It is convenient to analyze the operation of an asynchronous electric motor on the basis of its mechanical characteristics, which are a graphically expressed dependence of the form P = f(M). In these cases, speed characteristics are used very rarely, since for an asynchronous electric motor the speed characteristic is the dependence of the speed on the rotor current, in determining which there are a number of difficulties, especially in the case of asynchronous electric motors with a squirrel-cage rotor.

For asynchronous electric motors, as well as for direct current electric motors, natural and artificial mechanical characteristics are distinguished. An asynchronous electric motor operates on a natural mechanical characteristic if its stator winding is connected to a three-phase current network, the voltage and frequency of which correspond to the nominal values, and if any additional resistances are not included in the rotor circuit.

On fig. 42 was given dependence M = f(s), which allows you to easily go to the mechanical characteristic n = f(M ), since, according to expression (82) , the rotor rotation speed depends on the amount of slip.

Substituting formula (81) into expression (91) and solving the resulting equation for P 2 we obtain the following equation for the mechanical characteristics of an asynchronous motor

Member r 1 s omitted due to its smallness. The mechanical characteristics corresponding to this equation are shown in fig. 44.

Equation (95) is inconvenient for practical constructions; therefore, simplified equations are usually used in practice. So, in the case of an electric motor operating on a natural characteristic with a torque not exceeding 1.5 of its nominal value, the slip usually does not exceed 0.1. Therefore, for this case, in equation (95) we can neglect the term x 2 s 2 /kr’ 2 · M , resulting in the following simplified natural characteristic equation:

which is the equation of a straight line inclined to the x-axis.

Although equation (97) is approximate, experience shows that for torque changes ranging from M= 0 to M=1,5M n the characteristics of asynchronous electric motors are really straightforward and equation (97) gives results that are in good agreement with the experimental data.

When additional resistances are introduced into the rotor circuit, the characteristic P = f(M) with sufficient accuracy for practical purposes can also be considered rectilinear within the specified limits for the torque and be constructed according to equation (97).

Thus, the mechanical characteristics of an induction motor range from M= 0 to M = 1,5 M n at various resistances of the rotor circuit, they represent a family of straight lines intersecting at one point corresponding to the synchronous number of revolutions (Fig. 45). As equation (97) shows, the slope of each characteristic to the abscissa axis is determined by the value of the active resistance of the rotor circuit r’ 2 . Obviously, the greater the resistance introduced into each phase of the rotor, the more the characteristic is inclined to the abscissa axis.

As mentioned, usually in practice, the speed characteristics of asynchronous motors are not used. The calculation of starting and adjusting resistances is carried out using equation (97). The construction of a natural characteristic can be performed by two points - by synchronous speed n­ 1 = 60f /R at zero torque and at rated speed at rated torque.

It should be borne in mind that for asynchronous electric motors, the dependence of the torque on the rotor current I 2 is more complex than the dependence of the torque on the armature current for

DC electric motors. Therefore, the speed characteristic of an induction motor is not identical to the mechanical characteristic. Characteristic P = f(I 2 ) has the form shown in Fig. 46. ​​There is also a characteristic n = f (I 1 ).

Dynamic mechanical characteristic an induction motor is called the relationship between the instantaneous values ​​of the speed (slip) and the moment of the electric machine for the same moment in time of the transient mode of operation.

The graph of the dynamic mechanical characteristic of an induction motor can be obtained from the joint solution of the system of differential equations of electrical equilibrium in the stator and rotor circuits of the motor and one of the equations of its electromagnetic torque, which are given without their derivation:

The system of equations (5.35) uses the following notation:

A

- component of the stator winding voltage vector, oriented along the axis b fixed coordinate system;

- equivalent inductive resistance of the stator winding, equal to the inductive resistance of the leakage of the stator winding and the inductive resistance from the main field;

- equivalent inductive resistance of the rotor winding, reduced to the stator winding, equal to the inductive resistance of the leakage of the rotor winding and the inductive resistance from the main field;

- inductive resistance from the main field (magnetization circuit), created by the total action of the stator currents;

A fixed coordinate system;

- component of the stator winding flux linkage vector, oriented along the axis b fixed coordinate system;

A fixed coordinate system;

is the component of the rotor winding flux linkage vector, oriented along the axis b fixed coordinate system;

A fixed coordinate system;

- component of the rotor winding current vector, oriented along the axis b fixed coordinate system.

Electromechanical processes in an asynchronous electric drive are described by the equation of motion. For the case

where is the moment of load resistance reduced to the motor shaft; - the total moment of inertia of the electric drive reduced to the motor shaft.

The analysis of dynamic processes of energy conversion in an induction motor is a difficult task due to the significant non-linearity of the equations describing the induction motor, due to the product of variables. Therefore, it is advisable to study the dynamic characteristics of an induction motor using computer technology.

The joint solution of the system of equations (5.62) and (5.63) in the MathCAD software environment allows you to calculate the graphs of transient processes of speed ω and torque M with numerical values ​​of the parameters of the equivalent circuit of an asynchronous motor, defined in example 5.3.

Since the dynamic mechanical characteristic of an induction motor can only be obtained from the results of calculations of transients, first we present the graphs of transients of speed (Fig. 5.9) and torque (Fig. 5.10) when starting an induction motor by direct connection to the network.

Rice. 5.9.

Rice. 5.10.

Rice. 5.11.

Graphs and transients allow you to build a dynamic mechanical characteristic of an asynchronous motor (Fig. 5.1 I, curve I) when starting by direct connection to the network. For comparison, the same figure shows the static mechanical characteristic - 2, calculated by expression (5.7) for the same parameters of the equivalent circuit of an asynchronous motor.

An analysis of the dynamic mechanical characteristic of an asynchronous motor shows that the maximum shock moments at start-up exceed the rated moment L / n of the static mechanical characteristic by more than 4.5 times and can reach values ​​that are unacceptably large in terms of mechanical strength. Impact torques during start-up, and especially during reversal of an asynchronous motor, lead to failure of the kinematics of production mechanisms and the asynchronous motor itself.

Modeling in the MathCAD software environment makes it quite easy to study the dynamic mechanical characteristics of an induction motor. It has been established that the dynamic characteristic is determined not only by the parameters of the equivalent circuit of an asynchronous motor, but also by the parameters of the electric drive, such as the equivalent moment of inertia, the moment of resistance on the motor shaft. Consequently, an asynchronous motor with given parameters of the supply network and the equivalent circuit has one static and many dynamic mechanical characteristics.

As follows from the analysis of the dynamic characteristics of Fig. 5.9-5.10, the transient process of starting a short-circuited asynchronous motor can have an oscillatory character not only in the initial, but also in the final section, and the motor speed exceeds the synchronous ω0. In practice, fluctuations in the angular velocity and torque of the engine in the final section of the transient process are not always observed. In addition, there is big number production mechanisms for which such fluctuations must be excluded. A typical example is the mechanisms of winches and the movement of cranes. For such mechanisms, asynchronous motors with soft mechanical characteristics or with increased slip are produced. It has been established that the softer the working section of the mechanical characteristic of an induction motor and the greater the equivalent moment of inertia of the electric drive, the smaller the amplitude of oscillations when reaching a steady speed and the faster they decay.

Studies of dynamic mechanical characteristics are of theoretical and practical importance, since, as shown in Section 5.1.1, taking into account only static mechanical characteristics can lead to not entirely correct conclusions and distort the nature of dynamic loads during start-ups of asynchronous motors. Studies show that the maximum values ​​of the dynamic torque can exceed the rated torque of the motor when starting by direct connection to the network by 2-5 times and by 4-10 times when the motor is reversed, which must be taken into account when developing and manufacturing electric drives.

38) Mechanical characteristic of an asynchronous motor.

Mechanical characteristic. The dependence of the rotor speed on the load (torque on the shaft) is called the mechanical characteristic of an induction motor (Fig. 262, a). At rated load, the speed for various engines is usually 98-92.5% of the 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 induction motor: a - natural; b - when the starting rheostat is turned on

in fig. 262, a, the rotational speed of an asynchronous motor only slightly decreases 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 at some slip s kp of 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 moment M ext applied to the shaft and the moment M developed by the engine. This condition corresponds to the upper part of the characteristic until M max is reached (up to point B). If the load moment M ext exceeds the moment M max, then the motor loses stability and stops, while the current 5-7 times the nominal current will pass through the windings of the machine, and they may burn out.

When a starting rheostat is included in 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 1p (curve 2), R 2p (curve 3) and R 3p (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. Starting torque M p also depends on R 2 . You can choose the resistance of the rheostat in such a way that the starting torque M p is equal to the largest 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 generated 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 much greater than the moment 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.

JUST A WORKING CHARACTERISTIC!!!

Operating characteristics. The performance characteristics of an induction motor are the dependences of the rotational speed n (or slip s), torque on the shaft M 2, stator current I 1 efficiency? and cos? 1, from useful power P 2 \u003d P mx at nominal 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 slip equal to zero to slip exceeding the nominal by 10-20%. The rotational speed n with an increase in the output power P 2 changes little, as well 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 torque 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 \u003d 0 there is some no-load current I 0. The efficiency varies approximately in the same way as in a transformer, maintaining a fairly large value over a relatively wide load range.

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

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

Rice. 264. Performance characteristics of an induction motor

At loads of 25-50% of the nominal, which are often encountered during the operation of various mechanisms, the power factor decreases to unsatisfactory values ​​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 it is impossible to allow the operation of asynchronous motors at idle and significant underloads.

Work at low voltage and breakage of one of the phases. Reducing the mains voltage does not have a significant effect on the rotor speed of the induction motor. However, in this case, the maximum torque that an asynchronous motor can develop is greatly reduced (when the voltage drops by 30%, it decreases by about 2 times). Therefore, with a significant voltage drop, the motor may stop, and with a low voltage, it may not start.

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

If one of the phases is broken, the motor 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 an open phase is not possible, 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 e. p.s. provides significant advantages over DC motors. With a decrease in voltage in the contact network, the rotational speed of asynchronous motors, and hence the supply of compressors, fans, and pumps, practically does not change. In DC motors, the rotational speed is proportional to the supply voltage, so the supply of these machines is significantly reduced.

The mechanical characteristics of induction motors can be expressed as n=f(M) or n=f(I). However, often the mechanical characteristics of induction motors are expressed as a dependence M = f (S), where S is the slip, S = (nc-n) / nc, where n s is the synchronous speed.

In practice, for the graphical construction of a mechanical characteristic, a simplified formula is used, called the Kloss formula:

here: Mk is the critical (maximum) value of the moment. This value of the moment corresponds to the critical slip

Where λm = Mk/Mn

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

Rice. 1. Asynchronous motor: a - schematic diagram, b - mechanical characteristic M \u003d f (S) - natural in motor and generator modes, c - natural mechanical characteristic n \u003d f (M) in motor mode, d - artificial rheostatic mechanical characteristics, e - mechanical characteristics for various voltages and frequencies.

As can be seen from fig. 1, mechanical characteristic of an induction motor located in the I and III quadrants. Part of the curve in the I quadrant corresponds to a positive slip value and characterizes the motor mode of operation of the induction motor, and in the III quadrant - the generator mode. The motor mode is of the greatest practical interest.

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

Point A corresponds rated motor torque and is determined by the formula Mn = 9.55 10 3 (P n/n n)

This moment corresponds to , which for engines of general industrial use has a value in the range from 1 to 7%, i.e. Sн=1 - 7%. At the same time, small engines have more slip, and large ones have less.

High slip motors, designed to work with shock loading, have S n ~ 15%. These include, for example, engines of a single AC series.

Point C on the characteristic corresponds to the value starting torque arising on the motor shaft during start-up. This moment Mn is called the initial, or starting. The slip in this case is equal to one, and the speed is equal to zero. it is easy to determine according to the reference table, which indicates the ratio of the starting torque to the nominal Mp / Mn.

The value of the starting torque at constant voltage and current frequency depends on the active resistance in the rotor circuit. In this case, at first, with an increase in active resistance, the starting torque increases, reaching its maximum when the active resistance of the rotor circuit is equal to the total inductive resistance of the motor. In the future, with an increase in the active resistance of the rotor, the value of the starting torque decreases, tending to zero in the limit.

Point B (Fig. 1, b and c) corresponds to maximum torque, which can develop the engine over the entire speed range from n = 0 to n = n s. This moment is called the critical (or overturning) moment Mk. critical moment corresponds to the critical slip Sc. The smaller the value of the critical slip Sk, as well as the value of the nominal slip S n, the greater the rigidity of the mechanical characteristic.

Both starting and critical moments are determined through the nominal. According to GOST for electrical machines for a squirrel-cage motor, the condition Mp / Mn \u003d 0.9 - 1.2, Mk / Mn \u003d 1.65 - 2.5 must 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 circuit, while the critical slip S k is directly proportional to this resistance. This means that with an increase in the active resistance of the rotor circuit, the value of the critical moment remains unchanged, however, the maximum of the torque curve shifts towards increasing slip values ​​(Fig. 1, d).

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

If, for example, the voltage supplied to the motor is equal to 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 opposite phenomenon is observed when the frequency changes. If, for example, a motor designed to operate with a current frequency f = 60 Hz is supplied with a current with a frequency f = 50 Hz, then the critical moment will receive a value (60/50) 2 = 1.44 times greater than at its formal frequency (Fig. 1, e).

The critical moment characterizes the instantaneous overload capacity of the engine, i.e. it shows what instantaneous (for a few seconds) overload the engine is able to transfer without any harmful consequences.

The section of the mechanical characteristic from zero to the maximum (critical) value (see Fig. 1, biv) is called stable part of the characteristic, and the BC section (Fig. 1, c) - unstable part.

This division is explained by the fact that on the increasing part of the OF characteristic with increasing slip, i.e. as the speed decreases, the torque developed by the engine increases. This means that with an increase in load, i.e. with an increase in braking torque, the engine speed decreases, and the torque developed by it increases. When the load is reduced, on the contrary, the speed increases, and the torque decreases. When the load changes over the entire range of the stable part of the characteristic, the rotation speed and torque of the engine change.

The engine is not able to develop a moment greater than the critical one, and if the braking torque is greater, the engine must inevitably stop. It happens, as they say, engine rollover.

The mechanical characteristic at constant U and I and the absence of additional resistance in the rotor circuit is called natural characteristic(characteristic of a squirrel-cage asynchronous motor with a phase rotor without additional resistance in the rotor circuit). Artificial, or rheostatic, characteristics are called those that correspond to the additional resistance in the rotor circuit.

All values ​​of starting torques are different and depend on the active resistance of the rotor circuit. The same nominal moment Mn corresponds to slips of various sizes. With an increase in the resistance of the rotor circuit, slip increases and, consequently, the engine speed decreases.

Due to the inclusion of active resistance in the rotor circuit, the mechanical characteristic in the stable part is extended in the direction of increasing slip, in proportion to the resistance. This means that the motor speed begins to change strongly depending on the load on the shaft and the characteristic becomes soft from hard.

Lecture 3

Asynchronous motors have been widely used in industry due to a number of significant advantages over other types of motors. The asynchronous motor is simple and reliable in operation, as it does not have a collector; asynchronous motors are cheaper and much lighter than DC motors.

To derive the equation for the mechanical characteristic of an induction motor, you can use the simplified equivalent circuit shown in Fig. 3.1, where the following designations are accepted:

Uf - primary phase voltage; I 1 - phase current of the stator; I / 2 - reduced rotor current; X 1 and X" 2 - primary and secondary reduced scattering reactances; Ro and X 0 - active and reactive resistance of the magnetization circuit; s == (w 0 - w) / w 0 - engine slip; w 0 = 2pn 0 /60 - synchronous angular speed of the motor; w 0 = 2pf 1 /p; R1 and R/2 - primary and secondary reduced active resistances; f 1 - network frequency; R - number of pairs of poles.

Rice. 3.1 Simplified equivalent circuit of an asynchronous motor.

In accordance with the above equivalent circuit, it is possible to obtain an expression for the secondary current

(2.1)

The torque of an induction motor can be determined from the loss expression Mw 0 s = 3 (I / 2) 2 R / 2 , whence

(2.2)

Substituting the value of the current I / 2 in (2.1), we obtain:

(2.3)

Moment curve M = f(s) has two maxima: one - in the generator mode, the other - in the motor mode 1 .

Equating dM/ds= 0, we determine the value of the critical slip Sg, at which the engine develops the maximum (critical) torque

(2.4)

With significant resistance of the rotor circuit, the maximum torque may be in the mode of braking by counter-switching.

Substituting the value of Sk in (3.3), we find the expression for the maximum moment

(2.5)

The sign "+" in equalities (2.4) and (2.5) refers to the motor mode (or braking by counter-inclusion), the sign "-" - to the generator mode of operation in parallel with the network (w>w 0)

If the expression (2.3) is divided by (2.5) and the corresponding transformations are made,

Rice. 3.2 Mechanical characteristics of an asynchronous motor.

then you can get:

(2.6)

where Mk - maximum engine torque; S K - critical slip corresponding to the maximum moment; A= R 1 / R / 2 .

Here it is necessary to emphasize a circumstance that is very important for practice - the effect of changing the mains voltage on the mechanical characteristics of an induction motor. As can be seen from (3.3), for a given slip, the motor torque is proportional to the square of the voltage, so this type of motor is sensitive to mains voltage fluctuations.

The critical slip and the angular velocity of an ideal idle are independent of voltage.

On fig. 3.2 shows the mechanical characteristics of an asynchronous motor. Her characteristic points:

1) s = 0; M = 0, while the motor speed is equal to synchronous;

2) s = s NOM; M = M nom which corresponds to the rated speed and rated torque;

3) s == sk; M == M max - maximum torque in motor mode;

Initial starting torque;

5) s = - s K ; M=M K.G. - the maximum torque in the generator mode of operation in parallel with the network.

With s> 1.0, the motor operates in the anti-switching braking mode, with s< 0 имеет место генераторный режим работы параллельно с сетью.

It must be emphasized that the absolute values ​​of S k in the motor and generator modes in parallel with the network are the same

However, from (2.6) it follows that the maximum moments in the motor and generator modes are different. In the generator mode of operation in parallel with the network, the maximum torque is greater in absolute value, which follows from the relation

If in equation (2.6) we neglect the active resistance of the stator, then we get a formula that is more convenient for calculations:

(2.7)

Substituting in expression (2.7) instead of the current values ​​of M and s their nominal values ​​and denoting the multiplicity of the maximum moment M K / M NOM, through l, we get:

In the last expression, the “+” sign should be taken before the root.

An analysis of formula (2.6) shows that for s>s k (the non-working part of the characteristic), a hyperbola equation will be obtained if, in this case, the second terms of the denominator in equations (3.6) are neglected, i.e.

This part of the characteristic practically corresponds only to starting and braking modes.

For small values ​​of slip (s< s k) для M=f (s) we get the equation of a straight line if we neglect the first term in the denominator (3.6):

This linear part of the characteristic is its working part, on which the engine usually operates in steady state. On the same part of the characteristic there are points corresponding to the nominal data of the motor: M NOM, I NOM, n NOM, s NOM.

The static drop (difference) of speed in relative units on the natural mechanical characteristic of an asynchronous motor at a rated torque is determined by its rated slip.

The nominal slip depends on the resistance of the rotor. Motors with a squirrel-cage rotor of normal design usually have the smallest rated slip for the same power and number of poles. For these motors, due to their design features, the rotor resistance has a relatively small value, which leads to a decrease in the values ​​of critical slip s k (3.4) and nominal slip s NOM. For the same reasons, with an increase in engine power, its nominal slip decreases and the stiffness of the natural characteristic increases. The latter is illustrated by the curve in Fig. 11, built on average data for engines of different power.

The maximum moment, as can be seen from (3.5), does not depend on the active resistance of the rotor R 2 , the critical slip, according to (3.4), increases as the rotor resistance increases. As a result, in motors with a phase rotor, when resistors are introduced into the rotor circuit, the maximum of the torque curve is shifted towards large slips.

The resistance value R 2 , necessary to build the natural and rheostatic characteristics of a motor with a phase rotor, is determined from the expression

where E 2k, I 2NOM - linear voltage with a stationary rotor and the rated current of the rotor.

On fig. 12 shows the family of rheostatic characteristics in the motor mode in the coordinate axes M and with for different values ​​of the resistance of the rotor circuit. With a known approximation, the rheostatic characteristics in their working part can be taken as linear. This makes it possible, when calculating the resistance of resistors included in the rotor circuit of an asynchronous motor, to use methods similar to those used

Rice. 11. Curve of the nominal Fig. 12 Natural and rheostatic mechanical

slip for asynchronous characteristics of an induction motor with phase-

engines of different power. rotor

to calculate the armature circuit resistance of a DC motor of independent excitation. Some inaccuracy in the determination of the resistance of the resistor is introduced in this case due to the fact that the characteristic of the asynchronous motor in the section of the graph from M = 0 to the maximum torque at start-up is considered linear.

A more accurate method is when the characteristics are straightened over a smaller area. The multiplicity of the maximum moment l \u003d M K.D. /M nom should be at least 1.8 for motors of normal design with a phase rotor, and at least 1.7 for motors with a squirrel-cage rotor. Crane motors are characterized by a higher ratio of maximum torque. For example, for motors with a squirrel-cage rotor of the MTK series l=2.3¸3.4.

Motors with a phase rotor of the mentioned series have approximately the same values ​​of l .

For motors with a squirrel-cage rotor, the multiplicity of the initial starting torque and the initial starting current are essential from the point of view of the electric drive.

On fig. 13 shows the approximate natural characteristics of a motor with a normal squirrel-cage rotor having circular slots. These characteristics show that a squirrel-cage motor, consuming a very large current from the network, has a relatively

Rice. 13. Characteristics co = = f(M) and u == D (/) for an induction motor with a squirrel-cage rotor with round slots.

low starting torque. The multiplicity of the initial starting torque of the engines

and for crane engines

Starting current ratio

The lack of proportionality between the motor torque and the stator current during start-up (Fig. 13) is explained by a significant decrease in the motor magnetic flux, as well as a decrease in the power factor of the secondary circuit during start-up.

The moment of an induction motor, like any electrical machine, is proportional to the magnetic flux Ф and the active component of the secondary current

(2.8)

With increasing slip, the EMF of the rotor increases E 2 \u003d E 2K s , the rotor current I / 2 increases in accordance with (3.1), asymptotically tending to a certain limit value, and cos y 2 decreases with increasing s (very little in the working section of the characteristic), asymptotically tending to zero at s ®¥. The motor flux also does not remain constant, decreasing as the current increases due to the voltage drop across the stator winding resistances. All this causes the lack of proportionality between the current and the motor torque.

To increase the initial starting torque and reduce the starting current, motors with a squirrel-cage rotor of special designs are used. Electric motor rotors have two concentric cages or deep surfacings with tall and narrow shafts. The rotor resistance of these motors in the starting

Rice. 14. Mechanical characteristics of an asynchronous motor with a squirrel-cage rotor with a dip at low angular speeds.

the period is much longer than at rated speed, due to the skin effect due to the increased frequency of the current in the rotor at large slips. Therefore, when switching to motors with a deep groove or a double winding of the rotor, the multiplicity of the starting torque increases significantly (cos y 2 flux increases) and the multiplicity of the starting current decreases. True, in this case, the power factor and efficiency corresponding to the rated load are somewhat reduced.

It should be noted that for motors with a squirrel-cage rotor, the starting torque is practically not always the smallest value of the torque in the region of the motor mode. As can be seen from fig. 14, the mechanical characteristic of a motor with a squirrel-cage rotor sometimes has a dip at low angular speeds, caused by the influence of higher harmonics of the tooth fields. This circumstance should be taken into account when starting the engine under load.

For motors with a phase rotor, the initial starting torque increases as it increases to the known resistance limits of the resistor (Fig. 12), and the starting current decreases with increasing resistance. The initial starting torque can be adjusted to the maximum torque. With a further increase in the resistance of the rotor circuit, an increase in cos y 2 compensates for a decrease in the rotor current and the starting torque decreases.

Mechanical characteristics

asynchronous motor in braking modes

In § 3.7, the mechanical characteristics of an asynchronous machine operating in a motor mode were considered. However, an asynchronous motor can also operate in braking modes: during braking with energy transfer to the network, during anti-switching braking and during dynamic braking.

1. Braking with energy return to the network(generator operation mode

Rice. 15. Mechanical characteristics of an asynchronous motor for various operating modes.

in parallel with the mains) is possible at speeds higher than synchronous. The mechanical characteristics of an asynchronous motor in the coordinates M and w) are shown in fig. 15. In quadrant 1 there are sections of the characteristics of the motor mode for three different resistances of the rotor circuit. As the engine speed approaches ideal idle speed, or synchronous speed, the engine torque approaches zero.

With a further increase in the angular velocity under the influence of an external moment, when w>w 0 , the engine operates in the generator mode in parallel with the network, to which it can supply electrical energy, while consuming reactive power for excitation. Braking with energy transfer to the network corresponds to the sections of characteristics located in the upper part of quadrant 2. In this mode, as can be seen from (3.5), the maximum torque is greater than in the motor mode. The braking mode with energy transfer to the network is used practically for pole-changing motors, as well as for drives of hoisting machines (lifts, excavators, etc.) and in some other cases.

2. Reverse current braking has much more practical application. The reverse current braking mode can be obtained, in the same way as for a DC motor, with a load driving torque Ms > M P (Fig. 15). To limit the current and obtain the corresponding torque, it is necessary, when using a motor with a phase rotor, to include an additional resistor in its rotor circuit. The steady-state mode during braking by counter-wiring corresponds, for example, to the point - w SET, M C on the characteristic (Fig. 15).

The mechanical characteristic for Rp 1 in the anti-current braking mode and M C == const does not provide stable operation. Reverse braking can also be obtained by switching two phases of the stator winding on the go, which leads to a change in the direction of rotation of the magnetic field (transition from the point A exactly IN in fig. 16). The rotor then rotates against the direction of the field and gradually slows down. When the angular velocity drops to zero (point C in Fig. 16), the motor must be disconnected from the network, otherwise it may again switch to motor mode, and its rotor will rotate in the opposite direction to the previous one (point D).

3. Dynamic braking of asynchronous motor is usually carried out by turning on the stator winding on the DC network; the rotor winding is then closed to external resistors. To switch from motor mode to dynamic braking mode, contactor K1 (Fig. 17) disconnects the stator from the AC network, and contactor K2 connects the stator winding to the DC network. External resistors are provided in the rotor circuit to limit the current and obtain various braking characteristics.

Passing through the stator winding, the direct current forms a fixed field, the main wave of which gives a sinusoidal distribution of induction. An alternating current arises in a rotating rotor, which creates its own field, which

also stationary relative to the stator. As a result of the interaction of the total magnetic flux with the rotor current, a braking torque arises, which depends on the stator MMF, rotor resistance and the angular velocity of the motor. The mechanical characteristics for this mode are given in the lower part of quadrant 2 (see Fig. 15). They pass through the origin of coordinates, since at an angular velocity equal to zero, the braking torque in this mode is also equal to zero. The maximum torque is proportional to the square of the voltage applied to the stator 1 and increases with increasing voltage. The critical slip depends on

Fig. 16. Mechanical characteristics 17 Wiring diagram