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Hysteresis loop sum of ferromagnetic materials

Inverse curve

Experimental purpose

1. Understand the magnetization law of ferromagnetic substances and compare the dynamic magnetization characteristics of two typical ferromagnetic substances.

2. Determine the basic magnetization curve of the sample and make the H curve.

3.Hc, Br, Bm and (Hm? Bm) and other parameters.

4. Draw the hysteresis loop of the sample.

Experimental principle

1. Initial magnetization curve and hysteresis loop

Ferromagnetic substance is a kind of material with special properties and wide applications. Iron, cobalt, nickel and their alloys, as well as iron-containing oxides (ferrites) are ferromagnetic substances. It is characterized by strong magnetization under the action of external magnetic field, so its permeability is high. Another feature is hysteresis, that is, ferromagnetic materials still maintain their magnetization state after the magnetization field stops. Fig. 2- 1 shows the relationship between magnetic induction b and magnetization h of ferromagnetic materials.

Figure 2- 1 Initial magnetization curve and hysteresis loop of ferromagnetic material 2-2 A set of hysteresis loops of the same ferromagnetic material

The original point o in the figure indicates that the ferromagnetic substance is in a magnetic neutral state before magnetization, that is, B=H=0. When the magnetic field H increases from zero, the magnetic induction intensity B rises slowly, as shown by the line segment Oa, and then B increases rapidly with H, as shown by ab, and then the growth of B slows down. When h increases to Hm, b reaches the saturation value Bm, and Oabs is called the initial magnetization curve. Fig. 2- 1 shows that when the magnetic field gradually decreases from Hm to zero, the magnetic induction intensity b does not return to the "o" point along the initial magnetization curve, but decreases along another new curve SR. Comparing the line segment OS and Sr, it can be seen that the decrease of H also decreases correspondingly, but the change of B lags behind the change of H, which is the so-called hysteresis phenomenon. The obvious feature of lag is that when H=0, b is not zero, but remains unchanged.

When the reverse magnetic field changes gradually from 0 to -Hc, the magnetic induction intensity B disappears, indicating that the reverse magnetic field must be applied to eliminate the remanence. HC is called coercivity, and its magnitude reflects the ability of ferromagnetic materials to maintain remanence, and the line segment RD is called demagnetization curve.

Fig. 2- 1 also shows that when the magnetic field changes in the order of hm → 0 →-HC →-hm → 0 → HC → hm, the corresponding magnetic induction intensity b changes along the closed curve SRDS'R'D'S, which is called hysteresis loop. Therefore, ferromagnetic materials will repeatedly magnetize → demagnetize → demagnetize → demagnetize along the hysteresis loop in an alternating magnetic field (such as the iron core in a transformer). In this process, extra energy is consumed and released from ferromagnetic materials in the form of heat, which is called hysteresis loss. It can be proved that the hysteresis loss is proportional to the area surrounded by the hysteresis loop.

2. Basic magnetization curve

It should be noted that when the ferromagnetic material with the initial state of H=B=0 is magnetized from weak to strong under the alternating magnetic field intensity, a cluster of hysteresis loops can be obtained. As shown in Figure 2-2, the hysteresis loops of vertices A 1, A2, A3, ... are the basic magnetization curves of ferromagnetic materials, from which the permeability can be approximately determined. Because b and h are nonlinear ferromagnetic materials. The relative permeability of ferromagnetic materials can be as high as thousands or even tens of thousands, which is one of the main reasons why they are widely used.

Fig. 2-3 Relationship Curve of Ferromagnetic Materials μ and H 2-4 Hysteresis Loop of Different Ferromagnetic Materials

It can be said that magnetization curve and hysteresis loop are the main basis for the classification and selection of ferromagnetic materials. Figure 2-4 shows two common typical hysteresis loops, among which soft magnetic materials are the main materials for manufacturing transformers, motors and AC magnets because of their long and narrow hysteresis loops, low coercivity and low remanence and hysteresis loss. However, hard magnetic materials have hysteresis linewidth, large coercivity and strong remanence, which can be used to manufacture permanent magnets.

3. Observe the principle of hysteresis loop with oscilloscope.

Figure 2-5 Principle Circuit Diagram

The principle circuit of observing hysteresis loop with oscilloscope is shown in Figure 2-5.

The sample to be tested is EI-type silicon steel sheet, on which magnetizing coil N and auxiliary coil N are evenly wound. Ac voltage u is applied to the magnetizing coil, and the sampling resistor R 1 is connected in series on the line. Add the voltage UH across R 1 to the x input of the oscilloscope (channel I of DC4322B oscilloscope). The secondary winding n is connected in series with a resistor R2 and a capacitor C to form a loop. The voltage UB across the capacitor C is applied to the Y input of the oscilloscope (channel II of the DC4322B oscilloscope). Let's explain why such a circuit can display and measure hysteresis loops.

(1) uh (x input) is proportional to the magnetic field strength H.

Let the average circumference of a rectangular sample be L, the number of turns of the magnetizing coil be N, and the magnetizing current be i 1 (note that this is the instantaneous value of AC current). According to Ampere's loop law, there are Hl=Ni 1, that is, I1= HL/N. And UH=R 1i 1, so it is available.

(2- 1)

Where R 1, l and n are constants, it can be seen that UH is directly proportional to h, indicating that the horizontal deflection of the electron beam on the oscilloscope screen is directly proportional to the magnetic field intensity in the sample.

⑵ UB(Y input) is directly proportional to magnetic induction intensity B under certain conditions.

Let the cross-sectional area of the sample be s, and according to the law of electromagnetic induction, the induced electromotive force in the secondary coil with n turns should be

(2-2)

If the current in the secondary circuit is i2 and the charge on the capacitor C is Q, there should be

(2-3)

In the above formula, it has been considered that the number of turns n of the secondary winding is small, so the self-induced electromotive force can be ignored. When selecting the line parameters, R2 and C are deliberately chosen to be large enough so that the voltage drop UB=q/C on the capacitor C is negligible compared with the voltage drop R2i2 on the resistor. Then equation (2-3) can be approximately rewritten as

(2-4)

Substitute this relationship into equation (2-4)

(2-5)

Comparing the above formula with formula (2-2), regardless of its negative sign (in alternating current, the negative sign is equivalent to the phase difference of π), it should be.

When the two sides of the equation integrate time, because B and UB alternate, the integration constant is 0. After completion

(2-6)

So far, it can be seen that the light spot of oscilloscope describes a complete hysteresis loop within a period of magnetization current change. After that, this process is repeated every cycle to produce a stable hysteresis loop pattern on the oscilloscope screen.

If UH and UB are added to the signal input of the tester, the saturation magnetic induction intensity Bm, remanence Br, coercivity HC, hysteresis loss (BH) and permeability of the sample can be measured.

Figure 2-6 Circuit schematic diagram in actual measurement

The circuit schematic diagram of the actual measurement is shown in Figure 2-6. In order to make the voltage drop UH across R 1 proportional to the instantaneous value of current i 1, R 1 must be a resistor with no inductance or minimal inductance. Secondly, for the sake of safe operation and convenient adjustment, isolation step-down transformer B is used in the line to avoid direct connection between subsequent circuit components and 220 V commercial power. The voltage regulating transformer is used to adjust the input voltage u to control the magnetizing current i 1.

Laboratory instrument

MHC hysteresis loop tester, hysteresis loop tester and oscilloscope.

Experimental contents and steps

1. Circuit connection: According to the circuit diagram given in Figure 2-9, select the sample 1 connection circuit, set R1= 2.5Ω, and "U Select" is 0. UH and UB (that is, U 1 and U2) are respectively connected to the X input and Y input of the oscilloscope, and "Jack ⊥" is the male * * * terminal.

2. sample demagnetization: turn on the power supply of the tester to demagnetize the sample, that is, turn the "U Select" knob clockwise to increase u from 0 to 3V, and then turn the knob counterclockwise to reduce u from the maximum value to 0, in order to eliminate remanence and ensure that the sample is in a magnetic neutral state, that is, B=H=0, as shown in Figure 2-7.

3. Observe the hysteresis loop: turn on the power supply of the oscilloscope, make the light spot in the center of the coordinate grid, make U= 1.5V, and adjust the sensitivity of the X axis and Y axis of the oscilloscope respectively, so that the hysteresis loop with appropriate graphic size appears on the display screen (if a small braided loop appears at the top of the graphic, as shown in Figure 2-8, the excitation voltage U can be reduced to eliminate).

Figure 2-7 schematic diagram of demagnetization Figure 2-8 Distortion caused by factors such as the phase difference between uh and b.

4. Observe the basic magnetization curve, demagnetize the sample according to step 2, and gradually increase the excitation voltage from U=0, and a cluster of hysteresis loops will be obtained on the display screen. The connecting line of the vertices of these hysteresis loops is the basic magnetization curve of the sample.

5. Observe and compare the magnetization characteristics of sample 1 and sample 2; Determine the soft magnetism and hard magnetism of the two samples. (U= 1.5 V or U=2.0 V, r 1 = 2.5ω)

6. Drawing H curve: Read the instructions of the tester carefully (see Resources) and connect the tester and the tester. Turn on the power supply, demagnetize the sample, and when U=0.5, 1.0, measure the Hm and Bm values of 10 group ... 3.0V in turn, and make an H curve.

7. Let U= 1.5V, r 1 = 2.5ω, and determine the parameters such as Bm, Br, Hc and [BH] of the sample 1.

8. Take H in step 7 and its corresponding B value, and draw a B-H curve with drawing paper (how to get the number? How many sets of data are taken? Think for yourself) and estimate the area around the curve.

data processing

Table 2- 1 Basic magnetization curve and H curve

U (v) hm×103a /m BM×10 Tesla =B/H Henry/m.

0.5

1.0

1.2

1.5

1.8

2.0

2.2

2.5

2.8