insulating

magnets.

slide-2
SLIDE 2

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

2

Magnetic losses are conveniently defined under given time periodic law for the rate of change of the magnetization. Typically, one has to deal with either sinusoidal or triangular B(t) waveform. The viscous character of the magnetization process makes attaining a given peak polarization under defined B(t) law increasingly difficult with increasing the magnetizing frequency. There is an obvious practical appeal to the study of magnetic losses, because there is a stringent need for ther prediction in most electrical/electronic

  • applications. Besides the unnecessary waste of energy, the fast increase of the

power loss with the magnetizing frequency (somewhat ∝ f2) can make overheating the main obstacle to high-frequency applications (P = cvdT/dt). For sample of volume V subjected to periodic excitation at the frequency f = 1/T, we can express the eddy-current energy loss per unit volume on a period as

dt t r V r d W

T V

∫ ∫

=

2 3

) , (

σ

j

The space-time behavior of the current density j(r, t) is hopelessly complicated. We need to focus on the general features of the loss behavior, to be treated from a statistical viewpoint.

slide-3
SLIDE 3

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

3

  • 150
  • 100
  • 50

50 100 150

  • 1.5
  • 1.0
  • 0.5

0.0 0.5 1.0 1.5 0.25 Hz 150 Hz 400 Hz Grain-oriented Fe-(3wt%)Si d = 0.30 mm Jp = 1.7 T

J (T) Hm (A/m)

100 200 300 400 100 200 300 400 500 600

W exc W cl W h

Grain-oriented Fe-(3wt%)Si d = 0.30 mm Jp = 1.7 T

Energy loss (J/m

3)

Frequency (Hz)

dJ H dJ H dH H dB H W

  • ∫

∫ ∫ ∫

= + = = µ

W = Whyst + Wcl + Wexc

2 / 1 exc cl p p

) ( ) , ( f k f k J W f J W

hyst

+ + =

Q HdX dU

δ + =

H and X conjugate work variables Isothermal cycle:

=

∫ dU ∫ ∫

− =

Q HdX

δ

slide-4
SLIDE 4

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

4

Amorphous ribbon Soft ferrite ring

slide-5
SLIDE 5

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

5

Soft ferrite ring Nanocrystalline ribbon ∼ 20 kW/kg

slide-6
SLIDE 6

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

6

100 200 300 400 500 50 100 Whyst Wcl Wexc

nonoriented Fe-Si Jp= 1.5 T, d = 0.35 mm

W (mJ/kg) f (Hz)

5 10 15 20 25 20 40 60 80

nonoriented Fe-Si Jp= 1.5 T, d = 0.35 mm

Wexc Whyst

(W - W cl) (mJ/kg) f

1/2 (Hz)

( )

2 / 1 2 / 3 p

  • 2

p 2 2 h

76 . 8 6 / f J GSV f J d W W

σ σ π + + =

Excess energy loss under generic polarization rate dJ/dt

∫ ∫

= =

T T

t d t J GSV dt t p W

2 / 3

  • exc

exc

| ) ( | ) ( 

σ

Sinusoidal induction

slide-7
SLIDE 7

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

7

The hysteresis (quasi-static) energy loss cannot be generally predicted from knowledge of the structural properties and the intrinsic magnetic parameters. At low inductions, however, magnetic hysteresis can usually be described by the analytical Rayleigh law.

  • 300
  • 200
  • 100

100 200 300

  • 0,06
  • 0,04
  • 0,02

0,00 0,02 0,04 0,06

(Hp, Jp) Pure Ni foil J (T)

H (A/m)

) ( 2 ) ( ) (

2 2

H H b H bH a H J

p p

− + =

2 p p p

bH aH J

+ =

a ≡ initial permeability, resulting from domain wall bending and moment rotations

slide-8
SLIDE 8

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

8

The dynamic loss can be formally assessed in a linear (or, in practice, quasi- linear) material, with defined DC permeability. Dissipative phenomena bring about a time delay of the B(t) waveform with respect to the H(t) waveform and the resulting hysteresis loop takes an elliptical shape

t cos H ) t ( H

p

ω =

( )

t B t B t B t B

p p p

ω δ ω δ δ ω

sin sin cos cos cos ) (

+ = = − =

The associated energy loss (area

  • f the elliptical loops) is

δ π

sin ) ( ) (

p p T

B H dt dt t dB t H W

= ⋅ = ∫

  • 4
  • 3
  • 2
  • 1

1 2 3 4

  • 0.010
  • 0.005

0.000 0.005 0.010

Co67Fe4B14.5Si14.5 Jp = 10 mT

Bm 20Hz B 20kHz B 200kHz B 500kHz B 1MHz B 2MHz B 5MHz

J (T) H (A/m)

slide-9
SLIDE 9

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

9

Rs Ls is Rsis jωLsis δ Rp Lp

When dealing with a linear system we can attack in a simple way the phenomenology of energy loss and the related concepts of complex permeability, quality factor, and equivalent L - R circuit

slide-10
SLIDE 10

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

10

2 / 1 exc cl p p

) ( ) , ( f k f k J W f J W

hyst

+ + =

The concept of loss separation can be given a solid physical justification in terms of characteristic space-time scales of the magnetization process

(G. Bertotti, Hysteresis in Magnetism). It is valid in both conducting and non-

conducting magnetic materials.

W = Whyst + Wcl + Wexc

Wcl is easily calculated in the simple case of a thin lamination (width >> thickness) under time-varying induction (e. g., B(t) = Bp sin ωt) uniform across the sheet cross-section.

B(t)

y x z

slide-11
SLIDE 11

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

11

The full approach to the classical eddy current losses, valid for whatever lamination thickness and material conductivity is based on the diffusion equation for the internal magnetic field.

dt dB E

− = × ∇

j H

− = × ∇

dt dH dy E

µ − = ∂

Ha(t)

y x z

σ

E j dy H

− = − = ∂

dt dH dy H

σ µ = ∂

2 2

and the boundary conditions

at / 2 / for ) ( ) (

a

= = ∂ ∂ ± = =

y y H d y t H t H

H (t) = Ha(t)-Heddy(t)

slide-12
SLIDE 12

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

12

The concept of magnetic losses and hysteresis are associated with that of lag in time of induction with respect to the field. We can therefore talk aboy a time constant (or a distribution of time constants). The simplest case of relaxation is one where the change of the magnetization with time is proportional to its deviation from the equilibrium value

)) ( ( / t M M k dt dM

− =

/ )

1 ( ) ( M e t M

t τ

−

− =

with τ = 1/k If relaxation is due to eddy currents, the time constant will depend on conductivity, permeability, and sample size.

1 2 3 4 5 6 0.0 0.2 0.4 0.6 0.8 1.0

M / M0 t / τ

slide-13
SLIDE 13

ISTITUTO NAZIONALE DI RICERCA METROLOGICA ISTITUTO NAZIONALE DI RICERCA METROLOGICA

European School on Magnetism ESM2013 European School on Magnetism ESM2013

13

Bibliography

  • G. Bertotti, Hysteresis in Magnetism, Academic Press, 1988.
  • G. Bertotti, IEEE Trans. Magn. 24 (1988) 621.
  • G. Bertotti, J. Appl. Phys. 57 (1985) 2110.
  • J.B. Goodenough, IEEE Trans. Magn. 38 (2002) 3398.
  • F. Fiorillo, C. Appino, M. Pasquale, in The Science of Hysteresis (G. Bertotti and I.

Mayergoyz, eds., Academic Press, 2006), vol III, p.1.

  • R.H. Pry and C.P. Bean, J. Appl. Phys. 29 (1958) 532.
  • H.J. Williams, W. Shockley, C. Kittel, Phys. Rev. 80 (1950) 1090.
  • B.D. Cullity and C.D. Graham, Introduction to magnetic materials, Wiley, 2011.
  • F. Fiorillo and A. Novikov, IEEE Trans. Magn. 26 (1990) 2904.
  • G. Bertotti and I. Mayergoyz, eds., The Science of Hysteresis, Academic Press,

2006.