In inductive electrical machines, the stator and rotor windings are connected by a magnetic field. In order to connect the rotating part of the machine with the machine stationary in the air gap through a system of stator windings, create rotating a magnetic field.
By rotating we mean a magnetic field whose induction vector moves in space (in a plane perpendicular to the rotor axis) with a certain angular velocity. If the amplitude of the induction vector is constant, then such a field is called circular. A rotating magnetic field can be created:
- alternating current in a two-phase system of windings shifted in space by 90°;
- three-phase alternating current in a three-phase system of windings shifted in space by 120°;
- direct current switched sequentially through windings distributed along the motor stator bore;
- direct current, switched using a commutator along winding branches located along the surface of the rotor (armature). Formation of a rotating magnetic field in a two-phase machine
- (rice. 1.2). IN In such a machine, the axes of the windings are shifted geometrically by 90° (a machine with one pair of poles is considered, r p = 1). The stator windings are powered by two-phase voltage, as shown in Fig. 1.2, i. Assuming the machine is symmetrical and unsaturated, we assume that the currents in the windings are also shifted by 90 electrical degrees (90° el.) and the magnetomotive force of the windings is proportional to the current (Fig. 1 .2,6). IN moment of time, = 0 winding current A is equal to zero, and the current in the winding b has the greatest negative value.
Rice. 1.2. Formation of a rotating magnetic field in a two-phase electric machine: a - winding connection diagram: b - system of two-phase currents in the stator windings: V- spatial vector diagram of magnetically moving forces created by the stator windings
Consequently, the total vector of magnetic motion forces (MFF) of the windings at an instant of time is equal to t and is located in space, as shown in Fig. 1.2, V. At the moment of time c 2 = 7s/ the currents in the windings will be Tl m / and, therefore, the total MMF vector will rotate by an angle To/ and will occupy the position in space indicated in Fig. 12, V, like 2 = 2 + 2. In the moment
time with 2 = i/2 the total vector of the MMF will be equal. Similarly, you can trace how the position of the total MMF vector changes at moments of time, etc. It can be seen that the vector rotates in space at a speed of co = 2ts, keeping its amplitude constant. The direction of field rotation is clockwise. We suggest making sure that if you apply to the phase A voltage = (co -), and per phase b voltage = co, then direction
rotation will be reversed.
Rice. 1.3. Schemes for connecting the windings of a three-phase motor: a - location of the motor windings at p p = 1; b - star connection of windings; V- diagrams of three-phase currents in the motor windings
Thus, the combination of a spatial shift of the winding axes by 90 geometric degrees (90°) and a phase shift of the alternating current in the windings by (90° el.) electrical degrees allows the formation of a magnetic field rotating along the circumference of the stator in the air gap of the machine.
The mechanism of formation of a rotating magnetic field in a three-phase alternating current machine. The windings of the machine are shifted in space by 120° (Fig. 1.3, a) and are powered by a three-phase voltage system. The currents in the machine winding are shifted by 120°el. (Fig. 1.3, V):
The resulting MMF vector of the stator windings is equal to:
Where w- number of turns of windings.
Let's consider the position in space of the vector at the moment of time (Fig. 1.4, o). The winding MMF vector o t is directed along the o axis in the positive direction and is equal to 0, w, those. ABOUT, . Vector MDS winding With, directed along the axis With and equals 0, . The sum of vectors j and j is directed along the axis b in the negative direction and with this sum the winding MMF vector is added b, equal The sum of three vectors forms a vector X= 3 /2, occupying at the moment of time the position shown in Fig. 1.4, o. After time = l/30 (at a frequency of 50 Hz after 1/300 s) there will be a moment in time 2 at which the MMF vector of the winding o is equal, and the MMF vectors of the windings b And With equal - 0.5. The resulting MMF vector 2 at time 2 will take the position shown in Fig. 1.4,5, i.e. will move relative to the previous position at at an angle of 60° clockwise. It is easy to verify that at time 3 the resulting MMF vector of the stator windings will take position 3, i.e. will continue to move clockwise. During the period of supply voltage = 2l/co = 1/ the resulting MMF vector will complete a full revolution, i.e. the speed of rotation of the stator field is directly proportional to the frequency of the current in its windings and inversely proportional to the number of pole pairs:
where n is the number of pole pairs of the machine.
If the number of motor pole pairs is greater than one, then the number of winding sections located around the circumference of the stator increases. So, if the number of pole pairs n = 2, then three phase windings will be located on one half of the stator circumference and three on the other. In this case, during one period of the supply voltage, the resulting MMF vector will make half a revolution and the rotation speed of the stator magnetic field will be half that of machines with „=1-
Rice. 1.4.A- с = 7с/ b- co = l/ V- с = 7с/
The operation of almost all alternating current motors: synchronous with electromagnetic excitation (SM), with excitation from permanent magnets (PMSM), synchronous reluctance motors (SRM), and asynchronous motors (IM) is based on the principle of creating a rotating magnetic field.
According to the principles of electrodynamics, in all electric motors (except reactive ones), the developed electromagnetic torque is the result of the interaction of magnetic fluxes (flux linkages) created in the moving and stationary parts of the electric motor. The moment is equal to the product of the vectors of these flows, as shown in Fig. 1.5, and the value of the moment is equal to the product of the modules of the flow vectors and the sine of the spatial angle 0 between the flow vectors:
Where To - design factor.
Rice. 1.5.
Synchronous(SD, SDPM, SRD) and asynchronous motors They have almost identical stator designs, but the rotors are different. The distributed stator windings of these electric motors fit into a relatively large number of semi-closed stator slots. If we do not take into account the influence of tooth harmonics, then the stator windings form a magnetic flux of constant amplitude, rotating at a constant speed determined by the frequency of the current. In real structures, the presence of grooves and teeth in the stator magnetic circuit leads to the appearance of higher harmonics of magnetizing forces, which leads to pulsations of the electromagnetic torque.
On the rotor of the LED there is an excitation winding, which is powered by direct current from an independent voltage source - the exciter. The excitation current creates an electromagnetic field, stationary relative to the rotor and rotating in the air gap together with the rotor at a speed of [see. (1.7)]. For synchronous motors with power up to 100 kW, excitation from permanent magnets is used, which are installed on the rotor.
The magnetic force lines of the rotor field, created by the excitation winding or permanent magnets, “couple” with the electromagnetic field of the stator rotating synchronously with it. Interaction of stator fields X and rotor 0 creates an electromagnetic torque on the shaft of a synchronous machine.
In the absence of load on the shaft, the field vectors of the stator and rotor 0 coincide in space and rotate together at a speed of 0 (Fig. 1.6, i).
When a moment of resistance is applied to the motor shaft, the vectors [ and 0 diverge (stretch like a spring) at an angle of 0, and both vectors continue to rotate at the same speed from 0 (Fig. 1 .6,6). If angle 0 is positive, then the synchronous machine operates in motor mode. A change in the load on the motor shaft corresponds to a change in angle 0 Maximum torque M will be at 0 = l;/ (0 - electrical degrees). If
the load on the motor shaft exceeds M then the synchronous mode is disrupted and the engine falls out of synchronism. If the angle is negative 0, the synchronous machine will operate as a generator.
Rice. 1.6.A- at ideal idle speed; b - with load on the shaft
Synchronous reluctance motor - This is a motor with pronounced rotor poles without an excitation winding, where the torque is determined by the desire of the rotor to occupy a position in which the magnetic resistance between the excited stator winding and the rotor takes on a minimum value.
In the RDS, the rotor is salient-pole (Fig. 1.7). It has different magnetic conductivity along its axes. Longitudinal axis d, passing through the middle of the pole, the conductivity is maximum, and along the transverse axis q- minimal. If the axis of the stator magnetizing forces coincides with the longitudinal axis of the rotor, there is no curvature of the magnetic flux lines and the torque is zero. When the flow of the stator axis is displaced relative to the longitudinal axis d When the magnetic field (MF) rotates, the flux lines of force become bent and an electromagnetic torque arises. The highest torque at the same stator current is obtained at angle 0 = 45°el.
The main difference between an asynchronous motor and a synchronous one is that the speed of rotation of the motor rotor is not equal to the speed of the magnetic field created by the currents in the stator windings. The difference in speed between the stator and rotor fields is called sliding= co - co. Thanks to sliding, the magnetic field lines of the rotating stator field cross the conductors of the rotor winding and induce emf and rotor current in it. The interaction of the stator field and rotor current determines the electromagnetic torque of an asynchronous motor.
Rice. 1.7.
Depending on the rotor design, asynchronous motors are distinguished with phase And short-circuited rotor. In slip-ring motors, a three-phase winding is located on the rotor, the ends of which are connected to slip rings, through which the rotor circuit is removed from the machine for connection to starting resistors with subsequent short-circuiting of the windings.
In an asynchronous motor, when there is no load on the shaft, only magnetizing currents flow through the stator windings, creating the main magnetic flux, and the amplitude of the flux is determined by the amplitude and frequency of the supply voltage. In this case, the rotor rotates at the same speed as the stator field. No EMF is induced in the rotor windings, there is no rotor current and, therefore, the torque is zero.
When a load is applied, the rotor rotates slower than the field, slip occurs, an EMF proportional to the slip is induced in the rotor windings, and rotor currents arise. The stator current, as in a transformer, increases by an appropriate value. The product of the active component of the rotor current and the stator flux modulus determines the motor torque.
What all motors have in common [except switched reluctance motors (SMR)] is that the main magnetic flux in the air gap rotates relative to a stationary stator at a given frequency and angular velocity co. This magnetic flux carries along the rotor, which rotates for synchronous machines with the same angular speed co = co, or for asynchronous machines with some lag - slip 5. The power lines forming the main flow have a minimum length when the engine is running idle (=). In this case, the vector axes of the magnetizing forces of the stator and rotor coincide. When a load appears on the motor shaft, the axes diverge, and the force lines bend and lengthen. Since lines of force always tend to shorten in length, tangential forces appear, creating torque.
In recent years, they have begun to be used switched reluctance motors. This type of motor has a salient pole stator with coil windings on each pole. The rotor is also salient pole, but with a different number of poles without windings. A unipolar current is alternately supplied to the stator windings from a special converter - a commutator, and a nearby rotor tooth is attracted to these excited poles. Then the next stator pole is excited in turn. The stator pole windings are switched in accordance with the signals from the rotor position sensor. This, as well as the fact that the current in the stator windings is regulated depending on the load torque, is the main difference between VID and a stepper motor.
In VIEW (Fig. 1.8), the torque is proportional to the amplitude of the main flow and the degree of curvature of the magnetic field lines. At the beginning, when the rotor pole (teeth) begins to overlap the stator pole, the curvature of the power lines is maximum and the flux is minimum. When the pole overlap is maximum, the bending of the field lines is minimal, and the amplitude of the flow increases, while the torque remains approximately constant. As the magnetic system of the VID becomes saturated, the increase in flux is limited, even with an increase in the current in the windings of the VID. The change in torque as the rotor poles pass relative to the stator poles causes uneven rotation of the VID shaft.
Rice. 1.8.
In a DC motor, the field winding is located on the stator and the field created by this winding is stationary. A rotating magnetic field is created in the armature, the rotation speed of which is equal to the speed of rotation of the armature, but is directed in the opposite direction. This is achieved by the fact that alternating current flows through the turns of the armature winding, switched by a mechanical frequency converter - collector apparatus.
The electromagnetic torque of a DC motor determines the interaction of the main flux created by the field winding and the current in the turns of the armature winding: M = k/ I
If we replace the brush-commutator apparatus of a DC motor with a semiconductor switch, we get brushless DC motor. A practical implementation of such motors is a valve motor. Structurally valve motor is a three-phase synchronous machine with electromagnetic excitation or excitation from permanent magnets. The stator windings are switched using a semiconductor controlled converter - a commutator, depending on the position of the motor rotor.
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. Thanks to sliding in the rotor, electricity, 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:
- Up from nominal. To do this, the magnetic flux is reduced using additional resistances or a voltage regulator;
- 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
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 rotates in the opposite direction relative to the rotating magnetic field.
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.
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.
A feature of multiphase systems is the ability to create a rotating magnetic field in a mechanically stationary device.
A coil connected to an alternating current source produces a pulsating magnetic field, i.e. a magnetic field that varies in magnitude and direction.
Let's take a cylinder with an internal diameter D. On the surface of the cylinder we will place three coils, spatially displaced relative to each other by 120 o. We connect the coils to a three-phase voltage source (Fig. 12.1). In Fig. Figure 12.2 shows a graph of changes in instantaneous currents forming a three-phase system.
Each of the coils creates a pulsating magnetic field. The magnetic fields of the coils, interacting with each other, form a resulting rotating magnetic field, characterized by the vector of the resulting magnetic induction
In Fig. 12.3 shows the magnetic induction vectors of each phase and the resulting vector constructed for three moments in time t1, t2, t3. The positive directions of the coil axes are designated +1, +2, +3.
At the moment t = t 1, the current and magnetic induction in the coil A-X are positive and maximum, in the coils B-Y and C-Z they are the same and negative. The vector of the resulting magnetic induction is equal to the geometric sum of the vectors of the magnetic induction of the coils and coincides with the axis of the coil A-X. At the moment t = t 2, the currents in the coils A-X and C-Z are equal in magnitude and opposite in direction. The current in phase B is zero. The resulting magnetic induction vector rotated clockwise by 30 o. At the moment t = t 3, the currents in the coils A-X and B-Y are equal in magnitude and positive, the current in the C-Z phase is maximum and negative, the vector of the resulting magnetic field is located in the negative direction of the axis of the C-Z coil. During the period of alternating current, the vector of the resulting magnetic field will rotate 360 o.
Magnetic field rotation speed or synchronous rotation speed
where P is the number of pole pairs.
The coils shown in Fig. 12.1, create a two-pole magnetic field, with the number of poles 2P = 2. The field rotation frequency is 3000 rpm.
To obtain a four-pole magnetic field, it is necessary to place six coils inside the cylinder, two for each phase. Then, according to formula (12.1), the magnetic field will rotate twice as slowly, with n 1 = 1500 rpm.
To obtain a rotating magnetic field, two conditions must be met.
1. Have at least two spatially offset coils.
2. Connect out-of-phase currents to the coils.
12.2. Asynchronous motors.
Design, principle of operation
The asynchronous motor has motionless
part called stator
, And rotating
part called rotor
. The stator contains a winding that creates a rotating magnetic field.
There are asynchronous motors with squirrel cage and wound rotor.
Aluminum or copper rods are placed in the slots of the short-circuited rotor. The ends of the rods are closed with aluminum or copper rings. The stator and rotor are made of electrical steel sheets to reduce eddy current losses.
The phase rotor has a three-phase winding (for a three-phase motor). The ends of the phases are connected into a common unit, and the beginnings are brought out to three slip rings placed on the shaft. Fixed contact brushes are placed on the rings. A starting rheostat is connected to the brushes. After starting the engine, the resistance of the starting rheostat is gradually reduced to zero.
Let's look at the operating principle of an asynchronous motor using the model shown in Figure 12.4.
Let's imagine the rotating magnetic field of the stator in the form of a permanent magnet rotating at a synchronous rotation speed n 1.
Currents are induced in the conductors of the closed rotor winding. The poles of the magnet move clockwise.
To an observer placed on a rotating magnet, it seems that the magnet is stationary, and the conductors of the rotor winding are moving counterclockwise.
The directions of rotor currents determined by the right-hand rule are shown in Fig. 12.4.
Rice. 12.4
Using the left-hand rule, we find the direction of the electromagnetic forces acting on the rotor and causing it to rotate. The motor rotor will rotate at a rotation speed n 2 in the direction of rotation of the stator field.
The rotor rotates asynchronously, i.e. its rotation frequency n 2 is less than the rotation frequency of the stator field n 1.
The relative speed difference between the stator and rotor fields is called slip.
The slip cannot be equal to zero, since at the same speeds of the field and the rotor the induction of currents in the rotor would cease and, therefore, there would be no electromagnetic torque.
The rotating electromagnetic torque is balanced by the counteracting braking torque M em = M 2.
As the load on the motor shaft increases, the braking torque becomes greater than the rotating torque, and slip increases. As a result, the induced in the rotor increases EMF winding and currents. The torque increases and becomes equal to the braking torque. The torque can increase with increasing slip up to a certain maximum value, after which, with a further increase in the braking torque, the torque decreases sharply and the engine stops.
The slip of a stalled motor is equal to one. The engine is said to be running in short circuit mode.
The rotational speed of an unloaded asynchronous motor n 2 is approximately equal to the synchronous frequency n 1. Slip of an unloaded engine S 0. The engine is said to be running in idle mode.
The slip of an asynchronous machine operating in motor mode varies from zero to one.
An asynchronous machine can operate in generator mode. To do this, its rotor must be rotated by a third-party motor in the direction of rotation of the stator magnetic field with a frequency n 2 > n 1. Slip of an asynchronous generator.
An asynchronous machine can operate in electric machine brake mode. To do this, it is necessary to rotate its rotor in the direction opposite to the direction of rotation of the stator magnetic field.
In this mode, S > 1. Typically, asynchronous machines are used in motor mode. The induction motor is the most common type of motor in industry. The field rotation frequency in an asynchronous motor is strictly related to the network frequency f 1 and the number of stator pole pairs. At frequency f 1 = 50 Hz, there is the following series of rotation frequencies.