Construction of the mechanical characteristics of an asynchronous motor with a squirrel-cage rotor. Equation of mechanical characteristics of an asynchronous motor. single phase equivalent circuit. Construction of the natural mechanical characteristics of the engine
It is convenient to analyze the operation of an asynchronous electric motor on the basis of its mechanical characteristics, which are a graphically expressed dependence of the form P = f(M). Speed characteristics in these cases are used very rarely, since for an asynchronous electric motor the speed characteristic is the dependence of the number of revolutions on the rotor current, in determining which a number of difficulties are encountered, especially in the case of asynchronous electric motors with a squirrel-cage rotor.
For asynchronous electric motors, as well as for DC electric motors, a distinction is made between natural and artificial mechanical characteristics. An asynchronous electric motor operates on a natural mechanical characteristic if its stator winding is connected to a three-phase current network, the voltage and frequency of which correspond to the rated values, and if no additional resistance is included in the rotor circuit.
In Fig. 42 the dependence was given M = f(s), which allows you to easily move on to the mechanical characteristics n = f(M ), since, according to expression (82), the rotor rotation speed depends on the amount of slip.
Substituting formula (81) into expression (91) and solving the resulting equation for P 2 we obtain the following equation for the mechanical characteristics of an asynchronous electric motor
Member r 1 s omitted due to its small size. The mechanical characteristics corresponding to this equation are shown in Fig. 44.
For practical constructions, equation (95) is inconvenient, so in practice simplified equations are usually used. Thus, in the case of an electric motor operating on a natural characteristic with a torque not exceeding 1.5 of its nominal value, the slip usually does not exceed 0.1. Therefore, for the indicated case in equation (95) we can neglect the term x 2 s 2 /kr’ 2 · M , as a result of which we obtain the following simplified equation of natural characteristics:
which is the equation of a straight line inclined to the x-axis.
Although equation (97) is approximate, experience shows that with torque changes ranging from M= 0 to M=1,5M n the characteristics of asynchronous electric motors are truly straightforward and equation (97) gives results that are in good agreement with experimental data.
When introducing additional resistances into the rotor circuit, the characteristic P = f(M) with sufficient accuracy for practical purposes can also be considered rectilinear within the specified limits for the torque and can be constructed using equation (97).
Thus, the mechanical characteristics of an asynchronous electric motor range from M= 0 to M = 1,5 M n at different resistances of the rotor circuit they represent a family of straight lines intersecting at one point corresponding to the synchronous speed (Fig. 45). As equation (97) shows, the slope of each characteristic to the abscissa axis is determined by the value of the active resistance of the rotor circuit r’ 2 . Obviously, the greater the resistance introduced into each phase of the rotor, the more the characteristic is inclined to the abscissa axis.
As indicated, usually in practice the speed characteristics of asynchronous electric motors are not used. The starting and control resistances are calculated using equation (97). The construction of a natural characteristic can be performed at two points - at synchronous speed n 1 = 60f /R at zero torque and at rated speed at rated torque.
It should be borne in mind that for asynchronous electric motors the dependence of torque on rotor current I 2 is more complex than the dependence of torque on armature current for
DC electric motors. Therefore, the speed characteristic of an asynchronous motor is not identical to the mechanical characteristic. Characteristic P = f(I 2 ) has the form shown in Fig. 46. Characteristics are also given there n = f (I 1 ).
Mechanical characteristics of the engine is called the dependence of the rotor speed on the torque on the shaft n = f (M2). Since the no-load torque is small under load, M2 ≈ M and the mechanical characteristic is represented by the dependence n = f (M). If we take into account the relationship s = (n1 - n) / n1, then the mechanical characteristic can be obtained by presenting its graphical dependence in coordinates n and M (Fig. 1).
Rice. 1. Mechanical characteristics of an asynchronous motor
Natural mechanical characteristic of an induction motor corresponds to the main (certificate) circuit of its connection and the nominal parameters of the supply voltage. Artificial characteristics are obtained if any additional elements are included: resistors, reactors, capacitors. When the motor is powered with a non-rated voltage, the characteristics also differ from the natural mechanical characteristics.
Mechanical characteristics are a very convenient and useful tool for analyzing the static and dynamic modes of an electric drive.
Main points of mechanical characteristics: critical slip and frequency, maximum torque, starting torque, rated torque.
Mechanical characteristic is the dependence of torque on slip, or, in other words, on the number of revolutions:
From the expression 
it is clear that this dependence is very complex, because, as the formulas show) 
And 
, sliding is also included in the expressions for I 2
And cos? 2. The mechanical characteristics of an asynchronous motor are usually given graphically
The starting point of the characteristic corresponds to n= 0 and s= 1: this is the first moment the engine starts. Starting torque value M n - a very important characteristic of the operational properties of the engine. If M n small, less than the rated operating torque, the engine can only be started idle or with a correspondingly reduced mechanical load.
Let us denote by the symbol Mnp counteracting (braking) torque created by the mechanical load on the shaft at which the engine starts. The obvious condition for the engine to be able to start is: M n > Mnp . If this condition is met, the engine rotor will begin to move, its speed will be n will increase, and the slip s decrease. As can be seen from the image above, the engine torque increases from M n up to maximum M m , corresponding to the critical slip s kp therefore, the excess available engine power, determined by the torque difference, also increases M And Mnp .
The greater the difference between the available engine torque (possible for a given slip along the operating characteristic) M and opposing M np , the easier the starting mode and the faster the engine reaches a steady rotation speed.
As the mechanical characteristics show, at a certain number of revolutions (at s = s kp) the available motor torque reaches the maximum possible for a given motor (at a given voltage U ) values 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.
38) Mechanical characteristics of an asynchronous motor.
Mechanical characteristics. The dependence of the rotor speed on the load (rotating torque on the shaft) is called the mechanical characteristic of an asynchronous motor (Fig. 262, a). At rated load, the rotation speed for various motors is usually 98-92.5% of the rotation speed n 1 (slip s nom = 2 - 7.5%). The greater the load, i.e. the torque that the engine must develop, the lower the rotor speed. As the curve shows
Rice. 262. Mechanical characteristics of an asynchronous motor: a - natural; b - when the starting rheostat is turned on
in Fig. 262a, the rotation speed of an asynchronous motor decreases only slightly with increasing load in the range from zero to its highest value. Therefore, such an engine is said to have a rigid mechanical characteristic.
The engine develops the greatest torque M max with some slip s kp amounting to 10-20%. The ratio M max /M nom determines the overload capacity of the engine, and the ratio M p /M nom determines its starting properties.
The engine can operate stably only if self-regulation is ensured, i.e., automatic equilibrium is established between the load torque M int applied to the shaft and the torque M developed by the engine. This condition corresponds to the upper part of the characteristic until M max is reached (to point B). If the load torque M in exceeds the torque M max, then the engine loses stability and stops, while a current 5-7 times greater than the rated current will pass through the windings of the machine for a long time, and they can burn out.
When the starting rheostat is connected to the rotor winding circuit, we obtain a family of mechanical characteristics (Fig. 262,b). Characteristic 1 when the engine is running without a starting rheostat is called natural. Characteristics 2, 3 and 4, obtained by connecting a rheostat with resistances R 1п (curve 2), R 2п (curve 3) and R 3п (curve 4) to the motor rotor winding, are called rheostatic mechanical characteristics. When the starting rheostat is turned on, the mechanical characteristic becomes softer (more steeply falling), as the active resistance of the rotor circuit R 2 increases and s kp increases. This reduces the starting current. The starting torque M p also depends on R 2. You can select the rheostat resistance so that the starting torque M p is equal to the maximum M max.
In an engine with increased starting torque, the natural mechanical characteristic approaches in its form the characteristic of an engine with the starting rheostat turned on. The torque of a double squirrel cage motor is equal to the sum of the two torques created by the working and starting cages. Therefore, characteristic 1 (Fig. 263) can be obtained by summing characteristics 2 and 3 created by these cells. The starting torque M p of such a motor is significantly greater than the torque M ' p of a conventional squirrel-cage motor. The mechanical performance of the deep slot motor is the same as that of the double squirrel cage motor.
WORKING CHARACTERISTICS JUST IN ANY CASE!!!
Performance characteristics. The operating characteristics of an asynchronous motor are the dependences of rotation speed n (or slip s), torque on the shaft M 2, stator current I 1 efficiency? and cos? 1, from useful power P 2 = P mx at rated values of voltage U 1 and frequency f 1 (Fig. 264). They are built only for the zone of practical stable operation of the engine, i.e. from a slip equal to zero to a slip exceeding the nominal by 10-20%. The rotational speed n changes little with increasing power output P2, just as in the mechanical characteristic; the torque on the shaft M 2 is proportional to the power P 2, it is less than the electromagnetic moment M by the value of the braking torque M tr created by friction forces.
The stator current I 1 increases with increasing power output, but at P 2 = 0 there is some no-load current I 0 . The efficiency varies in approximately the same way as in a transformer, maintaining a fairly large value over a relatively wide load range.
The highest efficiency value for medium and high power asynchronous motors is 0.75-0.95 (high power machines have a correspondingly higher efficiency). Power factor cos? 1 of medium and high power asynchronous motors at full load is 0.7-0.9. Consequently, they load power plants and networks with significant reactive currents (from 70 to 40% of the rated current), which is a significant disadvantage of these motors.
Rice. 263. Mechanical characteristics of an asynchronous motor with increased starting torque (with a double squirrel cage)
Rice. 264. Performance characteristics of an asynchronous motor
At loads of 25-50% of the nominal load, which are often encountered during the operation of various mechanisms, the power factor decreases to values that are unsatisfactory from an energy point of view (0.5-0.75).
When the load is removed from the engine, the power factor decreases to values of 0.25-0.3, therefore Asynchronous motors should not be allowed to operate at idle speed or at significant underloads.
Operation at low voltage and failure of one of the phases. Reducing the network voltage does not have a significant effect on the rotor speed of an asynchronous motor. However, in this case, the maximum torque that an asynchronous motor can develop is greatly reduced (when the voltage decreases by 30%, it decreases by approximately 2 times). Therefore, if the voltage drops significantly, the engine may stop, and if the voltage is low, it may not start working.
On e. p.s. alternating current, when the voltage in the contact network decreases, the voltage in the three-phase network, from which the asynchronous motors driving the rotation of auxiliary machines (fans, compressors, pumps), also decreases accordingly. In order to ensure normal operation of asynchronous motors at reduced voltage (they must operate normally when the voltage is reduced to 0.75U nom), the power of all auxiliary machine motors is at . p.s. is taken approximately 1.5-1.6 times greater than is necessary to drive them at rated voltage. Such a power reserve is also necessary due to some asymmetry of the phase voltages, since at the e.g. p.s. asynchronous motors are powered not from a three-phase generator, but from a phase splitter. If the voltages are unbalanced, the phase currents of the motor will be unequal and the phase shift between them will not be equal to 120°. As a result, more current will flow through one of the phases, causing increased heating of the windings of this phase. This forces the engine to limit its load compared to operating it at symmetrical voltage. In addition, with voltage asymmetry, not a circular, but an elliptical rotating magnetic field arises and the shape of the mechanical characteristics of the engine changes somewhat. At the same time, its maximum and starting torques are reduced. Voltage asymmetry is characterized by an asymmetry coefficient, which is equal to the average relative (in percent) deviation of voltages in individual phases from the average (symmetrical) voltage. A three-phase voltage system is considered to be practically symmetrical if this coefficient is less than 5%.
If one of the phases breaks, the engine continues to operate, but increased currents will flow through the undamaged phases, causing increased heating of the windings; such a regime should not be allowed. Starting a motor with a broken phase is impossible, since this does not create a rotating magnetic field, as a result of which the motor rotor will not rotate.
The use of asynchronous motors to drive auxiliary machines. p.s. provides significant advantages over DC motors. When the voltage in the contact network decreases, the rotation speed of asynchronous motors, and therefore the supply of compressors, fans, and pumps, practically does not change. In DC motors, the rotation speed is proportional to the supply voltage, so the supply of these machines is significantly reduced.
Asynchronous motors (IM) are the most common type of motor, because... they are simpler and more reliable in operation, with equal power they have less weight, dimensions and cost in comparison with DPT. The circuit diagrams for switching on the blood pressure are shown in Fig. 2.14.
Until recently, IMs with squirrel-cage rotors were used in unregulated electric drives. However, with the advent of thyristor frequency converters (TFCs) of the voltage supplying the stator windings of the IM, squirrel-cage motors began to be used in adjustable electric drives. Currently, power transistors and programmable controllers are used in frequency converters. The speed control method is called pulse and its improvement is the most important direction in the development of electric drives.
Rice. 2.14. a) circuit diagram for switching on an IM with a squirrel-cage rotor;
b) circuit diagram for switching on an IM with a phase-wound rotor.
The equation for the mechanical characteristics of the blood pressure can be obtained based on the equivalent circuit of the blood pressure. If we neglect the active resistance of the stator in this circuit, then the expression for the mechanical characteristic will have the form:
,
Here M k – critical moment; S to- the corresponding critical slip; U f– effective value of the phase voltage of the network; ω 0 =2πf/p– angular speed of the rotating magnetic field of the IM (synchronous speed); f– supply voltage frequency; p– number of pairs of poles of the IM; x k– inductive phase resistance of the short circuit (determined from the equivalent circuit); S=(ω 0 -ω)/ω 0– slip (rotor speed relative to the speed of the rotating field); R 2 1– total active resistance of the rotor phase.
The mechanical characteristics of an IM with a squirrel-cage rotor are shown in Fig. 2.15.
Rice. 2.15. Mechanical characteristics of an induction motor with a squirrel-cage rotor.
Three characteristic points can be distinguished on it. Coordinates of the first point ( S=0; ω=ω 0 ; M=0). It corresponds to the ideal idle mode, when the rotor speed is equal to the speed of the rotating magnetic field. Coordinates of the second point ( S=S to; M=M k). The engine is running at maximum torque. At M s >M k the motor rotor will be forced to stop, which is a short circuit for the motor. Therefore, the engine torque at this point is called critical M k. Coordinates of the third point ( S=1; ω=0; M=M p). At this point, the engine operates in start mode: rotor speed ω=0 and the starting torque acts on the stationary rotor M p. The section of the mechanical characteristic located between the first and second characteristic points is called the working section. On it the engine operates in steady state. For an IM with a squirrel-cage rotor, if the conditions are met U=U n And f=f n the mechanical characteristic is called natural. In this case, on the working section of the characteristic there is a point corresponding to the nominal operating mode of the engine and having coordinates ( S n; ω n; M n).
Electromechanical characteristics of blood pressure ω=f(I f), which is shown as a dashed line in Fig. 2.15, in contrast to the electromechanical characteristic of the DPT, coincides with the mechanical characteristic only in its working section. This is explained by the fact that during startup due to the changing frequency of the emf. in the rotor winding E 2 the frequency of the current and the ratio of the inductive and active resistance of the winding changes: at the beginning of the start-up, the frequency of the current is higher and the inductive resistance is greater than the active one; with increasing rotor speed ω the frequency of the rotor current, and hence the inductive resistance of its winding, decreases. Therefore, the starting current of the IM in direct start mode is 5–7 times higher than the rated value I fn, and the starting torque M p equal to nominal M n. Unlike DPT, where when starting it is necessary to limit the starting current and starting torque, when starting an IM, the starting current must be limited and the starting torque increased. The last circumstance is the most important, since the DPT with independent excitation starts when M s<2,5М н , DPT with sequential excitation at M s<5М н , and blood pressure when working at a natural characteristic at M s<М н .
For an IM with a squirrel-cage rotor, the increase M p is ensured by a special design of the rotor winding. The groove for the rotor winding is made deep, and the winding itself is arranged in two layers. When starting the engine, frequency E 2 and the rotor currents are large, which leads to the appearance of a current displacement effect - the current flows only in the upper layer of the winding. Therefore, the winding resistance and the starting torque of the motor increase M P. Its value can reach 1.5M n.
For an IM with a wound rotor, the increase M P is ensured by changing its mechanical characteristics. If resistance R P, included in the rotor current flow circuit, is equal to zero - the engine operates at a natural characteristic and M P =M N. At R P >0 the total active resistance of the rotor phase increases R 2 1. Critical slip S to as it increases R 2 1 also increases. As a result, in an IM with a wound rotor, the introduction R P into the rotor current flow circuit leads to a displacement M K towards large slips. At S K =1 M P =M K. Mechanical characteristics of IM with wound rotor at R P >0 are called artificial or rheostat. They are shown in Fig. 2.16.
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.
An example of calculating the mechanical characteristics of an asynchronous motor
A three-phase asynchronous motor with a squirrel-cage rotor is powered from a network with a voltage of = 380 V at = 50 Hz. Engine parameters: P n = 14 kW, n n = 960 rpm, cos φн = 0.85, ηн = 0.88, maximum torque ratio k m = 1.8.
Determine: rated current in the stator winding phase, number of pole pairs, rated slip, rated torque on the shaft, critical torque, critical slip and construct a mechanical characteristic of the motor.
Solution. Rated power consumed from the network
P1 n = P n / ηn = 14 / 0.88 = 16 kW.
Rated current consumed from the network
Number of pole pairs
p = 60 f / n1 = 60 x 50 / 1000 = 3,
Where n1 = 1000 – synchronous speed closest to the rated frequency n n = 960 rpm.
Nominal slip
s n = (n1 - n n) / n1 = (1000 - 960) / 1000 = 0.04
Nominal torque on the motor shaft
Critical moment
Mk = k m x Mn = 1.8 x 139.3 = 250.7 N m.
We find the critical slip by substituting M = Mn, s = s n and Mk / Mn = k m.
To construct the mechanical characteristics of the engine using n = (n1 - s), we determine the characteristic points: idle point s = 0, n = 1000 rpm, M = 0, nominal mode point s n = 0.04, n n = 960 rpm, Mn = 139.3 N m and the critical mode point s k = 0.132, n k = 868 rpm, Mk = 250.7 N m.