National Taiwan University

Hysteresis Curves章意昇 B01504120/化工一Group Number: 24Professor: 趙治宇 Teacher Assistant: 駱冠宇

201322 April

I. Purpose:

1. To understand more about Hysteresis Curve.

II. AbstractHysteresis refers to systems that have memory, where the effects of the current input (or stimulus) to the system are experienced with a certain delay in time. Such a system may exhibit path dependence, or "rate-independent memory" (Mielke & Roubicek 2003). Hysteresis phenomena occur in magnetic materials, ferromagnetic materials and ferroelectric materials, as well as in the elastic, electric, and magnetic behavior of materials, in which a lag occurs between the application and the removal of a force or field and its subsequent effect. Electric hysteresis occurs when applying a varying electric field, and elastic hysteresis occurs in response to a varying force. The term "hysteresis" is sometimes used in other fields, such as economics or biology, where it describes a memory, or lagging effect.

III. Principle

A great deal of information can be learned about the magnetic properties of a material by studying its hysteresis loop. A hysteresis loop shows the relationship between the induced magnetic flux density (B) and the magnetizing force (H). It is often referred to as the B-H loop. An example hysteresis loop is shown below.

The loop is generated by measuring the magnetic flux of a ferromagnetic material while the magnetizing force is changed. A ferromagnetic material that has never been previously magnetized or has been thoroughly demagnetized will follow the dashed line as H is increased. As the line demonstrates, the greater the amount of current applied (H+), the stronger the magnetic field in the component (B+). At point "a" almost all of the magnetic domains are aligned and an additional increase in the magnetizing force will produce very little increase in magnetic flux. The material has reached the point of magnetic saturation. When H is reduced to zero, the curve will move from point "a" to point "b." At this point, it can be seen that some magnetic flux remains in the material even though the magnetizing force is zero. This is referred to as the point of retentivity on the graph and indicates the remanence or level of residual magnetism in the material. (Some of the magnetic domains remain aligned but some have lost their alignment.) As the magnetizing force is reversed, the curve moves to point "c", where the flux has been reduced to zero. This is called the point of coercivity on the curve. (The reversed magnetizing force has flipped enough of the domains so that the net flux within the material is zero.) The force required to remove the residual magnetism from the material is called the coercive force or coercivity of the material.

As the magnetizing force is increased in the negative direction, the material will again become magnetically saturated but in the opposite direction (point "d"). Reducing H to zero brings the curve to point "e." It will have a level of residual magnetism equal to that achieved in the other direction. Increasing H back in the positive direction will return B to zero. Notice that the curve did not return to the origin of the graph because some force is required to remove the residual magnetism. The curve will take a different path from point "f" back to the saturation point where it with complete the loop.

From the hysteresis loop, a number of primary magnetic properties of a material can be determined.

1. Retentivity - A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words, it is a material's ability to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. (The value of B at point b on the hysteresis curve.)

2. Residual Magnetism or Residual Flux - the magnetic flux density that remains in a material when the magnetizing force is zero. Note that residual magnetism and retentivity are the same when the material has been magnetized to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetizing force did not reach the saturation level.

3. Coercive Force - The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero. (The value of H at point c on the hysteresis curve.)

4. Permeability, m - A property of a material that describes the ease with which a magnetic flux is established in the component.

5. Reluctance - Is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.

The shape of the hysteresis loop tells a great deal about the material being magnetized. The hysteresis curves of two different materials are shown in the graph.

Relative to other materials, a material with a wider hysteresis loop has:

Lower Permeability Higher Retentivity Higher Coercivity Higher Reluctance Higher Residual Magnetism

Relative to other materials, a material with the narrower hysteresis loop has:

Higher Permeability Lower Retentivity Lower Coercivity Lower Reluctance Lower Residual Magnetism.

In magnetic particle testing, the level of residual magnetism is important. Residual magnetic fields are affected by the permeability, which can be related to the carbon content and alloying of the material. A component with high carbon content will have low permeability and will retain more magnetic flux than a material with low carbon content.

Magnetic Field Orientation and Flaw Detectability

To properly inspect a component for cracks or other defects, it is important to understand that the orientation between the magnetic lines of force and the flaw is very important. There are two general types of magnetic fields that can be established within a component.

A longitudinal magnetic field has magnetic lines of force that run parallel to the long axis of the part. Longitudinal magnetization of a component can be accomplished using the longitudinal field set up by a coil or solenoid. It can also be accomplished using permanent magnets or electromagnets.A circular magnetic field has magnetic lines of force that run circumferentially around the perimeter of a part. A circular magnetic field is induced in an article by either passing current through the component or by passing current through a conductor surrounded by the component.

The type of magnetic field established is determined by the method used to magnetize the specimen. Being able to magnetize the part in two directions is important because the best detection of defects occurs when the lines of magnetic force are established at right angles to the longest dimension of the defect. This orientation creates the largest disruption of the magnetic field within the part and the greatest flux leakage at the surface of the part. As can be seen in the image below, if the magnetic field is parallel to the defect, the field will see little disruption and no flux leakage field will be produced.

An orientation of 45 to 90 degrees between the magnetic field and the defect is necessary to form an indication. Since defects may occur in various and unknown directions, each part is normally magnetized in two directions at right angles to each other. If the component below is considered, it is known that passing current through the part from end to end will establish a circular magnetic field that will be 90 degrees to the direction of the current. Therefore, defects that have a significant dimension in the direction of the current (longitudinal defects) should be detectable. Alternately, transverse-type defects will not be detectable with circular magnetization.

IV. Experiment Procedure

The proceeds of the deflection angle for tan and current graphics, have hysteresis curve.θ

The same, and saturated, reduce the current of 0.2 amps each, record the yaw angle, until the current is zero, the 0N commutator switch position, and then continue to increase the

current of 0.2 amps each, record the yaw angle, until saturation, a hysteresis loop to complete the steps.

Up to saturation, then the same in order to reduce the current of 0.2 amps each, record the yaw angle. Until the current is zero, the commutator switch ON position to another

ON Department, to change the current direction, and then continue to increase the current of 0.2 amps each, record the yaw angle, until saturated.

Be adjusted once every 0.2 amperes current, and record the angle of deflection magnetometer.

Will be transferred to 0N commutator position, and open the DC power supply, adjust the current so that no more than 2 amps, so both sides of the solenoid to adjust the location

of the pointer to magnetometer to stay fixed in place, that the two magnetic field generated in the Statistics Department entirely offset.

Take two identical solenoids home shelves, so both the same distance from the magnetometer, and its vertical pointer. Figure 4, connected to the DC power supply,

current account and the commutator, pay attention to the two solenoid current direction opposite to be offset by both the magnetic field.

V. Data

Teta1 Tan(teta1) teta2 Tan(teta2)0 0 0 0

200.36397023

4 150.26794919

2

350.70020753

8 300.57735026

945 1 47 1.07236871

54 1.37638192 581.60033452

9

601.73205080

8 662.24603677

4

652.14450692

1 733.27085261

8

702.74747741

9 774.33147587

4

723.07768353

7 784.70463010

9

774.33147587

4 795.14455401

6

764.01078093

4 80 5.67128182

784.70463010

9 81.56.69115623

8

795.14455401

6 838.14434642

880 5.67128182 85 11.4300523

80 5.67128182 8614.3006662

6

816.31375151

5 8614.3006662

6

827.11536972

2 8614.3006662

6

816.31375151

5 8614.3006662

6

80 5.67128182 8614.3006662

6

80 5.67128182 8614.3006662

6

80 5.67128182 84.510.3853970

8

80 5.67128182 849.51436445

4

784.70463010

9 849.51436445

4

764.01078093

4 827.11536972

2

753.73205080

8 80 5.67128182

753.73205080

8 795.14455401

6

702.74747741

9 774.33147587

4

702.74747741

9 753.73205080

8

652.14450692

1 723.07768353

7

601.73205080

8 702.74747741

9

501.19175359

3 642.05030384

2

400.83909963

1 521.27994163

2

200.36397023

4 330.64940759

3

-35

-0.70020753

8 100.17632698

1

-65

-2.14450692

1 -12

-0.21255656

2

-75

-3.73205080

8 -35

-0.70020753

8

-80-

5.67128182 -47-

1.07236871

-82

-7.11536972

2 -55.5

-1.45500902

9

-83

-8.14434642

8 -62

-1.88072646

5

-85-

11.4300523 -70

-2.74747741

9

-85-

11.4300523 -70.5

-2.82391288

6

-86

-14.3006662

6 -71

-2.90421087

8

-89

-57.2899616

3 -72

-3.07768353

7-89 - -73 -

57.28996163

3.270852618

-89

-57.2899616

3 -74

-3.48741444

4

-89

-57.2899616

3 -76

-4.01078093

4

-89

-57.2899616

3 -77

-4.33147587

4

-88

-28.6362532

8 -77

-4.33147587

4

-88

-28.6362532

8 -78

-4.70463010

9

-88

-28.6362532

8 -77

-4.33147587

4

-87

-19.0811366

9 -77

-4.33147587

4

-86

-14.3006662

6 -77

-4.33147587

4

-86

-14.3006662

6 -76

-4.01078093

4

-86

-14.3006662

6 -76

-4.01078093

4

-86

-14.3006662

6 -75

-3.73205080

8

-85-

11.4300523 -74

-3.48741444

4

-85-

11.4300523 -73

-3.27085261

8

-85-

11.4300523 -71

-2.90421087

8

-85-

11.4300523 -70

-2.74747741

9-83 -

8.14434642-68 -

2.47508685

8 3

-80-

5.67128182 -65

-2.14450692

1

-76

-4.01078093

4 -60.5

-1.76749401

6

-70

-2.74747741

9 -55

-1.42814800

7

-55

-1.42814800

7 -44

-0.96568877

5

-30

-0.57735026

9 -29

-0.55430905

1

400.83909963

1 -3

-0.05240777

9

400.83909963

1 200.36397023

4

501.19175359

3 410.86928673

8

551.42814800

7 56.51.51083519

4

621.88072646

5 662.24603677

4

652.14450692

1 702.74747741

9

682.47508685

3 753.73205080

8

702.74747741

9 784.70463010

9

723.07768353

7 795.14455401

6

743.48741444

4 816.31375151

5

764.01078093

4 827.11536972

2

764.01078093

4 85 11.4300523

784.70463010

9 85 11.4300523

784.70463010

9 85 11.430052380 5.67128182 85 11.4300523

-4 -3 -2 -1 0 1 2 3 4

-100-80-60-40-20

020406080

100

Experiment 1

Series2

I(A)

teta

-4 -3 -2 -1 0 1 2 3 4

-70

-60

-50

-40

-30

-20

-10

0

10

20

Experiment 1

Series2

I(A)

TA

N(t

eta)

-4 -3 -2 -1 0 1 2 3 4

-100-80-60-40-20

020406080

100

Experiment 2

Series2

I(A)

teta

-4 -3 -2 -1 0 1 2 3 4

-10

-5

0

5

10

15

20

Experiment 2

Series2

I(A)

TA

N(t

eta)

VI. Error AnalysisAs you can see above, after we try to draw the graph the graph doesn’t look like a hysteresis graph. Only graph 2 teta vs I that look like a hysteresis curve. The error of this may graph may be caused by this:

1. To AC magnetic coil for the iron bar to when one should be careful not to place too long, otherwise the heat as the relationship between the electronic movement, although to magnetic entirely; but due to thermal expansion's sake, make iron bars can not get stuck in the circle out. The power required to pay close attention to avoid damage to equipment.

2. Slow increase in current increases when the note not to be excessive, or the draw of the curve may not be smooth, resulting in considerable error. 2 See discussion principle.

3. Observation of hard and soft iron bar iron bar hysteresis curves. Hard iron bars of the curve can be found in large, soft iron bar smaller narrow curve. Namely the hard iron bars were more obvious hysteresis, this material is suitable for a more suitable for moving coil loudspeaker, and the header part of the permanent magnet. The hysteresis loops of soft iron bar less obvious, less energy consumption curve of the small size, said. Soft iron in the transformers, electromagnets, magnetic tapes and computer disks very useful.

4. Use of the experimental principle, in order to make an object to the magnetic (demagnetize), for example: tape heads, need to make it through a series of magnetic field has been to reduce the hysteresis curve. Shock magnetic field by the AC current through a coil to generate. Coil start close to the object to be magnetized, and then slowly go away from the magnetic objective can be achieved.

VII. Problems

1. 磁性物質為什麼會有磁性？Why magnetic material has magnetic power? Magnetic and electronic material as long as the movement is related to a motion of electrons in atoms to establish the atomic current, and the formation of magnetic dipole moment and magnetic field. Atomic angular momentum quantum mechanics is the quantum of the (quantized), that is only an integer multiple of the basic unit appears: L = nh = 0, h, 2h ... ..., to L = h on behalf of the orbit angular momentum L, spin and revolution The relationship between = eL/2m = eh/4m. μ This amount is called Bohr magnetic element (Bohr magneton), its value is 9.27×10-24Am2. In most of the material, each atom of the angular momentum in a different direction, so then all the atomic magnetic dipole moment to the average, be equal to zero, but there is a magnetic source.

According to quantum mechanics, each electron has a definite spin angular momentum (spin angular momentum). We can e around an imaginary axis within the spin, it generates an internal current of change. Because the spin magnetic dipole moment born just mean Bohr magnetic element. In many atoms and ions, the spin angular momentum are reversed in pairs, the result would be no net magnetic dipole moment. Sometimes one or two electronic to pairs, this time change was a permanent atomic magnetic dipole. The presence or absence of this magnetic dipole, the number and intensity of the effects and cause anti-magnetic, paramagnetic, ferromagnetic material.

2. 在實驗過程中，若電流一下加的太大．有何影響？原因為何？In the experiment, if the current look too much added. What impact? Why not?Current size of the control of the external magnetic field strength, if the current is too much at once added, the samples were magnetized in the magnetic field change increased at this time if the current book value in the

back, then the measured magnetic field will be slightly larger than actual value, because the induced magnetic field 1, but bigger, and not the original magnetization curve along the back, resulting in experimental error. Therefore, experiments should be carefully and slowly increase the current.

3. 在實驗過程中，當每增大 0.2安培電流所停留的時間相差較大時．會有何現象產生？原因為何？In the experiment, every increase of 0.2 amps to stay current by the time difference is large. What will the phenomenon? Why not?

In ferromagnetic materials, each atom is because one or two electrons and a magnetic moment since; the size of 1mm size of these magnetic moments of the magnetic line field (magnetic domain) completely parallel. In a magnetic field applied parallel to the magnetic field domain will increase, while the other magnetic field will be narrowed; when larger 0.2 amps per stay by the difference in time increases, allowing an external magnetic field and magnetic field the sample will yield more complete heat balance; reverse magnetic field of the sample because of time better than a long field with the same tendency to. Induction of the magnetic field caused by large hysteresis curve outward expansion of the experiment more accurate.

4. 鐵磁性材料中有分軟磁性材料和硬磁性材料，他們分別在生活當眾有哪些應用？Ferromagnetic material in a hand of soft magnetic materials and hard magnetic materials, they were living in public in what application?

Soft Ferromagnets

The general range of applications for soft magnets is clear from the table above. It is also clear that we want the hystereses loop as "flat" as possible, and as steeply inclined as possible. Moreover, quite generally we would like the material to have a high resistivity.

The requirements concerning the maximum frequency with which one can run through the hystereses loop are more specialized: Most power applications do not need high frequencies, but the microwave community would love to have more magnetic materials still "working" at 100 Ghz or so.

Besides trial and error, what are the guiding principles for designing soft magnetic materials? There are simple basic answers, but it is not so simple to turn these insights into products:

Essentially, remanence is directly related to the ease of movement of domain walls. If they can move easily in response to magnetic fields, remanence (and coercivity) will be low and the hystereses loop is flat.

The essential quantities to control, partially mentioned before, therefore are:The density of domain walls. The fewer domain walls you have to move around, the easier it is going to be.The density of defects able to "pin" domain walls. These are not just the classical lattice defects encountered in neat single- or polycrystalline material, but also the cavities, inclusion of second phases, scratches,

microcracks or whatever in real sintered or hot-pressed material mixtures.The general anisotropy of the magnetic properties; including the anisotropy of the magnetization ("easy" and "hard" direction, of the magnetostriction, or even induced the shape of magnetic particles embedded in a non-magnetic matrix (we must expect, e.g. that elongated particles behave differently if their major axis is in the direction of the field or perpendicular to it). Large anisotropies generally tend to induce large obstacles to domain movement.

Hard FerromagnetCATEGORY #1Applications that make use of the tractive and/or repelling force of the magnet, i.e., the attraction between a magnet and a soft magnetic material, such as a piece of iron or steel, or the attraction or repulsion between two magnets, is used to do mechanical work. The following applications are in this category:

Magnetic separators, magnetic holding devices, such as magnetic latches. Magnetic torque drives Magnetic bearing devices

CATEGORY #2Applications that make use of the magnetic field of the magnet to convert mechanical energy to electrical energy. Some of these applications are:

Magnetos Generators and alternators Eddy current brakes (used widely for watt-hour meter damping). (This application could

be listed under electrical to mechanical energy conversion; but as mechanical energy is used to create the eddy currents, it will be discussed with this group.)

CATEGORY #3Applications that make use of the magnetic field of the magnet to convert electrical energy to mechanical energy. Some of these applications are:

Motors Meters Loudspeakers Relays Actuators, linear, and rotational

CATEGORY #4Applications that use the magnetic field of the magnet to direct, shape and control electron or ion beams. Some of these applications follow:

Magnetic focused cathode-ray tubes Traveling Wave Tubes Magnetrons, BWO’s, Klystrons Ion Pumps Cyclotrons