The speed of rotation of the magnetic field is slip. Obtaining a rotating magnetic field

Conditions for receiving:

1) the presence of at least two windings;

2) the currents in the windings must be different in phase

3) the axes of the windings must be displaced in space.

In a three-phase machine, with one pair of poles (p=1), the axes of the windings must be shifted in space by an angle of 120°, with two pairs of poles (p=2), the axes of the windings must be shifted in space by an angle of 60°, etc.

Let's consider a magnetic field that is created using a three-phase winding that has one pair of poles (p = 1). The axes of the phase windings are displaced in space by an angle of 120° and the magnetic inductions of individual phases created by them (BA, BB, BC) are also displaced in space by an angle of 120°.

The magnetic induction fields created by each phase, as well as the voltages supplied to these phases, are sinusoidal and differ in phase by an angle of 120°.

Operating principle

Voltage is applied to the stator winding, under the influence of which current flows through these windings and creates a rotating magnetic field. The magnetic field acts on the rotor rods and, according to the law of magnetic induction, induces an emf in them. Under the influence of the induced EMF, a current arises in the rotor rods. The currents in the rotor bars create their own magnetic field of the bars, which interact with the rotating magnetic field of the stator. As a result, a force acts on each rod, which, adding up around the circle, creates a rotating electromagnetic moment of the rotor.

Taking the initial induction phase in phase A (φA) equal to zero, we can write:

The magnetic induction of the resulting magnetic field is determined by the vector sum of these three magnetic inductions.

Let's find the resulting magnetic induction using vector diagrams, constructing them for several moments in time.

Draw vector diagrams

As follows from the diagrams, the magnetic induction B of the resulting magnetic field of the machine rotates, remaining unchanged in magnitude. Thus, the three-phase stator winding creates a circular rotating magnetic field in the machine. The direction of rotation of the magnetic field depends on the order of phase alternation. The magnitude of the resulting magnetic induction.

The frequency of rotation of the magnetic field depends on the frequency of the network and the number of pairs of poles of the magnetic field.

, [rpm].

In this case, the rotation frequency of the magnetic field does not depend on the operating mode of the asynchronous machine and its load.

When analyzing the operation of an asynchronous machine, the concept of magnetic field rotation speed ω0 is often used, which is determined by the relation:

, [rad/sec].

To compare the rotation frequency of the magnetic field and the rotor-ravel, the coefficient was called slip and designated by a letter. Slip can be measured in relative units and as a percentage.

or

Processes in an asynchronous machine Stator circuit

a) stator EMF.

The magnetic field created by the stator winding rotates relative to the stationary stator with a frequency and will induce an EMF in the stator winding. The effective value of the EMF induced by this field in one phase of the stator winding is determined by the expression:

where: =0.92÷0.98 – winding coefficient;

– network frequency;

– number of turns of one phase of the stator winding;

–resulting magnetic field in the machine.

b) Equation of electrical equilibrium of the stator winding phase.

This equation is made by analogy with a coil with a core operating on alternating current.

Here and are the mains voltage and the voltage supplied to the stator winding.

– active resistance of the stator winding associated with losses due to heating of the winding.

– inductive resistance of the stator winding associated with leakage flux.

– impedance of the stator winding.

– current in the stator winding.

When analyzing the operation of asynchronous machines, it is often adopted. Then we can write:

From this expression it follows that the magnetic flux in an asynchronous machine does not depend on its operating mode, and at a given network frequency it depends only on the effective value of the applied voltage. A similar relationship occurs in another alternating current machine - in a transformer.

In the previous paragraph it was shown that the speed of rotation of the magnetic field is constant and is determined by the frequency of the current. In particular, if the three-phase motor winding is placed in six slots on the inner surface of the stator (Fig. 5-7), then, as shown (see Fig. 5-4), the magnetic flux axis will rotate

for half a period of alternating current by half a turn, and for a full period - by one turn. The rotation speed of the magnetic flux can be represented as follows:

In this case, the stator winding creates a magnetic field with one pair of poles. This winding is called bipolar.

If the stator winding consists of six coils (two series-connected coils per phase), laid in twelve slots (Fig. 5-8), then as a result of constructions similar to those for a two-pole winding, it can be obtained that the magnetic flux axis rotates by a quarter turn, and for a full period - half a turn (Fig. 5-9). Instead of two poles with three

windings, the stator field now has four poles (two pairs of poles). The rotation speed of the stator magnetic field in this case is equal to

By increasing the number of slots and windings and making similar arguments, we can conclude that the speed of rotation of the magnetic field in the general case for pairs of poles is equal to

Since the number of pole pairs can only be an integer (the number of coils in the stator winding is always a multiple of three), the speed of rotation of the magnetic field can have not arbitrary, but quite definite values ​​(see Table 5.1).

Table 5.1

In practice, to obtain a constant value of the torque acting on the rotor during one revolution, the number of slots in the stator is significantly increased (Fig. 5-10) and each side of the coil is placed in several slots, with each winding consisting of several sections connected between ourselves consistently. Windings are usually made of two layers. In each groove, two sides of sections of two different coils are laid one above the other, and if one active side lies at the bottom of one groove, then the other active side of this section lies at the top of another groove, the sections and coils are connected to each other so that in most of the conductors For each slot, the direction of the currents was the same.

An important advantage of three-phase current is the possibility of obtaining a rotating magnetic field, which underlies the principle of operation of electrical machines - asynchronous and synchronous motors of three-phase current.

Rice. 7.2. Diagram of the arrangement of coils when obtaining a rotating magnetic field (a) and wave diagram of a three-phase symmetrical system of currents flowing through the coils (b)

A rotating magnetic field is obtained by passing a three-phase current system (Fig. 7.2,b) through three identical coils A, B, C(Fig. 7.2,a), the axes of which are located at an angle of 120° relative to each other.

Figure 7.2a shows the positive directions of currents in the coils and the directions of magnetic field inductions IN A , IN IN , IN WITH, created by each of the coils separately.

Figure 7.3 shows the actual directions of currents for instants of time
and directions of induction IN res the resulting magnetic field created by the three coils.

Analysis of Figure 7.3 allows us to draw the following conclusions:

a) induction IN res the resulting magnetic field changes its direction (rotates) over time;

b) the frequency of rotation of the magnetic field is the same as the frequency of change of current. Yes, when f = 50 Hz the rotating magnetic field makes five to ten revolutions per second or three thousand revolutions per minute.

The induction value of the resultant IN res = 1,5B m constant magnetic field

Where B m– induction amplitude of one coil.

at different times

7.3 Asynchronous machines

7.3.1 Operating principle of an asynchronous motor (IM). Let us place between the fixed coils (Fig. 7.4) in the region of the rotating magnetic field, a movable metal cylinder mounted on an axis - a rotor.

Let the magnetic field rotate “clockwise”, then the cylinder relative to the rotating magnetic field rotates in the opposite direction.

Taking this into account, using the right-hand rule we will find the direction of the currents induced in the cylinder.

In Figure 7.4, the directions of induced currents (along the generatrices of the cylinder) are shown by crosses (“from us”) and dots (“towards us”).

Applying the left-hand rule (Fig. 7.1, b), we find that the interaction of induced currents with the magnetic field generates forces F, causing the rotor to rotate in the same direction in which the magnetic field rotates.

Rotor speed
less than the magnetic field rotation frequency , because at the same angular speeds, the relative speed of the rotor and the rotating magnetic field would be zero and there would be no induced emf and currents in the rotor. Therefore, there would be no strength F, creating torque. The simplest device considered explains the principle of operation asynchronous motors. The word "asynchronous" (Greek) means non-simultaneous. This word emphasizes the difference in the frequencies of the rotating magnetic field and the rotor - the moving part of the engine.

Rice. 7.4. To the principle of operation of an asynchronous motor

The rotating magnetic field created by three coils has two poles and is called bipolar rotating magnetic field(single phase poles).

During one period of sinusoidal current, a bipolar magnetic field makes one revolution. Therefore, at standard frequency f 1 = 50 Hz this field makes three thousand revolutions per minute. The rotor speed is slightly less than this synchronous speed.

In cases where an asynchronous motor with a lower speed is required, a multi-pole stator winding consisting of six, nine, etc. is used. coils Accordingly, the rotating magnetic field will have two, three, etc. pairs of poles.

In general, if a field has R pairs of poles, then its rotation speed will be

.

7.3.2 Construction of an asynchronous motor. The magnetic system (magnetic circuit) of an asynchronous motor consists of two parts: an outer stationary one, shaped like a hollow cylinder (Fig. 8.5), and an inner one - a rotating cylinder.

Both parts of the asynchronous motor are assembled from sheets of electrical steel 0.5 mm thick. These sheets are insulated from each other by a layer of varnish to reduce eddy current losses.

The stationary part of the machine is called stator, and rotating – rotor(from Latin stare - stand and rotate – rotate).

Rice. 7.5. Diagram of an asynchronous motor: cross-section (a);

rotor winding(b): 1 – stator; 2 – rotor; 3 – shaft; 4 – turns of the stator winding;

5 – turns of the rotor winding

A three-phase winding is placed in the grooves on the inside of the stator, the currents of which excite the rotating magnetic field of the machine. A second winding is located in the rotor slots, the currents in which are induced by a rotating magnetic field.

The stator magnetic circuit is enclosed in a massive housing, which is the outer part of the machine, and the rotor magnetic circuit is mounted on the shaft.

Rotors of asynchronous motors are manufactured in two types: squirrel-cage and with slip rings. The first of them are simpler in design and are more often used.

The winding of a squirrel-cage rotor is a cylindrical cage (“squirrel wheel”) made of copper tires or aluminum rods, short-circuited at the ends with two rings (Fig. 7.5, b). The rods of this winding are inserted without insulation into the grooves of the magnetic circuit.

The method of filling the grooves of the rotor magnetic circuit with molten aluminum with simultaneous casting of the closing rings is also used.

7.3.3 Characteristics of an asynchronous motor. The speed of rotation of the rotating magnetic field is determined either by the angular frequency , n, or number of revolutions P in a minute. These two quantities are related by the formula

. (7.3)

A characteristic quantity is the relative speed of the rotating magnetic field, called slidingS:

or

Where
– rotor angular frequency, rad/s;

– number of revolutions per minute, rpm.

The closer the rotor speed to the speed of the rotating magnetic field , the lower the EMF induced by the field in the rotor, and therefore the lower the currents in the rotor.

The decrease in currents reduces the torque acting on the rotor, so the motor rotor must rotate slower than the rotating magnetic field - asynchronously.

It can be shown that the torque of the IM is determined by the following expression:

, (7.4)

Where , , x 1 , – parameters of the electrical equivalent circuit, which are given in reference books on IM;

– effective phase voltage on the stator winding.

In modern asynchronous motors, slip even at full load is small - about 0.04 (four percent) for small ones and about 0.015...0.02 (one and a half to two percent) for large motors.

Typical dependence curve M from slipping S shown in Figure 7.6,a.

Maximum torque splits the curve
to the stable part from S = 0 to and the unstable part from before S = 1, within which the torque decreases with increasing slip.

On the site from S = 0 to when the braking torque decreases
On the shaft of an asynchronous motor, the rotation speed increases, slip decreases, so that in this section the operation of the asynchronous motor is stable.

On the site from before S= 1 decreasing
the rotation speed increases, the slip decreases and the torque increases, which leads to an even greater increase in the rotation speed, so that the operation of the engine is unstable.

Thus, while the braking torque
, dynamic moment balance is automatically restored. When
, with a further increase in load, an increase in slip leads to a decrease in rotating torque M and the engine stops due to the predominance of the braking torque over the rotating torque.

Meaning M To can be calculated using the formula

.

For practice, the dependence of engine speed is of great importance from the load on the shaft
. This dependence is called mechanical characteristics(Fig. 7.6,b).

As the curve of Figure 7.6, b shows, the speed of an asynchronous motor decreases only slightly as the torque increases in the range from zero to the maximum value
The starting torque corresponding to S = 1 can be obtained from (7.4), taking S= 1. Typically starting torque M start = (0.8 1,2)M nom, M nom – nominal torque. This dependence is called tough.

Rice. 7.6. Dependence of torque on the shaft of an asynchronous motor

from slipping (a); mechanical characteristics (b)

Asynchronous motors have become widespread due to the following advantages: simplicity of the device; high reliability in operation; low cost.

With the help of asynchronous motors, cranes, winches, elevators, escalators, pumps, fans and other mechanisms are driven.

Asynchronous motors have the following disadvantages:

regulating the rotor speed is difficult.

When designing equipment, it is necessary to know the speed of the electric motor. To calculate the rotation speed, there are special formulas that are different for AC and DC motors.

Synchronous and asynchronous electric machines

There are three types of AC motors: synchronous, the angular speed of the rotor coincides with the angular frequency of the stator magnetic field; asynchronous - in them the rotation of the rotor lags behind the rotation of the field; commutator motors, the design and operating principle of which are similar to DC motors.

Synchronous speed

The rotation speed of an AC electric machine depends on the angular frequency of the stator magnetic field. This speed is called synchronous. In synchronous motors, the shaft rotates at the same speed, which is an advantage of these electric machines.

To do this, the rotor of high-power machines has a winding to which a constant voltage is applied, creating a magnetic field. In low power devices, permanent magnets are inserted into the rotor, or there are pronounced poles.

Slip

In asynchronous machines, the number of shaft revolutions is less than the synchronous angular frequency. This difference is called the “S” slip. Due to sliding, an electric current is induced in the rotor and the shaft rotates. The larger S, the higher the torque and the lower the speed. However, if the slip exceeds a certain value, the electric motor stops, begins to overheat and may fail. The rotation speed of such devices is calculated using the formula in the figure below, where:

• n – number of revolutions per minute,
• f – network frequency,
• p – number of pole pairs,
• s – slip.

There are two types of such devices:

• With squirrel-cage rotor. The winding in it is cast from aluminum during the manufacturing process;
• With wound rotor. The windings are made of wire and are connected to additional resistances.

Speed ​​adjustment

During operation, it becomes necessary to adjust the speed of electrical machines. This is done in three ways:

• Increasing additional resistance in the rotor circuit of electric motors with a wound rotor. If it is necessary to greatly reduce the speed, it is possible to connect not three, but two resistances;
• Connecting additional resistances in the stator circuit. It is used to start high-power electrical machines and to regulate the speed of small electric motors. For example, the speed of a table fan can be reduced by connecting an incandescent lamp or capacitor in series with it. The same result is achieved by reducing the supply voltage;
• Changing the network frequency. Suitable for synchronous and asynchronous motors.

Attention! The rotation speed of commutator electric motors operating from an alternating current network does not depend on the frequency of the network.

DC motors

In addition to AC machines, there are electric motors connected to a DC network. The speed of such devices is calculated using completely different formulas.

Rated rotation speed

The speed of a DC machine is calculated using the formula in the figure below, where:

• n – number of revolutions per minute,
• U – network voltage,
• Rya and Iya – armature resistance and current,
• Ce – motor constant (depending on the type of electric machine),
• Ф – stator magnetic field.

These data correspond to the nominal values ​​of the parameters of the electric machine, the voltage on the field winding and the armature or the torque on the motor shaft. Changing them allows you to adjust the rotation speed. It is very difficult to determine the magnetic flux in a real motor, so calculations are made using the current flowing through the field winding or armature voltage.

The speed of commutator AC motors can be found using the same formula.

Speed ​​adjustment

Adjustment of the speed of an electric motor operating from a DC network is possible within a wide range. It is possible in two ranges:

1. Up from nominal. To do this, the magnetic flux is reduced using additional resistances or a voltage regulator;
2. Down from par. To do this, it is necessary to reduce the voltage on the armature of the electric motor or connect a resistance in series with it. In addition to reducing the speed, this is done when starting the electric motor.

Knowing what formulas are used to calculate the rotation speed of an electric motor is necessary when designing and setting up equipment.

Video

One of the most common electric motors, which is used in most electric drive devices, is the asynchronous motor. This motor is called asynchronous (non-synchronous) for the reason that its rotor rotates at a lower speed than that of a synchronous motor, relative to the speed of rotation of the magnetic field vector.

It is necessary to explain what synchronous speed is.

Synchronous speed is the speed at which the magnetic field rotates in a rotary machine; to be precise, it is the angular speed of rotation of the magnetic field vector. The speed of rotation of the field depends on the frequency of the flowing current and the number of poles of the machine.

An asynchronous motor always operates at a speed lower than the synchronous rotation speed, because the magnetic field that is formed by the stator windings will generate a counter magnetic flux in the rotor. The interaction of this generated counter magnetic flux with the stator magnetic flux will cause the rotor to start rotating. Since the magnetic flux in the rotor will lag behind, the rotor will never be able to independently achieve synchronous speed, that is, the same speed as the stator magnetic field vector rotates.

There are two main types of induction motor, which are determined by the type of power supplied. This:

• single-phase asynchronous motor;
• three-phase asynchronous motor.

It should be noted that a single-phase asynchronous motor is not capable of independently starting movement (rotation). In order for it to start rotating, it is necessary to create some displacement from the equilibrium position. This is achieved in various ways, using additional windings, capacitors, and switching at the time of start-up. Unlike a single-phase asynchronous motor, a three-phase motor is capable of starting independent movement (rotation) without making any changes to the design or starting conditions.

Induction motors are structurally different from direct current (DC) motors in that power is supplied to the stator, in contrast to a DC motor, in which power is supplied to the armature (rotor) through a brush mechanism.

Operating principle of an asynchronous motor

By applying voltage only to the stator winding, the asynchronous motor begins to operate. Interested to know how it works, why this happens? This is very simple if you understand how the induction process occurs when a magnetic field is induced in the rotor. For example, in DC machines, you have to separately create a magnetic field in the armature (rotor) not through induction, but through brushes.

When we apply voltage to the stator windings, an electric current begins to flow through them, which creates a magnetic field around the windings. Further, from many windings that are located on the stator magnetic circuit, a common magnetic field of the stator is formed. This magnetic field is characterized by a magnetic flux, the magnitude of which changes over time; in addition, the direction of the magnetic flux changes in space, or rather, it rotates. As a result, it turns out that the stator magnetic flux vector rotates like a spun sling with a stone.

In full accordance with Faraday's law of electromagnetic induction, in a rotor that has a short-circuited winding (short-circuited rotor). An induced electric current will flow in this rotor winding since the circuit is closed and it is in short circuit mode. This current, just like the supply current in the stator, will create a magnetic field. The motor rotor becomes a magnet inside the stator, which has a magnetic rotating field. Both magnetic fields from the stator and rotor will begin to interact, obeying the laws of physics.

Since the stator is motionless and its magnetic field rotates in space, and a current is induced in the rotor, which actually makes it a permanent magnet, the movable rotor begins to rotate because the magnetic field of the stator begins to push it, dragging it along with it. The rotor seems to mesh with the magnetic field of the stator. We can say that the rotor tends to rotate synchronously with the magnetic field of the stator, but this is unattainable for it, since at the moment of synchronization the magnetic fields cancel each other out, which leads to asynchronous operation. In other words, when an asynchronous motor operates, the rotor slides in the magnetic field of the stator.

Sliding can be either delayed or advanced. If there is a delay, then we have a motor mode of operation, when electrical energy is converted into mechanical energy; if sliding occurs with the rotor advancing, then we have a generator mode of operation, when mechanical energy is converted into electrical energy.

The torque generated on the rotor depends on the frequency of the alternating current supply to the stator, as well as on the magnitude of the supply voltage. By changing the frequency of the current and the magnitude of the voltage, you can influence the rotor torque and thereby control the operation of the asynchronous motor. This is true for both single-phase and three-phase asynchronous motors.

Types of asynchronous motor

Single-phase asynchronous motor is divided into the following types:

• With separate windings (Split-phase motor);
• With a starting capacitor (Capacitor start motor);
• With start capacitor and run capacitor (Capacitor start capacitor run induction motor);
• With a displaced pole (Shaded-pole motor).

Three-phase asynchronous motor is divided into the following types:

• With a squirrel cage induction motor;
• With slip rings, wound rotor (Slip ring induction motor);

As mentioned above, a single-phase asynchronous motor cannot start moving (rotating) on ​​its own. What should be understood by independence? This is when the machine starts working automatically without any influence from the external environment. When we turn on a household electrical appliance, such as a fan, it starts working immediately upon pressing a key. It should be noted that in everyday life a single-phase asynchronous motor is used, for example a motor in a fan. How does such an independent start occur, if it was said above that this type of engine does not allow it? In order to understand this issue, you need to study methods of starting single-phase motors.

Why is a three-phase asynchronous motor self-starting?

In a three-phase system, each phase relative to the other two has an angle of 120 degrees. All three phases are thus evenly spaced in a circle; the circle has 360 degrees, which is three times 120 degrees (120+120+120=360).

If we consider three phases, A, B, C, then we will notice that only one of them at the initial moment of time will have the maximum value of the instantaneous voltage value. The second phase will increase its voltage value following the first, and the third phase will follow the second. Thus, we have the order of phase alternation A-B-C as their value increases, and another order is possible in the order of decreasing voltage C-B-A. Even if you write the alternation differently, for example, instead of A-B-C, write B-C-A, the alternation will remain the same, since the alternation chain in any order forms a vicious circle.

How will the rotor of an asynchronous three-phase motor rotate? Since the rotor is entrained by the stator's magnetic field and slides in it, it is quite obvious that the rotor will move in the direction of the stator's magnetic field vector. In which direction will the stator magnetic field rotate? Since the stator winding is three-phase and all three windings are located evenly on the stator, the generated field will rotate in the direction of the phase alternation of the windings. From this we draw a conclusion. The direction of rotation of the rotor depends on the phase sequence of the stator windings. By changing the alternation order of the phases, we get the motor rotating in the opposite direction. In practice, to change the rotation of the motor, it is enough to swap any two supply phases of the stator.

Why doesn't a single-phase asynchronous motor start rotating on its own?

For the reason that it is powered from one phase. The magnetic field of a single-phase motor is pulsating, not rotating. The main task of the launch is to create a rotating field from a pulsating field. This problem is solved by creating a phase shift in the other stator winding using capacitors, inductors and the spatial arrangement of the windings in the motor design.

It should be noted that single-phase asynchronous motors are effective in use in the presence of a constant mechanical load. If the load is less and the engine is running below its maximum load, its efficiency is significantly reduced. This is a disadvantage of a single-phase asynchronous motor and therefore, unlike three-phase machines, they are used where the mechanical load is constant.