Rotating magnetic field of an asynchronous machine (for non-electricians). Asynchronous motor

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.

The simplicity of the technical implementation of circular motion for rotating the magnetic field is the basis for the operation of all 3-phase machines, including electric generators and motors.

Conditions for creating a rotating magnetic field. Its creation is achieved by simultaneously fulfilling two conditions:

1. By placing three windings with the same electrical parameters in the same plane of rotation with equal angular displacement (Δα=360°/3=120°);

2. By passing through these windings sinusoidal harmonic currents of equal magnitude and shape, which are shifted in time by a third of the period (in angular frequency by 120°).

The formed circular magnetic field will begin to rotate. The constant induction of the created field has a maximum amplitude with a value Bmax directed along the field axis with a speed of constant angular rotation ωп.

The location of the three coil windings in the same plane of rotation is shown in the figure and meets the requirements of the first condition.

By coil windings OH, B-Y, C-Z from their beginning (entrance) A, IN, WITH to the end (exit) X, Y, Z An electrical symmetrical 3-phase current is passed through, the value of which for any instant of time is calculated using the expressions:

iA=Im∙sin(ωt+0);
iВ=Im∙sin(ωt-120°);
iС=Im∙sin(ωt+120°).

Each turn of the coil winding forms its own individual magnetic field, the induction of which is proportional to the current passing through the turn (B=k*i). The summation of the fields of all turns in each coil forms a system of three inductions, symmetrical relative to the center of rotation (the origin of coordinates):

BA=Вm∙sin(ωt+0);
ВB=Вm∙sin(ωt+0);
ВC=Вm∙sin(ωt+0).

Magnetic fields in the form of induction vectors VA, BB, VS have a strictly defined orientation in space, determined by the well-known gimlet rule in relation to the positive direction of the current in the coil winding.

The total (resulting) vector of magnetic induction B from the created magnetic field in an electric machine is calculated by geometric addition of phase vectors VA, BB, VS from all coils.

In a particular case, for the temporary assessment of the magnetic induction vector, several points of the period are selected, for example, those that correspond to 0, 30 and 60 degrees of its rotation relative to the initial ordinate.

The spatial arrangement of the induction vectors of each phase and the resulting vector obtained from their geometric addition for each case on the complex plane is demonstrated by graphs.

It is convenient to analyze the results of graphical addition after they are presented in a separate table:

The results of the analysis indicate that the total induction vector B of all magnetic fields of the machine phases has one constant value at all points under consideration. Similar conclusions will be obtained by mathematically solving a similar problem for any other time points.

Properties of the magnetic induction vector IN :

The direction of its rotation in space corresponds to movement in the nearest direction from the coil A towards the coil IN;

It is known that a magnetic field is always formed around a conductor carrying current. Its direction is determined by the rule of the right-hand screw ("gimlet").

Let's draw a magnetic field line around conductors C and Y and, accordingly, B and Z (see dashed lines in Fig. 5.2.2 a).

Let us now consider the moment of time t 2. At this time there will be no current in phase B. In conductor A of phase A-X it will have a sign (+), and in conductor C of phase C-Z it will have a sign (·). Now let’s put down the signs: in conductor X - (·), and in conductor Z - (+).

represents the total mechanical power developed by the engine.

5.8. INDUCTION MOTOR SWITCH DIAGRAM

The EMF and current equations correspond to an equivalent equivalent circuit (Fig. 5.8.1.). Thus, the complex magnetic circuit of an electrical machine can be replaced by an electrical circuit. Resistance r 2 "(1 - S)/S can be considered as an external resistance included in the rotor winding. It is the only variable parameter of the circuit. A change in this resistance is equivalent to a change in the load on the motor shaft, and therefore a change in slip S.

5.9. LOSSES AND EFFICIENCY OF AN INDUCTION MOTOR

The stator winding receives power P 1 from the network. Part of this power goes to losses in the steel Pcl, as well as losses in the stator winding P e1:

The remaining power is transferred to the rotor through magnetic flux and is called electromagnetic power:

Part of the electromagnetic power is spent to cover electrical losses in the rotor winding:

The remaining power is converted into mechanical power, called total mechanical power:

P 2 "=P em -P e2

Using the previously obtained formula

Let's write down the expression for the total mechanical power:

Р e2 = SP em,

those. the power of electrical losses is proportional to slip.

The power on the motor shaft P 2 is less than the total mechanical power P 2 ' by the amount of mechanical P mechanical and additional P additional losses:

P 2 = P 2 '-(P mech. + P ext.).

Thus:

SP=P cl +P e1 +P e2 +P mech. +P ext.

The efficiency is the ratio of the power on the shaft P 2 to the power consumption P 1:

5.10. TORQUE EQUATION

The torque in an asynchronous motor is created by the interaction of the rotor current with the magnetic field of the machine. Torque can be expressed mathematically in terms of the electromagnetic power of the machine:

where w 1 =2pn 1 /60 is the angular frequency of the field rotation.

In turn, n 1 =f 1 60/P, then

Let's substitute the expression P em = P e2 / S into formula M 1 and divide by 9.81, we get:

It follows that the motor torque is proportional to the electrical losses in the rotor. Let's substitute the value of current I 2 ' into the last formula:

However, the widespread development of technology and technical creativity of students requires knowledge of a number of additional possibilities for using these materials. Let's look at just a few of them.

5.18.2 Induction regulators and phase regulators

Induction voltage regulators are a braked induction motor with a phase rotor. They can regulate the voltage over a wide range. The stator and rotor windings in the regulator are electrically connected, but in such a way that they can be offset relative to each other by turning the rotor. When the induction controller is connected to the network, the rotating magnetic flux induces EMF E 1 and E 2 in the stator and rotor windings. When the axes in the windings coincide, the EMFs E 1 and E 2 are in phase, and the maximum voltage value is set at the output terminals of the regulator.

When the rotor turns, the axes of the windings rotate through a certain angle a. The vector E 2 is also shifted by the same angle. In this case, the output voltage decreases. By turning the rotor through an angle of 180°, we set the minimum voltage at the output.

The phase regulator is designed to change the phase of the secondary voltage relative to the primary. In this case, the value of the secondary voltage remains unchanged.

The phase regulator is an asynchronous machine, inhibited by a special rotary device. Voltage is supplied to the stator winding and removed from the rotor winding. Unlike the induction regulator, the stator and rotor windings are not electrically connected here. The phase of the secondary voltage is changed by rotating the rotor relative to the stator.

It is used in automation and measuring technology.

5.18.3 Asynchronous frequency converter

As is known, the frequency of the current in the rotor circuit of an asynchronous motor depends on slip, i.e. is determined by the difference between the rotor speed and the stator field.

This property allows the motor to be used as a frequency converter (Fig. 5.18.3.1). If the stator winding is connected to an industrial frequency network f 1, and the rotor is driven into rotation against the stator field by means of an external motor, then the slip increases, and the frequency of the rotor current f 2 accordingly increases several times compared to the network frequency f 1. If it is necessary to reduce the frequency of the current, then the rotor of the converter must be rotated in the direction of the rotating field of the stator.

5.18.4 Electromagnetic asynchronous clutch

An electromagnetic asynchronous clutch (Fig. 5.18.4.1) is designed on the principle of an asynchronous motor and serves to connect two parts of the shaft. On the driving part of the shaft 1 there is a pole system 2, which is a system of salient poles with excitation coils. Direct current in the excitation coil is supplied through slip rings 4. The driven part of the coupling 3 is designed like a rotor winding of a motor.

The principle of operation of the coupling is similar to that of an asynchronous motor, only the rotating magnetic flux here is created by the mechanical rotation of the pole system. Torque from the driving part of the shaft to the driven part is transmitted electromagnetically. The coupling is disconnected by turning off the excitation current.

A circular rotating magnetic field has the following characteristic properties:

a) the maximums of the resulting MMF and induction waves always coincide with the axis of the phase in which the current has a maximum. This position can be easily verified by specifying the value ωt, corresponding to the maximum current in the phase, and determining by (3.15) the coordinate of the point X, in which MDS F" x maximum;

b) the magnetic field moves towards the axis of the phase in which the nearest maximum is expected. This property follows directly from the previous one;

c) to change the direction of rotation of the field, it is necessary to change the order of current alternation in the phases. In three-phase machines, to do this, swap the wires that supply current from the three-phase network to any two phases of the winding. In two-phase machines, you need to switch the wires connecting the winding phases to the two-phase network.

Elliptical field. A circular rotating magnetic field occurs with symmetry of currents passing through the phases (symmetry of the MMF of the coils of individual phases), a symmetrical arrangement of these phases in space, a time shift between phase currents equal to the spatial shift between the phases and a sinusoidal distribution of induction in the air gap of the machine along the circumference of the stator (rotor). If at least one of the specified conditions is not met, not a circular, but an elliptical rotating field arises, in which the maximum value of the resulting MMF and induction for different moments of time does not remain constant, as in the case of a circular field. In such a field, the spatial vector of the MMF describes an ellipse (see Fig. 3.12, V).

An elliptical field can be thought of as two equivalent circular fields rotating in opposite directions. A field rotating in the direction of rotation of the resulting elliptical field is called straight; field rotating in the opposite direction - reverse The decomposition of an elliptic field into direct and inverse circular fields is carried out by the method of symmetric components, with the help of which the MMF of the direct and inverse sequences is determined.

Consider, for example, a two-phase machine in which two phase windings (phases) are located on the stator OH And BY, the axes of which are shifted in space by a certain angle α (Fig. 3.16, A). Currents passing through these phases and the corresponding MMF vectors FxA And FxB shifted in time by a certain angle β. Phases OH And BY create pulsating magnetic fields sinusoidally distributed in space. MMF of these phases, acting at any point X air gap,

FxA = FmA sin ωt cos(πx/τ); FxB = FmB sin(ωt + β)cos(πx/τ + α).

The MMF of the AX and BY phases, similarly to (3.15), can be represented as the sum of two traveling MMF waves of opposite directions:

In expressions (3.21), time and space angles are added or subtracted, i.e. they become equivalent. This is explained by the fact that the spatial position of the MMF vector of the rotating field is determined by the time and frequency of the current supplying the phases - in one period the field moves by a pair of poles. The resulting magnetic field created by the combined action of the two windings can be obtained by adding the component positive sequence MMF vectors rotating clockwise (forming a direct field):

F"xA = 0.5FmA sin(ωt - πx/τ) and F"xB = 0.5FmB sin(ωt + β - πx/τ ± α),

As well as negative sequence MMF vectors rotating counterclockwise (forming a reverse field)

Total MMF of fields rotating in opposite directions, i.e. F"x = F"xA + F"xB And F""x = F"xA + F"xB, are not equal in magnitude (Fig. 3.16.6), and therefore the resulting field of the machine is not pulsating, but rotating. In this field, the maximum value of the resulting MMF at different times does not remain constant, as with a circular field, i.e., the field is elliptical. In a two-phase machine it is also possible to obtain a circular rotating field; while one of the components of the MDS F"x or F"x should be missing. The conditions for obtaining a circular field in such a machine are reduced to mutual compensation of one of the MDS pairs F"xA And F"xB or F"xA And F"xB. The latter can happen if the indicated MMFs are equal in amplitude but opposite in phase, i.e. if α ± β = π .

Depends on the frequency of the supply voltage, on the power of the current load on the shaft, and on the number of electromagnetic poles of a given motor. This real rotation speed (or operating frequency) is always less than the so-called synchronous frequency, which is determined only by the parameters of the power source and the number of poles of the stator winding of a given asynchronous motor.

Thus, synchronous motor speed I- this is the rotation frequency of the magnetic field of the stator winding at the rated frequency of the supply voltage, and it is slightly different from the operating frequency. As a result, the number of revolutions per minute under load is always less than the so-called synchronous revolutions.

The figure below shows how the synchronous rotation speed for an asynchronous motor with a certain number of stator poles depends on the frequency of the supply voltage: the higher the frequency, the higher the angular speed of rotation of the magnetic field. For example, by changing the frequency of the supply voltage, the synchronous frequency of the motor is changed. At the same time, the operating speed of the engine rotor under load also changes.

Typically, the stator winding of an asynchronous motor is supplied with three-phase alternating current, which creates a rotating magnetic field. And the more pairs of poles, the lower the synchronous rotation speed will be - the rotation frequency of the stator magnetic field.

Most modern asynchronous motors have from 1 to 3 pairs of magnetic poles, in rare cases 4, because the more poles, the lower the efficiency of the asynchronous motor. However, with fewer poles, the rotor rotation speed can be changed very, very smoothly by changing the frequency of the supply voltage.

As noted above, the actual operating frequency of an asynchronous motor differs from its synchronous frequency. Why is this happening? When the rotor rotates at a frequency less than synchronous, the rotor conductors cross the stator's magnetic field at a certain speed and an emf is induced in them. This EMF creates currents in the closed conductors of the rotor, as a result, these currents interact with the rotating magnetic field of the stator, and a torque arises - the rotor is dragged by the magnetic field of the stator.

If the torque is sufficiently large to overcome the friction forces, then the rotor begins to rotate, and the electromagnetic torque is equal to the braking torque created by the load, friction forces, etc.

In this case, the rotor always lags behind the magnetic field of the stator, the operating frequency cannot reach the synchronous frequency, since if this happened, then the EMF would cease to be induced in the rotor conductors, and the torque simply would not appear. As a result, the “slip” value is introduced for the motor mode (usually 2-8%), and therefore the following engine inequality is valid:

But if the rotor of the same asynchronous motor is spun using some external drive, for example an internal combustion engine, to such a speed that the rotor speed exceeds the synchronous frequency, then the EMF in the rotor conductors and the active current in them will acquire a certain direction, and the asynchronous motor will turn into .

The total electromagnetic torque will turn out to be braking, and slip s will become negative. But in order for the generator mode to manifest itself, it is necessary to supply the asynchronous motor with reactive power, which would create a magnetic field of the stator. At the moment of starting such a machine in generator mode, the residual induction of the rotor and capacitors, which are connected to the three phases of the stator winding supplying the active load, may be sufficient.

The principle of obtaining a rotating magnetic field. The operation of asynchronous motors is based on a rotating magnetic field created by the MMF of the stator windings.

The principle of obtaining a rotating magnetic field using a stationary system of conductors is that if phase-shifted currents flow through a system of stationary conductors distributed in space around a circle, then a rotating field is created in space. If the system of conductors is symmetrical, and the phase shift angle between the currents of neighboring conductors is the same, then the amplitude of the induction of the rotating magnetic field and the speed are constant. If a circle with conductors is turned onto a plane, then using such a system it is possible to obtain a “running” field.

Rotating field of alternating current of a three-phase circuit. Let's consider obtaining a rotating field using the example of a three-phase asynchronous motor with three windings shifted along the circumference by 120° (Fig. 3.5) and connected by a star. Let the stator windings be powered by a symmetrical three-phase voltage with a phase shift of voltages and currents by 120°.

If for winding OH take the initial phase of the current equal to zero, then the instantaneous values ​​of the currents have the form

The current graphs are shown in Fig. 3.6. Let us assume that in each winding there are only two wires, occupying two diametrically located slots.

Rice. 3.5 Fig. 3.6

As can be seen from Fig. 3.6, at time to phase current A positive, and in phases IN And WITH– negative.

If the current is positive, then we take the direction of the current from the beginning to the end of the winding, which corresponds to the designation with the sign “x” at the beginning of the winding and the sign “ · "(dot) at the end of the winding. Using the right-hand propeller rule, it is easy to find the pattern of magnetic field distribution for a moment in time to(Fig. 3.7, a). Axis of the resulting magnetic field with induction In the face located horizontally.

In Fig. 3.7, b shows the picture of the magnetic field at a moment in time ti, corresponding to a change in the phase of the current by an angle = 60°. At this moment in time, the currents in the phases A And IN positive, i.e. the current flows in them from beginning to end, and the current is in phase WITH – negative, that is, it goes from the end to the beginning. The magnetic field turns out to be rotated clockwise by an angle = 60°. If the angular frequency of the current is , then . (Here , where is the frequency of the current in the network). At moments in time t 2 And t 3 the axis of the magnetic field will accordingly rotate through angles and (Fig. 3.6, c and G). After a time equal to the period T , the field axis will take its original position. Therefore, over the period T the field makes one revolution (Fig. 3.7, d) ( ()). In the case considered, the number of poles 2р = 2 and the magnetic field rotates with frequency n 1 =60 f 1 =60∙50=3000 rpm ( f 1 =50 Hz – industrial frequency). It can be proven that the resulting magnetic induction is a rotating field with amplitude

Where W – maximum induction of one phase; Intrusion– maximum induction of three phases; – the angle between the horizontal axis and the straight line connecting the center with an arbitrary point between the stator and the rotor.

Direction of field rotation. In the case considered, the direction of field rotation coincides with the direction of clockwise movement. If you swap the terminals of any two phases of the supply voltage, for example B And WITH , which corresponds to the reverse sequence of phases, the direction of rotation of the field will be opposite (counterclockwise), i.e. the magnetic field is reversed (cf. Fig. 3.8).

Formula for field rotation frequency. If the number of coils in each phase is increased and the phase shift between the currents is kept at 120°, then the frequency of rotation of the field will change. For example, with two coils in each phase, located as shown in Fig. 3.9, the field will rotate 180° in space in one period.

Rice. 3.8 Fig. 3.9 Fig. 3.10

To obtain a picture of the field, let’s take a moment in time to, when the current is in phase A positive, and the currents are in phases B and C negative. Using the rule of signs for currents, we find that in this case the number of poles 2р = 4 or p = 2 and then n 1 = 60 f 1 / p = 3000/2 =1500 rpm Reasoning in a similar way, for three coils in each phase we find the field pattern shown in Fig. 3.10. Here p = 3 and, therefore, n 1 = 1000 rpm.

The general formula for determining the rotation speed, rpm, will be

n 1 = 60 f 1 / p (3.1)

In all the cases considered, the coils of each phase were connected to each other in series. It is with this connection that the stator field rotation frequency for R= 1, 2 and 3 at f 1 = 50 Hz was 3000, 1500 and 1000 rpm, respectively.

Parallel connection of coils. Let us show that when the coils are switched from one phase to another and when they are connected in parallel, the number of field poles and, therefore, the field rotation frequency will be different from those considered. As an example, let's take two coils in each phase and connect them to each other in parallel as shown in Fig. 3.11, A and in expanded form in Fig. 3.11, 6 . From the picture of the field it is clear that R= 1, and rotation speed n 1 = 3000 rpm. It was shown above that when the same coils were connected in series, the rotation speed was 1500 rpm. When the current frequency in the network is 50 Hz, the rotation frequency of the stator field is determined from the expression

n 1 = 60 f 1 / p = 60 ∙50 / p .

Given a different number of pole pairs R = 1, 2, 3, 4, 5, 6, 8, 10, we find the frequency of field rotation. The calculation results are summarized in table. 3.1.

Table 3.1

Electrogravity is easy