Equation of mechanical characteristics of an asynchronous motor. single phase equivalent circuit. Mechanical characteristics of the motor Mechanical characteristics of an asynchronous motor with a short-circuit rotor
Mechanical characteristics of asynchronous motors
Induction motors are the main motors that are most widely used in both industry and agro-industrial production. They have significant advantages over other types of engines: they are easy to operate, reliable and low cost.
In a three-phase asynchronous motor, when the stator winding is connected to a three-phase alternating voltage network, a rotating magnetic field is created, which, crossing the conductors of the rotor winding, induces an emf in them, under the influence of which current and magnetic flux appear in the rotor. The interaction of the magnetic fluxes of the stator and rotor creates the torque of the motor. The appearance of EMF, and therefore torque, in the rotor winding is possible only if there is a difference between the rotation speeds of the magnetic field of the stator and rotor. This difference in speed is called slip.
The slip of an induction motor is a measure of how much the rotor lags in its rotation behind the rotation of the stator's magnetic field. It is denoted by the letter S and is determined by the formula
, (2.17)
where w 0 is the angular speed of rotation of the stator magnetic field (synchronous angular speed of the motor); w is the angular velocity of the rotor; ν – engine rotation speed in relative units.
The rotation speed of the stator magnetic field depends on the frequency of the supply network current f and number of pole pairs R engine: . (2.18)
The equation for the mechanical characteristics of an asynchronous motor can be derived based on the simplified equivalent circuit shown in Fig. 2.11. The following designations are used in the equivalent circuit: U f- primary phase voltage; I 1- phase current in the stator windings; I 2- reduced current in the rotor windings; X 1– reactance of the stator winding; R 1, R 1 2– active resistances in the windings of the stator and reduced rotor, respectively; X 2΄ - reduced reactance in the rotor windings; R0, X 0- active and reactive resistance of the magnetization circuit; S– sliding.
In accordance with the equivalent circuit in Fig. 2.11, the expression for the rotor current has the form
Rice. 2.11. Replacement diagram of an asynchronous motor
The torque of an induction motor can be determined from the expression Мw 0 S=3(I 2 ΄) 2 R 2 according to the formula
Substituting the current value I 2 ΄ from formula (2.19) to formula (2.20), we determine the engine torque depending on the slip, i.e. the analytical expression of the mechanical characteristics of an asynchronous motor has the form
Dependency graph M= f (S) for the motor mode is presented in Fig. 2.12. During acceleration, the engine torque changes from the starting torque M n up to the maximum moment, which is called critical moment M to. The slip and engine speed corresponding to the greatest (maximum) torque are called critical and are designated accordingly S to, w to. Equating the derivative to zero in expression (2.21), we obtain the value of the critical slip S k, at which the engine develops maximum torque:
Where X k = (X 1 + X 2 ΄) – motor reactance.
For motor mode S to taken with a “plus” sign, for supersynchronous - with a “minus” sign.
Substituting the value S to(2.22) into expression (2.21), we obtain the formulas for the maximum moment:
a) for motor mode
b) for supersynchronous braking
The plus sign in equalities (2.22) and (2.23) refers to the motor mode and back-switching braking; the minus sign in formulas (2.21), (2.22) and (2.24) - to the supersynchronous mode of a motor operating in parallel with the network (with w>w 0).
As can be seen from (2.23) and (2.24), the maximum torque of a motor operating in supersynchronous braking mode will be greater compared to the motor mode due to the voltage drop across R 1(Fig. 2.11).
If expression (2.21) is divided by (2.23) and a number of transformations are made taking into account equation (2.22), we can obtain a simpler expression for the dependence M= f (S):
Where – coefficient.
Neglecting the active resistance of the stator winding R 1, because for asynchronous motors with a power of more than 10 kW, the resistance R 1 is significantly less X k, can be equated a ≈ 0, we obtain a more convenient and simpler for calculations formula for determining the engine torque by its sliding (Kloss formula):
. (2.26) If in expression (2.25) instead of the current values M And S substitute the nominal values and indicate the multiplicity of moments M to /M n through k max, we obtain a simplified formula for determining the critical slip:
In (2.27), take any result of the solution under the root with a “+” sign, because with a “-” sign, the solution of this equation does not make sense. Equations (2.21), (2.23), (2.24), (2.25) and (2.26) are expressions that describe the mechanical characteristics of an asynchronous motor (Fig. 2.12).
Artificial mechanical characteristics of an asynchronous motor can be obtained by changing the voltage or frequency of the current in the supply network or by introducing additional resistances into the stator or rotor circuit.
Let us consider the influence of each of these parameters ( U, f, R d) on the mechanical characteristics of an asynchronous motor.
Influence of supply voltage. Analysis of equations (2.21) and (2.23) shows that changing the network voltage affects the motor torque and does not affect its critical slip. In this case, the torque developed by the motor changes in proportion to the square of the voltage:
M≡ kU 2, (2.28)
Where k– coefficient depending on engine and slip parameters.
The mechanical characteristics of an asynchronous motor when the network voltage changes are presented in Fig. 2.13. In this case U n= U 1 >U 2 >U 3.
The influence of additional external active resistance included in the stator circuit. Additional resistances are introduced into the stator circuit to reduce the starting current and torque values (Fig. 2.14a). The voltage drop across the external resistance is in this case a function of the motor current. When starting the engine, when the current value is high, the voltage on the stator windings decreases.
Fig.2.14. Connection diagram (a) and mechanical characteristics (b) of an asynchronous motor when active resistance is connected to the stator circuit
In this case, according to equations (2.21), (2.22) and (2.23), the starting torque changes M p, critical moment M k and angular velocity ω To. Mechanical characteristics for various additional resistances in the stator circuit are presented in Fig. 2.14b, where R d 2 >R d 1 .
The influence of additional external resistance included in the rotor circuit. When additional resistance is included in the rotor circuit of a motor with a wound rotor (Fig. 2.15a), its critical slip increases, which is explained by the expression.
Fig.2.15. Connection diagram (a) and mechanical characteristics (b) of an asynchronous motor with a wound rotor when additional resistance is connected to the rotor circuit
The value R / 2 is not included in expression (2.23), since this value does not affect MK, therefore the critical moment remains unchanged for any R / 2. The mechanical characteristics of an asynchronous motor with a wound rotor with various additional resistances in the rotor circuit are presented in Fig. 2.15b.
Influence of mains frequency. Changing the frequency of the current affects the value of inductive reactance X to asynchronous motor and, as can be seen from equations (2.18), (2.22), (2.23) and (2.24), affects the synchronous angular velocity w 0, critical slip S to and critical moment M to. Moreover ; ; w 0 ºf, Where C 1, C 2- coefficients determined by motor parameters independent of current frequency f.
Mechanical characteristics of the motor when changing the frequency of the current f are presented in Fig. 2.16.
Fig.2.16. Mechanical characteristics of an asynchronous motor when changing the frequency of the supply network
Dynamic mechanical characteristic of an asynchronous motor is the relationship between the instantaneous values of speed (slip) and torque of an electric machine for the same moment in time of the transient operating mode.
A graph of the dynamic mechanical characteristics of an asynchronous motor can be obtained from a 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 voltage vector of the stator winding, oriented along the axis b fixed coordinate system;
– equivalent inductive reactance of the stator winding, equal to the inductive leakage resistance of the stator winding and the inductive reactance from the main field;
– equivalent inductive reactance of the rotor winding, reduced to the stator winding, equal to the inductive leakage resistance of the rotor winding and the inductive reactance from the main field;
– inductive reactance from the main field (magnetization circuit), created by the total action of stator currents;
A fixed coordinate system;
– component of the flux linkage vector of the stator winding, oriented along the axis b fixed coordinate system;
A fixed coordinate system;
– component of the flux linkage vector of the rotor winding, 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 occasion
where is the load resistance moment reduced to the motor shaft; – total moment of inertia of the electric drive reduced to the motor shaft.
Analysis of the dynamic processes of energy conversion in an asynchronous motor is a complex task due to the significant nonlinearity of the equations describing the asynchronous motor, caused by the product of variables. Therefore, it is advisable to study the dynamic characteristics of an asynchronous motor using computer technology.
The joint solution of the system of equations (5.62) and (5.63) in the MathCAD software environment makes it possible to calculate 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 characteristics of an asynchronous motor can be obtained only from the results of calculations of transient processes, we first present graphs of the transient processes of speed (Fig. 5.9) and torque (Fig. 5.10) when starting an asynchronous motor by direct connection to the network.
Rice. 5.9.
Rice. 5.10.
Rice. 5.11.
Graphs and transient processes make it possible to construct a dynamic mechanical characteristic of an asynchronous motor (Fig. 5.1 I, curve I) when started by direct connection to the network. For comparison, the same figure shows the static mechanical characteristic - 2, calculated using expression (5.7) for the same parameters of the equivalent circuit of an asynchronous motor.
Analysis of the dynamic mechanical characteristics of an asynchronous motor shows that the maximum impact torques during startup exceed the nominal torque L/n of the static mechanical characteristics by more than 4.5 times and can reach values that are unacceptably high in terms of mechanical strength. Shock 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 asynchronous 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 and the moment of resistance on the motor shaft. Consequently, an asynchronous motor, with given parameters of the supply network and 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 squirrel-cage asynchronous motor can have an oscillatory nature not only at the initial, but also at the final section, and the motor speed exceeds the synchronous speed ω0. In practice, fluctuations in the angular velocity and torque of the engine at the final section of the transient process are not always observed. In addition, there are a large number of production mechanisms for which such fluctuations must be eliminated. A typical example is the mechanisms of winches and 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 characteristics of an asynchronous 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 fade.
Studies of dynamic mechanical characteristics are of theoretical and practical importance, since, as was shown in Section 5.1.1, taking into account only static mechanical characteristics can lead to not entirely correct conclusions and to a distortion of the nature of dynamic loads when starting asynchronous motors. Research shows that the maximum values of dynamic torque can exceed the rated torque of the motor when starting with direct connection to the network by 2-5 times and by 4-10 times when reversing the motor, which must be taken into account when developing and manufacturing electric drives.
Mechanical characteristics of the engine is called the dependence of the rotor speed on the torque on the shaft n = f (M2). Since the no-load torque is small under load, M2 ≈ M and the mechanical characteristic is represented by the dependence n = f (M). If we take into account the relationship s = (n1 - n) / n1, then the mechanical characteristic can be obtained by presenting its graphical dependence in coordinates n and M (Fig. 1).
Rice. 1. Mechanical characteristics of an asynchronous motor
Natural mechanical characteristic of an induction motor corresponds to the main (certificate) circuit of its connection and the nominal parameters of the supply voltage. Artificial characteristics are obtained if any additional elements are included: resistors, reactors, capacitors. When the motor is powered with a non-rated voltage, the characteristics also differ from the natural mechanical characteristics.
Mechanical characteristics are a very convenient and useful tool for analyzing the static and dynamic modes of an electric drive.
Main points of mechanical characteristics: critical slip and frequency, maximum torque, starting torque, rated torque.
Mechanical characteristic is the dependence of torque on slip, or, in other words, on the number of revolutions:
From the expression 
it is clear that this dependence is very complex, because, as the formulas show) 
And 
, sliding is also included in the expressions for I 2
And cos? 2. The mechanical characteristics of an asynchronous motor are usually given graphically
The starting point of the characteristic corresponds to n= 0 and s= 1: this is the first moment the engine starts. Starting torque value M n - a very important characteristic of the operational properties of the engine. If M n small, less than the rated operating torque, the engine can only be started idle or with a correspondingly reduced mechanical load.
Let us denote by the symbol Mnp counteracting (braking) torque created by the mechanical load on the shaft at which the engine starts. The obvious condition for the engine to be able to start is: M n > Mnp . If this condition is met, the engine rotor will begin to move, its speed will be n will increase, and the slip s decrease. As can be seen from the image above, the engine torque increases from M n up to maximum M m , corresponding to the critical slip s kp therefore, the excess available engine power, determined by the torque difference, also increases M And Mnp .
The greater the difference between the available engine torque (possible for a given slip along the operating characteristic) M and opposing M np , the easier the starting mode and the faster the engine reaches a steady rotation speed.
As the mechanical characteristics show, at a certain number of revolutions (at s = s kp) the available motor torque reaches the maximum possible for a given motor (at a given voltage U ) values Mt . Next, the engine continues to increase its rotation speed, but its available torque quickly decreases. At some values n And s the engine torque becomes equal to the countermotor: the engine start ends, its speed is set to a value corresponding to the ratio:
This ratio is mandatory for all engine load modes, that is, for all values Mnp , within the maximum available engine torque M t . Within these limits, the engine itself automatically adapts to all load fluctuations: if during engine operation its mechanical load increases, for a moment M n.p. there will be more torque developed by the engine. The engine speed will begin to decrease and the torque will increase.
The rotation speed will be established at a new level corresponding to the equality M And Mnp . When the load decreases, the process of transition to a new load mode will be reversed.
If the load moment Mnp will exceed M t , the engine will stop immediately, since with a further decrease in speed, the engine torque decreases.
Therefore, the maximum engine torque M T also called the overturning or critical moment.
If in the moment formula 
substitute:
then we get:
Taking the first derivative of M by and equating it to zero, we find that the maximum value of the torque occurs under the condition:
that is, with such sliding s = s kp , at which the active resistance of the rotor is equal to the inductive reactance
Values s kp for most asynchronous motors they range from 10 to 25%.
If in the torque formula written above, instead of active resistance r 2 substitute the inductive by the formula
The maximum torque of an asynchronous motor is proportional to the square of the magnetic flux (and therefore the square of the voltage) and inversely proportional to the leakage inductance of the rotor winding.
When the voltage supplied to the motor is constant, its flow F remains virtually unchanged.
The leakage inductance of the rotor circuit is also practically constant. Therefore, when the active resistance in the rotor circuit changes, the maximum value of the torque Mt will not change, but will occur at different slips (with an increase in the active resistance of the rotor - at large slip values).
Obviously, the maximum possible engine load is determined by the value of its Mt . The working part of the engine characteristics lies in a narrow range of speeds from n, corresponding Mt , before. At n = n 1 (characteristic end point) M = 0, since at synchronous rotor speed s = 0 and I 2 = 0.
The rated torque, which determines the nameplate power of the engine, is usually taken equal to 0.4 - 0.6 of Mt . Thus, asynchronous motors allow short-term overloads of 2 - 2.5 times.
The main parameter characterizing the operating mode of an asynchronous motor is slip s - the relative difference between the motor rotor speed n and its field n o: s = (n o - n) / n o .
The region of mechanical characteristics corresponding to 0 ≤ s ≤ 1 is the region of motor modes, and at s< s кр работа двигателя устойчива, при s >s cr - unstable. When s< 0 и s >1 engine torque is directed against the direction of rotation of its rotor (regenerative braking and counter-initiation braking, respectively).
A stable section of the mechanical characteristics of an engine is often described by the Kloss formula, by substituting the parameters of the nominal mode into which the critical slip scr can be determined:
,
where: λ = M kp / M n - overload capacity of the engine.
A mechanical characteristic according to a reference book or catalog can be approximately constructed using four points (Fig. 7.1):
Point 1 - ideal idle speed, n = n o = 60 f / p, M = 0, where: p - number of pole pairs of the motor magnetic field;
Point 2 - nominal, mode: n = n n, M = M n = 9550 P n / n n, where P n is the rated power of the engine in kW;
Point 3 - critical mode: n = n cr, M = M cr =λ M n;
Point 4 - start mode: n = 0, M = M start = β M n.
When analyzing engine operation in a load range up to Mn and slightly more, a stable section of the mechanical characteristic can be approximately described by the equation of a straight line n = n 0 - vM, where the coefficient “b” is easily determined by substituting the nominal mode parameters n n and M n into the equation.
Design of stator windings. Single-layer and double-layer loop windings.
Based on the design of the coils, the windings are divided into loose windings with soft coils and windings with hard coils or half-coils. Soft coils are made from round insulated wire. To give the required shape, they are first wound onto templates and then placed in insulated trapezoidal grooves (see Fig. 3.4, V, G and 3.5, V); interphase insulating spacers are installed during winding installation. Then the coils are strengthened in the grooves with the help of wedges or covers, they are given their final shape (the frontal parts are formed), the winding is banded and impregnated. The entire process of manufacturing random windings can be completely mechanized.
Rigid coils (half-coils) are made from rectangular insulated wire. They are given their final shape before being placed in the grooves; At the same time, shell and phase-to-phase insulation is applied to them. The coils are then placed in pre-insulated open or semi-open slots , strengthened and impregnated.
1. Single layer windings- most suitable for mechanized installation, since in this case the winding must be concentric and placed in the stator slots on both sides of the coil simultaneously. However, their use leads to increased consumption of winding wire due to the significant length of the frontal parts. In addition, in such windings it is not possible to shorten the pitch, which leads to a deterioration in the shape of the magnetic field in the air gap, an increase in additional losses, the occurrence of dips in the mechanical characteristics and increased noise. However, due to their simplicity and low cost, such windings are widely used in asynchronous motors of low power up to 10-15 kW.
2. Double layer windings- allow you to shorten the winding pitch by any number of tooth divisions, thereby improving the shape of the magnetic field created by the winding and suppressing higher harmonic EMF curves. In addition, with two-layer windings, a simpler shape of end connections is obtained, which simplifies the manufacture of windings. Such windings are used for motors with power over 100 kW with rigid coils that are laid manually.
Stator windings. Single-layer and double-layer wave windings
A multiphase winding is placed in the slots of the stator core, which is connected to the alternating current network. Multiphase symmetrical windings with the number of phases T include T phase windings that are connected into a star or polygon. So, for example, in the case of a three-phase stator winding, the number of phases t = 3 and the windings can be connected in star or triangle. The phase windings are offset from each other by an angle of 360/ T hail; for a three-phase winding this angle is 120°.
The phase windings are made of separate coils connected in series, parallel or series-parallel. In this case, under coil refers to several series-connected turns of the stator winding, placed in the same slots and having common insulation relative to the walls of the slot. In its turn coil two active (i.e., located in the stator core itself) conductors are considered, laid in two slots under adjacent opposite poles and connected to each other in series. The conductors located outside the stator core and connecting the active conductors to each other are called the end parts of the winding. The straight parts of the winding coils placed in the slots are called coil sides or slot parts.
The stator grooves into which the windings are placed form so-called teeth on the inside of the stator. The distance between the centers of two adjacent teeth of the stator core, measured along its surface facing the air gap, is called dentate division or groove division.
Multilayer cylindrical coil windings (Figure 3) are wound from round wire and consist of multilayer disk coils located along the rod. Radial channels for cooling can be left between the coils (through each coil or through two or three coils). Such windings are used on the high voltage side when S st ≤ 335 kV×A, I st ≤ 45 A and U l.n ≤ 35 kV.
Single-layer and double-layer cylindrical windings (Figure 4) are wound from one or more (up to four) parallel rectangular conductors and are used when S st ≤ 200 kV×A, I st ≤ 800 A and U l.n ≤ 6 kV.
The mechanical characteristic is usually understood as the dependence of the rotor speed as a function of the electromagnetic torque n = f(M). This characteristic (Fig. 2.15) can be obtained using the dependence M = f(S) and recalculating the rotor speed at different slip values.
Since S = (n0 - n) / n0, hence n = n0(1 - S). Let us recall that n0 = (60 f) / p is the rotation frequency of the magnetic field.
Section 1-3 corresponds to stable operation, section 3-4 – unstable operation. Point 1 corresponds to the ideal idle speed of the engine when n = n0. Point 2 corresponds to the nominal operating mode of the engine, its coordinates are Mn and nn. Point 3 corresponds to the critical moment Mcr and the critical rotation speed ncr. Point 4 corresponds to the starting torque of the engine Mstart. The mechanical characteristic can be calculated and constructed using the passport data. Point 1:
n0 = (60 f) / p,
where: p – number of pole pairs of the machine;
f – network frequency.
Point 2 with coordinates nn and Mn. The rated rotation speed nн is specified in the passport. The rated torque is calculated using the formula:
here: Рн – rated power (shaft power).
Point 3 with coordinates Mkr nkr. The critical moment is calculated using the formula Mkr = Mn λ. The overload capacity λ is specified in the motor passport ncr = n0 (1 - Skr), 
, Sн = (n0 - nn) / n0 – nominal slip.
Point 4 has coordinates n=0 and M=Mstart. The starting torque is calculated using the formula
Mstart = Mn λstart,
where: λstart – the starting torque multiplicity is specified in the passport.
Asynchronous motors have a rigid mechanical characteristic, because The rotor speed (section 1–3) depends little on the load on the shaft. This is one of the advantages of these engines.
Asynchronous motors (IM) are the most common type of motor, because... they are simpler and more reliable in operation, with equal power they have less weight, dimensions and cost in comparison with DPT. The circuit diagrams for switching on the blood pressure are shown in Fig. 2.14.
Until recently, IMs with squirrel-cage rotors were used in unregulated electric drives. However, with the advent of thyristor frequency converters (TFCs) of the voltage supplying the stator windings of the IM, squirrel-cage motors began to be used in adjustable electric drives. Currently, power transistors and programmable controllers are used in frequency converters. The speed control method is called pulse and its improvement is the most important direction in the development of electric drives.
Rice. 2.14. a) circuit diagram for switching on an IM with a squirrel-cage rotor;
b) circuit diagram for switching on an IM with a phase-wound rotor.
The equation for the mechanical characteristics of the blood pressure can be obtained based on the equivalent circuit of the blood pressure. If we neglect the active resistance of the stator in this circuit, then the expression for the mechanical characteristic will have the form:
,
Here M k – critical moment; S to- the corresponding critical slip; U f– effective value of the phase voltage of the network; ω 0 =2πf/p– angular speed of the rotating magnetic field of the IM (synchronous speed); f– supply voltage frequency; p– number of pairs of poles of the IM; x k– inductive phase resistance of the short circuit (determined from the equivalent circuit); S=(ω 0 -ω)/ω 0– slip (rotor speed relative to the speed of the rotating field); R 2 1– total active resistance of the rotor phase.
The mechanical characteristics of an IM with a squirrel-cage rotor are shown in Fig. 2.15.
Rice. 2.15. Mechanical characteristics of an induction motor with a squirrel-cage rotor.
Three characteristic points can be distinguished on it. Coordinates of the first point ( S=0; ω=ω 0 ; M=0). It corresponds to the ideal idle mode, when the rotor speed is equal to the speed of the rotating magnetic field. Coordinates of the second point ( S=S to; M=M k). The engine is running at maximum torque. At M s >M k the motor rotor will be forced to stop, which is a short circuit for the motor. Therefore, the engine torque at this point is called critical M k. Coordinates of the third point ( S=1; ω=0; M=M p). At this point, the engine operates in start mode: rotor speed ω=0 and the starting torque acts on the stationary rotor M p. The section of the mechanical characteristic located between the first and second characteristic points is called the working section. On it the engine operates in steady state. For an IM with a squirrel-cage rotor, if the conditions are met U=U n And f=f n the mechanical characteristic is called natural. In this case, on the working section of the characteristic there is a point corresponding to the nominal operating mode of the engine and having coordinates ( S n; ω n; M n).
Electromechanical characteristics of blood pressure ω=f(I f), which is shown as a dashed line in Fig. 2.15, in contrast to the electromechanical characteristic of the DPT, coincides with the mechanical characteristic only in its working section. This is explained by the fact that during startup due to the changing frequency of the emf. in the rotor winding E 2 the frequency of the current and the ratio of the inductive and active resistance of the winding changes: at the beginning of the start-up, the frequency of the current is higher and the inductive resistance is greater than the active one; with increasing rotor speed ω the frequency of the rotor current, and hence the inductive resistance of its winding, decreases. Therefore, the starting current of the IM in direct start mode is 5–7 times higher than the rated value I fn, and the starting torque M p equal to nominal M n. Unlike DPT, where when starting it is necessary to limit the starting current and starting torque, when starting an IM, the starting current must be limited and the starting torque increased. The last circumstance is the most important, since the DPT with independent excitation starts when M s<2,5М н , DPT with sequential excitation at M s<5М н , and blood pressure when working at a natural characteristic at M s<М н .
For an IM with a squirrel-cage rotor, the increase M p is ensured by a special design of the rotor winding. The groove for the rotor winding is made deep, and the winding itself is arranged in two layers. When starting the engine, frequency E 2 and the rotor currents are large, which leads to the appearance of a current displacement effect - the current flows only in the upper layer of the winding. Therefore, the winding resistance and the starting torque of the motor increase M P. Its value can reach 1.5M n.
For an IM with a wound rotor, the increase M P is ensured by changing its mechanical characteristics. If resistance R P, included in the rotor current flow circuit, is equal to zero - the engine operates at a natural characteristic and M P =M N. At R P >0 the total active resistance of the rotor phase increases R 2 1. Critical slip S to as it increases R 2 1 also increases. As a result, in an IM with a wound rotor, the introduction R P into the rotor current flow circuit leads to a displacement M K towards large slips. At S K =1 M P =M K. Mechanical characteristics of IM with wound rotor at R P >0 are called artificial or rheostat. They are shown in Fig. 2.16.