Asynchronous motors (IM) are the most common type of motor, because... they are simpler and more reliable in operation, with equal power they have less weight, dimensions and cost in comparison with DPT. The circuit diagrams for switching on the blood pressure are shown in Fig. 2.14.

Until recently, IMs with squirrel-cage rotors were used in unregulated electric drives. However, with the advent of thyristor frequency converters (TFCs) of the voltage supplying the stator windings of the IM, squirrel-cage motors began to be used in adjustable electric drives. Currently, power transistors and programmable controllers are used in frequency converters. The speed control method is called pulse and its improvement is the most important direction in the development of electric drives.

Rice. 2.14. a) circuit diagram for switching on an IM with a squirrel-cage rotor;

b) circuit diagram for switching on an IM with a phase-wound rotor.

The equation for the mechanical characteristics of the blood pressure can be obtained based on the equivalent circuit of the blood pressure. If we neglect the active resistance of the stator in this circuit, then the expression for the mechanical characteristic will have the form:

,

Here M k – critical moment; S to- the corresponding critical slip; U f– effective value of the phase voltage of the network; ω 0 =2πf/p– angular speed of the rotating magnetic field of the IM (synchronous speed); f– supply voltage frequency; p– number of pairs of poles of the IM; x k– inductive phase resistance of the short circuit (determined from the equivalent circuit); S=(ω 0 -ω)/ω 0– slip (rotor speed relative to the speed of the rotating field); R 2 1– total active resistance of the rotor phase.

The mechanical characteristics of an IM with a squirrel-cage rotor are shown in Fig. 2.15.

Rice. 2.15. Mechanical characteristics of an induction motor with a squirrel-cage rotor.

Three characteristic points can be distinguished on it. Coordinates of the first point ( S=0; ω=ω 0 ; M=0). It corresponds to the ideal idle mode, when the rotor speed is equal to the speed of the rotating magnetic field. Coordinates of the second point ( S=S to; M=M k). The engine is running at maximum torque. At M s >M k the motor rotor will be forced to stop, which is a short circuit for the motor. Therefore, the engine torque at this point is called critical M k. Coordinates of the third point ( S=1; ω=0; M=M p). At this point, the engine operates in start mode: rotor speed ω=0 and the starting torque acts on the stationary rotor M p. The section of the mechanical characteristic located between the first and second characteristic points is called the working section. On it the engine operates in steady state. For an IM with a squirrel-cage rotor, if the conditions are met U=U n And f=f n the mechanical characteristic is called natural. In this case, on the working section of the characteristic there is a point corresponding to the nominal operating mode of the engine and having coordinates ( S n; ω n; M n).

Electromechanical characteristics of blood pressure ω=f(I f), which is shown as a dashed line in Fig. 2.15, in contrast to the electromechanical characteristic of the DPT, coincides with the mechanical characteristic only in its working section. This is explained by the fact that during startup due to the changing frequency of the emf. in the rotor winding E 2 the frequency of the current and the ratio of the inductive and active resistance of the winding changes: at the beginning of the start-up, the frequency of the current is higher and the inductive resistance is greater than the active one; with increasing rotor speed ω the frequency of the rotor current, and hence the inductive resistance of its winding, decreases. Therefore, the starting current of the IM in direct start mode is 5–7 times higher than the rated value I fn, and the starting torque M p equal to nominal M n. Unlike DPT, where when starting it is necessary to limit the starting current and starting torque, when starting an IM, the starting current must be limited and the starting torque increased. The last circumstance is the most important, since the DPT with independent excitation starts when M s<2,5М н , DPT with sequential excitation at M s<5М н , and blood pressure when working at a natural characteristic at M s<М н .

For an IM with a squirrel-cage rotor, the increase M p is ensured by a special design of the rotor winding. The groove for the rotor winding is made deep, and the winding itself is arranged in two layers. When starting the engine, frequency E 2 and the rotor currents are large, which leads to the appearance of a current displacement effect - the current flows only in the upper layer of the winding. Therefore, the winding resistance and the starting torque of the motor increase M P. Its value can reach 1.5M n.

For an IM with a wound rotor, the increase M P is ensured by changing its mechanical characteristics. If resistance R P, included in the rotor current flow circuit, is equal to zero - the engine operates at a natural characteristic and M P =M N. At R P >0 the total active resistance of the rotor phase increases R 2 1. Critical slip S to as it increases R 2 1 also increases. As a result, in an IM with a wound rotor, the introduction R P into the rotor current flow circuit leads to a displacement M K towards large slips. At S K =1 M P =M K. Mechanical characteristics of IM with wound rotor at R P >0 are called artificial or rheostat. They are shown in Fig. 2.16.

The most common electric motors in industry, agriculture and all other applications are asynchronous motors. It can be said that squirrel-cage induction motors are the main means of converting electrical energy into mechanical energy. The operating principle of an asynchronous motor was discussed in § 1.2 and 6.1.

The electromagnetic field of the stator rotates in the air gap of the machine at a speed of co = 2 nf ( /r p. At a standard frequency of 50 Hz, the rated rotor speed depends on the number of pole pairs r p(Table 6.1).

Table 6.1

Dependence of rotation speed of asynchronous motors on the number of pairs

poles

Depending on the design of the rotor of an asynchronous motor, asynchronous motors with phase And squirrel cage rotor. In motors with a wound rotor, a three-phase distributed winding is located on the rotor, usually connected in a star; the ends of the windings are connected to slip rings, through which the electrical circuits of the rotor are removed from the machine for connection to starting resistances with subsequent short-circuiting of the windings. In squirrel-cage motors the winding is made in the form squirrel cage - rods short-circuited on both sides by rings. Despite the specific design, the squirrel cage can also be considered as a three-phase short-circuited winding.

Electromagnetic torque M in an asynchronous motor is created due to the interaction of the rotating magnetic field of the stator F with the active component of the rotor current:

Where To - constructive constant.

The rotor current arises due to EMF E 2, which is induced in the rotor windings by a rotating magnetic field. When the rotor is stationary, the asynchronous motor is a three-phase transformer with windings short-circuited or loaded with starting resistance. The EMF that occurs when the rotor is stationary in its windings is called rated phase EMF rotor E 2n. This EMF is approximately equal to the stator phase voltage divided by the transformation ratio to t:

When the motor is rotating, the rotor EMF E 2 and the frequency of this EMF (and therefore the frequency of the current in the rotor windings) depends on the frequency of the rotating field crossing the conductors of the rotor winding (in a squirrel-cage motor - rods). This frequency is determined by the difference between the speeds of the stator field co and the rotor field co, which is called absolute glide:

When analyzing the operating modes of an asynchronous motor with a constant supply voltage frequency (50 Hz), the relative slip value is usually used

When the engine rotor is stationary, s = 1. The greatest EMF of the rotor when operating in motor mode will be with a stationary rotor ( E 2n), as the speed increases (slip decreases) EMF E 2 will decrease:

Similarly, the frequency of the EMF and rotor current / 2 with a stationary rotor will be equal to the frequency of the stator current /, and as the speed increases it will decrease in proportion to slip:

In the nominal mode, the rotor speed differs slightly from the field speed, and the nominal slip is only 2...3% for general purpose motors with a power of 1.5...200.0 kW, and about 1% for motors of higher power. Accordingly, in the nominal mode the rotor EMF is 1...3% of the nominal value of this EMF at 5 = 1. The frequency of the rotor current in the nominal mode will be only 0.5... 1.5 Hz. At 5 = 0, when the rotor speed is equal to the field speed, the rotor emf E 2 and rotor current / 2 will be equal to zero, the motor torque will also be equal to zero. This mode is ideal idle mode.

The dependence of the EMF frequency and rotor current on slip determines the unique mechanical characteristics of an asynchronous motor.

Operation of an asynchronous motor with a wound rotor, the windings of which are short-circuited. As shown in (6.16), the motor torque is proportional to the flux Ф and the active component of the rotor current / 2 "a, reduced to the stator. The flux created by the windings depends on the value and frequency of the supply voltage

The rotor current is

where Z 2 is the impedance of the rotor winding phase.

It should be taken into account that the inductive reactance of the rotor winding x 2 is a variable value that depends on the frequency of the rotor current, and, therefore, on the slip: x 2 = 2p 2 2 = 2k t 2.

With a stationary rotor at s = 1 inductive reactance of the rotor winding is maximum. As the speed increases (slip decreases), the rotor inductive reactance x 2 decreases and upon reaching the rated speed is only 1...3% of the resistance at 5 = 1. Designating x 2s=l = x 2n, we get

Let us reduce the parameters of the rotor circuit to the stator winding, taking into account the transformation ratio and based on the conservation

power equality:

And the active component of the rotor current has the form:

Dividing the numerator and denominator of formula (6.26) by s, we get

The mathematical operation performed is dividing the numerator and denominator by s, of course, does not change the validity of equality (6.29), but is of a formal nature, which must be taken into account when considering this relationship. In fact, as follows from the original formula (6.26), the inductive reactance of the rotor depends on slip x 2, and active resistance g 2 remains constant. Using expression (6.29), by analogy with a transformer, we can create an equivalent circuit for an asynchronous motor, which is shown in Fig. 6.4 ,A.

Rice. 6.4.Equivalent circuits of an asynchronous motor: a - complete circuit; b- diagram with a remote magnetizing circuit

To analyze an unregulated electric drive, this circuit can be simplified by transferring the magnetization circuit to the motor terminals. A simplified U-shaped equivalent circuit is shown in Fig. 6.4D based on which, the rotor current will be equal to:

Where x k =x + x" 2i- inductive short circuit resistance. The active component of the rotor current taking into account (6.28) will be:

Substituting (6.22) and (6.31) into (6.16), we obtain an expression for the torque of an asynchronous motor

Natural mechanical characteristic of an asynchronous motor oz = f(M) with a wound rotor, the windings of which are short-circuited, is shown in Fig. 6.5. The electromechanical characteristic of the motor ω = /(/j) is also shown here, determined from the vector diagram of the asynchronous motor in Fig. 6.6, I x = I + / 2 ".

Rice. AT 5. Natural mechanical and electromechanical characteristics of an asynchronous motor

Rice. V.V. Simplified vector diagram of an induction motor

Assuming the magnetizing current to be reactive, we obtain where

Equating the derivative dM/ds= , let's find the maximum value of the torque of an asynchronous motor M k = M n and the corresponding critical slip value s K:

Where sK- critical slip; the sign “+” means that this value refers to the motor mode, the sign “-” - to the generator mode of regenerative braking.

Taking into account (6.34) and (6.35), the formula of the mechanical characteristic (6.32) can be transformed into a more convenient expression - Kloss formula:

For motors with a power of more than 15 kW, the resistance of the stator winding is small and at a frequency of 50 Hz is significantly less x k. Therefore, in the previously given expressions, the value of r can be neglected:

Using the obtained formulas, you can calculate the mechanical characteristics of an asynchronous motor, using its passport data, knowing the rated torque Mn, nominal slip s h and motor overload capacity X.

Note that by analyzing the electromagnetic processes in an asynchronous motor for a steady state, we arrived at the same relations (6.9) and (6.10) that were obtained in § 6.1 based on the differential equations of a generalized two-phase machine.

Analysis of the features of the mechanical characteristics of an asynchronous motor (see Fig. 6.5). It is non-linear and consists of two parts. The first - working part - within the sliding range from 0 to s K . This part of the characteristic is close to linear and has negative stiffness. Here the torque developed by the motor is approximately proportional to the stator current 1 X and rotor / 2. Since on this part the characteristics s then the second term of the denominator in formula (6.39) is significantly less than the first, and it can be neglected. Then the working part of the mechanical characteristic can be approximately represented in linear form, where the moment is proportional to the sliding:

The second part of the mechanical characteristics of an asynchronous motor with slips of large s K (s>s K) curvilinear, with a positive stiffness value (3. Despite the fact that the motor current increases as the slip increases, the torque, on the contrary, decreases. If the rotor windings of an asynchronous motor with a wound rotor are short-circuited in the external circuit, then the starting current of such a motor (with = 0 and 5 =1) will be very large and will exceed the rated one by 10-12 times. At the same time, the starting torque will be about 0.4...0.5 of the rated one. As will be shown below, for squirrel-cage motors the starting current will be ( 5...6)/n, and the starting torque is (1.1...1.3)A/n.

To explain this discrepancy between the starting current and torque, consider the vector diagrams of the rotor circuit (Fig. 6.7) for two cases: when the slip is large (the starting part of the characteristic); when the slip is small (the working part of the characteristic). At start-up, when 5=1, the rotor current frequency is equal to the mains frequency (f 2 = 50 Hz). Inductive reactance of the rotor winding [see. (6.24)] is large and significantly exceeds the active resistance of the rotor /* 2, the current lags behind the rotor EMF by a large angle φ, i.e. The rotor current is mainly reactive. Since the rotor EMF in this case will be large 2 = 2n, then the starting current will be very large, however, due to the small value of cp 2, the active component of the rotor current 1 2a will be small, therefore, the torque developed by the engine will also be small.

When the engine accelerates, slip decreases, the rotor EMF, rotor current frequency, and rotor inductive reactance decrease proportionally. Accordingly, the value of the total rotor and stator current decreases, however, due to an increase in f 2, the active component of the rotor current increases and the motor torque increases.

When engine slip becomes less sK, the frequency of the rotor current will decrease so much that the inductive reactance will become less active, and the rotor current will be practically active (Fig. 6.7,6), The motor torque will be proportional to the rotor current. So, if the rated motor slip is 5 n = 2%, then compared to the starting parameters, the frequency of the rotor current will decrease by 50 times, and the inductive reactance of the rotor will correspondingly decrease. Therefore, despite the fact that the rotor EMF will also decrease by 50 times, it will be sufficient to create the rated rotor current, providing the rated motor torque. Thus, the originality of the mechanical characteristics of an asynchronous motor is determined by the dependence of the rotor inductive reactance on slip.

Rice. AT 7. Vector diagram of the rotor circuit of an asynchronous motor: a - with large slip: b - with small slip

Based on the above, to start an asynchronous motor with a wound rotor, measures must be taken to increase the starting torque and reduce starting currents. For this purpose, additional active resistance is included in the rotor circuit. As follows from formulas (6.34), (6.35), the introduction of additional active resistance does not change the maximum motor torque, but only changes the value

critical slip: , where /?" ext - reduced to

the stator is an additional resistance in the rotor circuit.

The introduction of additional active resistance increases the total resistance of the rotor circuit, as a result the starting current decreases and the cf of the rotor circuit increases, which leads to an increase in the active component of the rotor current and, consequently, the starting torque of the engine.

Typically, a sectioned resistance is introduced into the rotor circuit of a wound-rotor motor, the stages of which are bridged by starting contactors. Rheostatic starting characteristics can be calculated using formula (6.39), using the value sK, appropriate R 2 b for each starting resistance stage. The circuit for connecting additional resistances and the corresponding rheostatic mechanical characteristics of the engine are shown in Fig. 6.8. The mechanical characteristics have a common point of ideal idle speed equal to the rotation speed of the stator electromagnetic field co, and the rigidity of the working part of the characteristics decreases as the total active resistance of the rotor circuit increases (2 + /? ext).

When starting the engine, the total additional resistance /? 1 ext. Upon reaching the speed at which the engine torque L/ becomes close to the resistance moment M s, part of the starting resistance is shunted by contactor K1, and the motor switches to a characteristic corresponding to the value of the additional resistance /? 2 ext. In this case, the engine torque increases to a value M 2. As the engine accelerates further, contactor K2 short-circuits the second stage of the starting resistance. After closing the short-circuit contactor contacts, the motor switches to a natural characteristic and will operate at a speed corresponding to point 1.

To calculate the starting characteristics, you need to set the torque value M ( at which the stages of starting resistors are switched M x = 1,2M s. Starting torque values M 2(Fig. 6.8) are found using the formula = A/, where T - number of steps.

To calculate the starting resistance stages, we find the nominal rotor resistance R 2h = 2n.lin/>/3 2n

Stage resistances:

With squirrel-cage asynchronous motors, it is impossible to introduce additional resistance into the rotor circuit. However, the same result can be obtained if we use the effect of displacement of current onto the surface of the conductor. The essence of this phenomenon is as follows. According to the law of electromagnetic induction, when alternating current flows through a conductor, a self-induction emf is induced in it, directed against the current:

The value of this EMF depends on the current I, its frequency and inductance, determined by the characteristics of the environment surrounding the conductor. If the conductor is in the air, then the magnetic permeability of the medium is very small, therefore, the inductance is small L. In this case, at a frequency of 50 Hz co=/s, the influence of the self-induction EMF is insignificant. It’s another matter when the conductor is placed in the body of the magnetic circuit. Then the inductance increases many times and the self-inductive emf, directed against the current, plays the role of inductive resistance, preventing the flow of current.

Rice. AT 9. Rotor design of an asynchronous squirrel-cage motor: A- with a deep groove; b - with a double cage; V- diagram explaining the effect of current displacement

Let us consider the manifestation of the action of self-induction EMF for the case of a conductor (rotor winding rod) placed in a deep groove in the magnetic circuit of the motor rotor (Fig. 6.9 ,A). Let us conditionally divide the cross-section of the rod into three parts, which are connected in parallel. The current flowing through the lower part of the rod forms a flux Ф, the magnetic field lines of which are closed along the magnetic circuit. In this part of the conductor a large self-inductive emf occurs eLV anti-current 1 2у

Current / 23 (Fig. 6.9, V), flowing along the upper part of the rotor winding rod forms a flow F 3, but since the power lines of this flow are closed through the air for a significant part of their length, the flow F 3 will be much less than the flow F,. Hence the EMF e 1b will be many times less than eLV

The indicated distribution of self-induction emf along the height of the rod is typical for the mode when the frequency of the rotor current is high - close to 50 Hz. In this case, since all three parts of the rotor bar are connected in parallel (see Fig. 6.9, V), then the rotor current / 2 will go along the top of the rod, where there is less back EMF e L . This phenomenon is called displacement of current onto the surface of the groove. In this case, the effective cross-section of the rod through which the current flows will be several times smaller than the total cross-section of the rotor winding rod. Thus, the active resistance of the rotor increases g 2. Note that since the self-induction emf depends on the frequency of the current (i.e., on slip), then the resistance g 2 And x 2 are sliding functions.

At start-up, when the slip is large, resistance r 2 increases (additional resistance is introduced into the rotor circuit, as it were). As the motor accelerates, the motor slip decreases, the current displacement effect weakens, the current begins to spread down the cross section of the conductor, the resistance g 2 decreases. When the operating speed is reached, the frequency of the rotor current is so low that the phenomenon of current displacement no longer has an effect, the current flows across the entire cross-section of the conductor, and the resistance g 2 minimal. Thanks to this automatic resistance change g 2, The start-up of asynchronous squirrel-cage motors proceeds favorably: the starting current is

5.0...6.0 nominal, and the starting torque is 1.1...1.3 nominal.

During design, you can vary the parameters of the starting characteristics of an asynchronous motor by changing the shape of the groove, as well as the resistance of the material of the rods (alloy composition). Along with deep grooves, double grooves are used, forming a double squirrel cage (Fig. 6.9,6), and also use pear-shaped grooves, etc.

In Fig. 6.10 presents typical mechanical characteristics of various modifications of asynchronous squirrel-cage motors.

Rice. AT 10 O'CLOCK. Approximate mechanical characteristics of asynchronous squirrel-cage motors: a - normal design; 6 - with increased slip; V- with increased starting torque; g- crane-metallurgical series

Normal squirrel-cage motors used to drive a wide class of working machines and mechanisms, primarily for drives operating in long-term operation. This design is characterized by high efficiency and minimal nominal slip. The mechanical characteristic in the area of ​​large slips usually has a small dip, characterized by a minimum moment M t(p.

High slip motors have a softer mechanical characteristic and are used in the following cases: when two or more engines operate on a common shaft, for mechanisms (for example, cranks) with a cyclically changing load, when to overcome movement resistance it is advisable to use the kinetic energy stored in the moving parts of the electric drive , and for mechanisms operating in intermittent mode.

Motors with increased starting torque designed for mechanisms with difficult starting conditions, for example, for scraper conveyors.

Engines of crane-metallurgical series Designed for mechanisms operating in intermittent mode with frequent starts. These motors have a high overload capacity, high starting torque, increased mechanical strength, but worse energy performance.

Analytical calculation of the mechanical characteristics of squirrel-cage asynchronous motors is quite complex, so the characteristic can be approximately constructed using four points: at idle (5 = 0), at maximum Mk, launcher M p and minimum M t[p moment at the beginning of the launch. Data for these characteristic points are given in catalogs and reference books for asynchronous motors. Calculation of the working part of the mechanical characteristics of a short-circuited asynchronous motor (with slips from 0 to 5 k) can be done using the Kloss formula (6.36), (6.39), since the effect of current displacement in the operating mode is almost not manifested.

Complete mechanical characterization of an asynchronous motor in all quadrants of the field M-s, shown in Fig. 6.11.

An asynchronous motor can operate in three braking modes: regenerative and dynamic braking and back-on braking. Capacitor braking is also a specific braking mode.

Regenerative regenerative braking possible when the rotor speed is higher than the rotation speed of the stator electromagnetic field, which corresponds to a negative slip value: oo>co 0 5

The slightly larger value of the maximum torque in generator mode is explained by the fact that the losses in the stator (at the resistance G () in motor mode, the torque on the shaft is reduced, and in generator mode, the torque on the shaft must be greater to cover the losses in the stator.

Note that in the regenerative braking mode, the asynchronous motor generates and supplies active power to the network, and in order to create an electromagnetic field, the asynchronous motor, even in generator mode, must exchange reactive power with the network. Therefore, an asynchronous machine cannot operate as an autonomous generator when disconnected from the network. It is possible, however, to connect an asynchronous machine to capacitor banks as a source of reactive power.

Dynamic braking method: the stator windings are disconnected from the AC mains and connected to a DC voltage source (Fig. 6.12). When the stator windings are powered with direct current, an electromagnetic field motionless in space is created, i.e. rotation speed of the stator field with dt = . The slip will be equal to 5 DT = -co/co n, where co n is the nominal angular velocity of rotation of the stator field.

Rice. 6 .12 A- enable dynamic braking; b - when connecting the windings in a star; V- when connecting the windings in a triangle

The type of mechanical characteristics (Fig. 6.13) is similar to the characteristics in the regenerative braking mode. The starting point of the characteristics is the origin of coordinates. The intensity of dynamic braking can be adjusted by changing the excitation current / dt in the stator windings. The higher the current, the greater the braking torque the motor develops. In this case, however, it must be taken into account that at currents / dt > / 1n the saturation of the motor magnetic circuit begins to affect.

For asynchronous motors with a wound rotor, the braking torque can also be controlled by introducing additional resistance into the rotor circuit. The effect of introducing additional resistance is similar to that which occurs when starting an asynchronous motor: thanks to the improvement of φ, the critical slip of the motor increases and the braking torque increases at high rotation speeds.

In dynamic braking mode, the stator windings are powered by a DC source. It should also be borne in mind that in a dynamic braking circuit, current / dt flows (when the windings are connected in a star) not through three, but through two phase windings.

To calculate the characteristics, you need to replace the real / equivalent current /, which, flowing through three phase windings,

creates the same magnetizing force as current I. For the diagram in Fig. 6.12 ,6 1 =0.816/ , and for the circuit in Fig. 6.12 ,in I =0,472/ .

A simplified formula for approximate calculation of mechanical characteristics (not taking into account engine saturation) is similar to the Kloss formula for motor mode:

Where - critical moment in dynamic braking mode;

It should be emphasized that the critical slip in the dynamic braking mode is significantly less than the critical slip in the motor mode, since » k. To obtain a maximum braking torque equal to the maximum torque in the motor mode, the current / eq must be 2-4 times higher than the rated magnetizing current / 0 . The voltage of the DC power source will be significantly less than the rated voltage and approximately equal to dt = (2, ... 4) / eq.

Energetically, in dynamic braking mode, an asynchronous motor operates as a synchronous generator loaded on the resistance of the motor rotor circuit. All mechanical power supplied to the motor shaft during braking is converted into electrical power and is used to heat the rotor circuit resistances. Back braking can be in two cases:

• when, when the engine is running, it is necessary to stop it urgently, and for this purpose the order of alternating phases of the power supply to the stator windings of the engine is changed;
• when the electromechanical system moves in the negative direction under the influence of a descending load, and the motor is turned on in the ascending direction to limit the descent speed (pulling load mode).

In both cases, the electromagnetic field of the stator and the motor rotor rotate in different directions. Engine slip in pro mode

inclusions are always greater than one:

In the first case (Fig. 6.14), the motor operating at point 1, after changing the order of the motor phases, goes into braking mode at point G, and the drive speed quickly decreases under the influence of the braking torque M T and static M s. When decelerating to near zero speed, the engine must be switched off, otherwise it will accelerate in the opposite direction of rotation.

Rice. 6.14.

In the second case, after removing the mechanical brake, the engine, turned on in the upward direction, under the influence of the gravity of the lowered load, will rotate in the opposite direction at a speed corresponding to point 2. Operation in the counter-switching mode under the action of a pulling load is possible when using motors with a wound rotor. In this case, a significant additional resistance is introduced into the rotor circuit, which corresponds to characteristic 2 in Fig. 6.14.

Energetically, the counter-switching regime is extremely unfavorable. The current in this mode for asynchronous squirrel-cage motors exceeds the starting current, reaching 10 times the value. Losses in the motor rotor circuit consist of motor short circuit losses and power that is transmitted to the motor shaft during braking: A R p = L/T co 0 + M t (o.

For squirrel-cage motors, the back-to-back mode is only possible for a few seconds. When using motors with a wound rotor in the counter-switching mode, it is necessary to include additional resistance in the rotor circuit. In this case, the energy losses remain just as significant, but they are transferred from the engine volume to the rotor resistances.

38) Mechanical characteristics of an asynchronous motor.

Mechanical characteristics. The dependence of the rotor speed on the load (rotating torque on the shaft) is called the mechanical characteristic of an asynchronous motor (Fig. 262, a). At rated load, the rotation speed for various motors is usually 98-92.5% of the rotation speed n 1 (slip s nom = 2 - 7.5%). The greater the load, i.e. the torque that the engine must develop, the lower the rotor speed. As the curve shows

Rice. 262. Mechanical characteristics of an asynchronous motor: a - natural; b - when the starting rheostat is turned on

in Fig. 262a, the rotation speed of an asynchronous motor decreases only slightly with increasing load in the range from zero to its highest value. Therefore, such an engine is said to have a rigid mechanical characteristic.

The engine develops the greatest torque M max with some slip s kp amounting to 10-20%. The ratio M max /M nom determines the overload capacity of the engine, and the ratio M p /M nom determines its starting properties.

The engine can operate stably only if self-regulation is ensured, i.e., automatic equilibrium is established between the load torque M int applied to the shaft and the torque M developed by the engine. This condition corresponds to the upper part of the characteristic until M max is reached (to point B). If the load torque M in exceeds the torque M max, then the engine loses stability and stops, while a current 5-7 times greater than the rated current will pass through the windings of the machine for a long time, and they can burn out.

When the starting rheostat is connected to the rotor winding circuit, we obtain a family of mechanical characteristics (Fig. 262,b). Characteristic 1 when the engine is running without a starting rheostat is called natural. Characteristics 2, 3 and 4, obtained by connecting a rheostat with resistances R 1п (curve 2), R 2п (curve 3) and R 3п (curve 4) to the motor rotor winding, are called rheostatic mechanical characteristics. When the starting rheostat is turned on, the mechanical characteristic becomes softer (more steeply falling), as the active resistance of the rotor circuit R 2 increases and s kp increases. This reduces the starting current. The starting torque M p also depends on R 2. You can select the rheostat resistance so that the starting torque M p is equal to the maximum M max.

In an engine with increased starting torque, the natural mechanical characteristic approaches in its form the characteristic of an engine with the starting rheostat turned on. The torque of a double squirrel cage motor is equal to the sum of the two torques created by the working and starting cages. Therefore, characteristic 1 (Fig. 263) can be obtained by summing characteristics 2 and 3 created by these cells. The starting torque M p of such a motor is significantly greater than the torque M ' p of a conventional squirrel-cage motor. The mechanical performance of the deep slot motor is the same as that of the double squirrel cage motor.

WORKING CHARACTERISTICS JUST IN ANY CASE!!!

Performance characteristics. The operating characteristics of an asynchronous motor are the dependences of rotation speed n (or slip s), torque on the shaft M 2, stator current I 1 efficiency? and cos? 1, from useful power P 2 = P mx at rated values ​​of voltage U 1 and frequency f 1 (Fig. 264). They are built only for the zone of practical stable operation of the engine, i.e. from a slip equal to zero to a slip exceeding the nominal by 10-20%. The rotational speed n changes little with increasing power output P2, just as in the mechanical characteristic; the torque on the shaft M 2 is proportional to the power P 2, it is less than the electromagnetic moment M by the value of the braking torque M tr created by friction forces.

The stator current I 1 increases with increasing power output, but at P 2 = 0 there is some no-load current I 0 . The efficiency varies in approximately the same way as in a transformer, maintaining a fairly large value over a relatively wide load range.

The highest efficiency value for medium and high power asynchronous motors is 0.75-0.95 (high power machines have a correspondingly higher efficiency). Power factor cos? 1 of medium and high power asynchronous motors at full load is 0.7-0.9. Consequently, they load power plants and networks with significant reactive currents (from 70 to 40% of the rated current), which is a significant disadvantage of these motors.

Rice. 263. Mechanical characteristics of an asynchronous motor with increased starting torque (with a double squirrel cage)

Rice. 264. Performance characteristics of an asynchronous motor

At loads of 25-50% of the nominal load, which are often encountered during the operation of various mechanisms, the power factor decreases to values ​​that are unsatisfactory from an energy point of view (0.5-0.75).

When the load is removed from the engine, the power factor decreases to values ​​of 0.25-0.3, therefore Asynchronous motors should not be allowed to operate at idle speed or at significant underloads.

Operation at low voltage and failure of one of the phases. Reducing the network voltage does not have a significant effect on the rotor speed of an asynchronous motor. However, in this case, the maximum torque that an asynchronous motor can develop is greatly reduced (when the voltage decreases by 30%, it decreases by approximately 2 times). Therefore, if the voltage drops significantly, the engine may stop, and if the voltage is low, it may not start working.

On e. p.s. alternating current, when the voltage in the contact network decreases, the voltage in the three-phase network, from which the asynchronous motors driving the rotation of auxiliary machines (fans, compressors, pumps), also decreases accordingly. In order to ensure normal operation of asynchronous motors at reduced voltage (they must operate normally when the voltage is reduced to 0.75U nom), the power of all auxiliary machine motors is at . p.s. is taken approximately 1.5-1.6 times greater than is necessary to drive them at rated voltage. Such a power reserve is also necessary due to some asymmetry of the phase voltages, since at the e.g. p.s. asynchronous motors are powered not from a three-phase generator, but from a phase splitter. If the voltages are unbalanced, the phase currents of the motor will be unequal and the phase shift between them will not be equal to 120°. As a result, more current will flow through one of the phases, causing increased heating of the windings of this phase. This forces the engine to limit its load compared to operating it at symmetrical voltage. In addition, with voltage asymmetry, not a circular, but an elliptical rotating magnetic field arises and the shape of the mechanical characteristics of the engine changes somewhat. At the same time, its maximum and starting torques are reduced. Voltage asymmetry is characterized by an asymmetry coefficient, which is equal to the average relative (in percent) deviation of voltages in individual phases from the average (symmetrical) voltage. A three-phase voltage system is considered to be practically symmetrical if this coefficient is less than 5%.

If one of the phases breaks, the engine continues to operate, but increased currents will flow through the undamaged phases, causing increased heating of the windings; such a regime should not be allowed. Starting a motor with a broken phase is impossible, since this does not create a rotating magnetic field, as a result of which the motor rotor will not rotate.

The use of asynchronous motors to drive auxiliary machines. p.s. provides significant advantages over DC motors. When the voltage in the contact network decreases, the rotation speed of asynchronous motors, and therefore the supply of compressors, fans, and pumps, practically does not change. In DC motors, the rotation speed is proportional to the supply voltage, so the supply of these machines is significantly reduced.

Mechanical characteristics of asynchronous motors

Induction motors are the main motors that are most widely used in both industry and agro-industrial production. They have significant advantages over other types of engines: they are easy to operate, reliable and low cost.

In a three-phase asynchronous motor, when the stator winding is connected to a three-phase alternating voltage network, a rotating magnetic field is created, which, crossing the conductors of the rotor winding, induces an emf in them, under the influence of which current and magnetic flux appear in the rotor. The interaction of the magnetic fluxes of the stator and rotor creates the torque of the motor. The appearance of EMF, and therefore torque, in the rotor winding is possible only if there is a difference between the rotation speeds of the magnetic field of the stator and rotor. This difference in speed is called slip.

The slip of an induction motor is a measure of how much the rotor lags in its rotation behind the rotation of the stator's magnetic field. It is denoted by the letter S and is determined by the formula

, (2.17)

where w 0 is the angular speed of rotation of the stator magnetic field (synchronous angular speed of the motor); w is the angular velocity of the rotor; ν – engine rotation speed in relative units.

The rotation speed of the stator magnetic field depends on the frequency of the supply network current f and number of pole pairs R engine: . (2.18)

The equation for the mechanical characteristics of an asynchronous motor can be derived based on the simplified equivalent circuit shown in Fig. 2.11. The following designations are used in the equivalent circuit: U f- primary phase voltage; I 1- phase current in the stator windings; I 2- reduced current in the rotor windings; X 1– reactance of the stator winding; R 1, R 1 2– active resistances in the windings of the stator and reduced rotor, respectively; X 2΄ - reduced reactance in the rotor windings; R0, X 0- active and reactive resistance of the magnetization circuit; S– sliding.

In accordance with the equivalent circuit in Fig. 2.11, the expression for the rotor current has the form

Rice. 2.11. Replacement diagram of an asynchronous motor

The torque of an induction motor can be determined from the expression Мw 0 S=3(I 2 ΄) 2 R 2 according to the formula

Substituting the current value I 2 ΄ from formula (2.19) to formula (2.20), we determine the engine torque depending on the slip, i.e. the analytical expression of the mechanical characteristics of an asynchronous motor has the form

Dependency graph M= f (S) for the motor mode is presented in Fig. 2.12. During acceleration, the engine torque changes from the starting torque M n up to the maximum moment, which is called critical moment M to. The slip and engine speed corresponding to the greatest (maximum) torque are called critical and are designated accordingly S to, w to. Equating the derivative to zero in expression (2.21), we obtain the value of the critical slip S k, at which the engine develops maximum torque:

Where X k = (X 1 + X 2 ΄) – motor reactance.

For motor mode S to taken with a “plus” sign, for supersynchronous - with a “minus” sign.

Substituting the value S to(2.22) into expression (2.21), we obtain the formulas for the maximum moment:

a) for motor mode

b) for supersynchronous braking

The plus sign in equalities (2.22) and (2.23) refers to the motor mode and back-switching braking; the minus sign in formulas (2.21), (2.22) and (2.24) - to the supersynchronous mode of a motor operating in parallel with the network (with w>w 0).

As can be seen from (2.23) and (2.24), the maximum torque of a motor operating in supersynchronous braking mode will be greater compared to the motor mode due to the voltage drop across R 1(Fig. 2.11).

If expression (2.21) is divided by (2.23) and a number of transformations are made taking into account equation (2.22), we can obtain a simpler expression for the dependence M= f (S):

Where – coefficient.

Neglecting the active resistance of the stator winding R 1, because for asynchronous motors with a power of more than 10 kW, the resistance R 1 is significantly less X k, can be equated a ≈ 0, we obtain a more convenient and simpler for calculations formula for determining the engine torque by its sliding (Kloss formula):

. (2.26) If in expression (2.25) instead of the current values M And S substitute the nominal values ​​and indicate the multiplicity of moments M to /M n through k max, we obtain a simplified formula for determining the critical slip:

In (2.27), take any result of the solution under the root with a “+” sign, because with a “-” sign, the solution of this equation does not make sense. Equations (2.21), (2.23), (2.24), (2.25) and (2.26) are expressions that describe the mechanical characteristics of an asynchronous motor (Fig. 2.12).

Artificial mechanical characteristics of an asynchronous motor can be obtained by changing the voltage or frequency of the current in the supply network or by introducing additional resistances into the stator or rotor circuit.

Let us consider the influence of each of these parameters ( U, f, R d) on the mechanical characteristics of an asynchronous motor.

Influence of supply voltage. Analysis of equations (2.21) and (2.23) shows that changing the network voltage affects the motor torque and does not affect its critical slip. In this case, the torque developed by the motor changes in proportion to the square of the voltage:

M≡ kU 2, (2.28)

Where k– coefficient depending on engine and slip parameters.

The mechanical characteristics of an asynchronous motor when the network voltage changes are presented in Fig. 2.13. In this case U n= U 1 >U 2 >U 3.

The influence of additional external active resistance included in the stator circuit. Additional resistances are introduced into the stator circuit to reduce the starting current and torque values ​​(Fig. 2.14a). The voltage drop across the external resistance is in this case a function of the motor current. When starting the engine, when the current value is high, the voltage on the stator windings decreases.

Fig.2.14. Connection diagram (a) and mechanical characteristics (b) of an asynchronous motor when active resistance is connected to the stator circuit

In this case, according to equations (2.21), (2.22) and (2.23), the starting torque changes M p, critical moment M k and angular velocity ω To. Mechanical characteristics for various additional resistances in the stator circuit are presented in Fig. 2.14b, where R d 2 >R d 1 .

The influence of additional external resistance included in the rotor circuit. When additional resistance is included in the rotor circuit of a motor with a wound rotor (Fig. 2.15a), its critical slip increases, which is explained by the expression.

Fig.2.15. Connection diagram (a) and mechanical characteristics (b) of an asynchronous motor with a wound rotor when additional resistance is connected to the rotor circuit

The value R / 2 is not included in expression (2.23), since this value does not affect MK, therefore the critical moment remains unchanged for any R / 2. The mechanical characteristics of an asynchronous motor with a wound rotor with various additional resistances in the rotor circuit are presented in Fig. 2.15b.

Influence of mains frequency. Changing the frequency of the current affects the value of inductive reactance X to asynchronous motor and, as can be seen from equations (2.18), (2.22), (2.23) and (2.24), affects the synchronous angular velocity w 0, critical slip S to and critical moment M to. Moreover ; ; w 0 ºf, Where C 1, C 2- coefficients determined by motor parameters independent of current frequency f.

Mechanical characteristics of the motor when changing the frequency of the current f are presented in Fig. 2.16.