The most common electric motors in industry, agriculture and in all other areas of use are asynchronous engines. It can be said that asynchronous motors with a short-circuit rotor are the main means of conversion electrical Energy in mechanical. The principle of operation of an asynchronous engine was considered 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 \u003d 2 nf ( /p P. . With a standard frequency of 50 Hz Rotational speed of the rotor depends on the number of pairs of poles p P. (Table 6.1).

Table 6.1.

The dependence of the speed of rotation of asynchronous engines from the number of couples

poles

Number of pairs of poles p P.	Angular velocity electronic magnetic field COQ stator. 1 / C.	Engine speed, rpm
Number of pairs of poles p P.		synchronous rotation l 0	sample nominal

Depending on the design of the asynchronous engine rotor, asynchronous engines are distinguished with phase and short-circuited rotor.In the motor-rotor engines, a three-phase distributed winding is located on the rotor, connected to the star, the windings are connected to the contact rings through which the rotor electrical circuits are displayed from the machine to connect to starting resistances, followed by incisioning windings. In short-circuited engines, the winding is made in the form delicious cells -rods, closed spin on both sides by rings. Despite the specific constructive device, the cell cell can also be viewed as a three-phase winding, closed in short.

Electromagnetic moment M. In an asynchronous engine, it 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 occurs due to EMF E 2, which is induced in the rotor windings with a rotating magnetic field. When the rotor is still, the asynchronous motor is a three-phase transformer with windings with closed spit or loaded on start-up resistance. Arising from a fixed rotor in his windings of EMS called nominal phase emfrotora E 2N. This EMF is approximately equal to the phase voltage of the stator divided into the transformation coefficient k T:

With rotating motor EMF rotor E 2. and the frequency of this EDC (and therefore the frequency of the current in the rotor windings) ^ depend on the frequency of the intersection of the rotor of the rotor winding (in a short-circuited engine - rods). This frequency determines the difference in the speeds of the field of the stator CO and the rotor of the CO, which is called absolute slipping:

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

When the engine rotor is still s \u003d. 1. The greatest emf of the rotor when working in the engine will be with a fixed rotor ( E. 2N), as the speed (reduction of sliding) EMF E 2. will decrease:

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

In the nominal mode, the rotor speed is slightly different from the field speed, and the nominal slide is for the general use of 1.5 ... 200.0 kW engines of only 2 ... 3%, and for more power engines of about 1%. Accordingly, in the nominal mode, the emf rotor is 1 ... 3% of the nominal value of this EDC at 5 \u003d 1. The rotor current frequency in the nominal mode will be only 0.5 ... 1.5 Hz. At 5 \u003d 0, when the rotor speed is equal to the field speed, EMF rotor E 2. And the rotor current / 2 will be zero, the motor moment will also be zero. This mode is mode of perfect idling.

The dependence of the EDC frequency and the rotor current of the slip determines the originality of the mechanical characteristics of the asynchronous engine.

The operation of an asynchronous engine with a phase rotor, the windings of which are closed in short.As shown in (6.16), the motor moment is proportional to the stream f and the active component of the rotor current / 2 "A, given to the Stator. The stream created by the windings depends on the value and frequency of the supply voltage

The rotor current is equal

where Z 2 is the total resistance of the rotor winding phase.

It should be borne in mind that the inductive impact of the rotor winding x 2 is a variable value depending on the frequency of the rotor current, and, therefore, from slipping: x 2 \u003d 2P 2 2 \u003d 2K T 2.

With a fixed rotor when s \u003d. 1 Inductive rotor winding resistance maximum. As the speed (reduction of slip) inductive rotor resistance x 2 It decreases and when the nominal speed is reached, only 1 ... 3% of the resistance at 5 \u003d 1. Notounted x 2s \u003d l \u003d x 2n, Receive

We present the parameters of the rotor chain to the stator winding, taking into account the transformation coefficient and on the basis of saving

power equality:

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

Sharing the numerator and denominator of formula (6.26) on s, Receive

Conducted mathematical operation - division of the numerator and denominator on s.Of course, the validity of equality (6.29) does not change, but is a formal nature that need to be considered when considering this relationship. In fact, as follows from the initial formula (6.26), the inductive resistance of the rotor depends on the sliding x 2 A active resistance g 2. It remains constant. Using the expression (6.29) allows by analogy with the transformer to make a scheme for replacing an asynchronous motor, which is presented in Fig. 6.4. ,but.

Fig. 6.4.Schemes for replacing an asynchronous engine: A - full scheme; B-scheme with rendered magnetizing contour

To analyze the unregulated electric drive, this scheme can be simplified, moved the magnetization circuit on the engine clips. The simplified P-shaped substitution scheme is presented in Fig. 6.4d based on which the rotor current will be equal to:

where x K \u003d x + x "2 - inductive resistance short circuit. The active component of the rotor current taking into account (6.28) will be:

Substituting (6.22) and (6.31) in (6.16), we obtain an expression for the moment of an asynchronous engine

Natural mechanical characteristics of asynchronous engine OZ \u003d f (M) With a phase rotor, the windings of which are closed in short, presented in Fig. 6.5. Here is also shown the electromechanical characteristic of the engine Y \u003d / (/ J), determined from the vector diagram of an asynchronous engine in Fig. 6.6, I x \u003d i + / 2 ".

Fig. AT 5.Natural mechanical and electromechanical characteristics of an asynchronous engine

Fig. V.V.Simplified vector asynchronous engine diagram

Believing the magnetization current reactive, we get where

Equating the derivative dM / DS \u003d, we will find the maximum value of the asynchronous engine M k \u003d m n and the corresponding value of critical slip s. K:

where s K. - critical slip; The "+" sign means that this value refers to the motor regime, the sign "-" - to the generator regime of recuperative braking.

Taking into account (6.34) and (6.35), the formula of mechanical characteristics (6.32) can be converted to more convenient to use expression - closse formula:

For engines with a capacity of more than 15 kW resistance of the stator winding, small and at a frequency of 50 Hz is significantly less x k Therefore, in the above expressions of the value of r, you can neglect:

According to the formulas obtained, it is possible to calculate the mechanical characteristics of an asynchronous motor using its passport data, knowing the nominal moment M n, Nominal slide s H and engine transshipment X.

Note that analyzing the electromagnetic processes in an asynchronous motor for the steady regime, came to the same ratios (6.9) and (6.10), which were obtained in § 6.1 based on differential equations A generalized two-phase machine.

Analysis of the characteristics of the mechanical characteristics of an asynchronous motor (see Fig. 6.5). It is non-linear character and consists of two parts. The first is the working part - within slip from 0 to s k. This part of the characteristic is close to linear and has a negative rigidity. Here is a moment developed by the engine, roughly proportional to the state of the stator 1 x. and rotor / 2. As on this part of the characteristics s, the second term of the denominator in Formula (6.39) is significantly less than the first, and they can be neglected. Then the working part of the mechanical characteristics can be approximately submitted in linear form, where the point is proportional to the slip:

The second part of the mechanical characteristics of an asynchronous engine with slides, large s k (s\u003e s k) curvilinear, with a positive hardness value (3. Although the engine current increases, the moment is increasing, the moment, on the contrary, decreases. If the rotor winding of an asynchronous motor with a phase rotor is closed in the outer circuit, the starting current of such an engine (with \u003d 0 and 5 \u003d 1) It will be very large and exceeds the nominal 10-12 times. At the same time, the starting point will be about 0.4 ... 0.5 nominal. As will be shown below, for short-circuited starting current engines will ( 5 ... 6) / N, and start-up (1,1 ... 1.3) a / n.

To explain this inconsistency between starting current and torque, we consider the vector chart chains of the rotor (Fig. 6.7) for two cases: when the slide is large (the starting part of the characteristics); When sliding is not enough (working part of the characteristics). When starting, when 5 \u003d 1, the rotor current frequency is equal to the frequency of the supply network (F 2 \u003d 50 Hz). Inductive resistance of the rotor winding [see (6.24)] Great and significantly exceeds the active resistance of the rotor / * 2, the current lags behind the emf of the rotor to the big angle f, i.e. The rotor current is mainly reactive. Since the emf of the rotor in this case will be 2 \u003d 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. It will be small, consequently, the moment developed by the engine will also be small.

When the engine is accelerated, the sliding decreases, the emission of the rotor, the rotor current frequency, the inductive resistance of the rotor is proportional to decrease. Accordingly, the value is reduced full current Rotor and stator, however, due to the increase in F 2, the active component of the rotor current is growing and the engine is growing.

When the engine sliding will become less s k The rotor current frequency will decrease so much that the inductive resistance will become less active, and the rotor current will be practically active (Fig. 6.7,6), The moment of the engine will be proportional to the current of the rotor. So, if the nominal slide of the engine 5 H \u003d 2%, then compared with the start parameters, the rotor current frequency will decrease by 50 times, the inductive resistance of the rotor will decrease accordingly. Therefore, despite the fact that the emf of the rotor will also decrease 50 times, it will be sufficient to create a rated current of the rotor, providing the nominal moment of the engine. Thus, the originality of the mechanical characteristics of the asynchronous engine is determined by the dependence of the inductive resistance of the rotor of the slide.

Fig. AT 7. Vector chain chart of an asynchronous engine rotor: A - with a large slide: b - with and small slide

Based on the above, to start an asynchronous motor with a phase rotor, you need to take steps to increase the starting point and reduce starting currents. To this end, the rotor circuit includes additional active resistance. As follows from formulas (6.34), (6.35), the introduction of additional active resistance does not change the maximum moment of the engine, but only changes the value

critical slip: where /? "Dob - given to

stator is added resistance in the rotor circuit.

The introduction of additional active resistance increases the impedance of the rotor chain, as a result, the starting current decreases and the CP rotary circuit increases, which leads to an increase in the active component of the rotor current and, therefore, the engine starting point.

Usually, a partitioned resistance is introduced into the rotary circuit of the engine with a phase rotor, the steps of which are brought by start contactors. Calculation of ropatory launchers can be calculated by formula (6.39) using the value s krelevant R 2. B for each stage of start-up resistance. The inclusion circuit of additional resistances and the corresponding risostat mechanical characteristics of the engine are shown in Fig. 6.8. Mechanical characteristics have a common point of the perfect idling, equal to the speed of rotation of the electromagnetic field of the stator CO, and the rigidity of the working part of the characteristics decreases as the total active resistance of the rotor chain increases (2 + /? DO).

When starting the engine, the complete addition resistance is first introduced first? 1DB Upon reaching the speed at which the torque of the engine l / becomes close to the moment of resistance M s, Part of the starting resistance is shunted by contactor K1, and the engine goes to the characteristic corresponding to the value of additional resistance /? 2DB At the same time, the motor moment increases to the value M 2. As the engine is further accelerated, the second stage of start-up resistance is captured by contactor. After closing contacts of the contactor KZ, the engine moves to a natural characteristic and will work at a speed corresponding to point 1.

To calculate the starting characteristics, you need to set the point value M ( in which the steps of starting resistors occurs M X. = 1,2M s. Starting torque values M 2. (Fig. 6.8) are found according to the formula, \u003d a /, where t - number of steps.

To calculate the steps of starting resistance, we find the nominal rotor resistance R 2H \u003d 2N.LIN /\u003e / 3 2N

Resistance steps:

B of short-circuited asynchronous engines The introduction of additional resistance to the rotor chain is impossible. However, the same result can be obtained if you use the effect of turning out the current on the surface of the conductor. The essence of this phenomenon is as follows. According to the law electromagnetic induction When the AC conductor occurs in it, self-induction is induced in it, aimed against the current:

The value of this EDC depends on the current I, Its frequency and inductance, determined by the characteristic of the environment surrounding the conductor. If the conductor is in the air, 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 \u003d / with the effect of self-induction EMF, slightly. Another thing is when the conductor is placed in the body of the magnetic pipeline. Then the inductance increases repeatedly and EMF self-induccus, directed against the current, plays the role of inductive resistance that impede current flow.

Fig. AT 9. The design of the rotor of an asynchronous short-circuit engine: but - with a deep groove; b - with a double cage; in - Scheme explaining the effect of current displacement

Consider the manifestation of the action of self-induction EMF for the case of the conductor (rod rotor winding) placed in a deep groove of the engine rotor magnetic pipeline (Fig. 6.9 ,but). Conditionally divide the cross section of the rod into three parts, which are connected in parallel. The current flowing at the bottom of the rod forms the flow F, magnetic power lines which is closed by magnetic pipeline. In this part of the conductor there is a big emf self-induction e LV. Directed against current 1 2

Current / 23 (Fig. 6.9, in), The rotary winding rod flowing along the top of the rod forms F 3, but, since the power lines of this flow in a significant part of their length closes through the air, the flow F 3 will be much smaller than the flow F,. From here and emf e 1 will be many times less than e LV.

The specified distribution of self-induction EMF in the height of the rod is characteristic of the mode when the frequency of the rotor current is large - close to 50 Hz. In this case, since all three parts of the rod rotor are connected in parallel (see Fig. 6.9, in), then the rotor current / 2 will go along the top of the rod where less anti-eads e L. This phenomenon is called withdraw the current on the surface of the groove. At the same time, the effective cross section of the rod, according to which the current goes, will be several times less than the overall section of the rotor winding rod. Thus, the active rotor resistance increases g 2. Note that since self-induction EMF depends on the frequency of the current (i.e., from slip), then resistance g 2. and x 2 are sliding functions.

When starting, when the slide is large, the resistance g 2 increases (in the rotor circuit, as it is introduced with additional resistance). As the engine is accelerated, the engine sliding decreases, the effect of current displacement is weakening, the current begins to spread down the cross section of the conductor, resistance g 2. decreases. When the operating speed is reached, the inclination of the rotor current is so small that the phenomenon of the current displacement no longer affects, the current flows throughout the cross section of the conductor, and resistance g 2. Minimum. Thanks to this automatic resistance change g 2, Start of asynchronous short-circuited engines proceeds favorably: the starting current is

5.0 ... 6.0 nominal, and launcher 1.1 ... 1.3 nominal.

You can vary the parameters of the asynchronous motor when designing the groove form, as well as the resistance of the material of the rods (alloy composition). Along with deep grooves, double grooves form a dual cellular cell (Fig. 6.9,6), And also use the grooves of the pear-shaped, etc.

In fig. 6.10 Presents typical mechanical characteristics of various modifications of asynchronous short-circuited engines.

Fig. AT 10 O'CLOCK. Exemplary mechanical characteristics of asynchronous short-circuited engines: A - normal performance; 6 - with high gliding; in - with an increased launcher; G-crane and metallurgical series

Short-accumulated normal execution engines Used to drive a wide class of work machines and mechanisms, especially for drives operating in long-term mode. This execution is characterized by the high efficiency of the efficiency and the minimum nominal slide. The mechanical characteristic in the region of large slides is usually a small failure, characterized by the minimum moment. M t (p.

Enhanced engines have a softer mechanical characteristic and are used in the following cases: when two or more engines are working on a common shaft, for mechanisms (for example, crank-connecting) with a cyclically changing load, when to overcome the resistance to movement, it is advisable to use kinetic energy to be used in moving parts of the electric drive , and for mechanisms working in re-short-term mode.

Engines with increased starting torque Designed for mechanisms with severe starting conditions, for example, for scraper conveyors.

Engines crane and metallurgical series Designed for mechanisms working in re-short-term mode with frequent starts. These engines have a greater overload capacity, a high starting point, increased mechanical strength, but the worst energy indicators.

Analytical calculation of the mechanical characteristics of short-circuited asynchronous motors is quite complicated, so approximately the characteristic can be built on four points: at idle course (5 \u003d 0), with the maximum M k Starting M P. and minimum Mt [n Moment at the beginning of the start. The data of these characteristic points are given in catalogs and directories on asynchronous motors. The calculation of the working part of the mechanical characteristics of a short-closed asynchronous motor (with slides from 0 to 5 k) can be made by the formula (6.36), (6.39), since the effect of turning out the current in the operating mode is almost no manifest.

Full mechanical characteristics of an asynchronous motor in all field quadrants M-s, Presented in Fig. 6.11.

The asynchronous engine can operate in three brake modes: recuperative and dynamic braking and braking with opposition. Specific brake mode is also condenser braking.

Recoperative generator braking It is possible when the rotor speed is higher than the speed of rotation of the electromagnetic field of the stator, which corresponds to the negative value of sliding: OO\u003e CO 0 5

A slightly greater value of the maximum moment in the generator mode is explained by the fact that the loss in the stator (on the resistance g () In engine mode, the moment on the shaft is reduced, and in the generator mode, the moment on the shaft should be greater to cover the loss in the stator.

Note that in the recovery braking mode, the asynchronous engine generates and gives it to the network active power, and to create an electromagnetic field, an asynchronous engine and in the generator mode must exchange with the network reactive power. Therefore, an asynchronous machine cannot work as an autonomous generator when disabled from the network. It is possible however, connecting an asynchronous machine to condenser batteries, as to the source of reactive power.

Method of dynamic braking: Stator windings are disconnected from the AC network and are connected to a constant voltage source (Fig. 6.12). When powering the stator windings, a constant current is created by an electromagnetic field in space, i.e. The speed of rotation of the stator field from DT \u003d. Slide will be equal to 5 dt \u003d -CO / C N, where with H is the nominal angular speed of rotation of the stator field.

Fig. 6 .12 but - inclusion of dynamic braking; b - when connecting windings in a star; in - when connecting windings in a triangle

The type of mechanical characteristics (Fig. 6.13) is similar to the characteristics in recovery braking mode. The initial point of characteristics is the origin of coordinates. You can adjust the intensity of dynamic braking by changing the excitation / dt current in the stator windings. The higher the current, the larger the braking moment develops the engine. At the same time, however, it should be borne in mind that at currents / dt\u003e / 1n begins to affect the engine magnetic circuit.

For asynchronous motors with a phase rotor, braking torque control can also be introduced by an additional resistance to the rotor chain. The effect of the introduction of additional resistance is similar to that, which takes place when the asynchronous engine is started: due to the improvement of f, the critical exclusion of the engine increases and the braking point increases at high speeds of rotation.

In the dynamic braking mode, the stator winding is powered by the source direct current. It should also be borne in mind that in the dynamic braking circuit of the current / d t flows (when connecting windings in a star) not in three, but by two phase windings.

To calculate the characteristics, it is necessary to replace the real / equivalent current /, which, passing along the three phase windings,

creates the same magnetizing force as the current I. For the scheme in fig. 6.12. ,6 1 \u003d 0.816 /, and for the scheme in Fig. 6.12. , in I. =0,472/ .

Simplified formula for approximate calculation of mechanical characteristics (not taking into account engine saturation) is similar to the Motor Motor Mode formula:

where - critical moment in dynamic braking mode;

It should be emphasized that the critical slip in the dynamic braking mode is significantly less critical slip in the engine mode, since "to. To obtain the maximum braking torque equal to the maximum torque in the motor mode, the current / ec should be 2-4 times higher than the nominal magnetization current / 0 . The voltage of the DC power supply will be significantly less than the nominal voltage and approximately equal to DT \u003d (2, ... 4) / eq,.

Energy in dynamic braking mode Asynchronous motor works as a synchronous generator loaded to the resistance of the rotor circuit of the engine. All mechanical powerentering the motor shaft when braking is converted to electrical and goes to heating the resistances of the rotor chain. Braking opposing Maybe in two cases:

When when the engine is running, it is necessary to stop it, and for this change the order of alternation phases of the power stator windings;
When the electromechanical system moves in a negative direction under the action of the descendable cargo, and the engine is turned on in the direction of the lift to limit the speed of the descent (the extensive cargo mode).

In both cases, the electromagnetic field of the stator and the engine rotor rotates in different directions. Motor sliding in the mode

conference is always more united:

In the first case (Fig. 6.14), the engine that operated at point 1, after changing the order of the alternation of the motor phases, passes into the braking mode at the point G, and the drive speed is quickly reduced under the action of the braking torque M T. and static M s. When slowing down to speed close to zero, the engine must be turned off, otherwise it will accelerate in the opposite direction of rotation.

Fig. 6.14.

In the second case, after removing the mechanical brake, the engine included in the upward direction, under the action of gravity of the descent cargo, will rotate in the opposite direction at a speed corresponding to the point 2. Operation in the mode of anti-evaluation under the action of the stretching cargo is possible when using engines with a phase rotor. In this case, a significant addition resistance is introduced into the rotor chain, which corresponds to the characteristic 2 in Fig. 6.14.

Energy is extremely unfavorable. The current in this mode for asynchronous short-circuited engines exceeds the launcher, reaching a 10-fold value. The losses in the rotor circuit of the engine are made up of a short circuit loss of the engine and power, which is transmitted to the engine shaft when braking: A P n \u003d L / t from 0 + Mt (o.

For short-circuited engines, the anti-key mode is possible only within a few seconds. When using engines with a phase rotor in opposition mode, it is necessary to switch on to the rotor chain of additional resistance. In this case, energy losses remain as significant, but they are taken out of the volume of the engine in rotary resistance.

Mechanical engine characteristic The dependence of the rotor speed is called from the moment on the shaft n \u003d f (m2). Since with the load moment of idling small, then M2 ≈ M.and the mechanical characteristic is represented by the dependence N \u003d F (M). If we take into account the relationship S \u003d (N1 - N) / N1, then the mechanical characteristic can be obtained by presenting it to a graphical dependence in the coordinates N and M (Fig. 1).

Fig. 1. Mechanical characteristics of asynchronous engine

Natural mechanical characteristic asynchronous engine Corresponds to the main (passportable) circuit of its inclusion and nominal parameters of the supply voltage. Artificial characteristics It turns out if any additional elements are included: resistors, reactors, capacitors. When powering the engine, the characteristic is also different from the natural mechanical characteristic.

Mechanical characteristics are a very convenient and useful tool when analyzing the static and dynamic modes of the electric drive.

An example of calculating the mechanical characteristics of an asynchronous engine

The three-phase asynchronous motor with a short-circuited rotor is powered by a network with voltage \u003d 380 V at \u003d 50 Hz. Engine parameters: P H \u003d 14 kW, N H \u003d 960 rpm, Cos Φn \u003d 0.85, ηn \u003d 0.88, the multiplicity of the maximum moment k m \u003d 1.8.

Determine: Rated current in the phase of the stator winding, the number of pairs of poles, nominal slip, nominal moment on the shaft, critical moment, critical slip and construct the mechanical characteristic of the engine.

Decision. Rated power consumed from the network

P1 H \u003d p n / ηn \u003d 14 / 0.88 \u003d 16 kW.

Rated current consumed from the network

Number of pairs of poles

p \u003d 60 f / n1 \u003d 60 x 50/1000 \u003d 3,

where n1 \u003d 1000 - the synchronous frequency of rotation immediately to the nominal frequency N H \u003d 960 rpm.

Nominal slide

s H \u003d (N1 - N H) / N1 \u003d (1000 - 960) / 1000 \u003d 0.04

Rated moment on the motor shaft

Critical moment

MK \u003d. k M X MN \u003d 1.8 x 139.3 \u003d 250.7 N m.

Critical sliding we find substituting M \u003d Mk, S \u003d S H and MK / MK \u003d K M.

To construct the mechanical characteristic of the engine with n \u003d (n1 - s) we define the characteristic points: the idle point s \u003d 0, n \u003d 1000 rpm, m \u003d 0, the point of the nominal mode S H \u003d 0.04, N n \u003d 960 rpm, mn \u003d 139.3 n m and point of critical mode S K \u003d 0.132, n K \u003d 868 rpm, MK \u003d 250.7 nm.

The mechanical characteristic of the engine is the dependence of the rotor rotation frequency from the moment on the shaft n \u003d f (m2). Since when loading the moment of idling is small, then M2? M and the mechanical characteristic is represented by the dependence N \u003d F (M). If we take into account the relationship S \u003d (N1 - N) / N1, then the mechanical characteristic can be obtained by presenting it to a graphical dependence in the coordinates N and M (Fig. 1).

Fig.1.

The natural mechanical characteristic of the asynchronous motor corresponds to the main (passportable) circuit of its inclusion and the nominal parameters of the supply voltage. Artificial characteristics are obtained if any additional elements are included: resistors, reactors, capacitors. When powering the engine, the characteristic is also different from the natural mechanical characteristic.

Mechanical characteristics are a very convenient and useful tool when analyzing the static and dynamic modes of the electric drive.

Data for calculating the mechanical characteristics for this drive and engine:

The three-phase asynchronous motor with a short-circuited rotor is powered by a network with voltage \u003d 380 V at \u003d 50 Hz.

Engine parameters 4am160s4:

PN \u003d 12.5 kW,

nn \u003d 1460 rpm,

cOSTSN \u003d 0.86, ZN \u003d 0.89, KN \u003d 2.2

(3.1) Rated power consumed from the network:

(3.2) Rated current consumed from the network:

(3.3) Pole Pole Number

where N1 \u003d 1500 is the synchronous frequency of rotation, nearest to the nominal frequency of Nn \u003d 1460 rpm.

(3.4) Nominal slide:

(3.5) Rated moment on the shaft of the engine:

(3.6) critical moment

MK \u003d KM x MN \u003d 1.5 x 249.5 \u003d 374.25 nm.

(3.7) Critical slipping found substituting M \u003d MN, S \u003d SN and MK / MK \u003d KM.

To construct the mechanical characteristics of the engine with n \u003d (N1 - S), we determine the characteristic points: the point of idling s \u003d 0, n \u003d 1500 rpm, m \u003d 0, the point of the nominal mode Sn \u003d 0.03, nn \u003d 1500 about / Min, MN \u003d 249.5 nm and point of critical mode SK \u003d 0.078, MK \u003d 374.25 nm.

For the starting point of SP \u003d 1, N \u003d 0 we find

According to the data obtained, the mechanical characteristic of the engine is built. For a more accurate construction of the mechanical characteristic, you should increase the number of calculation points and for the specified slides to determine the moments and speed of rotation.

Building a natural mechanical engine characteristic

The mechanical characteristic of the engine is called, the dependence of the rotational speed N from the moment M of the load on the shaft.

Distinguish natural I. artificial characteristics electric motors.

Natural the mechanical characteristic is called - the dependence of the engine speed from the moment on the shaft under the nominal models of the engine in relation to its parameters (rated voltages, frequency, resistance, and the like). Changing one or more parameters calls the corresponding change in the mechanical engine characteristic. Such a mechanical characteristic is called artificial.

To build the equation of the mechanical characteristics of the asynchronous motor, we use the formula of the Ros (4.1):

where M K is the critical moment of the engine (4.1.1) :;

S K is a critical engine sliding (4.1.2);

Engine transshipment (\u003d 3);

S N - engine nominal slide (4.1.3):

where N n is the rotational speed of the rotor;

n 1 is the synchronous speed of the stator field (4.1.4);

where F is the industrial power frequency of the supply network, (F \u003d 50 Hz) (4.1.5);

P - number of pairs of poles (for engine 4am132S4 p \u003d 2)

Nominal engine sliding 4am132S4

Critical engine sliding

Critical moment of engine

To build, the characteristics in the coordinates are moving from sliding to the number of revolutions based on the equation

Slide is set from 0 to 1

S \u003d 0 n \u003d 1500. (1 - 0) \u003d 1500 rpm;

When constructing an automated electric drive models, it is necessary to take into account the complexity of electromechanical processes occurring in the engine during its operation. The results obtained in mathematical calculation should be checked by an experimental way. Thus, the need to determine the characteristics of the electric motors during the invention experiment. The information obtained during such an experiment make it possible to approve the constructed mathematical model. The article discusses the method of constructing the mechanical characteristics of an asynchronous engine with a short-circuited rotor, an experimental check of the calculated mechanical characteristic is carried out on the example of a system consisting of an asynchronous motor, the DC motor of the DC independent excitation is connected as a load as the load, the calculation error is evaluated, the calculation error is evaluated The results obtained for further research. During the experiment, the laboratory stand of NTC-13.00.000 is used.

asynchronous engine

dC motor

mechanical characteristic

scheme of substitution

magnetic system saturation.

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2. Moskalenko V.V. Electric drive: Textbook for stud. Higher. studies. establishments. - M.: Publishing Center "Academy", 2007. - 368 p.

3. Moshinsky Yu. A., Bespalov V. Ya., Kiryakin A. A. Determination of the parameters of the scheme of replacement of an asynchronous machine according to catalog data // Electricity. - №4 / 98. - 1998. - P. 38-42.

4. Technical catalog, second, revised and complemented / Vladimir Electromotor factory. - 74 p.

5. Austin Hughes Electric Motors and Drives Fundamentals, Types and Applications. - Third Edition / School of Electronic and Electrical Engineering, University of Leeds. - 2006. - 431 p.

Introduction

Asynchronous engine (AD) is an electric motor that has found very wide use in various industries and agriculture. Hell with a short-circuited rotor possesses the peculiarities of its widespread: simplicity in the manufacture, and this means low initial cost and high reliability; High efficiency together with low maintenance costs result in low total operating costs; The ability to work directly from the AC network.

Modes of operation of an asynchronous electric motor

The engines with a short-circuited rotor are asynchronous machines, the speed of which depends on the frequency of the supply voltage, the number of pairs of poles and the load on the shaft. As a rule, when maintaining constant supply voltage and frequency, if the change in temperature is ignored, the moment on the shaft will depend on slip.

The torque pressure can be determined by the formula:

where, - a critical moment - a critical slip.

In addition to the motor regime, the asynchronous engine has three more brake modes: a) the generator brake with the return of energy to the network; b) braking by opposing; c) dynamic braking.

With a positive slide, the machine with a short-circuited rotor will act as an engine, with a negative slide - as a generator. It follows from this that the current anchor anchor with a short-circuited rotor will depend only on slip. When the machine exits, the current speed will be minimal.

The generator braking hell with the return of energy to the network occurs at a rotor speed exceeding synchronous. In this mode, the electric motor gives to the network active energyAnd from the network to the electric motor comaves the reactive energy required to create an electromagnetic field.

The mechanical characteristic for the generator mode is to continue the characteristics of the motor regime into the second quadrant of the coordinate axes.

Braking with the opposition corresponds to the direction of rotation of the magnetic field of the stator opposite to the rotation of the rotor. In this mode, the sliding is greater than the unit, and the rotor speed of the rotor relative to the frequency of rotation of the stator field is negative. Current in the rotor, and therefore, in the stator reaches a large value. To limit this current into the rotor chain, adding resistance is administered.

The braking mode by opposing occurs when the direction of rotation of the magnetic field of the stator is changed, while the electric motor rotor and the mechanisms connected to it continue to rotate in the inertia. This mode is also possible in the case when the stator field does not change the direction of rotation, and the rotor under the action of the outer moment changes the direction of rotation.

In this article, consider the construction of the mechanical characteristics of the asynchronous motor in the engine.

Construction of mechanical characteristics using the model

Passport details ADT DMT F 011-6U1: UF \u003d 220 - nominal phase voltage, in; p \u003d 3 - number of pairs of windings poles; n \u003d 880 - rotation speed nominal, rpm; PN \u003d 1400 - Power Nominal, W; In \u003d 5.3 - the rotor current is nominal, and; η \u003d 0.615 - kpd. Nominal,%; cosφ \u003d 0.65 - cos (φ) nominal; J \u003d 0.021 - the moment of inertia of the rotor, kg · m 2; Ki \u003d 5.25 - the multiplicity of the start current; Kp \u003d 2.36 - the multiplicity of the starting point; KM \u003d 2.68 - Critical moment multiplicity.

For the study of operational modes of asynchronous engines, workers and mechanical characteristics are used, which are determined experimentally or calculated on the basis of the substitution scheme (SZ). For the use of SZ (Fig. 1) it is necessary to know its parameters:

R 1, R 2 ", R M is the active resistances of the phases of the stator, the rotor and the branches of the magnetization;
X 1, x 2 ", x m - inductive scattering resistance phases of the rotor stator and magnetization branches.

These parameters are required to determine starting currents when selecting magnetic starters and contactors, when performing overload protection, to adjust and set up an electric drive control system, to simulate transient processes. In addition, they are necessary for calculating the Starting CD, determining the characteristics of an asynchronous generator, as well as in the design of asynchronous machines in order to compare the source and design parameters.

Fig. 1. Scheme of the substitution of an asynchronous engine

We use the method of calculating the parameters of the substitution scheme to determine the active and reactive resistances of the phases of the stator and rotor. The values \u200b\u200bof the efficiency and power factor with partial loads required for the calculations are given in the technical directory: PF \u003d 0.5 - partial load coefficient,%; PPF \u003d PN · PF - Power with partial load, W; η _PF \u003d 0.56 - kpd. with partial load,%; cosφ_pf \u003d 0.4 - cos (φ) with partial load.

Resistance values \u200b\u200bin the substitution scheme: x 1 \u003d 4.58 - the reactive resistance of the stator, Ohm; X 2 "\u003d 6.33 - Rotor reactive resistance, Ohm; R 1 \u003d 3.32 - the active resistance of the stator, Ohm; R 2" \u003d 6.77 is the active resistance of the rotor, Ohm.

We construct the mechanical characteristic of the asynchronous motor using the formula of the Kloss (1).

Slide is determined from the expression of the form:

where - the rotation speed of the rotor hell, rad / s,

synchronous rotation speed:

Critical rotation speed:

. (4)

Critical slide:

The point of the critical moment is determined from the expression

Starting time Determined by the formula of the Kloss at S \u003d 1:

. (7)

According to the calculations produced, we construct a mechanical characteristic of the blood pressure (Fig. 4). To check it in practice, we will conduct an experiment.

Construction of experimental mechanical characteristics

When carrying out the experiment, the Laboratory Stand of the NTC-13.00.000 "Electric Drive" is used. There is a system consisting of blood pressure to the shaft of which the DC motor (DPT) of independent excitation is connected to the shaft. It is necessary to construct a mechanical characteristic of an asynchronous motor using the passport details of asynchronous and synchronous machines and sensor readings. We have the ability to change the voltage of the DPT excitation winding, measure the currents on the anchor of the synchronous and asynchronous motor, the rates of rotation of the shaft. Connect hell to the power source and will load it by changing the current of the DPT excitation. After conducting an experiment, make a table of values \u200b\u200bfrom sensor readings:

Table 1 Sensor readings when loading asynchronous motor

where IV is the current of the motor excitation of the DC motor, I - the current anchor anchor of the DC motor, Ω is the rotation speed of the asynchronous motor rotor, I 2 - the rotor of the asynchronous motor.

Passport data for synchronous machine type 2P H90L UHL4: PN \u003d 0.55 - Rated power, kW; Ur \u003d 220 - Rated voltage, in; Uv \u003d 220 - the excitation voltage is nominal, in; II.The \u003d 3.32 - the rated current of the anchor, and; Can \u003d 400 - the excitation current nominal, ma; RY \u003d 16.4 - anchor resistance, Ohms; nn \u003d 1500 - rotation speed nominal, rpm; JDV \u003d 0.005 - the moment of inertia, kg · m 2; 2p n \u003d 4 - number of pairs of poles; 2a \u003d 2 - the number of parallel branches of the anchor winding; N \u003d 120 - the number of active conductors of the anchor winding.

In the DPT rotor, the current comes through one brush, flows through all the coils of the rotor winding and goes through another brush. The point of contact of the stator winding with the rotor winding is through a collector plate or segments to which the brush presses at this time (the brush is usually more wide than one segment). Since each individual round of rotor winding is interconnected with the collector segment, the current actually passes through all the turns and through all the collector plates on its path through the rotor.

Fig. 2. Currents flowing in a DC motor rotor with two poles

Figure 2 shows that all conductors lying in the pole n have positive charge, while all conductors under the pole s carry negative charge. Therefore, all conductors under the poles n will receive downward strength (which is proportional to the radial density of the flow in and current of the rotor), while all conductors under the pole s will receive equal ascending force. As a result, a torque is created on the rotor, the magnitude of which is proportional to the product of the magnetic flux and current density. In practice, the magnetic flux density will not be absolutely uniform under the pole, so the force on some rotor conductors will be greater than on others. A complete moment, developing on the shaft, will be equal to:

M \u003d K T fi, (8)

where F is a complete magnetic flux, the coefficient K T is permanent for this engine.

In accordance with the formula (8), the regulation (limit) of the moment can be achieved by changing the current I or the magnetic flux F. In practice, the moment regulation is more often carried out by regulating the current. Adjusting the motor current is performed by its level of packaging (or by the operator) due to the change in the voltage converters by means of electric power transducers or the inclusion of additional resistors in its circuit.

Calculate the structural constant of the engine included in equation (8):

. (9)

Set the connection between the motor flow and the excitation winding current. As is known from the theory of electrical machines, due to the effect of the saturation of the magnetic system, this connection is non-linear and has the form shown in Figure 3. In order to better use Iron Machine is designed so that in the nominal mode the working point is on the inflection of the magnetization curve. We accept the magnetic flux value of the proportional excitation current.

FPR. \u003d IV, (10)

where IV is the excitation current.

F - the actual value of the flow; F pr. - The value of the flow adopted for the calculations

Fig. 3. The ratio of the values \u200b\u200bof the magnetic flux, adopted and real

Since the blood pressure and DPT in the experiment conducted one common shaft, we can calculate the moment created by the DPT, and on the basis of the values \u200b\u200bobtained and the indications of the speed sensor construct an experimental mechanical characteristic of the blood pressure (Figure 4).

Fig.4. Mechanical characteristics of an asynchronous engine: Calculated and experimental

The resulting experimental characteristic in the field of low moment values \u200b\u200bis located below the characteristics calculated theoretically, and above - in the field of high values. Such a deviation is associated with the difference of the magnetic flux taken for calculations and the real values \u200b\u200bof the magnetic flux (Fig. 3). Both graphics intersect with FPR. \u003d IV. nom.

We introduce amendment into calculations by setting a nonlinear dependence (Fig. 5):

F \u003d A · IV, (11)

where a is the coefficient of nonlinearity.

Fig. 5. The ratio of the magnetic flux to the excitation current

The resulting experimental characteristic will take the view shown in Fig. 6.

Fig.6. Mechanical characteristics of an asynchronous engine: Calculated and experimental

Calculate the error of the experimentally obtained data for the case in which the magnetic flow linearly depends on the current of the excitation (10), and the case in which this relationship is non-linear (11). In the first case, the total error is 3.81%, in the second 1.62%.

Output

The mechanical characteristic, built according to experimental data, differs from the characteristic constructed using the formula of the Closse (1) due to the adopted assumption of the FPR. \u003d IV, the discrepancy is 3.81%, with IV \u003d Iv. \u003d 0.4 (a) These characteristics coincide. Upon reaching the nominal value, the saturation of the DPT magnetic system occurs, as a result, the further increase in the excitation current is less affected by the magnetic flux value. Therefore, to obtain more accurate values \u200b\u200bof the moment, it is necessary to introduce a saturation coefficient, which makes it possible to increase the accuracy of the calculation 2.3 times. The mechanical characteristic, built by model, adequately reflects the operation of the real engine, can be taken as the basis in further research.

Reviewers:

Pücke Georgy Aleksandrovich, Doctor of N., Professor of the Department of Management Systems of Kamchatgtu, Petropavlovsk-Kamchatsky.
Potapov Vadim Vadimovich, Dr. N., Professor of the branch of the Feto, Petropavlovsk-Kamchatsky.

Bibliographic reference

Lyodedov A.D. Construction of the mechanical characteristics of an asynchronous engine and its testing // Modern problems science and education. - 2012. - № 5;
URL: http://science-education.ru/ru/Article/View?id\u003d6988 (Date of handling: 02/01/2020). We bring to your attention the magazines publishing in the publishing house "Academy of Natural Science"

The mechanical characteristics of asynchronous motors can be expressed in the form of n \u003d f (m) or n \u003d f (i). However, often the mechanical characteristics of asynchronous motors are expressed as a dependence M \u003d F (S), where S is sliding, S \u003d (NC-N) / NC, where N C is synchronous speed.

In practice, for graphic construction of mechanical characteristics, a simplified formula called the Formula of the Closse is used:

here: MK - Critical (maximum) moment value. This value of the moment is responsible for a critical slip.

where λm \u003d MK / MN

The formula of the Kloss is used in solving issues related to the electric drive, carried out using an asynchronous engine. Using the formula of the Klossa, you can construct a graph of mechanical characteristics according to the passport data of the asynchronous engine. For practical calculations in the formula in determining the critical moment, only a plus sign should be taken into account.

Fig. 1. Asynchronous engine: A - Schematic diagram, B - mechanical characteristic M \u003d F (S) - Natural in engine and generator modes, B is a natural mechanical characteristic N \u003d F (m) in engine mode, G - artificial rheostat mechanical characteristics, D - mechanical characteristics for different voltages and frequencies.

As can be seen from fig. one, mechanical characteristics of asynchronous engine Located in I and III quadrants. A portion of the curve in i quadrant corresponds to the positive value of the slip and characterizes the motor mode of operation of an asynchronous engine, and in the III quadrant - generator mode. Motor mode represents the greatest practical interest.

The graph of mechanical characteristics of the motor regime contains three characteristic points: A, B, C and conditionally can be divided into two sections: OV and Sun (Fig. 1, B).

Point A correspond to nominal moment of the engine and determined by the formula MN \u003d 9.55 10 3 (P H / N H)

This point corresponds to which for engines of general industrial use has a value ranging from 1 to 7%, i.e. Sn \u003d 1 - 7%. At the same time, small engines have a greater slide, and large - less.

Enhanced enginesdesigned to work with the impact load have S H ~ 15%. These include, for example, engines of the Unified AC series.

The point C on the characteristic corresponds to the magnitude initial torquearising from the motor shaft when started. This moment MP is the name of the initial, or launcher. The sliding is equal to one, and the speed is zero. Easily determine according to the reference table, which indicates the ratio of the starting point to the nominal MP / MP.

The magnitude of the starting torque at constant voltage values \u200b\u200band the current frequency depends on the active resistance in the rotor circuit. At the same time, initially with an increase in active resistance increases the magnitude of the starting point, reaching its maximum in the equality of the active resistance of the rotor chain and the total inductive resistance of the engine. In the future, with an increase in the active resistance of the rotor, the magnitude of the starting moment decreases, striving at the limit to zero.

Point in (Fig. 1, b and c) corresponds maximum momentwhich can develop the engine on the entire velocity range from n \u003d 0 to n \u003d n s. This moment is called the name of the critical (or tipping) moment MK. Critical moment Corporate SC critical slip. The smaller the value of the critical slip SC, as well as the value of the nominal slide S H, the greater the rigidity of the mechanical characteristic.

Both launcher and critical moments are determined through the nominal. According to GOST on electric machines for a short-circuited engine, the condition of MP / MK \u003d 0.9 - 1.2, MK / MK \u003d 1.65 - 2.5 should be observed.

It should be borne in mind that the value of the critical moment does not depend on the active resistance of the rotor chain, while the critical slip S is directly proportional to this resistance. This means that with an increase in the active resistance of the rotary circuit, the value of the critical moment remains unchanged, but the maximum of the moment curve is shifted towards increasing slip values \u200b\u200b(Fig. 1, d).

The magnitude of the critical moment is directly proportional to the square of the voltage summing up to the stator, and is inversely proportional to the square of the voltage frequency and the current frequency in the stator.

If, for example, the voltage caused to the engine will be 85% of the nominal value, then the value of the critical moment will be 0.85 2 \u003d 0.7225 \u003d 72.25% of the critical moment at rated voltage.

The reverse phenomenon is observed when the frequency changes. If, for example, to an engine designed to work with the frequency of current F \u003d 60 Hz, tested the current frequency F \u003d 50 Hz, then the critical moment will be obtained in (60/50) 2 \u003d 1.44 times more value than with its formal frequency (Fig. 1, e).

The critical moment is characterized by an instantaneous engine transshipment, i.e. it shows which instantaneous (for a few seconds) overload is able to transfer the engine without any harmful effects.

Section of the mechanical characteristic from zero to the maximum (critical) value (see Fig. 1, Biv) is called sustainable part of the characteristic, and a plot of Sun (Fig. 1, c) - unstable part.

This division is explained by the fact that on the increasing part of the characteristics of the OB with increasing sliding, i.e. With a decrease in speed, the motor developed by the engine is growing. This means that with an increase in the load, i.e., with an increase in the braking torque, the speed of rotation of the engine decreases, and the moment-developed moment increases. When a load decreases, on the contrary, the speed increases, and the moment decreases. When the load changes, on the entire range of stable part, the characteristic changes the speed of rotation and the moment of the engine.

The engine is not able to develop the moment more critical, and if the braking moment is greater, the engine must inevitably stop. Going on how to say engine tipping.

Mechanical characteristic with constant U and I and the absence of additional resistance in the rotor circuit is called natural characteristic (Characteristics of a short-circuited asynchronous engine with a phase rotor without additional resistance in the rotor circuit). Artificial, or rheostat, characteristics These are called that correspond to additional resistance in the rotor circuit.

All values \u200b\u200bof starting moments are different between themselves and depend on the active resistance of the rotor chain. The same nominal moment MN corresponds to slides of various sizes. With an increase in the resistance of the rotor circuit, the slide increases and, therefore, the speed of rotation of the engine is reduced.

Due to the inclusion in the rotor circuit of the active resistance, the mechanical characteristic in the steady part is pulled downwards in the direction of increasing the slip, proportional to the resistance. This means that the engine speed begins to change greatly depending on the load on the shaft and the characteristic of the tight is made soft.

Building a natural mechanical engine characteristic

Bibliographic reference

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