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 Mm , 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 M t . 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 M t 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 M t . The working part of the engine characteristics lies in a narrow range of speeds from n, corresponding M t , 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 M t . 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.
AC drive
Classification of AC electric drives
Based on synchronous motors.
a) LED with electromagnetic excitation,
b) LED with excitation from permanent magnets.
Synchronous machines can operate in three modes: generator, motor and synchronous compensator mode.
The most common operating mode of synchronous machines is the generator mode. Thermal power plants have turbogenerators with a capacity of 1200 MW at 3000 rpm and 1600 MW at 1500 rpm. Unlike high-speed turbogenerators, hydrogenerators are low-speed machines, usually with a vertical axis of rotation. To increase the dynamic stability of power systems and improve the quality of electricity, synchronous compensators are used, made on the basis of salient and non-salient pole synchronous machines.
In motor mode, synchronous machines are used as drive motors for powerful pumps, fans, and blowers. The maximum power of synchronous motors reaches several hundred megawatts. Also, synchronous micromotors, in which permanent magnets are used to create an excitation field, are widely used in various electric drives.
Typically, synchronous generators and motors are operated with cos φ= 0.8 ÷ 0.9.
Based on asynchronous motors with short-circuit rotor.
a) three-phase blood pressure,
b) biphasic blood pressure.
Based on asynchronous motors with a wound rotor.
Asynchronous machines are most widely used as motors. The maximum power of asynchronous motors is several tens of megawatts. Asynchronous motors with power up to 20 MW are produced for pumps and wind tunnels. Indicator systems use asynchronous motors ranging from fractions of a watt to hundreds of watts.
Currently, asynchronous motors are produced in single series. The main series of 4A asynchronous machines includes motors from 0.4 to 400 kW. A single series of asynchronous machines AI, AIR, 5A and RA has been developed. Motors of the ATD series are made with a squirrel cage massive rotor and water cooling of the stator winding.
Series 4A squirrel-cage induction motors can be divided into two types according to the degree of protection and cooling method. The machines are closed, protected from splashes from any direction and objects with a diameter of more than 1 mm getting inside, and have external ventilation with a fan. According to GOST, this version is designated IP44. The second type of design is machines with protection degree IP23. These machines provide protection against the possibility of contact of objects with a diameter of more than 12.5 mm with live rotating parts of the machine. The IP23 version provides protection against drops falling inside the machine falling at an angle of 60° to the vertical (drip-proof version).
A distinctive feature of machines with a wound rotor is the presence on the rotor of a winding made of conductors of round or rectangular cross-section, the beginnings of which are brought out to slip rings. The slip ring assembly is removed from the frame, and the slip rings are covered with a casing. The current collector consists of brushes and brush holders. Ventilation system and degree of protection of wound rotor motors - IP23 and IP44.
Equation of mechanical characteristics of an asynchronous motor. single phase equivalent circuit.
Unlike DC motors, the magnetic excitation flux of a three-phase motor is created by the alternating current of the windings and is rotating. The appearance of EMF and current in the rotor winding, and therefore torque on the shaft, is possible, as is known, only if there is a difference between the field rotation speed and the rotor rotation speed, called slip
Where ω – rotor rotation speed.
The mechanical characteristics of an asynchronous electric motor are plotted as a dependence of slip on the torque developed by the motor s=f(M) at a constant voltage and frequency of the supply network.
To obtain an analytical expression for the mechanical characteristics of a three-phase motor, an equivalent circuit of one phase of the motor is used when the stator and rotor windings are connected in a star. In the equivalent circuit (Figure 5.2), the magnetic connection between the stator and rotor windings is replaced by an electrical one, and the magnetizing current and the corresponding inductive and active resistances are presented in the form of an independent circuit connected to the mains voltage.
|
Rice. 5.1. Equivalent circuit of one phase of the motor.
For this drawing
Uph– primary phase voltage;
I 1– stator phase current;
I 2/ – reduced rotor current;
X 1 And X 2 /– primary and secondary reduced leakage reactance;
R0 And X 0– active and reactive resistance of the magnetization circuit;
s – engine slip;
– synchronous angular speed of the motor, ;
R 1 and R 2 / – primary and reduced secondary active resistance;
f 1– network frequency,
R– number of pairs of poles.
Rotor winding parameters (inductive, active resistance and rotor current I 2) are given to the turns of the stator winding and to the mode with a stationary rotor. In addition, the equivalent circuit is considered under the condition that the parameters of all circuits are constant and the magnetic circuit is unsaturated.
In accordance with the above equivalent circuit, we can obtain an expression for the secondary current:
(5.2)
The torque of an asynchronous motor can be determined from the loss expression
, where
(5.3)
Substituting the current value I 2/ into this expression, we get:
(5.4)
Expression for maximum torque:
(5.5)
The “+” sign refers to the motor mode (or back-on braking), the “-” sign refers to regenerative braking.
Having designated it, we get:
(5.6)
M to- maximum torque (critical torque) of the engine,
s to- critical slip corresponding to the maximum moment.
From formula 5.5 it is clear that for a given slip the motor torque is proportional to the square of the voltage, therefore the motor is sensitive to fluctuations in the network voltage.
Figure 5.2 shows the mechanical characteristics of an asynchronous motor in various operating modes. The characteristic points of the characteristic are:
1) - motor rotation speed is equal to synchronous speed;
2) 
- nominal operating mode of the engine;
3) 
- critical moment in motor mode;
4) 
- initial starting torque.
Designating the multiplicity of the maximum moment, we get:
.
When the engine operates only in starting and braking modes, this is the non-working part of the characteristic (hyperbole).
When the function is linear, its graph is a straight line, which is called the working part of the mechanical characteristics of an asynchronous motor. At this segment of the mechanical characteristics, the engine operates in steady state. On the same part there are points corresponding to the nominal data of the engine: 
.
Rice. 5-2. Mechanical characteristics of an asynchronous motor.
Initial data
Characteristics of the working machine: (rotation speed nnm = 35 rpm; gear ratio ipm = 14; calculated torque Msm = 19540 Nm; efficiency factor sm = 80%; moment of inertia Jm = 2200 kg m2; mechanical characteristics Msm( n) = 11200 + 16.8n power supply voltage Ul = 660 V.
Power calculation and selection of a three-phase asynchronous electric motor with a squirrel-cage rotor.
Moment of resistance of the working machine reduced to the motor shaft:
Mc = Mcm·(1/ ipm)·(1/ zm) = 19540·(1/14)·(1/0.8) = 1744.6 Nm
Estimated engine speed:
nр = nnm · ipm =35·14=490 rpm
Estimated engine power:
Pр = Mc·nр /9550=1744.6·490/9550=89.5 kW
Based on calculated power values Pр, rotation speed nр and the specified network voltage Ul We select from the catalog a three-phase asynchronous electric motor with a squirrel-cage rotor 4A355M12U3. We record the technical data of the selected engine in Table 1:
Table 1
Determination of electric motor parameters necessary for calculation and construction of mechanical characteristics:
- - number of motor pole pairs p;
- - frequency of rotation of the magnetic field n0;
- - rated motor slip sn;
- - critical engine slip skr;
- - rated motor torque Mn;
- - critical torque (maximum) of the engine Mcr(max);
- - engine starting torque MP.
To determine the number of pairs of poles of the electric motor, we use the expression that describes the relationship between the rotational speed of the magnetic field n0, rpm(synchronous speed) with mains frequency f, Hz and the number of pole pairs p:
n0=60f/p, rpm,
where p=60f/n0. Since the synchronous speed n0 unknown to us, it is possible to determine the number of pole pairs with a small error p, replacing n0 passport value of the rated engine speed nн(since the value nн differs from n0 by 2% - 5%), therefore:
p?60f/nn=60·50/490=6,122
The number of pole pairs cannot be fractional, so we round the resulting value p up to a whole number. We get p=6.
Magnetic field rotation speed (synchronous motor speed):
n0=60f /p=60·50/6=500 rpm
Rated motor slip:
sн = (n0 - nn)/n0 =(500 -490)/500=0.02
Critical engine slip
skr= sn (l+)=0,02(1,8+) =0,066
The rated torque of the motor is determined through the rated (certified) power values Pn=90 kW, and rotation speed nn=490 rpm
Mn=9550 Pn/nn =9550·90/490=1754.082 N·m
The starting torque is determined through the rated torque Mn and the value of the starting torque coefficient taken from the catalog kp= Mp / Mn=1
Mp=kp Mn=1 1754.082=1754.082 Nm
The critical (maximum) torque of the engine is determined through the rated torque Mn and the value of the motor overload coefficient taken from the catalog
l = Mmax / Mn =1.8
Mkr(max)= l Mn=1.8 1754.082=3157.348 Nm
For a three-phase asynchronous electric motor 4A355M12U3 (selected in step 1), construct a mechanical characteristic using the values found in task 2.
To construct the working section of the mechanical characteristics of the values of the moments developed by the engine at slip values s< sкр, let's calculate by expression M=2Mmax /(s /scr+ scr /s).
Taking sequential values s=0; sn= 0,02; skr=0.066, let's determine the values of the moments M, corresponding to these slips (we assign a slip value index to each moment):
M0=2·3157.348/(0/0.066+0.066/0)=0;
Mn=2·3157.348/(0.02/0.066+0.066/0.02)=1752.607 N·m;
M01=2·3157.348/(0.1/0.066+0.066/0.1)=2903.106 N m
Mkr=2·3157.348/(0.066/0.066+0.066/0.066)=3157.348 N·m.
Finding the correction factor b to calculate the moment values in the characteristic section with large slip values ( s > skr):
b=Mп - 2Mmax/((1/scr)+scr)= 1754.082-2·3157.348/((1/0.066)+0.066)=1339.12 N·m.
3.3 For the engine acceleration section (at s > scr), the values of the torques developed by the engine are determined by the expression M=(2Mmax /(s /scr+ scr /s))+b·s. Given the slip values s=0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9; 1.0, let’s calculate the values of the moments:
M02=2·3157.348/(0.2/0.066+0.066/0.2)+ 1339.12 ·0.2=2147.028 N·m;
M03=2·3157.348/(0.3/0.066+0.066/0.3)+ 1339.12 ·0.3=1726.834 Nm;
М04=2·3157.348/(0.4/0.066+0.066/0.4)+ 1339.12 ·0.4=1549.958 N·m;
M05=2·3157.348/(0.5/0.066+0.066/0.5)+ 1339.12 ·0.5=1488.825 Nm;
M06=2·3157.348/(0.6/0.066+0.066/0.6)+ 1339.12 ·0.6=1489.784 Nm;
M07=2·3157.348/(0.7/0.066+0.066/0.7)+ 1339.12 ·0.7=1527.523 Nm;
М08=2·3157.348/(0.8/0.066+0.066/0.8)+ 1339.12 ·0.8=1588.737 N·m;
M09=2·3157.348/(0.9/0, 0.066+0.066/0.9)+ 1339.12 ·0.9=1665.809 Nm;
M1=2·3157.348/(1.0/0.066+0.066/1.0)+ 1339.12 ·1.0=1754.082 Nm.
The calculation results are recorded in Table 3.
Using the expression n =n0 (1-s), for each slip value s calculate the engine shaft rotation speed n:
n0=500 (1 - 0)= 500 rpm;
nн=500 (1 - 0.02)=490 rpm;
ncr=500 (1-0.066)=467 rpm;
n01=500 (1 - 0,1)= 450 rpm;
n02=500 (1 - 0.2)= 400 rpm;
n03=500 (1 - 0,3)= 350 rpm;
n04=500 (1 - 0,4)= 300 rpm;
n05=500 (1 - 0,5)= 250rpm;
n06=500 (1 - 0,6)= 200 rpm;
n07=500 (1 - 0,7)= 150 rpm;
n08=500 (1 - 0,8)= 100 rpm;
n09=500 (1 - 0.9)=50 rpm;
n1=500 (1 - 1)= 0 rpm.
The calculation results are recorded in Table 3.
Based on the calculation results, we build a scale graph of the mechanical characteristics n(M):
4. Justify the method of connecting the phase windings of the previously selected 4A355M12U3 motor with rated voltage Un=380/660 IN to the electrical network with voltage Ul=660y V. Determine the starting, phase and linear rated currents of the motor for the selected method of connecting its windings. Calculate starting, phase and linear currents, starting and critical torques, motor power corresponding to the rated slip, if the method of connecting phase windings is incorrectly chosen.
The windings of a three-phase motor can be connected to the supply network in star or delta depending on the rated voltage of the phase winding Un and line voltage Ul. The motor data sheet usually indicates 2 voltages to which the motor can be connected. When connecting, it is necessary to take into account that the phase windings are designed for the lower of the two voltages (in our case, 380 V). Our motor should be connected to the network using a star connection, because Uph = Ul /(Uph = 660V / = 380V). asynchronous electric motor rotor shaft
The linear rated current of the motor is determined from the expression for the power of a three-phase circuit:
P1н= Uл Iл cosсн, where Ul=660 V- linear (nominal) voltage of the electrical network; P1n, W,- rated active electrical power of the engine, which
determined through the rated nameplate power on the motor shaft Pn taking into account losses in the engine:
P1n= Pn/ zn=90·10 3/0.915=98.361·10 3 W.
Motor rated linear current:
Il(n)=P1n /( Ul costn) = 98.361 10 3 / 660 0.77 = 111.745 A.
The rated phase currents when connected by a star are equal to linear:
If= Il=111.745 A.
The starting current of the motor is determined through the rated linear current In =66.254 A and starting current coefficient kI=Iп/Iн =5.5:
Iп= Iн·кI =111.745·5.5=614.598 A.
We determine the main characteristics of the motor if the method of connecting the motor is incorrectly chosen, i.e. when connecting phase windings triangle (?). Let us denote the characteristics of the engine if the method of connecting the engine is incorrect X!(I!, U!, M! ,R!). When connecting in a delta, the phase voltages Uph equal to linear Ul=660 V . Therefore, the voltage on the phase windings will be equal U!f = Ul=660V, which is several times higher than the rated voltage and can lead to breakdown of the insulation of the motor windings.
Phase currents, in accordance with Ohm's law, are directly proportional to the phase voltage Uph and inversely proportional to the impedance of the phase windings zph: Iph = Uph/zph. Consequently, the actual values of phase currents, as well as phase voltages, will greatly exceed the nominal values, i.e.
I!f =· Iф=·111.745=193.548 A.
Linear currents with delta connection Iн =· If. Consequently, the actual values of the linear currents will be equal to:
I!n=·I!ф =··Iф=3·111.745= 335.235 A, which is three times the rated values of line currents.
Starting currents will be determined through the actual values of linear currents I!n and inrush current ratio kI=Iп/Iн =5.5
I!p = I!n · kI =335.235·5.5=1843.793 A,
times the value of inrush currents when connected by a star.
Torques developed by the engine (starting MP, maximum Mmax) change proportionally to the square of the voltage on the phase windings, i.e. M = km U2f , Where km- coefficient that takes into account the main parameters of the engine, connecting the torque developed by the engine with voltage. Since the voltage on the phase windings with the wrong method of connecting the motor (triangle) increased by a factor, the motor torques will increase () 2 times, i.e. 3 times.
When connecting the motor phase windings with a star:
M = km U2f = km 3802, where km =M/3802.
When connecting the motor windings in a triangle:
M! = km (U!f)2 =M 6602 /3802 =3M.
Starting torque when connecting the motor with a triangle (incorrect method):
M!p=3MP =3·1754.082 =5262.246 Nm.
Critical moment when connecting a motor with a star:
M!kr=Microdistrict · 3=3·3157.348=9472.044 N·m.
The power at the motor shaft is expressed Pn= Ul In sign coscn. Of the quantities included in this expression, if the motor connection method is incorrectly chosen, only the linear current changes Il(mains voltage Ul =660 V does not change). According to the calculation result in clause 4.5.2. if the motor is mistakenly connected to a star, the linear currents increase by 3 times, therefore, the motor power at rated slip will increase by 3 times and will be:
P!n =3Pn =3·90=270 kW.
5. Determine start time tstart and plot the acceleration curve of an electric drive with a 4A355M12U3 electric motor and a working machine with a moment of inertia Jm= 9,68 kg m2 and mechanical characteristics
Ms= 11200+16.8n , Nm.
The acceleration time of the electric drive is determined from the equation of drive motion
M - Ms = (1/9.55)J dn/dt,
replacing infinitesimal values dn And dt to final values ?n And ?t:
?t=(1/9.55) J·?n /(M - Ms)
The resulting expression is valid provided that the moments are static M And Ms, and the moment of inertia do not depend on speed, i.e. (M - Ms)=const And J= const. Therefore, we will use an approximate graph-analytical calculation method, for which the joint mechanical characteristics of the engine n(M) and working machine Ms(n) We divide it into acceleration periods, at each of which we accept (M - Ms)=const.
We present the equation for the moment of static resistance of the working machine to the motor shaft:
Mc=Mcm·(1/i)·(1/zp)=(11200+16.8n)/(14·0.915); Ms =874.317+1.312·n, N·m.
We determine the values of the moment of static resistance of the working machine Ms for different speeds n given in Table 3. Supplementing Table 3 with the results of calculating the values Ms, we get table 4.
Mc=874.317+1.312·500=1530.317 Nm
Mc=874.317+1.312·490=1517.197 Nm
Mc=874.317+1.312·467=1487.021 Nm
Mc=874.317+1.312·450 =1464.717 Nm
Mc=874.317+1.312·400=1399.117 Nm
Mc=874.317+1.312·350=1333.517 Nm
Mc=874.317+1.312·300=1267.917 Nm
Mc=874.317+1.312·250=1202.317 Nm
Mc=874.317+1.312·200=1136.717 Nm
Mc=874.317+1.312·150=1071.117 Nm
Mc=874.317+1.312·100=1005.517 Nm
Mc=874.317+1.312·50=939.917 Nm
Mc=874.317+1.312 0=874.317 Nm
Based on the calculation results given in Table 4, we construct joint mechanical characteristics n(M) And n(Mс).
We determine the moment of inertia of the system reduced to the motor shaft:
J=Jd + Jm(nm/ nd)2=9.58+2200(35/490)2=20.805 kg m2
Joint mechanical characteristics of the engine n(M) and working machine Ms(n) we divide it into 10 acceleration periods in such a way that at each period it is easier and as accurately as possible to determine the average values of the torques over the period Mk, developed by the engine, and Moscow time-static resistance on the motor shaft from the side of the working machine. We assume that at each period the rotation frequency increases ?nk at constant dynamic torque (M - Ms), equal to the average for the period, and according to the expression ?t=(1/9.55) J·?n /(M - Ms) determine the acceleration time ?tк for each period. The calculation results are recorded in Table 5.
- ?tк=(1/9.55) 20.805·50/802.829=0.136
- ?tк=(1/9.55) 20.805·50/654.556=0.166
- ?tк=(1/9.55) 20.805·50/519.813=0.21
- ?tк=(1/9.55) 20.805·50/408.737=0.268
- ?tк=(1/9.55 )· 20.805·50/410.788=0.265
- ?tк=(1/9.55) 20.805·50/289.275=0.377
- ?tк=(1/9.55) 20.805·50/342.679=0.318
- ?tк=(1/9.55) 20.805·50/570.614=0.191
- ?tк=(1/9.5520.805·50/1093.15=0.1
- ?tк=(1/9.55) 20.805·45/836.895=0.13
We determine the acceleration time of the electric drive by summing the acceleration duration in each period:
tstart =0.136+0.166+0.21+0.268+0.265+0.377+0.318+0.191+0.1+0.13=2.161 sec
List of used literature
1. Electrical engineering, electronics and electric drive: method. instructions for performing calculations.-graph. works / P. T. Ponomarev; ed. E. V. Lesnykh; Sib. state University of Communications - Novosibirsk: SGUPS, 2014. - p.
2. General electrical engineering: textbook / ed. V. S. Pantyushin. - M.: Higher. school, 1970. - 568 p.
3. Electrical engineering and electronics: textbook. for non-electrical specialist. universities / V.G. Gerasimov, E.V. Kuznetsov, O.V. Nikolaeva [and others]; edited by V.G. Gerasimova. - M.: Energoatomizdat. Electrical and magnetic circuits. - 1996. - 288 p.
Federal Agency for Education
State educational institution of higher professional education
Petrozavodsk State University
Kola branch
Department of High-Voltage Electrical Power Engineering and Electrical Engineering
Discipline “_Electromechanics_”
Device asynchronous machine.
Test
__2___ year student
(group AVEE - /06/3.5)
correspondence department
Faculty of Physics and Energy
speciality: 140201– “High-voltage power engineering and electrical engineering”
Vakhovsky Vladimir Alexandrovich
teacher -
prof., doc. tech. sciences A.I. Rakaev
Apatity
Mechanical characteristics of an asynchronous motor (IM).
1. Introduction.
2. Asynchronous machines.
3. Equation of mechanical characteristics of an asynchronous motor.
4. Linearization of the mechanical characteristics of an asynchronous motor.
5. Mechanical characteristics of asynchronous motors under symmetrical modes
8. Device asynchronous machine.
9. Operating principleAsynchronous machines.
10. Bibliography
Mechanical characteristics of an asynchronous motor (IM).
1. Introduction.
AC electric drives are widely used in industry, transport, construction industry and other sectors of the national economy. Their predominant distribution is due to: the high reliability of an alternating current machine due to the absence of a commutator, the ease of control of unregulated drives, since most of them are directly connected to the network, the low cost of electrical machines and simple requirements for their maintenance and operating rules.
Depending on the type of motor used, not only AC and DC drives are distinguished, but also asynchronous, synchronous, stepper and other types of drives. However, one should not think that AC drives can be used everywhere instead of DC drives. For each type of drive there are established areas of promising use. Moreover, it is difficult to unambiguously and definitely list in advance all the factors that determine the choice of the type of current for the drive. Along with traditional drives built on the basis of asynchronous and synchronous machines, in recent decades AC drives with universal and stepper motors, dual-power motors and electromagnetic speed reduction have been used.
2. Asynchronous machines.
The principle of operation of an asynchronous machine in its most general form is as follows: one of the elements of the machine - the stator - is used to create a magnetic field moving at a certain speed, and in the closed conducting passive circuits of the other element - the rotor - an emf is induced, causing the flow of currents and the formation of forces (torques) when they interact with a magnetic field. All these phenomena take place during non-synchronous-asynchronous movement of the rotor relative to the field, which is what gave machines of this type the name - asynchronous.
The stator is usually made in the form of several coils located in grooves, and the rotor is in the form of a “squirrel cage” (squirrel-cage rotor) or in the form of several coils (wound rotor), which are interconnected, brought out onto rings located on the shaft, and with the help of sliding along them the brushes can be shorted to external resistors or other circuits.
Despite the simplicity of the physical phenomena and the constructs that materialize them, a complete mathematical description of the processes in an asynchronous machine is very complex:
firstly, all voltages, currents, flux linkages are variable, i.e. characterized by frequency, amplitude, phase or corresponding vector quantities;
secondly, moving contours interact, the relative positions of which change in space;
thirdly, the magnetic flux is nonlinearly related to the magnetizing current (saturation of the magnetic circuit appears), the active resistance of the rotor circuit depends on frequency (current displacement effect), the resistance of all circuits depends on temperature, etc.
Let's consider the simplest model of an asynchronous machine, suitable for explaining the main phenomena in an asynchronous electric drive.
The mechanical characteristics of the engine completely determine the quality of operation of the electromechanical system in steady state and its performance. They also affect the dynamic modes of the electric drive, characterizing the excess dynamic torque that determines the acceleration or deceleration of the engine.
3. Equation of mechanical characteristics of an asynchronous motor
In modern design practice, programs are used that take into account the magnetization of the machine’s magnetic system when calculating mechanical characteristics. But in this case, the clarity of their study is lost. Therefore, all further dependencies will be found if this basic assumption is met.
The electrical power supplied to the motor from the network is spent to cover losses in the magnetization circuit p μ , in stator copper p M 1, and the remainder of it is converted into electromagnetic power. Thus,
(4-12)
In its turn,
where ω 0 = 2π f 1 /p- the number of pairs of poles of the machine stator.
After minor transformations, we find
(4-14)
Therefore, the dependence M = f(s) is a complex function of sliding. Let us examine it to its extremum by taking the derivative
(4-15)
Equating the numerator of expression (4-15) to zero, we find the value of the critical slip s K , at which the dependence M =f(s) has a maximum:
(4-16)
Physically decreasing M at s sK And s > s K is explained as follows. At s s K, a decrease in slip is associated with a decrease in motor current and torque, and when s > s K, although the motor current increases, its active component, which determines the electromagnetic torque, does not increase, but decreases, which also leads to a decrease in the torque developed by the engine.
Positive sign s K corresponds to the motor mode, and negative - to the generator mode of operation of the machine.
It should be borne in mind that, like a DC machine, the relative magnitude r 1 decreases with increasing machine power and already for engines with a power of 100 kW is 10-15% of the value x 1 + x 2 ". Therefore, formula (4-16) can be used in a simplified form, neglecting r 1
Where x K.Z - inductive reduced short circuit resistance.
This cannot be done for machines of medium and especially low power, which have resistance r 1 commensurate with x K.Z.
Using formulas (4-14) and (4-16), you can get a different record of the mechanical characteristics of an asynchronous motor if you find the values of its critical moments in motor M K.D and generator M K.G operating modes:
(4-18)
Critical moment ratio
(4-19)
The commonly used notation used here is:
(4-20)
Formula (4-19) shows that the value of the critical torque of a machine in generator mode can be significantly greater than in motor mode (see Fig. 4-8).
For practical use, it is more convenient to express the mechanical characteristics of an asynchronous motor other than in formula (4-14). Let's find it using formulas (4-14), (4-17) and (4-20):
(4-21)
If we neglect the influence of the stator active resistance, then ε = 0, and formula (4-21) takes on this form (at M K.D = M K.G = M TO):
(4-22)
Expression (4-22) was first obtained by M. Kloss, which is why it is called Kloss’s formula.
Formulas (4-21) or (4-22) are more convenient for calculations than (4-14), since they do not require knowledge of the engine parameters. In this case, all calculations are made according to the catalog data. Due to the fact that the value s K is not indicated in the catalogues, it has to be determined based on other information, for example, the value of the machine’s overload capacity M TO / M NOM = λ M. Then from formula (4-21) we get:
(4-23)
from where, solving the quadratic equation, we find
where γ = λ M + (1 - λ M)ε.
In expression (4-24), you should take a plus sign in front of the root, since another value s K contradicts the physical meaning.
An approximate solution to equation (4-24) can be obtained with the coefficient ε = 0, but it is better to determine its value. The most reliable results will be obtained if, having the machine parameters, the value of ε is determined from formula (4-20), a s K - from expression (4-16). For asynchronous motors with a wound rotor, expressions (4-14) and (4-21) give more reliable results, since in these machines the effects of steel saturation and current displacement in the rotor windings (skin effect) are less noticeable.
4. Linearization of the mechanical characteristics of an asynchronous motor
In the working area of the mechanical characteristic, the slip value s much less than critical s K. Therefore, in equation (4-21) we neglect the term ss K -1 and set ε = 0. Then we get
(4-25)
Thus, expression (4-25) represents the linearized part of the mechanical characteristics of the engine. It can be used for sliding variations within 0 s s NOM.
Rice. 4-5. Linearized mechanical characteristics of asynchronous motors
To obtain artificial characteristics, it is enough to write down two equations of straight lines with the same slip values s i (Fig. 4-5):
where the indices “i” and “e” indicate artificial and natural characteristics, from where it is easy to find
(4-26)
Using formula (4-26), you can construct the initial sections of any mechanical characteristic. In this case, the slip should not exceed the specified limits.
If a total resistance is introduced into the rotor circuit R 2 NOM, then at s= 1 a current will flow in the rotor corresponding to the rated torque M NOM . Then expression (4-26) will take the form
The last expression allows us to write the following relation for any artificial or natural characteristic:
where ρ P is the relative value of the total resistance included in the rotor circuit of the machine ρ P = ρ 2 + ρ DOB; s - sliding on the corresponding mechanical characteristic.
It should be borne in mind that when R 2 = R 2 NOM nominal slip value s N NOM =1 on this artificial characteristic .
5 Mechanical characteristics of asynchronous motors in symmetrical modes
Motor characteristics when changing the supply voltage or resistance in the stator circuit .
Symmetrical are those modes of operation of asynchronous motors (IM), in which the supply network is symmetrical in value and phase shift of voltages, the active or reactive resistances introduced into the electrical circuits of all phases are the same and their internal parameters are symmetrical (the number of turns in phases, angular shifts of slots and other factors).
First, let's look at the changes to the network. From relation (4-9) it follows that the current I 2 "is proportional to the applied voltage, and the moment is [see expression (4-14)] to its square. This allows you to construct the mechanical characteristics of the engine at any voltage (Fig. 4-6). Obviously, formula (4-16) confirms the constancy of the critical slip s K. Already when the voltage drops to 0.7 U NOM critical moment is
Rice. 4-6. Mechanical characteristics of an asynchronous motor at various supply voltages.
only 49% M K nominal mode. In practice, the voltage drop is even greater when starting the engine due to the large starting current. All this leads to the fact that with long power lines or for large machines with their power commensurate with the power of transformer substations, it is necessary to perform special calculations confirming the possibility of normal starting of the IM and its operation with reduced voltage.
For the same reasons, a special GOST 13109-87 was established for the quality of electrical energy, which provides for a post-emergency change in voltage in the industrial network only within ±10% of its nominal value.
A decrease in voltage is especially dangerous for drives that, due to operating conditions, must start under load (drives of conveyors, lifting devices, converters and many other mechanisms). For example, when starting without load (idle), the static moment of the conveyor does not exceed (0.2-0.3) M NOM. If the conveyor drive was switched off while operating at full load, then when restarted with reduced voltage it will have to overcome M C ≈ M NOM .
To limit the starting currents of large asynchronous machines or to obtain a smooth start of an asynchronous drive, they use the inclusion of active or inductive reactors in the stator circuit, which are output at the end of the start (Fig. 4-7). A feature of such circuits is the dependence of the voltage at the motor terminals on the current value.
The inclusion of active resistance, although it slightly increases the power factor of the drive in starting modes, but at the same time increases energy losses compared to “reactor” starting.
Rice. 4-7. Mechanical characteristics of an asynchronous motor at rated and reduced voltage or active ( r DOB) and reactive ( x DOB) additional resistances in the stator.
In recent decades, for high-power motors that are frequently turned on and off, “frequency” starting has been used, which is more economical. For this purpose, a special converter is installed that smoothly changes the frequency of the motor power supply during startup, i.e., the value of ω 0. At the same time, the voltage decreases, which also limits the starting current.
Characteristics of an asynchronous motor when active resistances are included in the rotor circuit.
Asynchronous motors with a wound rotor are widely used in drives of hoisting and transport and metallurgical installations; powerful motors are used in drives of fans, wind tunnels and pumps. Thanks to the inclusion of active resistances in the rotor circuit, it is possible to change the critical slip of such an IM, the type of its mechanical characteristics, starting current and torque.
The use of wound-rotor motors in pump and fan drives makes it possible to economically regulate their performance, which brings a great economic effect. Let us recall that the critical moment does not depend on the active resistance introduced into the rotor circuit, therefore, by choosing r Additionally, it is possible to change the mechanical characteristics of the IM in such a way that the drive will have a maximum torque at start-up (ω = 0), or even in the back-on mode s K > 1 (Fig. 4-8).
Increase r DOB leads to an increase in the active component of the rotor current I 2 a " = I 2 "cosψ 2, since
(4-30)
Where R 2 " = r 2 " + r" DOB - total reduced active resistance of the secondary circuit of the machine.
For the same reason, motors with a wound rotor, unlike squirrel-cage motors, have higher starting torques at lower currents. This property of such machines serves as the main condition for their primary use in drives with severe starting conditions (cranes, metallurgical plants, rotary machines and other energy-intensive mechanisms). It should be borne in mind that excessive increase r DOB leads to a sharp decrease in the active component of the current I 2 ". Then the engine starting torque M P becomes less static moment when starting off M TR . As a result, starting the drive will be impossible.
The artificial mechanical characteristic can be calculated using formula (4-14) or (4-18), (4-20), (4-24) and (4-27). The method for calculating the artificial characteristics of an IM with a wound rotor can be simplified based on the following relationships. Let us write down expressions for equal values of moments M i on natural and any artificial characteristic based on formula (4-21):
The value of ε does not depend on the value of the active resistance component in the secondary circuit of the machine, therefore it remains unchanged for natural and artificial mechanical characteristics. Therefore, from formula (4-31) we have
The given values can be considered: critical slips on artificial and natural characteristics s K .I And s K .E and sliding on a natural characteristic s ei. Then from expression (4-32) we obtain
(4-33)
Thus, the basis for a simplified calculation is the natural mechanical characteristics of the engine. As stated earlier for machines with a wound rotor, it can be obtained approximately from expression (4-22) and more accurately from (4-21). Some of the machine parameters required for these calculations are indicated in catalogs or reference books, and some can be determined using the above formulas.
Rice. 4-8. Mechanical characteristics of a wound rotor motor
6. Braking modes of asynchronous motors
Braking modes for many drives with asynchronous machines are more important than starting modes in relation to the requirements for reliability and reliability of implementation. Often it is necessary to stop precisely at a given position or to brake the drive for a certain period of time.
For asynchronous motors, the following modes are used: regenerative braking with energy output to the network; opposition; dynamic braking with various stator excitation systems with direct (rectified) current, when the machine operates as a generator, dissipating energy in the secondary circuit; dynamic capacitor or magnetic braking with self-excitation. Therefore, braking modes, according to the method of excitation of the stator magnetic field, can be divided into two groups: independent excitation, carried out from an alternating or direct current network (regenerative, back-switching and dynamic braking) and with self-excitation, carried out as a result of energy exchange with a capacitor bank or when the motor stator is short-circuited when a magnetic flux is created by a self-inductive emf. According to the definition of L.P. Petrov, we will call the latter type magnetic braking.
All of the listed modes are used for machines with both phase and squirrel-cage rotors.
In connection with the use of powerful power semiconductor devices (thyristors and transistors), new schemes for implementing typical braking modes of asynchronous drives have appeared.
Increasing the efficiency of braking can be achieved by using combined methods of its implementation. It should be especially emphasized that most combined braking systems are fully controlled. This further increases their effectiveness.
The most effective are back-switching and capacitor-dynamic braking (CDB). The last method has many circuit solutions. It is recommended to be used for drives with large reduced moments of inertia, for example, exceeding twice the moment of inertia of the motor.
For low-inertia drives, capacitor-magnetic braking (CMB) can be used. Magneto-dynamic braking (MDB) will be no less effective. Other combined types of two and even three-stage braking are also rational for individual drives: counter-inclusion - dynamic braking (DCB), capacitor braking and counter-inclusion (CTB), etc.
Thus, the implementation of modern methods of braking IM largely depends on the experience and knowledge of the electric drive developer. Therefore, let's consider the braking modes in detail.
Braking with energy release into the network. The reversibility of an asynchronous motor, like other machines using the principle of electromagnetic induction (Maxwellian type), allows it to operate in generator mode. If there is no load on the motor shaft, then the energy consumed from the network is spent to cover losses in the stator, as well as losses in steel and mechanical losses in the rotor. By applying an external torque to the machine shaft, acting in the direction of rotation of the rotor, synchronous speed can be achieved. In this case, losses in the rotor are covered by an external energy source, and only the energy used to cover losses in the stator will be consumed from the network. A further increase in speed above synchronous speed leads to the fact that the asynchronous machine switches to generator mode.
When operating in this mode, the stator conductors are crossed by the magnetic field in the same direction, and the rotor conductors are crossed in the opposite direction, therefore the rotor EMF E 2 changes sign, i.e. E 2 "s = (- s)E 2 " ≈ - E 2 "s. The current in the rotor will accordingly be equal to
(4-34)
Rice. 4-13. Vector diagram of an asynchronous motor operating in generator mode
From expression (4-34) it is clear that when the IM switches to the generator mode, only the active component of the rotor current changes direction, since the torque on the shaft has changed its direction compared to what occurred in the motor mode. This is illustrated by the vector diagram in Fig. 4-13. Here the angle φ 1 > π/2, which confirms the change in the cause of the current I 1 in the form of EMF E 1 (not mains voltage U 1 , as in motor mode), although the direction of the magnetizing current I μ remained the same. Change of sign of the active current component I" 2 a leads to the fact that the electromagnetic power becomes negative, i.e. it is transferred to the network, since s 0:
The sign of the reactive power of the secondary circuit remains unchanged regardless of the operating mode of the machine, which follows from the expression
Due to the presence of active static moments, braking is used in lifting installations (Fig. 4-14, a), in transport drives (Fig. 4-14, b). The difference in these braking modes is that in the first case (Fig. 4-14, a) the engine, when lowering a large load, switches to lowering it (ω 3 in the fourth quadrant with |ω| > |ω 0 |). Load torque limit M WITH should not exceed M NOM. When a vehicle moves “downhill,” the potential energy of the transported load begins to promote movement and creates an external driving moment applied to the engine shaft. Thus, in this case, due to the increase in drive speed (ω > ω 0) and the change in the sign of the EMF E 2, the engine directly, without switching the stator windings, goes into generator mode with energy output to the network (point 2 in Fig. 4-14, b).
Rice. 4-14. Mechanical characteristics of an asynchronous motor with an active static torque: a - lowering a heavy load; b - vehicle operation “downhill”
In the presence of reactive static torque, regenerative braking with energy recovery into the network can be obtained in asynchronous motors with switching the number of poles or in drives with frequency, frequency-current and vector control of the rotation speed of the IM.
In the first case (Fig. 4-15, a), switching the machine stator from a smaller number of poles to a larger one, the synchronous speed ω 02 decreases
With frequency speed control, reducing the frequency of the stator supply from the main f 1 to f 2 f 1 and f 3 f 2, gradually switch the engine from one mechanical characteristic to another (Fig. 4-15, b). The drive operates in braking mode, releasing energy into the network while its operating point moves along the sections of the mechanical characteristics located in the second quadrant. By smoothly and automatically changing the frequency of the motor supply, it is possible to obtain a braking mode of the drive with a slightly varying braking torque. However, it is necessary to regulate the supply voltage in a certain way.
Rice. 4-15. Mechanical characteristics of an asynchronous motor in regenerative braking mode with a reactive static torque: a - switching the number of pole pairs; b - frequency speed control
Back braking. This type of braking occurs when the motor rotor rotates under the influence of a static torque in the direction opposite to the rotation of the stator field. In the presence of reactive torque, the duration of braking is short, after which the machine again switches from braking to motor mode (Fig. 4-16a). Initially the engine ran at the point 1 motor mode, and then after switching two phases of the stator winding, the direction of rotation of the magnetic field of the machine and its electromagnetic torque (point 2 ). The drive movement slows to a point ABOUT, and then the rotor is reversed and the engine accelerates in the opposite direction until steady motion at the point 3 .
For motors with a wound rotor, in the presence of a large additional resistance, a complete stop of the drive with braking torque is possible M TR (dot 5 in Fig. 4-16,a).
In the presence of an active torque (Fig. 4-16,b), if the direction of rotation of the magnetic field changes, as in the previous case, the engine also changes the operating mode, i.e., counter-switching braking takes place - second quadrant, motor mode with reversal of the direction of rotation rotor - the third quadrant and the new mode - generator mode with energy output to the network - the fourth quadrant, where the point of steady long-term movement lies 3 .
For motors with a wound rotor with an active static torque, the counter-switching mode can be achieved without switching stator phases, only by introducing large additional resistances into the rotor (Fig. 4-16, b). Then the car is in motor mode from the point 1 translated to point 4 with the introduction of additional resistance r D, and then it changes its movement according to an artificial mechanical characteristic, moving into the fourth quadrant. Dot 5 corresponds to long-term steady motion of an asynchronous motor in back-to-back mode.
Rice. 4-16. Switching circuit and mechanical characteristics of an asynchronous motor: a - in counter-switching mode with a reactive static torque; b - the same, with an active static torque
The counter-braking mode is often used in lifting and transport installations. Switching stator phases, without introducing additional resistance, is used only in asynchronous motors with a squirrel-cage rotor due to the fact that the initial values of the currents at the point 2 (Fig. 4-16) is slightly more than the starting one, which is (5-6) I NOM. For wound-rotor motors, such current peaks are generally unacceptable. The disadvantage of the braking characteristics of the back-off is their high steepness and significant energy losses, which are completely converted into heat dissipated in the secondary circuit of the engine. Due to the large slope of the mechanical characteristics, large fluctuations in drive speed are possible with minor changes in load.
If the moment is known M C, at which it is necessary to perform braking, it is easy to calculate the slip value at this point using formula (4-25), and then using formula (4-29) to determine the additional resistance.
Electrodynamic (dynamic) braking. If you disconnect the IM stator from the network, then the magnetic flux of residual magnetization generates an insignificant EMF and current in rotor.
With independent excitation, a stationary stator flux is obtained, which induces EMF and current in the windings of the rotating rotor.
Rice. 4-17. Schemes for connecting the stator windings of an asynchronous motor to a DC (rectified) voltage network
To connect the stator windings to a direct current network, various connection schemes are used, some of which are shown in Fig. 4-17.
To analyze the dynamic braking mode, it is more convenient to replace the MDS F P created by direct current, variable equivalent to MMF F~ formed jointly by the stator and rotor windings, as in a conventional asynchronous motor. Then the synchronous generator mode is replaced by the equivalent mode of an asynchronous machine. With such a replacement the equality must be observed: F P = F ~ .
Rice. 4-18. Connection diagrams of the beginning (H) and end (K) of the stator windings “in a star” (a), determination of the directions of the MMF of the stator windings (b), geometric addition of the MMF (c)
The interaction of small values of magnetic flux and current in the rotor is not capable of creating a large electromagnetic torque. Therefore, it is necessary to find ways to significantly increase the magnetic flux. This can be done by connecting the machine stator in dynamic braking mode to a DC or rectified voltage source. You can also create a motor self-excitation circuit by connecting capacitors to its stator winding. As a result, we obtain dynamic braking modes of an asynchronous machine with independent excitation and self-excitation
Determination of DC MMF for the circuit in Fig. 4-17,a Fig. explains. 4-18.
When the stator winding is connected three-phase to the AC network, it is necessary to determine the maximum MMF of the machine, equal to:
(4-36)
Where I 1 - effective value of alternating current; ω is the number of turns of the winding of one stator phase.
First, let's look at the DC power supply to the stator winding. If when the machine is operating in motor mode its slip and magnetizing current change little, then in dynamic braking mode the rotor slip changes over a wide range. Consequently, with a change in speed, the rotor EMF, the current in the rotor and the MMF created by it change, which has a significant impact on the resulting MMF.
Rice. 4-19. Vector diagram of an asynchronous machine in dynamic braking mode
Obviously, the resulting magnetizing current given to the stator will be equal to
Using the vector diagram (Fig. 4-19), we write the following relationships for currents:
(4-37)
Taking the value of the EMF in the rotor of the machine, as before, equal to E 2 at the angular speed of rotation of the rotor ω 0, at other speeds we have
Accordingly, the inductive reactance of the rotor
Where X 2 - inductive reactance of the rotor at frequency ω 0.
Now for the secondary circuit of the machine we can write
After bringing the EMF E 2 to the parameters of the primary circuit we will have E 1 = E 2" and then
Substituting expressions (4-38) into formula (4-37), we obtain:
(4-39)
Solving equation (4-39) for current I 2 ", we find
(4-40)
The value of the electromagnetic torque of the machine is determined by the losses in its secondary circuit, namely:
(4-41)
By examining this expression for an extremum, it is easy to obtain the critical relative rotor speed ν KP at which there is a maximum torque:
(4-42)
(4-43)
Based on formulas (4-41) - (4-43), the following expression can be obtained for the mechanical characteristics of the IM:
(4-44)
Expression (4-44) is similar to Kloss's formula, which makes it easier to understand. Analysis of formulas (4-40) - (4-44) and physical phenomena characteristic of dynamic inhibition of blood pressure allows us to draw the following conclusions.
1. In the dynamic braking mode, the properties of the mechanical characteristics of an asynchronous machine are similar to the properties of similar characteristics of the motor mode, i.e., the critical torque does not depend on the active resistance of the secondary circuit, and the critical speed ν KP is the same as s KP in motor mode, proportional r 2 ".
2. Parameter xμ and current I 1 may differ significantly from similar values of the motor mode, since they depend on the saturation of the stator magnetic circuit.
3. The stator current of the machine in motor mode is a function of rotor slip, and during dynamic braking it is constant.
4. The resulting magnetic flux during dynamic braking and low rotor speed increases, since this reduces the demagnetizing effect of the rotor reaction, and in motor mode it remains approximately constant.
Rice. 4-20. Mechanical characteristics of an asynchronous motor under dynamic braking and various values of excitation current or additional resistances in the rotor circuit
In Fig. 4-20 presents the characteristics, of which 1 And 2 obtained at two values of the stator current I 11 I 12 and constant resistance r 21, and characteristics 3 And 4 found at the same currents, but a different value r 22 > r 21 . For comparison, the mechanical characteristics of the machine operating in motor mode are presented. If it is possible to change the active resistance in the rotor circuit, then it is possible to obtain characteristics with approximately constant torque over a wide range of changes in drive speed.
Magnetizing circuit reactance x μ determined by the universal characteristics of the idle speed of the machine or experimental data. In the latter case, without taking into account the saturation of the magnetic circuit, the value x μ is found by the formula:
Where U 0 , I 0 - phase voltage and current when the machine is idling.
More precisely, dependence x μ = f(Iμ) can be found as follows. If a phase voltage varying in magnitude is supplied to an asynchronous machine, the rotor of which is rotated by an external motor at a synchronous speed, then it corresponds to the EMF E 1 . Therefore, measuring the current Iμ, it is easy to calculate the dependence x μ = E 1 Iμ -1, which will take into account the saturation of the machine’s magnetic system. In this case, the construction of a mechanical characteristic is carried out point by point. In this case, the values are set M KP, ν KP and calculate using formulas (4-42) and (4-43) the value r 2 " and current I 1 . Then find ν i by changing Iμi from zero to I 1 at corresponding values xμi, according to the formula:
(4-45)
Expression (4-45) was obtained after operations with formulas (4-37) - (4-38). Using formula (4-41), you can calculate the mechanical characteristic, taking into account the influence of saturation of the magnetic circuit of the machine.
This type of braking is used in hoisting and transport and machine drives powered from an unregulated AC network in frequency-controlled drives.
In recent decades, capacitor braking of asynchronous motors has been used in machine drives. The possibility of such a regime was established back in 1895 by M. Leblanc, but in the 20-40s of the 20th century this type of braking was considered irrational. Only in 1944 A.T. Golovan and I.N. Barbash showed the promise of its use. However, only in the late 50s, thanks to the works of L.P. Petrov, practical results were achieved in the use of both capacitor and other types of combined braking. This became possible due to the reduction in the cost and size of capacitors and the development of new circuits that provide intensive self-excitation of asynchronous machines in a wide range of changes in their rotation speed. Currently, various schemes for implementing capacitor braking are used.
Rice. 4-21. Dependence of self-excitation of an asynchronous machine with capacitor braking
The principle of self-excitation of blood pressure is illustrated by the images shown in Fig. 4-21. When disconnecting machines with a rotating rotor from the network and connecting a battery of capacitors to the stator (Fig. 4-26a) due to residual EMF E 0 the capacitors begin to charge with current I μ 0 (Figure 4-21). This current increases the emf of the machine to E 1 i , which, in turn, increases the capacitor charge current to the value Iμi , and then the process would continue as indicated in the figure until the point 1 (at a constant speed of rotation of the motor field), where E 1 i = E 1 and Iμi = I μ .
According to the equivalent circuit (Fig. 4-22) EMF E 1 will be equal
where φ = f X f 0 -1 and f 0 - nominal frequency in the circuit.
Assuming that at the beginning of self-excitation the current in the rotor is equal to zero and I 1 ≈ Iμ, you can find the initial relative self-excitation frequency φ INITIAL. Then from formula (4-46) we find
And x μ , x 1 , x C - reactive components of equivalent circuit resistance (Fig. 4-22) at network frequency (50 Hz).
Rice. 4-22. Equivalent circuit of an asynchronous machine with capacitor excitation
Neglecting values IN And x 1 2 compared with xμ 2 and solving the biquadratic equation (4-47), we obtain:
Or (4-48)
Rice. 4-23. Static characteristics of the capacitor self-excitation mode of an asynchronous machine F - magnetic flux; I 1 , I 2 " , Iμ - current in the stator, current in the rotor (given value), magnetizing current, respectively; φ - frequency of free current oscillations in the stator; ω - angular speed of the rotor; s - slip; M- electromagnetic torque
Thus, the initial frequency of the self-excitation process of an asynchronous generator is approximately equal to the natural frequency of the oscillatory circuit of an unsaturated machine. This is also illustrated by the curves in Fig. 4-23 (in relative units). They allow us to draw the following conclusions.
1. The mode is limited in terms of the angular speed of the rotor by the values of ω NAC, where self-excitation of the machine begins and ω K, where this process ends, and ω K > ω 0.
2. In a significant range of changes in the rotor speed, the magnetic circuit of the machine remains saturated and the flux maintains an approximately constant value (1.5-2.0) F NOM.
3. The values of the rotor and stator currents significantly exceed the nominal values.
Considering the physical processes occurring in the machine, we can establish the following. If the rotor rotation speed exceeds ω IN, then the frequency of the free component of the stator current increases due to saturation of the magnetic system of the machine (see Fig. 4-23) and φ will be greater than φ IN. The stator current vector rotates clockwise (Fig. 4-24), but its amplitude increases. At the same time, the increase in current in the rotor I 2 leads to the appearance of a demagnetizing component of the magnetic flux in the air gap. At rotor rotation speed ω K, equality of reactive current components occurs I 1 and I 2 "and the process of self-excitation of the machine stops.
Considering equal I 1 and I 2 "due to the smallness of their active components, and using expression (4-49), we find:
where φ K is the critical value of the relative frequency of the stator field.
Rice. 4-24. Vector diagram of self-excitation of an asynchronous generator
The motor phase equivalent circuit and its vector diagram make it possible to find dependencies for electromagnetic power and torque, the latter is determined by heat losses in the stator and rotor of the machine. However, these calculations involve very complex and cumbersome calculations of all the dependencies shown in Fig. 4-23. Therefore, we will use a simplified method for calculating the mechanical characteristics, which is determined by the following dependence:
Where M 0 - initial (calculated) braking torque at speed ω 0.
Magnitude M 0 obtained experimentally in the form of the product M NOM kC° , Where k - coefficient depending on the type of specific engine. It can be taken equal to 0.7 for four- and six-pole machines and 0.5 for two-pole machines, С° - phase capacitance of capacitors in relative units from C NOM. By setting the value of φ START, you can calculate С° according to the formula
Nominal capacity of capacitor bank (phase)
Where Iμ NOM - magnetizing current of the machine at the rated (phase) stator voltage; ω 0 - synchronous rotation speed of the magnetic field at a network frequency of 50 Hz.
Rice. 4-25. Static mechanical characteristics of an asynchronous machine with capacitor braking: with capacitance in phase WITH 1 (curve 1), with capacitance in phase WITH 2 (curve 2 and 3) and different values of magnetizing current Iμ 2 " Iμ 3
Mechanical characteristics (Fig. 4-25) show that increasing the capacitor capacity reduces the value of the angular velocities ω NACH and ω K, as well as the maximum braking torque. With increasing magnetizing current (curve 3 ) the saturation of the magnetic circuit increases, which leads to a decrease in the inductive reactance of the machine and an increase in the maximum braking torque and angular speed ω K.
Rice. 4-26. Combined capacitor-dynamic braking: a - circuit diagram; b - mechanical characteristics
As stated above, combined braking methods are effective in obtaining a complete stop of the drive. Depending on the closing moments of the brake contactor contacts CT in such a system it is possible to obtain even three sequentially changing braking modes (Fig. 4-26,b): capacitor (curve 1 ), magnetic (curve 2 ) and dynamic (curve 3 ) or only the first and last. The transition of the drive from the motor mode to the braking mode and the switching of various braking modes is indicated in the figure by arrows. For example, if contact closure CT occurs at the moment corresponding to the point With, then it undergoes a transition from capacitor to magnetic braking, which ends at the point d, then dynamic braking occurs almost until the drive stops.
7. Technical implementations. Applications
An asynchronous motor with a squirrel-cage rotor has been used for about 100 years and will be used as practically the only implementation of a mass-produced unregulated electric drive, which to date makes up more than 90% of all industrial electric drives. In the last 10-20 years, many companies in America and Europe have been attempting to develop and release to the wide market so-called energy-efficient engines, in which, by increasing the mass of active materials by 30%, the nominal efficiency is increased by 1-5% with a corresponding increase in cost. In recent years, the UK has undertaken a major project to create energy efficient engines without increasing the cost.
In the last decade, thanks to advances in electronics (FC), the squirrel-cage induction motor has become the basis of variable-frequency electric drives, successfully replacing the previously dominant DC electric drive in many areas. Particularly interesting is the use of such an electric drive in traditionally unregulated pumps, fans, and compressors. Experience shows that this technical solution allows saving up to 50% of electricity, up to 20% of water and more than 10% of heat.
The transition from an unregulated electric drive to a controlled one in many technologies is considered as the main direction of electric drive development, since this significantly improves the quality of technological processes and saves up to 30% of electricity. This determines the prospects for the development of variable frequency electric drives.
Electric drives with wound rotor motors with rheostatic control are traditionally used in cranes and are used in other technologies. Cascade circuits and dual-power machines can be found in powerful electric drives of gas pumping stations with a small control range, and in electric propulsion devices for ships.
Construction of asynchronous machines
The operating principle of an asynchronous machine is based on the use of a rotating magnetic field, which induces an electromotive force (EMF) in the rotor winding. When the rotor current interacts with a rotating magnetic field, an electromagnetic torque is created, causing the rotor to rotate (in motor mode) or braking it (in braking modes)
8-The principle of operation of an asynchronous machine
The operating principle of an asynchronous machine is based on the law of electromagnetic induction, discovered
M. Faraday, and the works of D. Maxwell and E. Lenz.
In an asynchronous machine, one of the windings is placed on stator 1 (Figure 1.1 a), and the second on rotor 5. There is an air gap between the rotor and stator, which is made as small as possible to improve the magnetic coupling between the windings. Stator winding 2 is a multiphase (or in a particular case three-phase) winding, the coils of which are placed evenly around the circumference of the stator. Stator winding phases OH,BY And CZ connected according to diagram Y or A and connected to a three-phase current network. Rotor winding 4 perform multi-phase short-circuit or three-phase and are placed evenly along the circumference of the rotor.
From the course of theoretical fundamentals of electrical engineering it is known that when a three-phase stator winding is supplied with a three-phase sinusoidal current, a rotating magnetic field appears, the rotation frequency (rpm) of which
П1=60f1|р Where f 1- mains frequency. R-. number of pole pairs
The rotating magnetic field induces an EMF E 2 in the conductors of the short-circuited rotor winding and current 1 2 passes through them.
Figure 1.1a shows (according to the right-hand rule) the direction of the EMF induced in the rotor conductors when the magnetic flux F rotates clockwise (in this case, the rotor conductors move relative to the flux F counterclockwise). If the rotor is stationary or its rotation frequency is less than frequency n1, then the active component of the rotor current is in phase with the induced EMF; With this in mind, the symbols (crosses and dots) in Fig. 1.1 show at the same time the direction of the active component of the current.
Rice. 1.1. Electromagnetic circuit of an asynchronous machine and the direction of its electrictromagnetic moment when the machine operates in modes: motor(A), generhetorical(b) and electr. braking(V)
Current-carrying conductors located in a magnetic field are subject to electromagnetic forces, the direction of which is determined by the left-hand rule. The total force F pe 3 applied to all conductors of the rotor forms an electromagnetic moment M, which drags the rotor behind the rotating magnetic field.
Electromagnetic torque arising from the interaction of the magnetic flux Fi of the rotor current I2
M=sФI2соsф2
where c is the proportionality coefficient; I2соsф2 - active component of the rotor current; φ2 - phase shift angle between current I2 and EMF E 2 in the rotor winding.
If the electromagnetic torque M is sufficiently large, then the rotor begins to rotate and its steady rotation speed n 2 corresponds to the equality of the electromagnetic torque to the braking torque created by the mechanism driven into rotation and internal friction forces. This mode of operation of an asynchronous machine is motor.
The rotation frequency of the rotor P2 always differs from the rotation frequency of the magnetic field P1, since if these frequencies coincide, the rotating field does not cross the rotor winding and no EMF is induced in it, and therefore no torque is created.
The relative difference in the rotation frequencies of the magnetic field and the rotor is called slip:
S=(P1- P1) | P1
It is expressed in relative units or percentages relative to P1 Rotor speed taking into account
Thus, a characteristic feature of an asynchronous machine is the presence of slipping, i.e. inequality of rotation frequencies P1 and P1 That is why the machine is called asynchronous (its rotor rotates asynchronously with the field).
When an asynchronous machine operates in motor mode, the rotor speed is less than the rotation speed of the magnetic field P1 In the machine, electrical energy is converted into mechanical energy.
If the rotor is braked (S = 1), this is a short circuit mode. If the rotor rotation frequency coincides with the rotation frequency of the magnetic field (synchronous frequency), i.e. S = 0, then no torque occurs.
If the rotor of an asynchronous machine is accelerated using an external torque (for example, by some motor) to a frequency P2, greater than the rotational frequency of the magnetic field P1, then the direction of the EMF in the rotor conductors and the active component of the rotor current will change. At the same time, the electromagnetic moment M will also change its direction, which will become braking, i.e., the asynchronous machine will switch to generator mode (Fig. 1.1, b). In generator mode, an asynchronous machine receives mechanical energy from the prime mover, converts it into electrical energy and supplies it to the network, while 0>S> - ∞.
If you rotate the rotor from an external motor in the direction opposite to the rotation of the magnetic field (Fig. 1.1, c), then the EMF and the active component of the current in the rotor conductors are directed in the same way as in motor mode, i.e. the machine receives electrical energy from the network . However, in this mode, the electromagnetic moment M is directed against the rotation of the rotor, i.e. it is braking. This mode of operation of an asynchronous machine is the electromagnetic braking mode. In this mode, the rotor rotates in the opposite direction (relative to the direction of the magnetic field), so P2
9-Design of asynchronous machines
Main types of engines. Asynchronous motors are divided into two main types: squirrel cage and wound rotor (the latter are called slip ring motors). The motors under consideration have the same stator design and differ only in the design of the rotor.
Squirrel cage motors are the most
common; The electrical industry produces tens of millions of them per year.
In Fig. 1.2, A shows a general view of the most common asynchronous motor with a squirrel-cage rotor of a closed, blown design. There is a three-phase winding on the stator. The rotor winding is made in the form of a squirrel cage, i.e. it is short-circuited.
The design of the shell (hull, shields, etc.) largely depends on the design of the machine in terms of the degree of protection and on the selected cooling system. In the design under consideration, the machine body is equipped with ribs for better cooling. A centrifugal fan located on the motor shaft outside the machine shell blows air over the ribbed motor housing. The fan is covered with an air guide casing.
Inside the machine, the air is mixed by ventilation blades cast together with short-circuiting rings. A terminal box is attached to the housing, in which a terminal panel is installed with the ends of the stator winding brought out.
In more powerful engines, to increase the cooling intensity, air is driven through the axial channels of the rotor by a separate fan or the same fan that blows on the outer surface of the machine. For this purpose, when using one common fan, air-conducting tubes are inserted into the axial holes of the rotor, secured in the holes of the support disks mounted on the rotor shaft (Fig. 1.2, b). This prevents outside air, which contains moisture, from penetrating the machine windings. The end shields have louvers for the passage and exit of air.
The stator core (magnetic core) is assembled from stamped ring-shaped sheets of electrical steel with a thickness of 0.35... 0.5 mm. The sheets have grooves stamped into them to accommodate the winding (Fig. 1.3). In large machines, the stator is assembled from sheets in the form of segments. Insulation (oxide film, varnish, etc.) is applied to the sheets on both sides. The sheets in the core package are held together by staples, welding, or in large machines, pins. In machines over 400 kW, the cores usually have radial channels for better cooling. They are formed by dividing the core along its length into a number of packages and installing steel spacers between them, which are welded to the outer sheets of the package.
Rice. 1.2. Asynchronous motors with squirrel-cage rotor: 1-short-circuiting rings of the rotor winding; 2, 10-bearing shields; 3 - ventilation blades; 4 - stator winding;
5 - terminal box; b - body (bed); 7 - stator core; 8-core rotor; 9-shaft; 11-fan casing; 12 - fan; 13-support disk; 14 - air supply tube
A winding made of rectangular or round wire is placed in the grooves of the stator magnetic circuit. Windings of rectangular wire are made in the form of rigid sections and placed in open or semi-open grooves (Fig. 1.4, a, b). Windings of round wire are usually poured into semi-closed slots through a slot in the slot (Fig. 1.5) using special stator winding machines. In high-voltage machines, the body insulation of the coils is usually made in the form of a compressed sleeve (see Figure 1.4). In modern asynchronous machines, electrical insulating materials of heat resistance classes B and F are used, and for special machines operating in difficult conditions, materials of class H are used.
Fig 1.3 Stator core and stamped sheet
In modern asynchronous machines, electrical insulating materials of heat resistance classes B and F are used, and for special machines operating in harsh conditions, materials of class H are used.
In machines, a distinction is made between turn-to-turn and body insulation. Interturn insulation (between the turns of the winding) is provided by the insulation of the conductor itself, applied to it during the manufacturing process at cable factories or during the manufacture of an electrical machine. Housing insulation separates the winding conductors from the body of the electrical machine. It uses various gaskets, sleeves or a number of layers of insulation applied to the corresponding coil before installing it in the machine
Fig 1.4Open(A)and half-open (b) stator slots for winding from rigid sections -
1.4.5 - insulating gaskets 2 - conductors 3 - coil insulation (case) 6-wedge The rotor of the machine consists of a package of electrical steel sheets with stamped grooves. In short-circuit rotors, the grooves are filled with aluminum. In this case, the rods of a squirrel cage are formed (Fig. 1.6 a). Short-circuiting end rings and ventilation blades are cast at the same time; the general view of such a rotor is shown in Fig. 1.6, b. In larger and special machines, copper (bronze, brass) rods are inserted into the rotor grooves, the ends of which are soldered (welded) into short-circuiting copper rings (Fig. 1.6, c). A package with an aluminum cage is pressed onto the shaft. For rotors with a copper cage, the sheets are assembled
directly on the shaft, and only then copper rods are inserted into the grooves of the package .
Engine rotors rotate in bearings; as a rule, rolling bearings are used; in machines over 1000 kW, plain bearings are also used. If necessary, a fan is installed on the shaft. Bearings are fixed in bearing shields, bearing shields are attached to the stator housing. Motors with a wound rotor find much less application than those with a squirrel-cage rotor, and are produced by industry mainly in the form of machines with a power of over 100 kW.
Fig 1.5 Rice. 1.5. Stator slots for bulk typenolayer(A) and two-layer(b) obmocurrent:
1 - conductors; 2 - groove insulation (casing); 3 - cover - wedge; 4 - gasket
In Fig. Figure 1.7 shows a general view of an asynchronous motor with a protected phase rotor. For better cooling, the magnetic cores of the stator and rotor in high- and medium-power machines are divided into separate packages, between which there are ventilation ducts. Ventilation blades, reinforced
Rice. 1.6. Squirrel-cage rotor design:
/ - rotor core; 2 - squirrel cage rods; 3 - ventilation blades
4 - short-circuit rings
on the frontal (outer) parts of the rigid winding sections, suck air into the machine through holes in the shields and
throw it out through the holes in the body. This type of ventilation is called symmetrical radial ventilation. The slip rings are located outside the machine shell.
Rice. 1.7. Asynchronous motor with wound rotor:
7 - terminal box; 2 -shaft; 3 - ventilation blades; 4 - rotor winding; 5 - stator winding;
6.11 bearing shields; 7-stator core; 8- rotor core; 9 - radial ventilation duct; 10 - diffuser; 12-brush traverse; 13 - casing; 14-pin rings
Rice. 1.8. Slots of a wound rotor with a random winding made of round wire(A) and with rigid winding(b):
1 - wedge; 2 - conductors; 3- gasket; 4 - groove insulation (casing)
the output ends of the rotor winding pass through a hole in the shaft and are connected to the slip rings with bolts. Brush holders with brushes are attached to the shield by a brush crossbar. In motors with a wound rotor, a loose winding of round wire is placed in the rotor slots (Fig. 1.8, a) or a winding consisting of rigid sections laid in the open slots of the rotor (Fig. 1.8,6), or a winding of rods inserted into semi-closed grooves at the end. The three ends from the phase windings are connected to slip rings mounted on the motor shaft.
10.References
1 I.P Kopylov - “Electric machines” - Moscow 2002
engine with wound rotor natural characteristic... Ohm. Fig 1. Mechanical characteristics, S =. M S Question No. 2 For engine DC parallel...Asynchronous engine with squirrel-cage rotor
Laboratory work >> PhysicsDetermine experimentally mechanical characteristics n(M), dependence mechanical moment on the shaft engine anti-slip M(S), working characteristics asynchronous engine n(P2...
When constructing models of an automated electric drive, it is necessary to take into account the complexity of the electromechanical processes occurring in the engine during its operation. The results obtained from mathematical calculations should be verified empirically. Thus, there is a need to determine the characteristics of electric motors during a full-scale experiment. The information obtained during such an experiment makes it possible to test the constructed mathematical model. The article discusses a method for constructing the mechanical characteristics of an asynchronous motor with a squirrel-cage rotor, conducts an experimental test of the calculated mechanical characteristics using the example of a system consisting of an asynchronous motor, to the shaft of which an independently excited DC motor is connected as a load, estimates the calculation error, and draws a conclusion about the possibility of using obtained results for further research. When conducting the experiment, the laboratory stand NTC-13.00.000 is used.
asynchronous motor
DC motor
mechanical characteristics
equivalent circuit
saturation of the magnetic system.
1. Voronin S.G. Electric drive of aircraft: Educational and methodological complex. - Offline version 1.0. - Chelyabinsk, 1995-2011.- ill. 493, list lit. - 26 titles
2. Moskalenko V.V. Electric drive: a textbook for students. higher textbook establishments. - M.: Publishing center "Academy", 2007. - 368 p.
3. Moshchinsky Yu. A., Bespalov V. Ya., Kiryakin A. A. Determination of the parameters of the equivalent circuit of an asynchronous machine using catalog data // Electricity. - No. 4/98. - 1998. - P. 38-42.
4. Technical catalog, second edition, corrected and expanded / Vladimir Electric Motor Plant. - 74 s.
5. Austin Hughes Electric Motors and Drives Fundamentals, Types and Applications. - Third edition / School of Electronic and Electrical Engineering, University of Leeds. - 2006. - 431 rub.
Introduction
An asynchronous motor (AM) is an electric motor that has found very wide application in various industries and agriculture. IM with a squirrel-cage rotor has features that make it widespread: ease of manufacture, which means low initial cost and high reliability; high efficiency combined with low maintenance costs ultimately result in low overall operating costs; possibility of working directly from the AC mains.
Operating modes of an asynchronous electric motor
Squirrel-cage motors are asynchronous machines, the speed of which depends on the frequency of the supply voltage, the number of pole pairs and the load on the shaft. Generally, by keeping the supply voltage and frequency constant, if the temperature change is ignored, the shaft torque will depend on the slip.
The torque of the arterial pressure can be determined using the Kloss formula:
where , is the critical moment, is the critical slip.
In addition to the motor mode, the asynchronous motor has three more braking modes: a) generator braking with energy output to the network; b) counter-switching braking; c) dynamic braking.
With positive slip the squirrel cage machine will act as a motor, with negative slip it will act as a generator. It follows from this that the armature current of a squirrel-cage motor will depend only on slip. When the machine reaches synchronous speed, the current will be minimal.
Generator braking of the IM with the release of energy into the network occurs when the rotor speed exceeds the synchronous speed. In this mode, the electric motor supplies active energy to the network, and reactive energy necessary to create an electromagnetic field is supplied to the electric motor from the network.
The mechanical characteristic for the generator mode is a continuation of the characteristic of the motor mode into the second quadrant of the coordinate axes.
Reverse braking corresponds to the direction of rotation of the stator magnetic field, opposite to the rotation of the rotor. In this mode, the slip is greater than unity, and the rotor speed in relation to the stator field speed is negative. The current in the rotor, and consequently in the stator, reaches a large value. To limit this current, additional resistance is introduced into the rotor circuit.
The reverse braking mode occurs when the direction of rotation of the stator magnetic field changes, while the electric motor rotor and the mechanisms connected to it continue to rotate by 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 influence of an external torque, changes the direction of rotation.
In this article we will consider the construction of the mechanical characteristics of an asynchronous motor in motor mode.
Constructing a mechanical characteristic using a model
Passport data of AD DMT f 011-6у1: Uф =220 - rated phase voltage, V; p=3 - number of pole pairs of windings; n=880 - nominal rotation speed, rpm; Pn=1400 - rated power, W; Iн=5.3 - rated rotor current, A; η = 0.615 - efficiency nominal, %; cosφ = 0.65 - cos(φ) nominal; J=0.021 - moment of inertia of the rotor, kg m 2; Ki = 5.25 - starting current multiple; Kp = 2.36 - multiplicity of starting torque; Km = 2.68 - critical moment multiplicity.
To study the operating modes of asynchronous motors, operating and mechanical characteristics are used, which are determined experimentally or calculated on the basis of an equivalent circuit (EC). To use SZ (Fig. 1), you need to know its parameters:
- R 1, R 2 ", R M - active resistance of the stator, rotor and magnetization branch phases;
- X 1, X 2 ", X M - inductive leakage resistance of the rotor stator phases and the magnetization branch.
These parameters are required to determine starting currents when selecting magnetic starters and contactors, when performing overload protection, to regulate and configure the electric drive control system, and to simulate transient processes. In addition, they are necessary for calculating the starting mode of the IM, determining the characteristics of an asynchronous generator, as well as when designing asynchronous machines in order to compare the initial and design parameters.
Rice. 1. Equivalent circuit of an asynchronous motor
We will use the methodology for calculating the parameters of the equivalent circuit to determine the active and reactive resistance of the stator and rotor phases. The values of efficiency and power factor at partial loads required for calculations are given in the technical catalog: pf = 0.5 - partial load factor, %; Ppf = Pн·pf - power at partial load, W; η _pf = 0.56 - efficiency at partial load, %; cosφ_pf = 0.4 - cos(φ) at partial load.
Resistance values in the equivalent circuit: X 1 =4.58 - stator reactance, Ohm; X 2 "=6.33 - rotor reactance, Ohm; R 1 =3.32 - stator active resistance, Ohm; R 2 "=6.77 - rotor active resistance, Ohm.
Let's construct a mechanical characteristic of an asynchronous motor using the Kloss formula (1).
Slip is determined from an expression of the form:
where is the rotation speed of the IM rotor, rad/sec,
synchronous rotation speed:
Critical rotor speed:
. (4)
Critical slide:
We determine the critical moment point from the expression
We determine the starting torque using the Kloss formula at s=1:
. (7)
Based on the calculations made, we will construct a mechanical characteristic of the blood pressure (Fig. 4). To test it in practice, we will conduct an experiment.
Construction of experimental mechanical characteristics
When conducting the experiment, the laboratory stand NTC-13.00.000 “Electrodrive” is used. There is a system consisting of an IM, to the shaft of which an independently excited direct current motor (DCM) is connected as a load. It is necessary to construct a mechanical characteristic of an asynchronous motor using the passport data of asynchronous and synchronous machines and sensor readings. We have the ability to change the voltage of the excitation winding of the DPT, measure the currents at the armature of a synchronous and asynchronous motor, and the shaft rotation frequency. Let's connect the IM to the power source and load it by changing the current of the excitation winding of the DPT. After conducting the experiment, we will compile a table of values from the sensor readings:
Table 1 Sensor readings when loading an asynchronous motor
where Iв is the field winding current of the DC motor, I I is the armature current of the DC motor, Ω is the rotor speed of the asynchronous motor, I 2 is the rotor current of the asynchronous motor.
Passport data of synchronous machine type 2P H90L UHL4: Pn=0.55 - rated power, kW; Unom=220 - rated voltage, V; Uv.nom=220 - nominal excitation voltage, V; Iya.nom=3.32 - rated armature current, A; Iv.nom=400 - rated excitation current, mA; Rя=16.4 - armature resistance, Ohm; nn=1500 - nominal rotation speed, rpm; Jdv=0.005 - moment of inertia, kg m 2; 2p p =4 - number of pole pairs; 2a=2 - number of parallel branches of the armature winding; N=120 - number of active conductors of the armature winding.
Current enters the DPT rotor through one brush, flows through all turns of the rotor winding and exits through the other brush. The point of contact of the stator winding with the rotor winding is through the commutator plate or segments that the brush presses on at the time (the brush is usually wider than one segment). Since each individual turn of the rotor winding is interconnected with a commutator segment, the current actually passes through all the turns and through all the commutator plates on its way through the rotor.
Rice. 2. Currents flowing in the rotor of a DC motor with two poles
Figure 2 shows that all the conductors lying at the N pole have a positive charge, while all the conductors under the S pole carry a negative charge. Therefore, all conductors under the N pole will receive a downward force (which is proportional to the radial flux density B and the rotor current), while all conductors under the S pole will receive an equal upward force. As a result, a torque is created on the rotor, the magnitude of which is proportional to the product of magnetic flux density and current. In practice, the magnetic flux density will not be completely uniform under the pole, so the force on some rotor conductors will be greater than on others. The total moment developing on the shaft will be equal to:
M = K T ФI, (8)
where Ф is the total magnetic flux, the coefficient K T is constant for a given motor.
In accordance with formula (8), torque regulation (limitation) can be achieved by changing the current I or magnetic flux F. In practice, torque regulation is most often carried out by adjusting the current. The motor current is regulated by its control system (or operator) by changing the voltage supplied to the motor using electrical power converters or by including additional resistors in its circuits.
Let us calculate the design constant of the motor included in equation (8):
. (9)
Let us establish a connection between the motor flux and the field winding current. As is known from the theory of electrical machines, due to the influence of saturation of the magnetic system, this relationship is nonlinear and has the form shown in Figure 3. In order to better use iron, the machine is designed so that in the nominal mode the operating point is at the inflection of the magnetization curve. Let us take the magnitude of the magnetic flux to be proportional to the excitation current.
Fpr.=Iв, (10)
where Iв is the excitation current.
F - real flow value; F pr. - flow value adopted for calculations
Rice. 3. Ratio of magnetic flux values, accepted and real
Since the IM and DPT have one common shaft in the experiment, we can calculate the torque created by the DPT and, based on the obtained values and speed sensor readings, construct an experimental mechanical characteristic of the IM (Figure 4).
Fig.4. Mechanical characteristics of an asynchronous motor: calculated and experimental
The obtained experimental characteristic in the region of low torque values is located below the characteristic calculated theoretically, and higher in the region of high values. This deviation is associated with the difference between the calculated and real values of the magnetic flux (Fig. 3). Both graphs intersect at Фр.=Iв. nom.
Let us introduce a correction to the calculations by establishing a nonlinear relationship (Fig. 5):
Ф=а·Iв, (11)
where a is the nonlinearity coefficient.
Rice. 5. Ratio of magnetic flux to excitation current
The resulting experimental characteristic will take the form shown in Fig. 6.
Fig.6. Mechanical characteristics of an asynchronous motor: calculated and experimental
Let us calculate the error of the experimental data for the case in which the magnetic flux depends linearly on the excitation current (10), and the case in which this dependence is nonlinear (11). In the first case, the total error is 3.81%, in the second - 1.62%.
Conclusion
The mechanical characteristic, constructed according to experimental data, differs from the characteristic constructed using the Kloss formula (1) due to the accepted assumption Fpr. = Iv, the discrepancy is 3.81%, with Iv = Iv.nom. = 0.4 (A) These characteristics are the same. When Iв reaches the nominal value, the magnetic system of the DPT becomes saturated; as a result, a further increase in the excitation current has less and less effect on the value of the magnetic flux. Therefore, to obtain more accurate torque values, it is necessary to introduce a saturation coefficient, which makes it possible to increase the calculation accuracy by 2.3 times. The mechanical characteristic constructed by modeling adequately reflects the operation of a real engine; it can be taken as a basis for further research.
Reviewers:
- Pyukke Georgy Aleksandrovich, Doctor of Technical Sciences, Professor of the Department of Control Systems of Kamchatka State Technical University, Petropavlovsk-Kamchatsky.
- Potapov Vadim Vadimovich, Doctor of Technical Sciences, Professor of the Far Eastern Federal University branch, Petropavlovsk-Kamchatsky.
Bibliographic link
Likhodedov A.D. CONSTRUCTION OF MECHANICAL CHARACTERISTICS OF AN INDUCTION MOTOR AND ITS TESTING // Modern problems of science and education. – 2012. – No. 5.;URL: http://science-education.ru/ru/article/view?id=6988 (access date: 02/01/2020). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"
