Ferromagnetic material

Characteristics of ferromagnetic materials

(1) Non-linear

(2) Saturation characteristics

curve

(1) Initial magnetization curve

$$B=f(H)$$

$THE\sim a$
$a\sim b$
$b\sim c$
$c\sim d$

$${\mu }_{FE}=f\left(H\right)$$

Magnetoresistance increases with increasing saturation

Paint point/saturation point: the point where the magnetization curve starts to bend. See point b in the picture.

(2) Hysteresis loop

Residual magnetic flux density/remanent magnetism:

Coercivity:

Hysteresis:

Hysteresis curve:

(3) Basic magnetization curve

Ferromagnetic material

According to the shape of the hysteresis loop

(1) Soft magnetic materials

Definition: narrow hysteresis loop, remanence $B_r$And coercivity $H_e$All small materials.

Common soft magnetic materials: electrical silicon steel sheet, cast iron, cast steel

Features: High magnetic permeability.

(2) Hard magnetic materials

Definition: the hysteresis loop is wider, the remanence $B_r$And coercivity $H_e$All big materials.

Common materials: aluminum nickel cobalt, ferrite, rare earth cobalt

Features: Remanence $B_r$Big.

Core loss

(1) Hysteresis loss [ $p_h$】

$$p_h=fV\oint HdB$$

• $f$ : the frequency of the alternating magnetic field.
• $V$ : The volume of the core.
• $\oint HdB$ : area of ​​hysteresis loop

$$p_h=C_{h}f{B}_m^{n}V$$

$C_h$: Hysteresis loss coefficient.

• The size depends on the nature of the material.

(2) Eddy current loss【$p_e$】

• $C_e$: Eddy current loss coefficient.

Depends on the resistivity of the material.

• $\Delta$ : the thickness of the steel sheet.

In order to reduce eddy current loss, the cores of motors and transformers are made of thin silicon steel sheets with higher silicon content.

(3) Core loss [ $p_{FE}$】

The sum of hysteresis loss and eddy current loss. Both the hysteresis loss and eddy current loss in the iron core will consume active power and heat the iron core.
$$p_{FE}=p_h+p_e=(C_{h}f{B}_m^n+C_e{\Delta }^2{f}^2{B.}_m^2)V$$

For general electrical steel sheets, the magnetic flux density at the normal operating point is $1T<B_m<.\; 1..\; 8T$ time, may be approximately
$$P_{FE}\approx C_{F\; ofa}{f}^{1.3}{B}_m^{2}G$$

• $G_{FE}$: Loss factor of core
• $G$ : core weight