Addition of external magnetic fluxes with a permanent magnet. Increasing the strength of the magnet. Experiments with neodymium magnets

Switching magnetic flux systems are based on magnetic flux switching relative to detachable coils.
The essence of the CE devices considered on the Internet is that there is a magnet for which we pay once, and there is a magnetic field of the magnet for which no one pays money.
The question is that it is necessary to create such conditions in transformers with switching magnetic fluxes under which the magnet field becomes controllable and we direct it. interrupt. redirect like this. so that the energy for switching is minimal or cost-free

In order to consider options for these systems, I decided to study and bring my thoughts on fresh ideas.

To begin with, I wanted to look at what magnetic properties a ferromagnetic material has, etc. Magnetic materials have a coercive force.

Accordingly, the coercive force obtained from the cycle, or from the cycle, is considered. are designated respectively

The coercive force is always greater. This fact is explained by the fact that in the right half-plane of the hysteresis graph, the value is greater than by the value:

In the left half-plane, on the contrary, it is less than , by the value . Accordingly, in the first case, the curves will be located above the curves, and in the second, below. This makes the hysteresis cycle narrower than the cycle.

Coercive force

Coercive force - (from lat. coercitio - holding), the value of the magnetic field strength necessary for the complete demagnetization of a ferro- or ferrimagnetic substance. It is measured in Ampere/meter (in the SI system). According to the magnitude of the coercive force, the following magnetic materials are distinguished

Soft magnetic materials are materials with a low coercive force that are magnetized to saturation and remagnetized in relatively weak magnetic fields of about 8–800 A/m. After magnetization reversal, they do not externally exhibit magnetic properties, since they consist of randomly oriented regions magnetized to saturation. An example would be various steels. The more coercive force a magnet has, the more resistant it is to demagnetizing factors. Hard magnetic materials are materials with a high coercive force that are magnetized to saturation and remagnetized in relatively strong magnetic fields with a strength of thousands and tens of thousands of a/m. After magnetization, magnetically hard materials remain permanent magnets due to high values ​​of coercive force and magnetic induction. Examples are rare earth magnets NdFeB and SmCo, barium and strontium hard magnetic ferrites.

With an increase in the mass of the particle, the radius of curvature of the trajectory increases, and according to Newton's first law, its inertia increases.

With an increase in magnetic induction, the radius of curvature of the trajectory decreases, i.e. the centripetal acceleration of the particle increases. Consequently, under the action of the same force, the change in particle velocity will be smaller, and the radius of curvature of the trajectory will be larger.

With an increase in the charge of the particle, the Lorentz force (magnetic component) increases, therefore, the centripetal acceleration also increases.

When the speed of the particle changes, the radius of curvature of its trajectory changes, the centripetal acceleration changes, which follows from the laws of mechanics.

If a particle flies into a uniform magnetic field by induction IN at an angle other than 90°, then the horizontal component of the velocity does not change, and the vertical component acquires centripetal acceleration under the action of the Lorentz force, and the particle will describe a circle in a plane perpendicular to the vector of magnetic induction and velocity. Due to the simultaneous movement along the direction of the induction vector, the particle describes a helix, and will return to the original horizontal at regular intervals, i.e. cross it at equal distances.

The retarding interaction of magnetic fields is caused by Foucault currents

As soon as the circuit in the inductor is closed, two oppositely directed flows begin to act around the conductor. According to Lenz's law, the positive charges of the electrogas (ether) begin their helical movement, setting in motion the atoms, according to which the electrical connection is established. From here it is mono to explain existence of magnetic action and counteraction.

By this I explain the inhibition of the exciting magnetic field and its counteraction in a closed circuit, the braking effect in the electric generator (mechanical braking or resistance to the rotor of the electric generator to the mechanically applied force and the opposition (braking) of the Foucault current to a falling neodymium magnet falling in a copper tube.

A little about magnetic motors

The principle of switching magnetic fluxes is also applied here.
But it's easier to go to the drawings.

How should this system work?

The middle coil is removable and operates on a relatively wide pulse length, which is created by the passage of magnetic fluxes from the magnets shown in the diagram.
The pulse length is determined by the inductance of the coil and the load resistance.
As soon as the time runs out and the core becomes magnetized, it is necessary to interrupt, demagnetize or remagnetize the core itself. to continue working with the load.

COILS OF ELECTROMAGNETS

The coil is one of the main elements of the electromagnet and must meet the following basic requirements:

1) ensure reliable switching on of the electromagnet under the worst conditions, i.e. in a heated state and at reduced voltage;

2) do not overheat above the permissible temperature in all possible modes, i.e. at high voltage;

3) with minimum dimensions to be convenient for production;

4) be mechanically strong;

5) have a certain level of insulation, and in some devices be moisture, acid and oil resistant.

During operation, stresses arise in the coil: mechanical - due to electrodynamic forces in the turns and between the turns, especially with alternating current; thermal - due to uneven heating of its individual parts; electrical - due to overvoltages, in particular during shutdown.

When calculating the coil, two conditions must be met. The first is to provide the required MMF with a hot coil and low voltage. The second is that the heating temperature of the coil should not exceed the permissible one.

As a result of the calculation, the following quantities necessary for winding should be determined: d- the diameter of the wire of the selected brand; w- number of turns; R- coil resistance.

According to the design, coils are distinguished: frame coils - winding is carried out on a metal or plastic frame; frameless banded - winding is carried out on a removable template, after winding the coil is bandaged; frameless with winding on the core of the magnetic system.

A permanent magnet is a piece of steel or some other hard alloy, which, being magnetized, steadily stores the stored part of the magnetic energy. The purpose of a magnet is to serve as a source of a magnetic field that does not noticeably change either with time or under the influence of factors such as shaking, temperature changes, external magnetic fields. Permanent magnets are used in a variety of devices and devices: relays, electrical measuring instruments, contactors, electrical machines.

There are the following main groups of alloys for permanent magnets:

2) alloys based on steel - nickel - aluminum with the addition of cobalt, silicon in some cases: alni (Fe, Al, Ni), alnisi (Fe, Al, Ni, Si), magnico (Fe, Ni, Al, Co);

3) alloys based on silver, copper, cobalt.

The quantities characterizing a permanent magnet are the residual induction IN r and coercive force H c. To determine the magnetic characteristics of finished magnets, demagnetization curves are used (Fig. 7-14), which are the dependence IN = f(– H). The curve is taken for the ring, which is first magnetized to saturation induction, and then demagnetized to IN = 0.

flow in the air gap. To use the energy of the magnet, it is necessary to make it with an air gap. The MMF component spent by the permanent magnet to conduct the flow in the air gap is called the free MMF.

The presence of an air gap δ reduces the induction in the magnet from IN r to IN(Fig. 7-14) in the same way as if a demagnetizing current was passed through a coil put on a ring, creating tension H. This consideration is the basis of the following method for calculating the flux in the air gap of a magnet.

In the absence of a gap, the entire MMF is spent on conducting the flow through the magnet:

where lμ is the length of the magnet.

In the presence of an air gap, part of the MDS Fδ will be spent on conducting the flow through this gap:

F=F μ + Fδ(7-35)

Let us assume that we have created such a demagnetizing magnetic field strength H, what

H l μ = Fδ(7-36)

and the induction became IN.

In the absence of scattering, the flux in the magnet is equal to the flux in the air gap

Bs μ = F δ Λ δ = Λ lμ Λ δ , (7-37)

where sμ is the section of the magnet; Λ δ = μ 0 sδ/δ; μ 0 is the magnetic permeability of the air gap.

From fig. 7-14 it follows that

B/H= l μ Λ δ / s μ=tgα (7-38)

Rice. 7-14. Demagnetization curves

Thus, knowing the data on the material of the magnet (in the form of a demagnetization curve), the dimensions of the magnet l μ , sμ and gap dimensions δ, sδ , you can use equation (7-38) to calculate the flow in the gap. To do this, draw a straight line on the diagram (Fig. 7-14). Ob at an angle a. Section bс defines induction IN magnet. From here, the flow in the air gap will be

When determining tg α, the scales of the y-axis and abscissa are taken into account:

where p = n/m- the ratio of the scales of the axes B and H.

Taking into account scattering, the flux Ф δ is determined as follows.

Carry out a straight line Ob at an angle α, where tg α == Λ δ l μ ( psµ). Received value IN characterizes the induction in the middle section of the magnet. Flux in the middle section of the magnet

Air Gap Flow

de σ is the scattering coefficient. Induction in working gap

Straight magnets. Expression (7-42) gives a solution to the problem for magnets of a closed shape, where the conductivity of the air gaps can be calculated with sufficient accuracy for practical purposes. For straight magnets, the problem of calculating the conductivities of the stray flux is very difficult. The flux is calculated using experimental dependencies relating the strength of the magnet field to the dimensions of the magnet.

Free magnetic energy. This is the energy that the magnet gives off in the air gaps. When calculating permanent magnets, choosing a material and the required ratios of dimensions, they strive for the maximum use of the material of the magnet, which is reduced to obtaining the maximum value of the free magnetic energy.

Magnetic energy concentrated in the air gap, proportional to the product of the flux in the gap and MMF:

Given that

We get

where V is the volume of the magnet. The material of a magnet is characterized by magnetic energy per unit of its volume.

Rice. 7-15. To the definition of the magnetic energy of a magnet

Using the demagnetization curve, one can construct a curve W m = f(IN) at V= 1 (Fig. 7-15). Curve W m = f(IN) has a maximum at some values IN And H, which we denote IN 0 and H 0 . In practice, the method of finding IN 0 and H 0 without plotting W m = f(IN). Intersection point of the diagonal of a quadrilateral whose sides are equal IN r and H c , with the demagnetization curve quite closely corresponds to the values IN 0 , H 0 . The residual induction V r fluctuates within relatively small limits (1-2.5), and the coercive force H c - within large limits (1-20). Therefore, materials are distinguished: low-coercive, in which W m is small (curve 2), high-coercivity, in which W m large (curve 1 ).

return curves. During operation, the air gap may change. Let us assume that before the introduction of the anchor, the induction was B 1tg a one . When the armature is introduced, the gap δ changes, and this state of the system corresponds to the angle but 2; (Fig. 7-16) and a large induction. However, the increase in induction does not occur along the demagnetization curve, but along some other curve b 1 cd, called the return curve. With complete closure (δ = 0), we would have induction B 2. When changing the gap in the opposite direction, the induction changes along the curve dfb one . return curves b 1 cd And dfb 1 are partial cycle curves of magnetization and demagnetization. The width of the loop is usually small, and the loop can be replaced with a straight b 1 d. Ratio Δ IN/Δ H is called the reversible permeability of the magnet.

Aging magnets. Aging is understood as the phenomenon of a decrease in the magnetic flux of a magnet over time. This phenomenon is determined by a number of reasons listed below.

structural aging. The magnet material after hardening or casting has an uneven structure. Over time, this unevenness passes into a more stable state, which leads to a change in the values IN And H.

Mechanical aging. Occurs due to shocks, shocks, vibrations and the influence of high temperatures, which weaken the flow of the magnet.

magnetic aging. Determined by the influence of external magnetic fields.

Stabilization of magnets. Any magnet before installing it in the apparatus must be subjected to an additional stabilization process, after which the resistance of the magnet to a decrease in flux increases.

structural stabilization. It consists in additional heat treatment, which is carried out before magnetization of the magnet (boiling the hardened magnet for 4 hours after hardening). Alloys based on steel, nickel and aluminum do not require structural stabilization.

mechanical stabilization. The magnetized magnet is subjected to shocks, shocks, vibrations in conditions close to the operating mode before being installed in the apparatus.

magnetic stabilization. A magnetized magnet is exposed to external fields of variable sign, after which the magnet becomes more resistant to external fields, to temperature and mechanical influences.

CHAPTER 8 ELECTROMAGNETIC MECHANISMS

Transgeneration of electromagnetic field energy

Essence of research:

The main direction of research is the study of the theoretical and technical feasibility of creating devices that generate electricity due to the physical process of transgeneration of electromagnetic field energy discovered by the author. The essence of the effect lies in the fact that when adding electromagnetic fields (constant and variable), not energies are added, but field amplitudes. The field energy is proportional to the square of the amplitude of the total electromagnetic field. As a result, with a simple addition of fields, the energy of the total field can be many times greater than the energy of all the initial fields separately. This property of the electromagnetic field is called the non-additivity of the field energy. For example, when adding three flat disk permanent magnets into a stack, the energy of the total magnetic field increases nine times! A similar process occurs during the addition of electromagnetic waves in feeder lines and resonant systems. The energy of the total standing electromagnetic wave can be many times greater than the energy of the waves and the electromagnetic field before addition. As a result, the total energy of the system increases. The process is described by a simple field energy formula:

When adding three permanent disk magnets, the volume of the field decreases by a factor of three, and the volumetric energy density of the magnetic field increases by a factor of nine. As a result, the energy of the total field of the three magnets together turns out to be three times the energy of the three disconnected magnets.

When adding electromagnetic waves in one volume (in feeder lines, resonators, coils, there is also an increase in the energy of the electromagnetic field compared to the original one).

The electromagnetic field theory demonstrates the possibility of energy generation due to the transfer (trans-) and addition of electromagnetic waves and fields. The theory of energy transgeneration of electromagnetic fields developed by the author does not contradict classical electrodynamics. The idea of ​​a physical continuum as a superdense dielectric medium with a huge latent mass energy leads to the fact that the physical space has energy and transgeneration does not violate the full energy conservation law (taking into account the energy of the medium). The non-additivity of the energy of the electromagnetic field demonstrates that for an electromagnetic field, the simple fulfillment of the law of conservation of energy does not occur. For example, in the theory of the Umov-Poynting vector, the addition of the Poynting vectors leads to the fact that the electric and magnetic fields are added simultaneously. Therefore, for example, when adding three Poynting vectors, the total Poynting vector increases by a factor of nine, and not three, as it seems at first glance.

Research results:

The possibility of obtaining energy by adding electromagnetic waves of research was investigated experimentally in various types of feeder lines - waveguides, two-wire, strip, coaxial. The frequency range is from 300 MHz to 12.5 GHz. Power was measured both directly - by wattmeters, and indirectly - by detector diodes and voltmeters. As a result, when performing certain settings in the feeder lines, positive results were obtained. When adding the amplitudes of the fields (in loads), the allocated power in the load exceeds the power supplied from different channels (power dividers were used). The simplest experiment illustrating the principle of amplitude addition is an experiment in which three narrowly directed antennas operate in phase on one receiver, to which a wattmeter is connected. The result of this experience: the power recorded at the receiving antenna is nine times greater than each transmitting antenna individually. At the receiving antenna, the amplitudes (three) from the three transmitting antennas are added, and the receive power is proportional to the square of the amplitude. That is, when adding three common-mode amplitudes, the receiving power increases nine times!

It should be noted that interference in air (vacuum) is multiphase, differs in a number of ways from interference in feeder lines, cavity resonators, standing waves in coils, etc. In the so-called classical interference pattern, both addition and subtraction of electromagnetic field amplitudes are observed . Therefore, in general, in case of multiphase interference, the violation of the energy conservation law is of a local nature. In a resonator or in the presence of standing waves in feeder lines, the superposition of electromagnetic waves is not accompanied by a redistribution of the electromagnetic field in space. In this case, in a quarter and half-wave resonators, only the addition of the field amplitudes occurs. The energy of the waves combined in one volume comes from the energy transmitted from the generator to the resonator.

Experimental studies fully confirm the theory of transgeneration. It is known from microwave practice that even with a normal electrical breakdown in feeder lines, the power exceeds the power supplied from the generator. For example, a waveguide designed for a microwave power of 100 MW is pierced by adding two microwave powers of 25 MW each - by adding two counterpropagating microwave waves in the waveguide. This can happen when microwave power is reflected from the end of the line.

A number of original circuit diagrams have been developed for generating energy using various types of interference. The main frequency range is meter and decimeter (UHF), up to centimeter. On the basis of transgeneration, it is possible to create compact autonomous sources of electricity.

There are two main types of magnets: permanent and electromagnets. It is possible to determine what a permanent magnet is based on its main property. The permanent magnet gets its name from the fact that its magnetism is always "on". It generates its own magnetic field, unlike an electromagnet, which is made from wire wrapped around an iron core and requires current to flow to create a magnetic field.

History of the study of magnetic properties

Centuries ago, people discovered that some types of rocks have original features: they are attracted to iron objects. The mention of magnetite is found in ancient historical chronicles: more than two thousand years ago in European and much earlier in East Asian. At first it was assessed as a curious object.

Later, magnetite was used for navigation, finding that it tends to take a certain position when it is given the freedom to rotate. A scientific study by P. Peregrine in the 13th century showed that steel could acquire these characteristics after being rubbed with magnetite.

Magnetized objects had two poles: "north" and "south", relative to the Earth's magnetic field. As Peregrine discovered, it was not possible to isolate one of the poles by cutting a fragment of magnetite in two - each separate fragment had its own pair of poles as a result.

In accordance with today's ideas, the magnetic field of permanent magnets is the resulting orientation of electrons in a single direction. Only some types of materials interact with magnetic fields, a much smaller number of them are able to maintain a constant magnetic field.

Properties of permanent magnets

The main properties of permanent magnets and the field they create are:

• the existence of two poles;
• opposite poles attract and like poles repel (like positive and negative charges);
• magnetic force imperceptibly propagates in space and passes through objects (paper, wood);
• there is an increase in the MF intensity near the poles.

Permanent magnets support MT without external help. Materials depending on the magnetic properties are divided into the main types:

• ferromagnets - easily magnetized;
• paramagnets - magnetized with great difficulty;
• diamagnets - tend to reflect the external MF by magnetization in the opposite direction.

Important! Soft magnetic materials such as steel conduct magnetism when attached to a magnet, but this stops when it is removed. Permanent magnets are made from magnetically hard materials.

How a permanent magnet works

His work is related to atomic structure. All ferromagnets create a natural, albeit weak, magnetic field, thanks to the electrons surrounding the nuclei of atoms. These groups of atoms are able to orient in a single direction and are called magnetic domains. Each domain has two poles: north and south. When a ferromagnetic material is not magnetized, its regions are oriented in random directions, and their MFs cancel each other out.

To create permanent magnets, ferromagnets are heated at very high temperatures and subjected to a strong external magnetic field. This leads to the fact that individual magnetic domains inside the material begin to orient themselves in the direction of the external magnetic field until all the domains align, reaching the magnetic saturation point. The material is then cooled and the aligned domains are locked into position. After the removal of the external MF, magnetically hard materials will retain most of their domains, creating a permanent magnet.

Characteristics of a permanent magnet

1. The magnetic force is characterized by residual magnetic induction. Designated Br. This is the force that remains after the disappearance of the external MT. Measured in tests (Tl) or gauss (Gs);
2. Coercivity or resistance to demagnetization - Ns. Measured in A / m. Shows what the intensity of the external MF should be in order to demagnetize the material;
3. Maximum energy - BHmax. Calculated by multiplying the residual magnetic force Br and the coercivity Hc. Measured in MGSE (megagaussersted);
4. The temperature coefficient of the residual magnetic force is Тс of Br. Characterizes the dependence of Br on the temperature value;
5. Tmax is the highest temperature value at which permanent magnets lose their properties with the possibility of reverse recovery;
6. Tcur is the highest temperature value when the magnetic material permanently loses its properties. This indicator is called the Curie temperature.

The individual characteristics of a magnet change with temperature. At different temperatures, different types of magnetic materials work differently.

Important! All permanent magnets lose a percentage of magnetism as the temperature rises, but at a different rate depending on their type.

Types of permanent magnets

There are five types of permanent magnets in total, each of which is made differently based on materials with different properties:

• alnico;
• ferrites;
• rare earth SmCo based on cobalt and samarium;
• neodymium;
• polymeric.

Alnico

These are permanent magnets composed primarily of a combination of aluminum, nickel, and cobalt, but may also include copper, iron, and titanium. Due to the properties of alnico magnets, they can operate at the highest temperatures while retaining their magnetism, however, they demagnetize more easily than ferrite or rare earth SmCo. They were the first mass-produced permanent magnets, replacing magnetized metals and expensive electromagnets.

Application:

• electric motors;
• heat treatment;
• bearings;
• aerospace vehicles;
• military equipment;
• high-temperature loading and unloading equipment;
• microphones.

Ferrites

For the manufacture of ferrite magnets, also known as ceramic, strontium carbonate and iron oxide are used in a ratio of 10/90. Both materials are abundant and economically available.

Due to low production costs, resistance to heat (up to 250°C) and corrosion, ferrite magnets are one of the most popular for everyday use. They have greater internal coercivity than alnico, but less magnetic force than neodymium counterparts.

Application:

• sound speakers;
• security systems;
• large plate magnets to remove iron contamination from process lines;
• electric motors and generators;
• medical instruments;
• lifting magnets;
• marine search magnets;
• devices based on the operation of eddy currents;
• switches and relays;
• brakes.

SmCo Rare Earth Magnets

Cobalt and samarium magnets operate over a wide temperature range, have high temperature coefficients and high corrosion resistance. This type retains its magnetic properties even at temperatures below absolute zero, making them popular for use in cryogenic applications.

Application:

• turbotechnics;
• pump couplings;
• wet environments;
• high temperature devices;
• miniature electric racing cars;
• electronic devices for operation in critical conditions.

Neodymium magnets

The strongest existing magnets, consisting of an alloy of neodymium, iron and boron. Due to their enormous strength, even miniature magnets are effective. This provides versatility of use. Each person is constantly next to one of the neodymium magnets. They are, for example, in a smartphone. The manufacture of electric motors, medical equipment, radio electronics rely on heavy-duty neodymium magnets. Due to their super strength, huge magnetic force and resistance to demagnetization, samples up to 1 mm can be produced.

Application:

• hard drives;
• sound-reproducing devices - microphones, acoustic sensors, headphones, loudspeakers;
• prostheses;
• magnetic coupling pumps;
• door closers;
• engines and generators;
• locks on jewelry;
• MRI scanners;
• magnetotherapy;
• ABS sensors in cars;
• lifting equipment;
• magnetic separators;
• reed switches, etc.

Flexible magnets contain magnetic particles inside a polymer binder. They are used for unique devices where it is impossible to install solid analogues.

Application:

• display advertising - quick fixation and quick removal at exhibitions and events;
• vehicle signs, educational school panels, company logos;
• toys, puzzles and games;
• masking surfaces for painting;
• calendars and magnetic bookmarks;
• window and door seals.

Most permanent magnets are brittle and should not be used as structural elements. They are made in standard forms: rings, rods, discs, and individual: trapezoids, arcs, etc. Due to the high iron content, neodymium magnets are susceptible to corrosion, therefore they are coated on top with nickel, stainless steel, teflon, titanium, rubber and other materials.

Video

a) General information. To create a constant magnetic field in a number of electrical devices, permanent magnets are used, which are made of magnetically hard materials with a wide hysteresis loop (Fig. 5.6).

The work of a permanent magnet occurs in the area from H=0 before H \u003d - H s. This part of the loop is called the demagnetization curve.

Consider the basic relationships in a permanent magnet, which has the shape of a toroid with one small gap b(fig.5.6). Owing to the shape of a toroid and a small gap, stray fluxes in such a magnet can be neglected. If the gap is small, then the magnetic field in it can be considered uniform.

Fig.5.6. Permanent Magnet Demagnetization Curve

If buckling is neglected, then the induction in the gap IN & and inside the magnet IN are the same.

Based on the total current law in closed-loop integration 1231 rice. we get:

Fig.5.7. Permanent magnet shaped like a toroid

Thus, the field strength in the gap is directed opposite to the field strength in the magnet body. For a DC electromagnet having a similar shape of the magnetic circuit, without taking into account saturation, you can write:.

Comparing it can be seen that in the case of a permanent magnet n. c, which creates a flow in the working gap, is the product of the tension in the magnet body and its length with the opposite sign - Hl.

Taking advantage of the fact that

, (5.29)

, (5.30)

where S- the area of ​​the pole; - conductivity of the air gap.

The equation is the equation of a straight line passing through the origin in the second quadrant at an angle a to the axis H. Given the scale of induction t in and tension t n angle a is defined by the equality

Since the induction and strength of the magnetic field in the body of a permanent magnet are connected by a demagnetization curve, the intersection of this straight line with the demagnetization curve (point BUT in Fig.5.6) and determines the state of the core at a given gap.

With a closed circuit and

With growth b conductivity of the working gap and tga decrease, the induction in the working gap decreases, and the field strength inside the magnet increases.

One of the important characteristics of a permanent magnet is the energy of the magnetic field in the working gap W t . Considering that the field in the gap is uniform,

Substituting value H we get:

, (5.35)

where V M is the volume of the magnet body.

Thus, the energy in the working gap is equal to the energy inside the magnet.

Product dependency B(-H) in the induction function is shown in Fig.5.6. Obviously, for point C, where B(-H) reaches its maximum value, the energy in the air gap also reaches its maximum value, and from the point of view of using a permanent magnet, this point is optimal. It can be shown that the point C corresponding to the maximum of the product is the point of intersection with the beam demagnetization curve OK, through a point with coordinates and .

Let us consider in more detail the influence of the gap b by the amount of induction IN(fig.5.6). If the magnetization of the magnet was carried out with a gap b, then after the removal of the external field in the body of the magnet, an induction will be established corresponding to the point BUT. The position of this point is determined by the gap b.

Decrease the gap to the value , then

. (5.36)

With a decrease in the gap, the induction in the magnet body increases, however, the process of changing the induction does not follow the demagnetization curve, but along the branch of a private hysteresis loop AMD. Induction IN 1 is determined by the point of intersection of this branch with a ray drawn at an angle to the axis - H(dot D).

If we increase the gap again to the value b, then the induction will drop to the value IN, and dependence B (H) will be determined by the branch DNA private hysteresis loop. Usually partial hysteresis loop AMDNA narrow enough and replaced by a straight AD, which is called the return line. The slope to the horizontal axis (+ H) of this line is called the return coefficient:

. (5.37)

The demagnetization characteristic of a material is usually not given in full, but only the saturation induction values ​​are given. B s , residual induction In g, coercive force N s. To calculate a magnet, it is necessary to know the entire demagnetization curve, which for most magnetically hard materials is well approximated by the formula

The demagnetization curve given by (5.30) can be easily plotted graphically if one knows B s , B r .

b) Determination of the flow in the working gap for a given magnetic circuit. In a real system with a permanent magnet, the flow in the working gap differs from the flow in the neutral section (in the middle of the magnet) due to the presence of scattering and buckling flows (Fig.).

The flow in the neutral section is equal to:

, (5.39)

where is the flow in the neutral section;

Bulging flow at the poles;

Flux scattering;

workflow.

The scattering coefficient o is determined by the equality

If we accept that flows created by the same magnetic potential difference, then

. (5.41)

We find the induction in the neutral section by defining:

,

and using the demagnetization curve Fig.5.6. The induction in the working gap is equal to:

since the flow in the working gap is several times less than the flow in the neutral section.

Very often, the magnetization of the system occurs in an unassembled state, when the conductivity of the working gap is reduced due to the absence of parts made of ferromagnetic material. In this case, the calculation is carried out using a direct return. If the leakage fluxes are significant, then the calculation is recommended to be carried out by sections, as well as in the case of an electromagnet.

Stray fluxes in permanent magnets play a much greater role than in electromagnets. The fact is that the magnetic permeability of hard magnetic materials is much lower than that of soft magnetic materials, from which systems for electromagnets are made. Stray fluxes cause a significant drop in the magnetic potential along the permanent magnet and reduce n. c, and hence the flow in the working gap.

The dissipation coefficient of the completed systems varies over a fairly wide range. The calculation of the scattering coefficient and scattering fluxes is associated with great difficulties. Therefore, when developing a new design, it is recommended to determine the value of the scattering coefficient on a special model in which the permanent magnet is replaced by an electromagnet. The magnetizing winding is chosen so as to obtain the necessary flux in the working gap.

Fig.5.8. Magnetic circuit with a permanent magnet and leakage and buckling fluxes

c) Determining the dimensions of the magnet according to the required induction in the working gap. This task is even more difficult than determining the flow with known dimensions. When choosing the dimensions of a magnetic circuit, one usually strives to ensure that the induction At 0 and tension H 0 in the neutral section corresponded to the maximum value of the product N 0 V 0 . In this case, the volume of the magnet will be minimal. The following recommendations are given for the choice of materials. If it is required to obtain a large value of induction at large gaps, then the most suitable material is magnico. If it is necessary to create small inductions with a large gap, then alnisi can be recommended. With small working gaps and a large value of induction, it is advisable to use an alni.

The cross section of the magnet is selected from the following considerations. The induction in the neutral section is chosen equal to At 0 . Then the flow in the neutral section

,

where is the cross section of the magnet

.
Induction values ​​in the working gap In r and the area of ​​the pole are given values. The most difficult is to determine the value of the coefficient scattering. Its value depends on the design and induction in the core. If the cross section of the magnet turned out to be large, then several magnets connected in parallel are used. The length of the magnet is determined from the condition for creating the necessary NS. in the working gap with tension in the body of the magnet H 0:

where b p - the value of the working gap.

After choosing the main dimensions and designing the magnet, a verification calculation is carried out according to the method described earlier.

d) Stabilization of the characteristics of the magnet. During the operation of the magnet, a decrease in the flow in the working gap of the system is observed - the aging of the magnet. There are structural, mechanical and magnetic aging.

Structural aging occurs due to the fact that after hardening of the material, internal stresses arise in it, the material acquires an inhomogeneous structure. In the process of work, the material becomes more homogeneous, internal stresses disappear. In this case, the residual induction In t and coercive force N s decrease. To combat structural aging, the material is subjected to heat treatment in the form of tempering. In this case, internal stresses in the material disappear. Its characteristics become more stable. Aluminum-nickel alloys (alni, etc.) do not require structural stabilization.

Mechanical aging occurs with shock and vibration of the magnet. In order to make the magnet insensitive to mechanical influences, it is subjected to artificial aging. The magnet specimens are subjected to such shocks and vibrations as are encountered in operation before installation in the apparatus.

Magnetic aging is a change in the properties of a material under the influence of external magnetic fields. A positive external field increases the induction along the return line, and a negative one reduces it along the demagnetization curve. In order to make the magnet more stable, it is subjected to a demagnetizing field, after which the magnet operates on a return line. Due to the lower steepness of the return line, the influence of external fields is reduced. When calculating magnetic systems with permanent magnets, it must be taken into account that in the process of stabilization, the magnetic flux decreases by 10-15%.