Design of an asynchronous motor with a squirrel-cage rotor. Coursework: Design of an asynchronous motor with a squirrel-cage rotor Design an asynchronous motor with a squirrel-cage rotor

MINISTRY OF EDUCATION AND SCIENCE

REPUBLIC OF KAZAKHSTAN

North Kazakhstan State University named after. M. Kozybaeva

Faculty of Energy and Mechanical Engineering

Department of Energy and Instrument Engineering

COURSE WORK

On the topic: “Design of an asynchronous motor with a squirrel-cage rotor”

discipline – “Electrical machines”

Completed by Kalantyrev

Scientific supervisor

Doctor of Technical Sciences, Prof. N.V. Shatkovskaya

Petropavlovsk 2010

Introduction

1. Selection of main sizes

2. Determination of the number of stator slots, turns in the winding phase, cross-section of the stator winding wire

4. Rotor calculation

5. Calculation of the magnetic circuit

6. Operating parameters

7. Calculation of losses

9. Thermal calculation

Appendix A

Conclusion

References

Introduction

Asynchronous motors are the main converters of electrical energy into mechanical energy and form the basis of the electric drive of most mechanisms. The 4A series covers a power rating range from 0.06 to 400 kW and has 17 axis heights from 50 to 355 mm.

In this course project the following engine is considered:

Execution according to the degree of protection: IP23;

Cooling method: IC0141.

Design according to installation method: IM1081 – according to the first digit – motor on feet, with bearing shields; according to the second and third numbers - with a horizontal shaft arrangement and a lower location of the paws; according to the fourth digit - with one cylindrical shaft end.

Climatic operating conditions: U3 – by letter – for moderate climates; by number - for placement in enclosed spaces with natural ventilation without artificially controlled climatic conditions, where fluctuations in temperature and air humidity, exposure to sand and dust, solar radiation are significantly less than in the open air of stone, concrete, wood and other unheated rooms.

1. Selection of main sizes

1.1 Determine the number of pole pairs:

Then the number of poles is .

1.2 Let us determine the height of the axis of rotation graphically: according to Figure 9.18, b, in accordance with, according to Table 9.8 we determine the outer diameter corresponding to the axis of rotation.

1.3 The inner diameter of the stator is calculated using the formula:

where is the coefficient determined according to table 9.9.

When lies in the interval: .

Let's choose the value, then

1.4 Define pole division:

(1.3)

1.5 Determine the design power, W:

, (1.4)

where is the power on the motor shaft, W;

– the ratio of the EMF of the stator winding to the rated voltage, which can be approximately determined from Figure 9.20. When and , .

We will take the approximate values from the curves constructed using the data from the 4A series engines. Figure 9.21, c. At kW and , , a

1.6 Electromagnetic loads A and B d are determined graphically using the curves in Figure 9.23, b. At kW and , , Tl.

1.7 Winding coefficient. For two-layer windings at 2p>2, = 0.91–0.92 should be taken. Let's accept.

1.8 Let us determine the synchronous angular velocity of the motor shaft W:

where is the synchronous rotation speed.

1.9 Calculate the length of the air gap:

, (1.6)

where is the field shape coefficient. .

1.10 The criterion for the correct choice of the main dimensions D is the ratio, which must be within acceptable limits, Figure 9.25, b.

. The l value lies within the recommended limits, which means the main dimensions are determined correctly.

2. Determination of the number of stator slots, turns in the winding phase and cross-section of the stator winding wire

2.1 Let’s determine the limit values: t 1 max and t 1 min Figure 9.26. When and , , .

2.2 Number of stator slots:

, (2.1)

(2.2)

Finally, the number of slots must be a multiple of the number of slots per pole and phase: q. Let's accept then

, (2.3)

where m is the number of phases.

2.3 We finally determine the tooth division of the stator:

(2.4)

2.4 Preliminary stator winding current

2.5 Number of effective conductors in the slot (provided):

(2.6)

2.6 We accept the number of parallel branches, then

(2.7)

2.7 Final number of turns in the winding phase and magnetic flux:

, (2.8)

2.8 Let’s determine the values of electrical and magnetic loads:

(2.11)

The values of electrical and magnetic loads differ slightly from those selected graphically.

2.9 The permissible current density is selected taking into account the linear load of the motor:

where is the heating of the slot part of the stator winding, we determine graphically Figure 9.27, d. At .

2.10 Let’s calculate the cross-sectional area of effective conductors:

(2.13)

We accept , then table P-3.1 , , .

2.11 Let us finally determine the current density in the stator winding:

3. Calculation of the dimensions of the stator tooth zone and air gap

3.1 First, we select the electromagnetic inductions in the stator yoke B Z 1 and in the stator teeth B a. When table 9.12, a.

3.2 Let us select the steel grade 2013, Table 9.13, and the steel filling factor of the stator and rotor magnetic circuits.

3.3 Using the selected inductions, we determine the height of the stator yoke and the minimum tooth width

3.4 Let's select the height of the slot and the width of the slot of the half-closed groove. For engines with axle height, mm. We select the slot width from table 9.16. When and , .

3.5 Determine the dimensions of the groove:

groove height:

dimensions of the groove in the die and:

Let's choose then

height of the wedge part of the groove:

Figure 3.1. Groove of the designed squirrel-cage motor

3.6 Let us determine the dimensions of the groove in the clear, taking into account allowances for the fusion and assembly of cores: and , table 9.14:

width, and:

and height:

Let us determine the cross-sectional area of the body insulation in the groove:

where is the one-sided insulation thickness in the groove, .

Let's calculate the cross-sectional area of the spacers to the groove:

Let us determine the cross-sectional area of the groove for placing conductors:

3.7 The criterion for the correctness of the selected dimensions is the groove fill factor, which is approximately equal to .

, (3.13)

so the selected values are correct.

4. Rotor calculation

4.1 Select the height of the air gap d graphically according to Figure 9.31. When and , .

4.2 Outer diameter of squirrel cage rotor:

4.3 The length of the rotor is equal to the length of the air gap: , .

4.4 We select the number of grooves from table 9.18,.

4.5 Determine the size of the rotor tooth division:

(4.2)

4.6 The value of the coefficient k B for calculating the shaft diameter will be determined from table 9.19. When and , .

The internal diameter of the rotor is:

4.7 Let us determine the current in the rotor rod:

where k i is a coefficient that takes into account the influence of the magnetizing current and winding resistance on the ratio, we will determine graphically at ; ;

The current reduction coefficient is determined by the formula:

Then the desired current in the rotor rod is:

4.8 Determine the cross-sectional area of the rod:

where is the permissible current density; in our case .

4.9 The rotor groove is determined according to Figure 9.40, b. We accept , , .

Let us select the magnetic induction in the rotor tooth from the gap table 9.12. Let's accept.

Let's determine the permissible tooth width:

Let's calculate the dimensions of the groove:

width b 1 and b 2:

, (4.9)

height h 1:

Let's calculate the total height of the rotor slot h P2:

Let us clarify the cross-sectional area of the rod:

4.10 Let us determine the current density in rod J 2:

(4.13)

Figure 4.1. Groove of the designed squirrel-cage motor

4.11 Calculate the cross-sectional area of the short-circuit rings q cl:

where is the current in the ring, determined by the formula:

4.12 Calculate the dimensions of the closing rings and the average diameter of the ring:

(4.18)

Let's clarify the cross-sectional area of the ring:

5. Calculation of magnetizing current

5.1 The value of inductions in the teeth of the rotor and stator:

, (5.1)

(5.2)

5.2 Let’s calculate the induction in the stator yoke B a:

5.3 Let us determine the induction in the rotor yoke B j:

, (5.4)

where h" j is the estimated height of the rotor yoke, m.

For engines with 2р≥4 with the rotor core seated on a bushing or on a ribbed shaft, h" j is determined by the formula:

5.4 Air gap magnetic voltage F d:

, (5.6)

where k d is the air gap coefficient, determined by the formula:

, (5.7)

Where

Air gap magnetic voltage:

5.5 Magnetic voltage of the stator tooth zones F z 1:

F z1 =2h z1 H z1 , (5.8)

where 2h z1 is the design height of the stator tooth, m.

H z1 is determined according to table P-1.7. At , .

5.6 Magnetic voltage of the rotor tooth zones F z 2:

, (5.9)

, table P-1.7.

5.7 Calculate the saturation coefficient of the tooth zone k z:

(5.10)

5.8 Let us find the length of the average magnetic line of the stator yoke L a:

5.9 Let us determine the field strength H a with induction B a using the magnetization curve for a yoke of the accepted steel grade 2013, Table P-1.6. At , .

5.10 Let’s find the magnetic voltage of the stator yoke F a:

5.11 Let us determine the length of the average magnetic flux line in the rotor yoke L j:

, (5.13)

where h j is the height of the rotor back, found by the formula:

5.12 The field strength H j during induction will be determined from the magnetization curve of the yoke for the adopted steel grade, Table P-1.6. At , .

Let us determine the magnetic voltage of the rotor yoke F j:

5.13 Let’s calculate the total magnetic voltage of the machine’s magnetic circuit (per pair of poles) F c:

5.14 Magnetic circuit saturation coefficient:

(5.17)

5.15 Magnetizing current:

Relative value of magnetizing current:

(5.19)

6. Operating parameters

The parameters of an asynchronous machine are the active and inductive resistance of the stator windings x 1, r 1, rotor windings r 2, x 2, mutual inductance resistance x 12 (or x m), and the calculated resistance r 12 (or r m), the introduction of which takes into account the effect of losses in stator steel on motor characteristics.

Phase replacement circuits for an asynchronous machine, based on bringing processes in a rotating machine to a stationary one, are shown in Figure 6.1. The physical processes in an asynchronous machine are more clearly reflected by the diagram shown in Figure 6.1. But for calculation it is more convenient to convert it into the diagram shown in Figure 6.2.

Figure 6.1. Phase replacement circuit for the winding of a reduced asynchronous machine

Figure 6.2. Transformed phase equivalent circuit of the winding of a reduced asynchronous machine

6.1 The active resistance of the stator winding phase is calculated using the formula:

, (6.1)

where L 1 is the total length of the effective conductors of the winding phase, m;

a is the number of parallel branches of the winding;

c 115 is the resistivity of the winding material (copper for the stator) at the design temperature. For copper ;

k r is the coefficient of increase in the active resistance of the winding phase due to the effect of current displacement.

In the conductors of the stator winding of asynchronous machines, the effect of current displacement is insignificant due to the small size of the elementary conductors. Therefore, in calculations of normal machines, as a rule, k r =1 is taken.

6.2 The total length of the conductors of the winding phase L 1 is calculated using the formula:

where l cf is the average length of the winding turn, m.

6.3 The average coil length l cp is found as the sum of the straight - grooved and curved frontal parts of the coil:

, (6.3)

where l P is the length of the groove part, equal to the design length of the machine cores. ;

l l - length of the frontal part.

6.4 The length of the front part of the stator random winding coil is determined by the formula:

, (6.4)

where K l is a coefficient, the value of which depends on the number of pole pairs, for Table 9.23;

b CT - the average width of the coil, m, determined by the arc of a circle passing through the midpoints of the height of the grooves:

, (6.5)

where b 1 is the relative shortening of the stator winding pitch. Usually accepted.

Coefficient for random windings placed in slots before the core is pressed into the housing.

Average Length:

Total length of effective winding phase conductors:

Active phase resistance of the stator winding:

6.5 Let’s determine the length of the overhang along the frontal part:

where Kvl is the coefficient determined according to table 9.23. at .

6.6 Let us determine the relative value of the phase resistance of the stator winding:

(6.7)

6.7 Let us determine the active resistance of the rotor winding phase r 2:

where r c is the resistance of the rod;

r cl - ring resistance.

6.8 We calculate the resistance of the rod using the formula:

6.9 Calculate the ring resistance:

Then the active resistance of the rotor is:

6.10 Let us reduce r 2 to the number of turns of the stator winding and determine:

6.11 Relative value of the rotor winding phase resistance.

(6.12)

6.12 Inductive resistance of the rotor winding phases:

, (6.13)

where l p is the magnetic conductivity coefficient of the slotted rotor.

Based on Figure 9.50, e l p is determined using the formula from Table 9.26:

, (6.14)

(conductors are secured with a groove cover).

, (6.15)

Frontal scattering magnetic conductivity coefficient:

The magnetic conductivity coefficient of differential scattering is determined by the formula:

, (6.17)

where is determined graphically, at , Figure 9.51, d, .

Using formula (6.13), we calculate the inductive reactance of the stator winding:

6.13 Let us determine the relative value of the inductive reactance of the stator winding:

(6.18)

6.14 Let us calculate the inductive reactance of the rotor winding phase using the formula:

where l p2 is the magnetic conductivity coefficient of the rotor slot;

l l2 – coefficient of magnetic conductivity of the frontal part of the rotor;

l d2 – coefficient of magnetic conductivity of differential rotor scattering.

The magnetic conductivity coefficient of the rotor slot is calculated using the formula based on Table 9.27:

6.15 The coefficient of magnetic conductivity of the frontal part of the rotor is determined by the formula:

6.16 The magnetic conductivity coefficient of differential rotor scattering is determined by the formula:

, (6.23)

Where .

6.17 Let’s find the value of inductive reactance using formula (6.19):

Let's reduce x 2 to the number of stator turns:

Relative value:

(6.25)

7. Calculation of losses

7.1 Let us calculate the main losses in the stator steel of an asynchronous machine using the formula:

, (7.1)

where are specific losses, table 9.28;

b – exponent, for steel grade 2013;

k yes and k d z – coefficients taking into account the effect on losses in steel, for steel grade 2013, ;

m a – yoke mass, calculated by the formula:

Where – specific gravity of steel.

Mass of stator teeth:

7.2 Let’s calculate the total surface losses in the rotor:

where p surface2 is the specific surface loss, determined by the formula:

, (7.5)

where is a coefficient that takes into account the effect of surface treatment of the heads of the rotor teeth on specific losses;

B 02 is the amplitude of induction pulsation in the air gap, determined by the formula:

where is determined graphically at Figure 9.53, b.

7.3 Let us calculate the specific surface losses using formula (7.5):

7.4 Let’s calculate pulsation losses in the rotor teeth:

, (7.7)

where m z 2 is the mass of steel of the rotor teeth;

B pool2 is the amplitude of magnetic pulsation in the rotor.

, (7.9)

7.5 Let us determine the amount of additional losses in steel:

7.6 Total losses in steel:

7.7 Let's determine mechanical losses:

where, at according to table 9.29.

7.8 Let's calculate the additional losses at nominal mode:

7.9 Motor no-load current:

, (7.14)

where I x.x.a. – active component of the no-load current, we will determine it using the formula:

where R e.1 x.x. – electrical losses in the stator at idle:

7.10 Let’s determine the power factor at idle:

(7.17)

8. Calculation of performance characteristics

8.1 Let us determine the real part of the resistance:

(8.1)

(8.2)

8.3 Motor constant:

, (8.3)

(8.4)

8.4 Let's determine the active component of the current:

8.5 Let’s determine the quantities:

8.6 Losses that do not change when slip changes:

We accept and calculate the performance characteristics when sliding is equal to: 0.005; 0.01; 0.015; 0.02; 0.0201. We write the calculation results in Table 8.1.

R 2n = 110 kW; U 1n =220/380 V; 2p=10 I 0 a =2.74 A; I 0 p =I m =61.99 A;

P c t + P fur = 1985.25 W; r 1 =0.0256 Ohm; r¢ 2 =0.0205 Ohm; c 1 =1.039;

а¢=1.0795; a=0.0266 Ohm; b¢=0; b=0.26 Ohm

Table 8.1

Performance characteristics of asynchronous motor

Calculation formula		Slip s
Calculation formula

Figure 8.1. Graph of engine power versus power P 2

Figure 8.2. Graph of engine efficiency versus power P 2

Figure 8.3. Graph of engine slip s versus power P 2

Figure 8.4. Graph of the dependence of the stator current I 1 of the motor on power P 2

9. Thermal calculation

9.1 Let us determine the excess of the temperature of the inner surface of the stator core over the air temperature inside the engine:

, (9.1)

where at and degree of protection IP23, table 9.35;

a 1 – heat transfer coefficient from the surface, we determine graphically Figure 9.68, b, .

, (9.2)

where is the coefficient of increase in losses for heat resistance class F.

9.2 Temperature difference in the insulation of the slot part of the stator winding:

, (9.4)

where P p1 is the perimeter of the cross section of the stator groove, determined by the formula:

l eq. – average equivalent thermal conductivity of the groove part, for heat resistance class F , page 452;

– average value of the thermal conductivity coefficient of internal insulation. define graphically at , , Figure 9.69.

9.3 Let us determine the temperature difference across the thickness of the insulation of the frontal parts:

, (9.6)

Where , .

The frontal parts of the stator winding are not insulated, therefore.

9.4 Let’s calculate the excess of the temperature of the outer surface of the frontal parts over the air temperature inside the car:

9.5 Let us determine the average temperature rise of the stator winding over the air temperature inside the machine:

(9.8)

9.6 Let’s calculate the average temperature rise of the air inside the machine over the ambient temperature:

where a in – we define graphically Figure 9.68, ;

– the sum of losses released into the air inside the engine:

where are the total losses in the engine at nominal mode;

Р e1 – electrical losses in the stator winding at rated mode;

Р e2 – electrical losses in the rotor winding at rated mode.

, (9.12)

where S cor. – surface area of the bed.

P r is determined graphically. At , Figure 9.70.

9.7 Let us determine the average temperature rise of the stator winding over the ambient temperature:

9.8 Let’s determine the air flow required for ventilation:

(9.14)

9.9 The air flow provided by the external fan with the design and dimensions adopted in the 4A series can be approximately determined by the formula:

, (9.15)

where and is the number and width, m, of radial ventilation ducts, page 384;

n - engine rotation speed, rpm;

Coefficient for engines with .

Those. The air flow provided by the outdoor fan is greater than the air flow required to ventilate the electric motor.

10. Calculation of performance characteristics using a pie chart

10.1 First, we determine the synchronous no-load current using the formula:

10.2 Let's calculate the active and inductive short circuit resistance:

10.3 Calculate the scale of the pie chart:

The current scale is:

where Dk is the diameter of the diagram circle, selected from the interval: , let's choose .

Power scale:

Moment scale:

(10.6)

The engine pie chart is shown below. A circle of diameter Dk with center O¢ is the geometric location of the ends of the motor stator current vector at various slips. Point A 0 determines the position of the end of the current vector I 0 during synchronous idling, and during real idling of the engine. The segment is equal to the power factor at idle. Point A 3 determines the position of the end of the stator current vector during a short circuit (s=1), the segment is the short-circuit current I. , and the angle is . Point A 2 determines the position of the end of the stator current vector at .

Intermediate points on the arc A 0 A 3 determine the position of the ends of the current vector I 1 under various loads in motor mode. The abscissa axis of the OB diagram is the line of primary power P1. The line of electromagnetic power P em or electromagnetic moments M em is line A 0 A 2. The line of useful power on the shaft (secondary power P 2) is line A ’ 0 A 3.

Figure 10.1. Pie chart

Conclusion

In this course project, an asynchronous electric motor with a squirrel cage rotor was designed. As a result of the calculation, the main indicators for an engine of a given power z and cosj were obtained, which satisfy the maximum permissible value of GOST for the 4A series of engines. The calculation and construction of the performance characteristics of the designed machine was carried out.

Thus, according to the calculation data, this engine can be given the following symbol:

4 – serial number of the series;

A – motor type – asynchronous;

315 – height of the axis of rotation;

M – nominal length of the bed according to IEC;

10 – number of poles;

U – climatic version for moderate climates;

Rated data of the designed motor:

P 2n =110 kW, U 1n =220/380 V, I 1n =216 A, cosj n =0.83, h n =0.93.

References

1. Design of electrical machines: Textbook. for universities / P79

I.P. Kopylov, B.K. Klokov, V.P. Morozkin, B.F. Tokarev; Ed. I.P. Kopylova. – 4th ed., revised. and additional - M.: Higher. school, 2005. – 767 p.: ill.

2. Voldek A.I., Popov V.V. Electrical machines. AC machines: Textbook for universities. – St. Petersburg,: – Peter, 2007. –350 p.

3. Katsman M.M. Handbook of Electrical Machines: A textbook for students of education. institutions prof. education / Mark Mikhailovich Katsman. – M.: Publishing Center “Academy”, 2005. – 480 p.

Appendix A

(required)

Figure 1. Diagram of a two-layer winding with a shortened pitch, , ,

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Electrical machines

Course project

“Design of an asynchronous motor with a squirrel-cage rotor”

Technical specifications

Design an asynchronous three-phase motor with a squirrel cage rotor:

P = 15 kW, U = 220/380 V, 2р = 2;

n = 3000 rpm, = 90%, cos = 0.89, S NOM = 3%;

h=160 M p / M n = 1.8, M max / M n = 2.7, I p / I n = 7;

design IM1001;

IP44 protection;

cooling method IC0141;

climatic version and placement category U3;

insulation heat resistance class F.

operating mode S1

Determination of basic geometric dimensions

1. First select the height of the rotation axis according to Fig. 8.17, and (hereinafter all formulas, tables and figures from) h = 150 mm.

From the table 8.6 we take the nearest smaller value h = 132 mm and a = 0.225 m (D a is the outer diameter of the stator).

2. Determine the internal diameter of the stator:

D=K D D a =0.560.225=0.126 (m)

K D - proportionality coefficient, determined according to table. 8.7.

3. Pole division

m

where 2p is the number of pole pairs.

4. Determine the estimated power:

P = (P 2 k E)/(cos)

k E - the ratio of the EMF of the stator winding to the rated voltage, determined from Fig. 8.20, k E = 0.983

- Efficiency of an asynchronous motor, according to Fig. 8.21,a, = 0.89, cos = 0.91

P 2 - power on the motor shaft, W

P = (1510 3 0.983) / (0.890.91) = 18206 (W)

5. Determine electromagnetic loads (preliminarily) according to Fig. 8.22, b:

Linear load (ratio of the current of all turns of the winding to the circumference) A = 25.310 3 (A/m)

Induction in the air gap B= 0.73 (T)

6. We select the preliminary winding coefficient depending on the type of stator winding. For single-layer windings k O1 = 0.95 0.96.

Let's take k O1 = 0.96.

7. The estimated length of the air gap is determined by the formula:

= P / (k V D 2 k O 1 AB)

k B is the field shape coefficient, preliminarily taken equal to

kV = / () = 1.11

- synchronous angular speed of the motor shaft, rad/s, calculated by the formula

rad/s

where 1 is the supply frequency, Hz

= 18206 / (1.110.126 2 3140.9625.310 3 0.73) = 0.19 (m)

8. Check the relation = / . It should be within the range of 0.19–0.87, determined from Fig. 8.25:

= 0,19 / 0,198 = 0,96

The obtained value is higher than the recommended limits, therefore we accept the next largest from the standard series (Table 8.6) height of the axis of rotation h = 160 mm. We repeat the calculations according to paragraphs. 1-8:

D a = 0.272 (m) P = (1510 3 0.984) / (0.910.89) = 18224 (W)

D = 0.560.272 = 0.152 (m) A = 3410 3 (A/m)

= (3,140,152) / 2 = 0.239 (m) B = 0.738 (T)

= 18224 / (1.110.152 2 3140.963610 3 0.738) = 0.091 (m)

= 0,091 / 0,239 = 0,38

Calculation of windings, slots and stator yoke

Definition Z 1 , 1 And sections wires windings stator

1. We determine the limiting values of tooth division 1 according to Fig. 6-15:

1 max = 18 (mm) 1 min = 13 (mm)

2. The limit values for the number of stator slots are determined by the following formulas

We accept 1 = 36, then q = Z 1 / (2pm), where m is the number of phases

q = 36 / (23) = 6

The winding is single-layer.

3. We finally determine the tooth division of the stator:

m = 1410 -3 m

4. Find the number of effective conductors in the groove (preliminarily, provided that there are no parallel branches in the winding (a = 1)):

u =

I 1H is the rated current of the stator winding, A, and is determined by the formula:

I 1H = P 2 / (mU 1H cos) = 1510 3 / (32200.890.91) = 28.06(A)

u= = 16

5. We accept a=2, then

u= au = 216 = 32

6. We get the final values:

number of turns in a winding phase

linear load

Vehicle

flow

Ф = (1) -1

k O1 - the final value of the winding coefficient, determined by the formula:

k О1 = k У k Р

k У - shortening coefficient, for a single-layer winding k У = 1

k P - distribution coefficient, determined from table. 3.16 for the first harmonic

k P = 0.957

Ф = = 0.01 (Wb)

induction in the air gap

Tl

Values A and B are within acceptable limits (Fig. 8.22b)

7. Current density in the stator winding (preliminary):

J 1 = (AJ 1)/ A= (18110 9)/ (33.810 3)= 5.3610 6 (A/m 2)

the product of the linear load and the current density is determined from Fig. 8.27, b.

Effective conductor cross-section (preliminary):

q EF = I 1 H / (aJ 1) = 28.06 / (25.1310 6) = 2.7310 -6 (m 2) = 2.73 (mm 2)

We accept n EL = 2, then

q EL = q EF / 2 = 2.73 / 2 = 1.365 (mm 2)

n EL - number of elementary conductors

q EL - section of an elementary conductor

We select the PETV winding wire (according to Table A3.1) with the following data:

nominal diameter of bare wire d EL = 1.32 mm

average diameter of insulated wire d IZ = 1.384 mm

cross-sectional area of bare wire q EL = 1.118 mm 2

cross-sectional area of the effective conductor q EF = 1.1182 = 2.236 (mm 2)

9. Current density in the stator winding (final)

Calculation sizes jagged zones stator And air gap

Groove stator - according to Fig. 1, a with a size ratio that ensures parallelism of the side edges of the teeth.

1. We accept in advance according to the table. 8.10:

the induction value in the stator teeth B Z1 = 1.9 (T) the induction value in the stator yoke B a = 1.6 (T), then the tooth width

b Z1 =

k C - coefficient of core filling with steel, according to table. 8.11 for oxidized steel sheets grade 2013 k C = 0.97

СТ1 - length of steel stator cores, for machines with 1.5 mm

ST1 = 0.091 (m)

b Z1 = = 6.410 -3 (m) = 6.4 (mm)

stator yoke height

2. The dimensions of the groove in the stamp are:

groove slot width b W = 4.0 (mm)

groove slot height h W = 1.0 (mm), = 45

groove height

h P = h a = =23.8 (mm) (25)

width of the bottom of the groove

b 2 = = = 14.5 (mm) (26)

width of the upper part of the groove

b 1 = = = 10.4 (mm) (27)

h 1 = h P - + = = 19.6 (mm) (28)

3. Clearance dimensions of the groove, taking into account assembly allowances:

for h = 160 250 (mm) b P = 0.2 (mm); h P = 0.2 (mm)

b 2 = b 2 - b P = 14.5 - 0.2 = 14.3 (mm) (29)

b 1 = b 1 - b P = 10.4 - 0.2 = 10.2 (mm) (30)

h 1 = h 1 - h P = 19.6 - 0.2 = 19.4 (mm) (31)

Cross-sectional area of the groove for placing conductors:

S P = S FROM S PR

cross-sectional area of gaskets S PR = 0

cross-sectional area of body insulation in the groove

S FROM = b FROM (2h P +b 1 +b 2)

b IZ - one-sided insulation thickness in the groove, according to table. 3.1 b IZ = 0.4 (mm)

S FROM = 0.4(223.8+14.5+10.4) = 29 (mm 2)

S P = 0.5(14.3+10.2)19.4 29 = 208.65 (mm 2)

4. Groove filling coefficient:

k Z = [(d IZ) 2 u n n EL ] / S P = (1.405 2 402)/ 208.65 = 0.757 (34)

The obtained value of k3 for mechanized winding installation is excessively high. The fill factor should be in the range of 0.70 - 0.72 (from Table 3-12). Let's reduce the fill factor by increasing the cross-sectional area of the groove.

Let's take B Z1 = 1.94 (T) and B a = 1.64 (T), which is acceptable, since these values exceed the recommended ones by only 2.5 - 3%.

5. Repeat the calculation according to paragraphs. 1-4.

b Z1 = = 0.0063(m)= 6.3(mm) b 2 = = 11.55 (mm)

h a = = 0.0353 (m) = 35.3 (mm) b 1 = = 8.46 (mm)

h P = = 24.7 (mm) h 1 = = 20.25 (mm)

b 2 = = 11.75 (mm)

b 1 = = 8.66 (mm)

h 1 = = 20.45 (mm)

S FROM = = 29.9 (mm 2)

S P = = 172.7 (mm 2)

k З = = 0.7088 0.71

The dimensions of the groove in the die are shown in Fig. 1, a.

Calculation of windings, slots and rotor yoke

1. Determine the air gap (according to Fig. 8.31): = 0.8 (mm)

2. Number of rotor slots (according to Table 8.16): Z 2 = 28

3. External diameter:

D 2 = D2 = 0.15220.810 -3 = 0.150 (m) (35)

4. Length of rotor magnetic circuit 2 = 1 = 0.091 (m)

5. Tooth division:

t 2 = (D 2)/ Z 2 = (3,140,150)/ 28 = 0.0168 (m) = 16.8 (mm) (36)

6. The internal diameter of the rotor is equal to the diameter of the shaft, since the core is directly mounted on the shaft:

D J = D B = k B D a = 0.230.272 = 0.0626 (m) 60 (mm) (37)

The value of the coefficient kB is taken from the table. 8.17: kV = 0.23

7. Preliminary current value in the rotor rod:

I 2 = k i I 1 i

k i is a coefficient that takes into account the influence of the magnetizing current and winding resistance on the I 1 / I 2 ratio. k i = 0.2+0.8cos = 0.93

i - current reduction coefficient:

i = (2m 1 1 k O 1) / Z 2 = (23960.957) / 28 = 19.7

I 2 = 0.9328.0619.7 = 514.1 (A)

8. Cross-sectional area of the rod:

q C = I 2 / J 2

J 2 - current density in the rotor rods; when filling the grooves with aluminum, it is selected within

J 2 = (2.53.5)10 6 (A/m 2)

q C = 514.1 / (3.510 6) = 146.910 -6 (m 2) = 146.9 (mm 2)

9. Rotor groove - as shown in Fig. 1. b. We design pear-shaped closed grooves with slot dimensions b W = 1.5 mm and h W = 0.7 mm. We choose the height of the jumper above the groove equal to h W = 1 mm.

Permissible tooth width

b Z2 = = = 7.010 -3 (m) = 7.0 (mm) (41)

B Z2 - induction in the rotor teeth, according to table. 8.10 V Z2 = 1.8 (T)

Groove dimensions

b 1 ===10.5 (mm)

b 2 = = = 5.54 (mm) (43)

h 1 = (b 1 - b 2)(Z 2 / (2)) = (10.5 - 5.54)(28/6.28) = 22.11 (mm) (44)

We take b 1 = 10.5 mm, b 2 = 5.5 mm, h 1 = 22.11 mm.

10. We specify the width of the rotor teeth

b Z2 = = 9.1 (mm)

b Z2 = = 3.14 9.1 (mm)

b Z2 = b Z2 9.1 (mm)

Full groove height:

h P 2 = h Ш + h Ш +0.5b 1 +h 1 +0.5b 2 = 1+0.7+0.510.5+22.11+0.55.5 = 31.81 (mm)

Rod cross section:

q C = (/8)(b 1 b 1 +b 2 b 2)+0.5(b 1 +b 2)h 1 =

(3.14/8)(10.5 2 +5.5 2)+0.5(10.5+5.5)22.11 = 195.2 (mm 2)

11. Current density in the rod:

J 2 = I 2 / q C = 514.1 / 195.210 -6 = 3.4910 6 (A/m 2)

12. Short circuit rings. Cross-sectional area:

qKL = IKL / JKL

JKL - current density in the closing rings:

JCL = 0.85J2 = 0.853.49106 = 2.97106 (A/m2) (51)

ICL - current in rings:

ICL = I2 /

= 2sin = 2sin = 0.224 (53)

ICL = 514.1 / 0.224 = 2295.1 (A)

qKL = 2295 / 2.97106 = 772.710-6 (m2) = 772.7 (mm2)

13. Dimensions of closing rings:

hKL = 1.25hP2 = 1.2531.8 = 38.2 (mm) (54)

bKL = qKL / hKL = 772.7 / 38.2 = 20.2 (mm) (55)

qKL = bKLhKL = 38.2 20.2 = 771.6 (mm2) (56)

DK. CP = D2 - hKL = 150 - 38.2 = 111.8 (mm) (57)

Magnetic circuit calculation

Steel magnetic core 2013; sheet thickness 0.5 mm.

1. Air gap magnetic voltage:

F= 1.5910 6 Bk, where (58)

k- air gap coefficient:

k= t 1 /(t 1 -)

= = = 2,5

k= = 1.17

F= 1.5910 6 0.7231.170.810 -3 = 893.25 (A)

2. Magnetic voltage of tooth zones:

stator

F Z1 = 2h Z1 H Z1

h Z1 - estimated height of the stator tooth, h Z1 = h P1 = 24.7 (mm)

H Z1 - the value of the field strength in the stator teeth, according to table P1.7 at B Z1 = 1.94 (T) for steel 2013 H Z1 = 2430 (A/m)

F Z1 = 224.710 -3 2430 = 120 (A)

calculated induction in teeth:

B Z1 = = = 1.934 (T)

since B Z1 is 1.8 (T), it is necessary to take into account the flow branch into the groove and find the actual induction in the tooth B Z1.

Coefficient k PH height h ZX = 0.5h Z:

k PH =

b PH = 0.5(b 1 + b 2) = 0.5(8.66+11.75) = 12.6

k PH = = 2.06

B Z1 = B Z1 - 0 H Z1 k PH

We accept B Z1 = 1.94 (T), check the ratio of B Z1 and B Z1:

1,94 = 1,934 - 1,25610 -6 24302,06 = 1,93

rotor

F Z2 = 2h Z2 H Z2

h Z2 - design height of the rotor tooth:

h Z2 = h P2 - 0.1b 2 = 31.8 - 0.15.5 = 31.25 (mm)

H Z2 - the value of the field strength in the rotor teeth, according to table P1.7 at B Z2 = 1.8 (T) for steel 2013 H Z2 = 1520 (A/m)

F Z2 = 231.25 10 -3 1520 = 81.02 (A)

tooth induction

B Z2 = = = 1.799 (T) 1.8 (T)

3. Saturation coefficient of the tooth zone

k Z = 1+= 1+= 1.23

4. Yoke magnetic voltage:

stator

F a = L a H a

L a - length of the average magnetic line of the stator yoke, m:

L a = = = 0.376 (m)

H a - field strength, according to table P1.6 at B a = 1.64 (T) H a = 902 (A/m)

F a = 0.376902 = 339.2 (A)

B a =

h a - design height of the stator yoke, m:

h a = 0.5(D a - D) - h P 1 = 0.5(272 - 152) - 24.7 = 35.3 (mm)

B a = = 1.6407 (T) 1.64 (T)

rotor

F j = L j H j

L j is the length of the average magnetic flux line in the rotor yoke:

Lj = 2hj

h j - height of the rotor back:

h j = - h P2 = - 31.8 = 13.7 (mm)

L j = 213.7 10 -3 = 0.027 (m)

B j =

h j - design height of the rotor yoke, m:

h j = = = 40.5 (mm)

B j = = 1.28 (T)

H j - field strength, according to table P1.6 at B j = 1.28 (T) H j = 307 (A/m)

F j = 0.027307 = 8.29 (A)

5. Total magnetic voltage of the magnetic circuit per pair of poles:

F C = F + F Z1 + F Z2 + F a + F j = 893.25 + 120 + 81.02 + 339.2 + 8.29 = 1441.83 (A)

6. Magnetic circuit saturation coefficient:

k = F C / F = 1441.83/893.25 = 1.6

7. Magnetizing current:

I = = = 7.3 (A)

relative value

I = I / I 1H = 7.3 / 28.06 = 0.26

Calculation of parameters of an asynchronous machine for nominal mode

1. Active resistance of the stator winding phase:

r 1 = 115

115 - specific resistance of the winding material at the design temperature, Ohm. For insulation heat resistance class F, the design temperature is 115 degrees. For copper 115 = 10 -6 /41 Ohm.

L 1 - total length of effective conductors of the stator winding phase, m:

L 1 = CP1 1

CP1 - average length of stator winding turn, m:

CP1 = 2(P1 + L1)

P1 - length of the groove part, P1 = 1 = 0.091 (m)

L1 - frontal part of the coil

L1 = K L b CT +2V

K L - coefficient, the value of which is taken from table 8.21: K L = 1.2

B is the length of the straight part of the coil extending from the groove from the end of the core to the beginning of the bend of the frontal part, m. We take B = 0.01.

b CT - average coil width, m:

b CT = 1

1 - relative shortening of the stator winding pitch, 1 = 1

b CT = = 0.277 (m)

L1 = 1.20.277+20.01 = 0.352 (m)

CP1 = 2(0.091+0.352) = 0.882 (m)

L 1 = 0.88296 = 84.67 (m)

r 1 = = 0.308 (Ohm)

Extension length of the front part of the coil

OUT = K OUT b CT +B = 0.260.277+0.01= 0.08202 (m)= 82.02 (mm) (90)

According to table 8.21 K OUT = 0.26

Relative value

r 1 = r 1 = 0.308 = 0.05

2. Active resistance of the rotor winding phase:

r 2 = r C +

r C - rod resistance:

r C = 115

for cast aluminum rotor winding 115 = 10 -6 / 20.5 (Ohm).

r C = = 22.210 -6 (Ohm)

r CL - resistance of the section of the closing ring enclosed between two adjacent rods

r CL = 115 = = 1.0110 -6 (Ohm) (94)

r 2 = 22.210 -6 + = 47.110 -6 (Ohm)

We reduce r 2 to the number of turns of the stator winding:

r 2 = r 2 = 47.110 -6 = 0.170 (Ohm) (95)

Relative value:

r 2 = r 2 = 0.170 = 0.02168 0.022

3. Inductive resistance of the stator winding phase:

x 1 = 15.8(P1 + L1 + D1), where (96)

P1 - coefficient of magnetic conductivity of slot scattering:

P1 =

h 2 = h 1 - 2b IZ = 20.45 - 20.4 = 19.65 (mm)

b 1 = 8.66 (mm)

h K = 0.5(b 1 - b) = 0.5(8.66 - 4) = 2.33 (mm)

h 1 = 0 (conductors are secured with a groove cover)

k = 1 ; k = 1 ; = = 0.091 (m)

P1 = = 1.4

L1 - coefficient of magnetic conductivity of frontal scattering:

L1 = 0.34(L1 - 0.64) = 0.34(0.352 - 0.640.239) = 3.8

D1 - coefficient of magnetic conductivity of differential scattering

D1 =

= 2k SK k - k O1 2 (1+ SK 2)

k = 1

SK = 0, since there is no bevel of the grooves

k SC is determined from the curves in Fig. 8.51,d depending on t 2 /t 1 and SC

= = 1.34 ; SK = 0; k SC = 1.4

= 21,41 - 0,957 2 1,34 2 = 1,15

D1 = 1.15 = 1.43

x 1 = 15.8(1.4+3.8+1.43) = 0.731 (Ohm)

Relative value

x 1 = x 1 = 0.731 = 0.093

4. Inductive reactance of the rotor winding phase:

x 2 = 7.9 1 (P2 + L2 + D2 + SK)10 -6 (102)

P2 = k D +

h 0 = h 1 +0.4b 2 = 17.5+0.45.5 = 19.7 (mm)

k D = 1

P2 = = 3.08

L2 = = = 1.4

D2 =

= = = 1,004

since with closed slots Z 0

D2 = = 1.5

x 2 = 7.9500.091(3.08+1.4+1.5)10 -6 = 21510 -6 (Ohm)

We reduce x 2 to the number of stator turns:

x 2 = x 2 = = 0.778 (Ohm)

Relative value

x 2 = x 2 = 0.778 = 0.099 (108)

Power loss calculation

1. Main losses in steel:

P ST. OSN. = P 1.0/50 (k Yes B a 2 m a +k DZ B Z1 2 +m Z1)

P 1.0/50 - specific losses at an induction of 1 T and a magnetization reversal frequency of 50 Hz. According to the table 8.26 for steel 2013 P 1.0/50 = 2.5 (W/kg)

m a - mass of stator yoke steel, kg:

m a = (D a - h a)h a k C1 C =

= 3.14(0.272 - 0.0353)0.03530.0910.977.810 3 = 17.67 (kg)

C - specific gravity of steel; in calculations we take C = 7.810 3 (kg/m 3)

m Z1 - mass of stator teeth steel, kg:

m Z1 = h Z1 b Z1 CP. Z 1 CT 1 k C 1 C =

= 24.710 -3 6.310 -3 360.0910.977.810 3 = 3.14 (kg) (111)

k Yes and k ДZ are coefficients that take into account the influence on losses in steel of uneven flux distribution across sections of magnetic core sections and technological factors. Approximately we can take k Da = 1.6 and k DZ = 1.8.

PCT. OSN. = 2.51(1.61.64217.67+1.81.93423.14) = 242.9 (W)

2. Surface losses in the rotor:

PPOV2 = pPOV2(t2 - bSH2)Z2ST2

pSOV2 - specific surface losses:

pPOV2 = 0.5k02(B02t1103)2

B02 - amplitude of induction pulsation in the air gap above the crowns of the rotor teeth:

B02=02

02 depends on the ratio of the slot width of the stator slots to the air gap. 02 (at bШ1/ = 4/0.5 = 8 according to Fig. 8.53, b) = 0.375

k02 is a coefficient that takes into account the effect of surface treatment of the heads of the rotor teeth on specific losses. Let's take k02 =1.5

B02 = 0.3571.180.739 = 0.331 (T)

pPOV2 = 0.51.5(0.33114)2 = 568 (16.8 - 1.5)24 0.091 = 22.2 (W)

3. Pulsation losses in the rotor teeth:

PPUL2 = 0.11mZ2

BPUL2 - amplitude of induction pulsations in the middle section of the teeth:

BPUL2 = BZ2

mZ2 - mass of steel rotor teeth, kg:

mZ2 = Z2hZ2bZ2СТ2kC2C =

= 2826.6510-39.110-30.0910.977.8103 = 3.59 (kg) (117)

BPUL2 = = 0.103 (T)

PPUL2 = 0.11= 33.9 (W)

4. Amount of additional losses in steel:

PCT. ADD. = PPOV1+PPUL1+PPOV2+PPUL2 = 22.2 + 33.9 = 56.1 (W

5. Total losses in steel:

PCT. = PST. OSN. + PST. ADD. = 242.9 + 56.1 = 299 (W

6. Mechanical losses:

PMECH = KTDa4 = 0.2724 = 492.6 (W) (120)

For engines with 2р=2 KT =1.

7. Engine idling:

IX. X.

IХ.Х.а. =

PE1 H.H. = mI2r1 = 37.320.308 = 27.4 (W)

IХ.Х.а. = = 1.24 (A)

IX.H.R. I = 7.3 (A)

IХ.Х. = = 7.405 (A)

cos xx = IX.X.a / IX.X. = 1.24/4.98 = 0.25

asynchronous three-phase motor squirrel cage rotor

Performance calculation

1. Parameters:

r 12 = P ST. OSN. /(mI 2) = 242.9/(37.3 2) = 3.48 (Ohm)

x 12 = U 1H /I - x 1 = 220/7.3 - 1.09 = 44.55 (Ohm)

c 1 = 1+x 1 / x 12 = 1+0.731/44.55 = 1.024 (Ohm)

= = =

= arctan 0.0067 = 0.38 (23) 1 o

Active component of the synchronous no-load current:

I 0a = (P ST. BASIC +3I 2 r 1) / (3U 1H) = = 0.41 (A)

a = c 1 2 = 1.024 2 = 1.048

b = 0

a = c 1 r 1 = 1.0240.308 = 0.402 (Ohm)

b = c 1 (x 1 +c 1 x 2) = 1.024(0.731+1.0241.12) = 2.51 (Ohm)

Losses that do not change when slip changes:

P ST. +P FUR = 299+492.6 = 791.6 (W)

Calculation formulas	Dimension	Slip S




Z = (R 2 +X 2) 0.5



I 1a = I 0a +I 2 cos 2
I 1p = I 0p +I 2 sin 2
I 1 = (I 1a 2 +I 1p 2) 0.5

P 1 = 3U 1 I 1a 10 -3
P E 1 = 3I 1 2 r 1 10 -3
P E 2 = 3I 2 2 r 2 10 -3
P ADD = 0.005P 1
P=P ST +P MECH +P E1 +P E2 +P ADD

Table 1. Induction motor performance characteristics

P2NOM = 15 kW; I0p = I = 7.3 A; PCT. +PMECH. = 791.6 W

U1NOM = 220/380 V; r1 =0.308 Ohm; r2 = 0.170 Ohm

2р=2 ; I0a = 0.41 A; c1 = 1.024; a = 1.048; b = 0 ;

a = 0.402 (Ohm); b = 2.51 (Ohm)

2. Calculate performance characteristics for sliding

S = 0.005;0.01;0.015

0.02;0.025;0.03;0.035, preliminary assuming that SNOM r2 = 0.03

The calculation results are summarized in table. 1. After constructing the performance characteristics (Fig. 2), we clarify the value of the nominal slip: SН = 0.034.

Rated data of the designed motor:

P2NOM = 15 kW cos NOM = 0.891

U1NOM = 220/380 V NOM = 0.858

I1NOM =28.5 A

Calculation of starting characteristics

Calculation currents With taking into account influence changes parameters under influence effect repression current (without accounting influence nasy tion from fields scattering)

Detailed the calculation is given for S = 1. The calculation data for the remaining points are summarized in table. 2.

1. Active resistance of the rotor winding taking into account the influence of the current displacement effect:

= 2h C = 63.61h C = 63.610.0255= 1.62 (130)

calc = 115 o C; 115 = 10 -6 /20.5 (Ohm); b C /b P =1; 1 = 50 Hz

h C = h P - (h W + h W) = 27.2 - (0.7+1) = 25.5 (mm)

- “reduced height” of the rod

according to fig. 8.57 for = 1.62 we find = 0.43

h r = = = 0.0178 (m)= 17.8 (mm)

since (0.510.5) 17.8 (17.5+0.510.5):

q r =

h r - depth of current penetration into the rod

q r - cross-sectional area limited by height h r

b r = = 6.91 (mm)

q r = = 152.5 (mm 2)

k r = q C /q r = 195.2 / 152.5 = 1.28 (135)

K R = = 1.13

r C = r C = 22.210 -6 (Ohm)

r 2 = 47.110 -6 (Ohm)

Reduced rotor resistance taking into account the influence of current displacement effect:

r 2 = K R r 2 = 1.130.235 = 0.265 (Ohm)

2. Inductive reactance of the rotor winding taking into account the influence of the current displacement effect:

for = 1.62 = kD = 0.86

KX = (P2 +L2 +D2)/(P2 +L2 +D2)

P2 = P2 - P2

P2 = P2(1- kD) = =

= = 0,13

P2 = 3.08 - 0.13 = 2.95

KX = = 0.98

x2 = KXx2 = 0.980.778 = 0.762 (Ohm)

3. Starting parameters:

Mutual induction reactance

x 12P = k x 12 = 1.644.55 = 80.19 (Ohm) (142)

with 1P = 1+x 1 / x 12P = 1+1.1/80.19 = 1.013 (143)

4. Calculation of currents taking into account the influence of the current displacement effect:

R P = r 1 +c 1 P r 2 /s = 0.308+1.0130.265 = 0.661 (Ohm)

Calculation formulas	Dimension	Slip S

63.61h C S 0.5



K R =1+(r C /r 2)(k r - 1)





R P = r 1 +c 1 P r 2 /s
X P = x 1 +c 1P x 2
I 2 = U 1 / (R P 2 +X P 2) 0.5
I 1 = I 2 (R P 2 + +(X P +x 12 P) 2) 0.5 /(c 1 P x 12 P)

Table 2. Calculation of currents in the starting mode of an asynchronous motor with a squirrel-cage rotor, taking into account the influence of the current displacement effect

P2NOM = 15 kW; U1 = 220/380 V; 2р=2 ; I1NOM = 28.5 A;

r2 = 0.170 Ohm; x12P = 80.19 Ohm; s1P = 1.013; SNOM = 0.034

XП = x1 + s1Пх2 = 0.731+1.0130.762 = 1.5 (Ohm)

I2 = U1 / (RP2+HP2)0.5= 220/(0.6612+1.52)0.5= 137.9 (A)

I1 = I2 (RP2+(HP+x12P)2)0.5/ (c1Px12P)=

=137.9(0.6612+(1.5+80.19)2)0.5/(1.01380.19)= 140.8 (A)

Calculation launchers characteristics With taking into account influence effect repression current And saturation from fields scattering

Calculation carry out for characteristic points corresponding to S=1; 0.8; 0.5;

0.2; 0.1, in this case we use the values of currents and resistances for the same slips, taking into account the influence of current displacement.

The calculation data are summarized in table. 3. Detailed calculation is given for S=1.

1. Inductive resistance of the windings. We accept k US =1.35:

Average MMF of the winding, related to one slot of the stator winding:

F P. SR. = = = 3916.4 (A)

C N = = 1.043

Fictitious leakage flux induction in the air gap:

B Ф =(F P. SR. /(1.6С N))10 -6 =(3916.410 -6)/(1.60.810 -3 1.043)=5.27(T)

for B Ф = 5.27 (T) we find k = 0.47

Magnetic conductivity coefficient of slot leakage of the stator winding taking into account the influence of saturation:

сЭ1 = (t1 - bШ1)(1 - к) = (14 - 4)(1 - 0.47) = 6.36

P1 US. =((hШ1 +0.58hK)/bШ1)(сЭ1/(сЭ1+1,5bШ1))

hK = (b1 - bШ1)/2 = (10.5 - 4)/2 = 3.25 (153)

P1 US. =

P1 US. = P1 - P1 US. = 1.4 - 0.37 = 1.03

Magnetic conductivity coefficient of differential leakage of the stator winding taking into account the influence of saturation:

D1 US. = D1k = 1.430.47 = 0.672

Inductive resistance of the stator winding phase taking into account the influence of saturation:

x1 US. = (x11 US)/ 1 = = 0.607 (Ohm)

Magnetic conductivity coefficient of slot leakage of the rotor winding taking into account the influence of saturation and current displacement:

P2. US. = (hШ2/bШ2)/(cЭ2/(сЭ2+bШ2))

сЭ2 = (t2 - bШ2)(1 - к) = (16.8 - 1.5)(1 - 0.47) =10.6

hШ2 = hШ +hШ = 1+0.7 = 1.7 (mm)

P2. US. =

P2. US. = P2 - P2. US. = 2.95 - 0.99 = 1.96

Magnetic conductivity coefficient of rotor differential leakage taking into account the influence of saturation:

D2. US. = D2k = 1.50.47 = 0.705

Reduced inductive reactance of the rotor winding phase taking into account the influence of current displacement and saturation effects:

x2 US = (x22 US)/ 2 = = 0.529 (Ohm)

s1P. US. = 1+ (x1 NAS./x12 P) = 1+(0.85/80.19) = 1.011

Calculation formulas	Dimension	Slip S



BФ =(FP.SR.10-6) / (1.6CN)

сЭ1 = (t1 - bШ1)(1 - к)
P1 US. = P1 - P1 US.
D1 US. = to D1
x1 US. = x11 US. / 1
c1P. US. = 1+x1 US. / x12P
сЭ2 = (t2 - bШ2)(1 - к)
P2 US. = P2 - P2 US.
D2 US. = to D2
x2 US. = x22 US. /2
RP. US. = r1+c1П. US. r2/s
XP.US=x1US.+s1P.US.x2US
I2US=U1/(RP.US2+HP.US2)0.5
I1 US=I2 US (RP.NAS2+(HP.NAS+ x12P) 2) 0.5/(c1P.NASx12P)
kUS. = I1 US. /I1
I1 = I1 US. /I1 NOM
M = (I2US/I2NOM)2КR(sHOM/s)

Table 3. Calculation of the starting characteristics of an asynchronous motor with a squirrel-cage rotor, taking into account the effect of current displacement and saturation from stray fields

P2NOM = 15 kW; U1 = 220/380 V; 2р=2 ; I1NOM = 28.06 A;

I2NOM = 27.9 A; x1 = 0.731 Ohm; x2 = 0.778 Ohm; r1 = 0.308 Ohm;

r2 = 0.170 Ohm; x12P = 80.19 Ohm; СN = 1.043; SNOM = 0.034

2. Calculation of currents and moments

RP. US. = r1+c1П. US. r2/s = 0.393+1.0110.265 = 0.661 (Ohm) (165)

XP.NAS.=x1NAS.+s1P.NAS.x2NAS. = 1.385 (Ohm) (166)

I2NAS.=U1/(RP.NAS2+HP.NAS2)0.5= 220/(0.6612+1.3852)0.5= 187.6 (A)

I1 US. = I2NAS.= = 190.8 (A) (168)

IP = = 6.8

M = = = 1.75

kUS. = I1 US. /I1 = 190.8/140.8 = 1.355

kUS. differs from the one accepted by US. = 1.35 by less than 3%.

To calculate other characteristic points, we set kNAS. , reduced depending on the current I1. We accept when:

s = 0.8 kUS. = 1.3

s = 0.5 kUS. = 1.2

s = 0.2 kUS. = 1.1

s = 0.1 kUS. = 1.05

The calculation data are summarized in table. 3, and the starting characteristics are presented in Fig. 3.

3. The critical slip is determined after calculating all points of the starting characteristics (Table 3) using the average resistance values x1 of the NAS. and x2 US. , corresponding to slips s = 0.2 0.1:

sKR = r2 / (x1 NAS / c1P NAS + x2 NAS) = 0.265/(1.085/1.0135+1.225) = 0.12

The designed asynchronous motor meets the requirements of GOST both in terms of energy indicators (and cos) and starting characteristics.

Thermal calculation

1. The temperature of the inner surface of the stator core exceeds the air temperature inside the engine:

pov1 =

PE. P1 - electrical losses in the slot part of the stator winding

PE. P1= kPE1= = 221.5 (W)

PE1 = 1026 W (from table 1 at s = sNOM)

k = 1.07 (for windings with insulation class F)

K = 0.22 (according to table 8.33)

1 - heat transfer coefficient from the surface; 1 = 152 (W/m 2 C)

pov1 =

2. Temperature difference in the insulation of the slot part of the stator winding:

from. n1 =

P P1 = 2h PC +b 1 +b 2 = 220.45+8.66+11.75 = 66.2 (mm) = 0.0662 (m)

EKV - average equivalent thermal conductivity of groove insulation, for heat resistance class F EKV = 0.16 W/(mS)

EKV - average value of the thermal conductivity coefficient, according to Fig. 8.72 at

d/d IZ = 1.32/1.405 = 0.94 EKV = 1.3 W/(m 2 C)

from. n1 = = 3.87 (C)

3. Temperature difference across the thickness of the insulation of the frontal parts:

from. l1=

PE. L1 - el. losses in the frontal part of the stator winding

PE. L1 = kPE1= = 876 (W)

PL1 = PP1 = 0.0662 (m)

bIZ. L1 MAX =0.05

from. l1= = 1.02 (C)

4. The temperature of the outer surface of the frontal parts exceeds the air temperature inside the engine:

pov l1 = = 16.19 (C)

5. Average temperature rise of the stator winding over the air temperature inside the engine

1 = =

= = 24.7 (C)

6. The air temperature inside the engine exceeds the ambient temperature

B =

P B - the sum of losses released into the air inside the engine:

P B = P - (1 - K)(P E. P1 +P ST. BASIC) - 0.9P MEC

P is the sum of all losses in the engine at rated mode:

P = P +(k - 1)(PE1+PE2) = 2255+(1.07 - 1)(1026+550) = 2365 (W)

PV = 2365 - (1 - 0.22)(221.5+242.9) - 0.9492.6 = 1559 (W)

SCOR - equivalent cooling surface of the housing:

SCOR = (Da+8PR)(+2OUT1)

PR - conditional perimeter of the cross section of the ribs of the engine housing, for h = 160 mm PR = 0.32.

B is the average value of the air heating coefficient, according to Fig. 8.70, b

B = 20 W/m2C.

SCOR = (3.140.272+80.32)(0.091+282.0210-3) = 0.96 (m2)

B = 1559/(0.9620) = 73.6 (C)

7. Average temperature rise of the stator winding over the ambient temperature:

1 = 1 +B = 24.7+73.6 = 98.3 (C)

8. Checking engine cooling conditions:

Air flow required for cooling

B =

km = = 9.43

For engines with 2р=2 m= 3.3

B = = 0.27 (m3/s)

Air flow provided by outdoor fan

B = = 0.36 (m3/s)

The heating of engine parts is within acceptable limits.

The fan provides the necessary air flow.

Conclusion

The designed engine meets the requirements set in the technical specifications.

List of used literature

1. I.P. Kopylov “Design of electrical machines” M.: “Energoatomizdat”, 1993. Part 1,2.

2. I.P. Kopylov “Design of electrical machines” M.: “Energy”, 1980.

3. A.I. Woldek “Electric machines” L.: “Energy”, 1978.

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COURSE PROJECT

in the discipline "Electrical machines"

DESIGN OF AN INDUCTION MOTOR WITH A SQUIRED ROTOR

Explanatory note

Annotation

The explanatory note for the course project in the discipline "Electromechanics" presents the electromagnetic, thermal and ventilation calculation of a six-pole three-phase asynchronous motor with a squirrel-cage rotor with a useful power of 2.2 kW for a network voltage of 220/380 V.

The calculation of the asynchronous motor was carried out manually and using a computer. As a result of engine design, a design version was obtained that meets the requirements of the technical specifications.

For the designed asynchronous motor, a mechanical calculation of the shaft was performed and bearings were selected. The dimensions of the engine structural elements have been determined.

The explanatory note contains 63 sheets of typewritten text, including 4 figures, 2 tables and a list of sources used from 3 titles.

Introduction………………………………………………………………………………….…………....5

1 Selection of main sizes………………………...……………………………7

2 Determination of stator parameters, calculation of the winding and dimensions of the stator tooth zone…………………………………………………………………………………..….9

3 Selection of air gap……………………………...………………….17

4 Calculation of a squirrel-cage rotor……………….....………………………..18

5 Calculation of the magnetic circuit……………………………….………………………...22

6 Operating mode parameters……………………………………………………………..27

7 Calculation of power losses in idle mode….…..…………………...34

8 Calculation of performance characteristics………………………………………….…..…38

9 Calculation of starting characteristics…………………………………………….....45

10 Thermal and ventilation calculation………………………………………………………..…..55

11 Engine design……………………………………………………………..60

Conclusion…………………………………………………………….………………………….62

List of sources used...................................................................63

Introduction

Asynchronous motors are the main motors in electric drives of almost all industrial enterprises. In the USSR, the production of asynchronous motors exceeded 10 million units per year. The most common are motors with rated voltages up to 660 V, the total installed power of which is about 200 million kW.

Engines of the 4A series were produced in mass quantities in the 80s of the 20th century and are currently in use at almost all industrial enterprises in Russia. The series covers a power range from 0.6 to 400 kW and is built in 17 standard pivot heights from 50 to 355 mm. The series includes basic engine versions, a number of modifications and specialized versions. The main version motors are designed for normal operating conditions and are general purpose motors. These are three-phase asynchronous motors with a squirrel-cage rotor, designed for a mains frequency of 50 Hz. They have a protection degree of IP44 over the entire range of heights of the rotation axis and IP23 in the range of heights of the rotation axes 160...355 mm.

Modifications and specialized versions of engines are built on the basis of the main version and have the same fundamental design solutions of the main elements. Such motors are produced in separate sections of the series at certain heights of the rotation axis, and are intended for use as drives of mechanisms that impose specific requirements on the motor or operate in conditions different from normal in terms of temperature or cleanliness of the environment.

Electrical modifications of the 4A series motors include motors with increased rated slip, increased starting torque, multi-speed, and a supply frequency of 60 Hz. Design modifications include wound-rotor motors, with a built-in electromagnetic brake, low noise, and with built-in temperature protection.

According to environmental conditions, modifications of engines are distinguished: tropical, moisture-freeze-resistant, chemical-resistant, dust-proof and agricultural.

Elevator motors have a specialized design, frequency-controlled, high-precision.

Most motors of the 4A series have a degree of protection IP44 and are produced in a design belonging to group IM1, i.e. with a horizontal shaft, on feet, with two bearing shields. The engine housing is made with longitudinal radial ribs, increasing the cooling surface and improving heat transfer from the engine to the surrounding air. At the opposite end of the shaft from the working end there is a fan that circulates cooling air along the ribs of the housing. The fan is covered with a casing with holes for air passage.

The magnetic core of the motors is laminated from sheets of electrical steel 0.5 mm thick, and motors with h = 50...250 mm are made of steel grade 2013, and motors with h = 280...355 mm are made of steel grade 2312.

In all engines of the series with h< 280 мм и в двигателях с 2p = 10 и 12 всех высот оси вращения обмотка статора выполнена из круглого провода и пазы статора полузакрытые. При h = 280…355 мм, кроме двигателей с 2p = 10 и 12, катушки обмотки статора намотаны прямоугольным проводом, подразделенные и пазы статора полуоткрытые.

The winding of the squirrel-cage rotor blades and rings are cast aluminum. Ventilation blades on the rotor rings serve to move the air inside the machine.

Bearing shields are attached to the housing using four or six bolts.

The terminal box is located on top of the frame, which facilitates installation work when connecting the motor to the network.

1 Selection of main sizes

Based on the requirements of the technical specifications sheet, for the base one we select the engine of the 4А100S6У3 series according to Appendix A /1/, design according to the degree of protection IP54, cooling method ICO141, design IM1001. Motor power 2.2 kW, 2р = 6, f = 60 Hz, U 1н = 230/400 V.

Base engine ratings:

; ; η= 81%; ; h = 100 mm.

Based on the height of the rotation axis, we select the outer diameter of the stator core according to Table 2.1 /1/.

The value of the diameter of the inner surface of the stator is determined by the outer diameter of the stator core, and the coefficient k d, equal to the ratio of the internal diameter to the external one. Coefficient value k d depending on the number of poles, select from table 2.2 in advance k d =0,70 .

Stator inner diameter:

where k d is the ratio of the internal and external diameter of the stator core;

D = 0.70 · 0.168 = 0.118 m.

Pole division:

where p is the number of pole pairs;

Rated machine power:

where is the power at the motor shaft;

The ratio of the EMF of the stator winding to the rated voltage is taken = 0.948;

Engine efficiency;

Power factor;

Electromagnetic loads are previously accepted:

A = 25·10 3 A/m; B δ = 0.88 T.

The preliminary winding coefficient for a single-layer winding is krev = 0.96.

Field shape factor:

Estimated length of the machine, m:

Magnetic induction in the air gap, T;

The ratio is within acceptable limits.

2 Determination of the number of slots and type of stator winding, calculation of the winding and dimensions of the stator tooth zone

Determining the size of the stator tooth zone begins with choosing the number of slots Z 1. The number of stator slots has an ambiguous effect on the technical and economic performance of the machine. If you increase the number of stator slots, the shape of the EMF curve and the distribution of the magnetic field in the air gap improves. At the same time, the width of the groove and teeth decreases, which leads to a decrease in the coefficient of filling the groove with copper, and in low-power machines it can lead to an unacceptable decrease in the mechanical strength of the teeth. An increase in the number of stator slots increases the labor intensity of winding work, increasing the complexity of the dies, and their durability decreases.

By choosing the number of stator slots according to Fig. 3.1 /1/ we determine the boundary values of the tooth division t z 1 max = 0.012 m; t z 1 min = 0.008 m.

Number of stator slots:

where is the minimum value of the stator tooth division, m;

Maximum value of stator tooth division, m;

From the resulting range of values, select the number of stator slots

Number of slots per pole and phase:

where m is the number of phases;

The stator tooth division is final:

Rated stator winding current:

where is the rated voltage of the motor, V;

Number of effective conductors in the slot:

We accept the number of parallel branches a = 1, then U p = 48 because single layer winding.

Number of turns in phase:

We choose a single-layer concentric winding. The stator winding is made of loose wire of round cross-section.

Distribution coefficient:

Winding coefficient:

k ob1 =k y ∙k p ; (2.9)

where k y is the shortening coefficient of the stator winding pitch, k y =1 is taken;

k rev1 =1∙0.966=0.966

The winding diagram is shown in Figure 1.

Figure 1 - Scheme of a single-layer three-phase winding with z 1 =36, m 1 =3, 2p=6, a 1 =1, q 1 =2.

Magnetic flux in the air gap of the machine:

Refined magnetic induction in the air gap:

Preliminarily for D a = 0.168 m we accept = 182∙10 9 .

Current density in the stator winding:

where is the product of the linear load and the current density, ;

The cross-sectional area of the effective conductor is preliminarily:

We accept PETV winding wire: d el = 0.95 mm, d iz = 1.016 mm, q el = 0.706 mm 2.

We preliminarily accept for 2p = 6 B’ z 1 = 1.9 T; B'a =1.55 Tesla.

According to table 3.2 /1/ for oxidized steel grade 2013 we accept.

Preliminary stator tooth width:

where is the filling factor of the package with steel;

Preliminary stator yoke height value:

The dimensions of the groove in the stamp are assumed to be b w = 3.0 mm; h w =0.5 mm; β = 45˚.

Preliminary stator slot height:

Stator slot dimensions:

where is the height of the slot, m;

- slot width, m;

Specified stator slot height value:

We accept = 0.1 mm and = 0.2 mm.

Clearance dimensions of the groove taking into account the assembly allowance:

where is the allowance for the width of the groove, m.

where is the height allowance, mm;

Cross-sectional area of groove insulation:

where is the insulation thickness, mm;

S from = 0.25∙10 -3 ∙(2∙1.37∙10 -2 +7.8∙10 -3 +5.9∙10 -3) = 1.032∙10 -5 m 2 .

Free groove area:

The criterion for evaluating the results of choosing the dimensions of the groove is the value of the fill factor of the free area of the groove with the winding wire:

where is the average diameter of the insulated wire, mm;

The obtained fill factor value is acceptable for mechanized winding installation.

Specified tooth width value:

Average stator tooth width:

Estimated stator tooth width:

Estimated stator tooth height:

Specified stator yoke height value:

3 Air gap selection

For engines with a power of less than 20 kW, the air gap size is found using formula 3.1.

Let's round the values to 0.05 mm δ=0.35 mm.

4 Calculation of a squirrel-cage rotor

For 2p = 6 and Z 1 = 36, select the number of rotor slots Z 2 = 28.

Rotor outer diameter:

D 2 = 0.118 - 2∙0.35∙10 -3 =0.1173 m.

Rotor tooth division:

For 2p = 6 and h = 100 mm we take K B =0.23.

Because we have 2.2 kW< 100 кВт, то сердечник ротора непосредственно насаивают на вал без промежуточной втулки. Применим горячую посадку сердечника на гладкий вал без шпонки.

With this design of the rotor, the internal diameter of the magnetic core is equal to the diameter of the shaft, m:

Rotor inner diameter:

d in = 0.23·0.168 = 0.0386 m.

Current reduction coefficient:

where is the groove bevel coefficient;

Bevel value: b sk =t 1 =0.01.

Bevel of the grooves in the rotor tooth segments:

Central bevel angle of grooves:

Bevel factor:

Preliminary current value in the rotor winding:

We take the current density in the rotor winding rods to be J 2 = 3.05∙10 6 A/m 2 .

Cross-sectional area of the rod:

q c = 255.12/3.05·10 6 = 8.36∙10 -5 m2.

For the rotor we select semi-closed slots.

Dimensions of the groove in the stamp: take b w = 1 mm; h w2 = 0.5 mm.

For 2p = 6; B z2 = 1.8 T.

Rotor slot dimensions:

where is the height of the slot, m;

Height of the jumper above the groove, m;

We accept b 21 = 5.8∙10 -3 m, b 22 = 1.6∙10 -3 m;

Specified stubble cross-section:

Groove height, mm:

We specify the width of the rotor teeth:

Design tooth width:

Squirrel-cage rotor ring current:

Ring cross-sectional area:

Average ring height:

Short ring width:

Average ring diameter:

5 Calculation of the magnetic circuit

The calculation of the magnetic circuit of an asynchronous motor is carried out for the nominal operating mode in order to determine the total magnetizing force required to create a working magnetic flux in the air gap.

The magnetic circuit of the machine is divided into five characteristic sections: the air gap, the stator and rotor teeth, the stator and rotor yoke. It is believed that within each section the magnetic induction has one most characteristic direction. For each section of the magnetic circuit, the magnetic induction is determined, the value of which determines the magnetic field strength. Based on the value of the magnetic field strength in sections of the magnetic circuit and the corresponding length of the field line, the magnetizing force is determined. The required magnetizing force is determined as the sum of the magnetizing forces of all sections of the magnetic circuit. The magnetic circuit of the machine is considered symmetrical, so the magnetizing force is calculated for one pair of poles.

Coefficient that takes into account the increase in the magnetic resistance of the air gap due to the toothed structure of the stator surface:

Coefficient that takes into account the increase in the magnetic resistance of the air gap due to the toothed structure of the rotor:

Resulting air gap coefficient:

Air gap magnetic voltage:

Calculated induction in the stator teeth:

Calculated induction in the rotor teeth:

We choose steel grade - 2013. For 1.88 T we take H z1 = 1970 A/m, for 1.79 T we take H z2 = 1480 A/m.

Magnetic voltage of tooth zones:

Saturation coefficient of the tooth zone:

The obtained value of the saturation coefficient of the tooth zone is within acceptable limits.

Induction in the stator yoke:

Rotor yoke height:

Because 2р=6, then the estimated height of the rotor yoke h’ a 2 = h a 2 .

For 1 = 1.56 T we take H a 1 = 654 A/m; for 2 = 1.06 T we take H a 2 = 206 A/m.

Length of the magnetic field line in the stator and rotor yoke:

Stator yoke magnetic voltage:

where is the field strength in the stator yoke, A/m;

Magnetic voltage per pair of poles:

Magnetic circuit saturation coefficient:

Magnetizing current:

Relative value of magnetizing current:

Main inductive reactance:

Where E= k e Usf=0.948∙230=218.04 V;

Main inductive reactance in relative units:

6 Operating mode parameters

6.1 Active resistance of the rotor and stator windings

Average width of stator winding coil:

where is the shortening of the stator winding pitch;

For a random winding placed in the slots before the core is pressed into the housing, we accept B= 0.01 m.

For 2p = 6 we accept,

Overhang of the front part of the stator winding:

Length of the frontal part of the stator winding:

Average length of stator winding turn:

For the stator winding made of copper conductors and the design temperature we take

Active resistance of the stator winding:

where is the resistivity of the winding material at the design temperature, ;

For a squirrel-cage rotor made of aluminum and the design temperature we take

Active resistance of the rotor winding rod:

Where k r- the coefficient of increase in the active resistance of the rod due to current displacement, we accept k r=1 ;

l cT= l 2- rod length;

Resistance of the section of the closing ring enclosed between two adjacent rods:

Rotor phase resistance:

Active phase resistance of the aluminum rotor winding, reduced to the number of turns of the stator winding:

where is the coefficient of reduction of the resistance of the rotor winding to the stator winding;

6.2 Inductive leakage reactances of an asynchronous motor

Relative winding pitch β=1, k β = k' β = 1.

Magnetic conductivity coefficient of slot dissipation of stator windings:

Frontal scattering conductivity coefficient:

For the selected stator slot configuration:

where is the bevel of the grooves, expressed in fractions of the tooth division of the rotor, β sk =0.76;

k'sk- coefficient depending on t 2 / t 1 And β ck, we accept k'sk = 1,85;

Inductive reactance of the stator winding phase:

Specific magnetic conductivity coefficient of slot dissipation of a squirrel-cage rotor:

where is the conductivity coefficient;

h’ sh2= 0;

Coefficient of specific magnetic conductivity of frontal scattering of the short-circuited rotor winding:

Specific magnetic conductivity coefficient of differential dissipation of the squirrel-cage rotor winding:

Inductive leakage resistance of the rotor winding:

Inductive leakage resistance of the rotor winding, reduced to the number of stator turns:

Base resistance:

Parameters of an asynchronous motor in relative units:

Coefficient for taking into account the influence of groove bevel:

Inductive leakage resistance of the machine taking into account the bevel of the grooves:

Adjusted coefficient value k e:

Difference between k e And k’ e, (k e - k’ e )%=((0,948-0,938)/0,948)∙100%=1,1 %.

7 Calculation of power losses in idle mode

Weight of stator teeth steel:

Weight of stator yoke steel:

For steel 2013 we accept.

For machines with a power of less than 250 kW they accept.

Main losses in the stator back:

where - specific losses in steel, W/kg;

Main losses in stator teeth:

Main losses in stator steel:

We accept k 01 =1.6, k 02 =1.6.

Amplitude of induction pulsation in the air gap above the tooth crowns:

Surface losses on the stator:

k01- coefficient taking into account the effect of surface treatment of the heads of the stator teeth on specific losses;

Surface losses on the rotor:

k02- coefficient taking into account the effect of surface treatment of the rotor tooth heads on specific losses;

Weight of rotor teeth steel:

Amplitude of pulsations of average values of magnetic induction in teeth:

Ripple power losses in stator teeth:

Pulsation losses in the rotor teeth:

Total additional losses in steel:

Total power loss in steel:

Mechanical losses:

Where kfur- friction coefficient, for engines with 2p=6

Electrical losses in the stator winding at no-load:

Active component of the engine no-load current:

No-load current:

Power factor at idle:

8 Performance calculation

Calculation of performance characteristics is carried out according to the equivalent circuit of an asynchronous motor, presented in Figure 2.

Figure 2 - Equivalent circuit of an asynchronous motor

Stator dissipation factor:

Calculated values of equivalent circuit parameters:

The short circuit resistances are:

Additional losses:

Mechanical power on the motor shaft:

Equivalent circuit resistances:

Impedance of the equivalent circuit operating circuit:

Nominal slip:

Rated rotor speed:

Active and reactive components of the stator current during synchronous

rotor rotation:

Rated rotor current:

Active and reactive components of the stator current:

Stator phase current:

Power factor:

Power losses in the stator and rotor windings:

Total power losses in the engine:

Power consumption:

Efficiency:

We calculate the performance characteristics for power: 0.25∙R 2n; 0.5∙P 2n; 0.75∙R 2n 0.9∙R 2n; 1.0∙P 2n; 1.25∙R 2n. The calculation results are summarized in Table 1.

Table 1 - Engine performance characteristics

	Calculated values	Power R 2, W.
	Calculated values

	R ext, W.
	R’ 2 ,W.
	Rn,Ohm.
	Zn,Ohm.
	sn, p.u.
	I 2'', A.
	I 1a, A.
Continuation of Table 1

	I 1p, A.
	I 1, A.

	R sum, W.
	P 1, W.
	η , p.u.
	n, rpm

Figure 3 - Performance characteristics of the designed engine

9 Calculation of starting characteristics

Height of the rod in the rotor groove:

Reduced rod height:

For accept, .

Depth of current penetration into the rod:

Width of the rotor slot at the calculated depth of current penetration into the rod:

Cross-sectional area of the rod at the calculated current penetration depth:

Calculated rod resistance increase factor:

The coefficient of increase in the active resistance of the rotor winding phase as a result of the current displacement effect:

Reduced rotor resistance taking into account the influence of current displacement effect:

Reducing the magnetic conductivity coefficient of slot leakage:

The coefficient of change in the inductive reactance of the rotor winding phase due to the current displacement effect:

The value of the inductive leakage resistance of the rotor winding reduced to the stator winding, taking into account the effect of current displacement:

Stator dissipation factor in starting mode:

Stator resistance coefficient:

Equivalent circuit parameters in start mode:

Starting impedance:

Preliminary value of the rotor current at start-up, taking into account the influence of saturation:

Where K n- saturation coefficient, we will first accept K n=1,6;

Estimated magnetizing force of stator and rotor slots:

Equivalent groove opening:

Reducing slot leakage conductivity:

Where ∆ bsh1= b 12 - bsh1=2.735 mm;

Slot leakage magnetic conductivity coefficient:

Differential scattering conductivity coefficient:

Calculated inductive leakage reactance of the stator winding:

Calculated inductive leakage resistance of the rotor winding, reduced to the stator winding, taking into account saturation and current displacement:

Resistance taking into account saturation and displacement at start-up:

Rated rotor current at start:

Active and reactive components of the stator current at start-up:

Stator current at start:

Starting current ratio:

Starting torque:

Starting torque multiplicity:

We calculate the starting characteristics for sliding s= 1; 0.8; 0.6; 0.4; 0.2; 0.1. We summarize the calculation results in Table 2.

Table 2 - Estimated starting characteristics.

	Calculated magnitude	Slip
	Calculated magnitude



	φ ’
	hr,m.
	b r, m.
	q r, m 2.


	r' 2ξ, Ohm.
	r” 2ξ, Ohm.
	Znξ, Ohm.
	I" 2n, A.
	I" 2nn, A.
	Fn, H.
	∆ bsh2, mm.
	∆λ n1
	∆λ n2
	λ n1.n
Continuation of Table 2

	λ n2ξ.n
	λ d1.n
	λ d 2 . n
	x” 1n, Ohm.
	x"2ξн, Ohm.
	Rn, Ohm.
	Xn, Ohm.
	Znξ.n, Ohm.
	I" 2nn, A.
	I n.A . , A.
	I n.r . , A.
	I 1 n, A.

	Mn, N∙m.

Figure 4 - Starting characteristics of the designed motor

The designed asynchronous motor meets the requirements of GOST both in terms of energy indicators (efficiency and) and starting characteristics.

10 Thermal and ventilation calculation of an asynchronous motor

For windings with insulation of heat resistance class B, we take kp = 1.15.

Electrical losses in the slot part of the stator winding:

where is the loss increase factor;

Electrical losses in the frontal part of the stator winding:

Calculated perimeter of the stator slot cross-section:

For insulation of heat resistance class B we accept. we accept.

Temperature difference in the insulation of the slot part of the stator winding:

where is the average equivalent thermal conductivity of the groove insulation;

The average value of the thermal conductivity coefficient of the internal insulation of a random winding coil made of enameled conductors, taking into account the loose fit of the conductors to each other;

For 2p = 6 we take K = 0.19. For we accept.

The temperature of the inner surface of the stator core exceeds the air temperature inside the engine:

Where K- coefficient taking into account that part of the losses in the stator core and in the slot part of the winding is transmitted through the frame directly to the environment;

Surface heat transfer coefficient;

Temperature difference across the thickness of the insulation of the frontal parts:

Where bfrom.l- one-sided insulation thickness of the frontal part of one coil;

The temperature of the outer surface of the frontal parts exceeds the air temperature inside the engine:

Average temperature rise of the stator winding over the air temperature inside the motor:

For h= 100 mm. we accept. For we accept.

Equivalent case cooling surface:

where is the conditional perimeter of the cross section of the ribs of the engine housing;

Amount of losses in the engine:

The amount of losses released into the air inside the engine:

The temperature of the air inside the engine exceeds the ambient temperature:

Average value of the temperature rise of the stator winding over the ambient temperature:

For engines with and h=100 mm. we accept.

Coefficient that takes into account changes in cooling conditions along the length of the surface of the housing blown by an external fan:

Air flow required for cooling:

Air flow provided by outdoor fan:

The fan provides the necessary air flow.

11 Engine design

Ventilation blades are cast simultaneously with the rods and closing rings, bl=3 mm., Nl=9 pcs., ll=30 mm., hl=15mm..

The frame is made of aluminum alloy with longitudinal transverse ribbing, bst=4 mm.. The output device is molded on top.

Rib height:

Number of fins per quarter of the stator surface:

The output device of the machine consists of a closed terminal box with an insulating terminal board located in it. The terminal box is equipped with a device for fastening the supplied wires.

For external airflow of the housing, a radial centrifugal fan is used, located at the end of the shaft on the side opposite to the drive. The fan is covered with a casing. The casing is equipped with a grille at the end for air inlet. The fan and casing are made of plastic. The fan is seated on a key.

Fan outer diameter:

Where Dbldg. = D a+2∙ bst=0.168+2∙4∙10 -3 =0.176 m. ;

Fan blade width:

Number of fan blades:

Long-term transmitted torque:

According to the torque obtained, we select the shaft dimensions: d 1 =24 mm.; l 1 =50mm.; b 1 =8 mm.; h 1 =7 mm.; t=4.0 mm.; d 2 =25 mm.; d 3 =32 mm..

According to the selected diameter for the shaft bearing d 2 =25 mm, Bearing 180605 is accepted.

Conclusion

The result of the electromagnetic calculation is a designed asynchronous motor with a squirrel-cage rotor, which meets the requirements of GOST both in terms of energy indicators (efficiency and) and starting characteristics.

Thermal calculations showed that the outdoor fan provides the air flow necessary for normal cooling.

During the design, the material chosen for the frame was aluminum alloy. The bed is made with longitudinal-transverse ribbing. Through long-term transmitted torque, the dimensions of the shaft are calculated, and ball bearing 180605 is selected.

Technical data of the designed squirrel-cage asynchronous motor: power P 2 = 2.2 kW, rated voltage 230/400 V, number of poles 2 p = 6 , rotation speed n=1148 rpm, efficiency η = 0.81, power factor cosφ = 0.74.

List of sources used

2 Design of electrical machines: Textbook. for universities / I.P. Kopylov, B.K. Klokov, V.P. Morozkin, B.F. Tokarev; Ed. I.P. Kopylova. - 3rd ed., rev. And additional - M.: Higher. Shk., 2002. - 757 p.: ill.

3 STO 02069024.101-2010. General requirements and design rules - Orenburg, 2010. - 93 p.

* This source is the main one; further reference to it will not be made.

DRAWING

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Ministry of Education and Science of the Russian Federation

Federal Agency for Education

IRKUTSK STATE TECHNICAL UNIVERSITY

Department of Electric Drive and Electric Transport

I admit to protection:

Head__ T.V. Klepikova __

DESIGN OF AN INDUCTION MOTOR WITH A SQUIRED ROTOR

EXPLANATORY NOTE

For a course project in the discipline

"Electric machines"

096.00.00P3

Completed by a student of group _EAPB 11-1 ________ __ Nguyen Van Vu____

Standard control ___________ _Associate Professor, Department of EET T.V. Klepikova __

Irkutsk 2013

Introduction

1. Main dimensions

2 Stator core

3 Rotor core

Stator winding

1 Stator winding with trapezoidal semi-closed slots

Squirrel-cage rotor winding

1 Dimensions of oval closed grooves

2 Dimensions of the short-circuit ring

Magnetic circuit calculation

1 MDS for air gap

2 MMF for teeth with trapezoidal semi-closed stator slots

3 MMF for rotor teeth with oval closed rotor slots

4 MDS for the stator back

5 MDS for the rotor back

6 Magnetic circuit parameters

Active and inductive resistance of windings

1 Stator winding resistance

2 Winding resistance of a squirrel-cage rotor with oval closed slots

3 Resistance of the windings of the converted equivalent circuit of the motor

Idle and nominal

1 Idle mode

2 Calculation of parameters of the nominal operating mode

Pie chart and performance characteristics

1 Pie chart

2 Performance characteristics

Maximum torque

Initial starting current and initial starting torque

1 Active and inductive resistances corresponding to the starting mode

2 Initial starting current and torque

Thermal and ventilation calculations

1 Stator winding

2 Ventilation calculation of a motor with protection degree IP44 and cooling method IC0141

Conclusion

List of sources used

Introduction

Electrical machines are the main elements of power plants, various machines, mechanisms, technological equipment, modern means of transport, communications, etc. They generate electrical energy, carry out highly economical conversion of it into mechanical energy, perform various functions of converting and amplifying various signals in automatic control systems and management.

Electric machines are widely used in all sectors of the national economy. Their advantages are high efficiency, reaching 95÷99% in powerful electric machines, relatively low weight and overall dimensions, as well as economical use of materials. Electrical machines can be made at different powers (from fractions of a watt to hundreds of megawatts), rotation speeds and voltages. They are characterized by high reliability and durability, ease of control and maintenance, convenient supply and removal of energy, low cost for mass and large-scale production, and are environmentally friendly.

Asynchronous machines are the most common electrical machines. They are mainly used as electric motors and are the main converters of electrical energy into mechanical energy.

Currently, asynchronous electric motors consume about half of all electricity generated in the world and are widely used as an electric drive for the vast majority of mechanisms. This is explained by the simplicity of design, reliability and high efficiency of these electric machines.

In our country, the most popular series of electrical machines is the general industrial series of 4A asynchronous machines. The series includes machines with power from 0.06 to 400 kW and is available in 17 standard rotation axis heights. For each rotation height, engines of two powers are available, differing in length. Based on a single series, various engine modifications are produced that meet the technical requirements of most consumers.

Based on a single series, various versions of engines are produced, designed to operate in special conditions.

Calculation of an asynchronous motor with a squirrel-cage rotor

Technical specifications

Design an asynchronous three-phase motor with a squirrel cage rotor: P = 45 kW, U = 380/660 V, n = 750 rpm; design IM 1001; IP44 protection type.

1. Motor magnetic circuit. Dimensions, configuration, material

1 Main dimensions

We accept the height of the engine rotation axis h=250 mm (Table 9-1).

We accept the outer diameter of the stator core DH1 = 450 mm (Table 9-2).

Stator core inner diameter (Table 9-3):

1= 0.72 DН1-3=0.72ˑ450-3= 321 (1.1)

We accept the coefficient (, Figure 9-1).

We accept the preliminary efficiency value (Figure 9-2, a)

We accept the preliminary value (Figure 9-3, a).

Design power

(1.2)

We accept preliminary linear load A/cm (, Figure 9-4, a and Table 9-5).

We accept pre-induction in the gap (, Figure 9-4, b and Table 9-5).

We accept the preliminary value of the winding coefficient (, page 119).

Estimated stator core length

We accept the design length of the stator core.

Maximum value of the ratio of core length to its diameter (Table 9-6)

Ratio of core length to its diameter

(1.5)

1.2 Stator core

We accept steel grade - 2013. We accept sheet thickness of 0.5 mm. We accept the type of sheet insulation - oxidation.

We accept the steel filling factor kC=0.97.

We take the number of slots per pole and phase (table 9-8).

Number of stator core slots (1.6)

1.3 Rotor core

We accept steel grade - 2013. We accept sheet thickness of 0.5 mm. We accept the type of sheet insulation - oxidation.

We accept the steel filling factor kC=0.97.

We accept the rotor core without bevel of the grooves.

We take the air gap between the stator and the rotor (Table 9-9).

Rotor core outer diameter

Inner diameter of rotor sheets

We take the length of the rotor core equal to the length of the stator core,

We take the number of slots in the rotor core (table 9-12).

2. Stator winding

We accept a two-layer winding with a shortened pitch, laid in trapezoidal semi-closed grooves (Table 9-4).

Distribution coefficient

(2.1)

Where

We accept the relative pitch of the winding.

The pitch of the resulting winding:

(2.2)

Shortening factor

Winding coefficient

Preliminary magnetic flux value

Preliminary number of turns in the phase winding

Preliminary number of effective conductors in the slot

(2.7)

where is the number of parallel branches of the stator winding.

We accept

Specified number of turns in the phase winding

(2.8)

Refined magnetic flux value

Refined value of induction in the air gap

(2.10)

Preliminary value of rated phase current

Deviation of the received linear load from the previously accepted one

(2.13)

The deviation does not exceed the permissible value of 10%.

We take the average value of magnetic induction in the stator back (Table 9-13).

Tooth division along the inner diameter of the stator

(2.14)

2.1 Stator winding with trapezoidal semi-closed slots

The stator winding and groove are determined according to Fig. 9.7

We take the average value of magnetic induction in the stator teeth (Table 9-14).

Tooth width

(2.15)

Stator back height

Groove height

Large groove width

Preliminary slot width

Smaller groove width

where is the height of the slot (, page 131).

And based on the requirement

Cross-sectional area of the groove in the die

Clear cross-sectional area of the groove

(2.23)

Where - allowances for the assembly of stator and rotor cores in width and height, respectively (page 131).

Cross-sectional area of shell insulation

where is the average value of the one-sided thickness of the body insulation (, page 131).

Cross-sectional area of the spacers between the top and bottom coils in the groove, at the bottom of the groove and under the wedge

Cross-sectional area of the slot occupied by the winding

Work

where is the permissible fill factor of the groove for manual laying (page 132).

We take the number of elementary wires in effective .

Diameter of elementary insulated wire

(2.28)

The diameter of an elementary insulated wire should not exceed 1.71 mm for manual laying and 1.33 mm for machine laying. This condition is met.

We accept the diameters of elementary insulated and non-insulated (d) wires (Appendix 1)

We take the cross-sectional area of the wire (Appendix 1).

Refined slot fill factor

(2.29)

The value of the specified groove fill factor satisfies the conditions of manual and machine laying (for machine laying the permissible ).

Adjusted slot width

We accept , because .

(2.31)

Product of linear load and current density

We accept the permissible value of the product of the linear load and the current density (Figure 9-8). Where coefficient k5=1 (Table 9-15).

Average stator tooth pitch

Average width of stator winding coil

Average length of one frontal part of the coil

Average length of winding turn

Extension length of the frontal part of the winding

3. Squirrel-cage rotor winding

We accept oval-shaped rotor slots, closed.

3.1 Dimensions of oval closed slots

The rotor slots are determined according to Fig. 9.10

We accept the height of the groove. (, Figure 9-12).

Estimated height of the rotor back

where is the diameter of the round axial ventilation ducts in the rotor core; they are not provided for in the designed engine.

Magnetic induction in the back of the rotor

Tooth division along the outer diameter of the rotor

(3.3)

We accept magnetic induction in the rotor teeth (Table 9-18).

Tooth width

(3.4)

Smaller groove radius

Larger groove radius

where is the height of the slot (, page 142);

Spline width (, page 142);

for a closed groove (, page 142).

Distance between centers of radii

Checking the correctness of the definition and based on the condition

(3.8)

The cross-sectional area of the rod equal to the cross-sectional area of the groove in the die

3.2 Dimensions of the short-circuit ring

We accept cast cage.

The rotor short-circuit rings are shown in Fig. 9.13

Cross section of the ring

Ring height

Ring length

(3.12)

Average ring diameter

4. Calculation of the magnetic circuit

1 MDS for air gap

Coefficient that takes into account the increase in the magnetic resistance of the air gap due to the toothed structure of the stator

(4.1)

Coefficient that takes into account the increase in magnetic resistance of the air gap due to the serration of the rotor structure

We accept a coefficient that takes into account the reduction in the magnetic resistance of the air gap in the presence of radial channels on the stator or rotor.

Overall air gap ratio

MMF for air gap

4.2 MMF for teeth with trapezoidal semi-closed stator slots

(Appendix 8)

We take the average length of the magnetic flux path

MDS for teeth

4.3 MMF for rotor teeth with oval closed rotor slots

Since, we take the magnetic field strength (Appendix 8).

MDS for teeth

4.4 MMF for the stator back

(Appendix 11).

Average magnetic flux path length

MMF for the stator back

4.5 MMF for the rotor back

We take the magnetic field strength (Appendix 5)

Average magnetic flux path length

MDS for the rotor back

4.6 Magnetic circuit parameters

Total MMF of a magnetic circuit per pole

Magnetic circuit saturation coefficient

(4.13)

Magnetizing current

Magnetizing current in relative units

(4.15)

No-load EMF

Main inductive reactance

(4.17)

Main inductive reactance in relative units

(4.18)

5. Active and inductive resistance of windings

1 Stator winding resistance

Active resistance of the phase winding at 20 0C

Where - specific electrical conductivity of copper at 200C (page 158).

Active resistance of the phase winding at 20 0C in relative units

(5.2)

Checking the correctness of the definition

We accept the dimensions of the stator groove (table 9-21)

Height: (6.4)

Coefficients taking into account step shortening

Leakage conductivity coefficient

(5.7)

We accept the stator differential dissipation coefficient (Table 9-23).

Coefficient taking into account the effect of opening the stator slots on the differential leakage conductivity

We accept a coefficient that takes into account the damping response of currents induced in the winding of a squirrel-cage rotor by higher harmonics of the stator field (Table 9-22).

(5.9)

Pole division:

(5.10)

Leakage conductivity coefficient of winding end parts

Stator winding leakage conductivity coefficient

Inductive reactance of the stator phase winding

Inductive reactance of the stator phase winding in relative units

(5.14)

Checking the correctness of the definition

5.2 Winding resistance of a squirrel-cage rotor with oval closed slots

Active resistance of the cell rod at 20 0C

Where - electrical conductivity of aluminum at 20 °C (page 161).

Coefficient of reduction of ring current to rod current

(5.17)

Resistance of short-circuiting rings reduced to rod current at 20 0C

magnetic circuit resistance winding

The central bevel angle of the grooves ask = 0 because there is no bevel.

Rotor slot bevel coefficient

Coefficient of reduction of rotor winding resistance to stator winding

Active resistance of the rotor winding at 20 0C, reduced to the stator winding

Active resistance of the rotor winding at 20 0C, reduced to the stator winding in relative units

Rotor bar current for operating mode

(5.23)

Leakage conductivity coefficient for an oval closed slot rotor

(5.24)

Number of rotor slots per pole and phase

(5.25)

We accept the rotor differential dissipation coefficient (Figure 9-17).

Differential leakage conductivity coefficient

(5.26)

Leakage conductivity coefficient of short-circuiting rings of cast cage

Relative bevel of the rotor grooves, in fractions of the rotor tooth division

(5.28)

Slot bevel leakage conductivity coefficient

Inductive reactance of the rotor winding

Inductive reactance of the rotor winding reduced to the stator winding

Inductive reactance of the rotor winding reduced to the stator winding, in relative units

(5.32)

Checking the correctness of the definition

(5.33)

The condition must be met. This condition is met.

5.3 Resistance of the windings of the converted equivalent circuit of the motor

Stator dissipation factor

Stator resistance coefficient

where is the coefficient (, page 72).

Converted winding resistances

Recalculation of the magnetic circuit is not required, since .

6. Idle and nominal

1 Idle mode

Because , in further calculations we will accept .

Reactive component of stator current during synchronous rotation

Electrical losses in the stator winding during synchronous rotation

Calculated mass of stator teeth steel with trapezoidal slots

Magnetic losses in stator teeth

Weight of stator back steel

Magnetic losses in the stator back

Total magnetic losses in the stator core, including additional losses in steel

(6.7)

Mechanical losses with degree of protection IP44, cooling method IC0141

(6.8)

where at 2p=8

The active component of the current x.x.

No-load current

Power factor at idle

6.2 Calculation of parameters of the nominal operating mode

Active short-circuit resistance

Inductive short-circuit reactance

Short-circuit impedance

Additional losses at rated load

Mechanical motor power

Equivalent circuit resistance

(6.17)

Equivalent circuit impedance

Checking the correctness of calculations and

(6.19)

Slip

Active component of the stator current during synchronous rotation

Rotor current

Active component of stator current

(6.23)

Reactive component of stator current

(6.24)

Stator phase current

Power factor

Current density in the stator winding

(6.28)

where is the winding coefficient for a squirrel-cage rotor (, page 171).

Current in the squirrel-cage rotor rod

Current density in the squirrel-cage rotor rod

Short circuit current

Electrical losses in the stator winding

Electrical losses in the rotor winding

Total losses in the electric motor

Power input:

Efficiency

(6.37)

Power input: (6.38)

The input powers calculated using formulas (6.36) and (6.38) must be equal to each other, up to rounding. This condition is met.

Output power

The output power must correspond to the output power specified in the technical specifications. This condition is met.

7. Pie chart and performance characteristics

1 Pie chart

Current scale

Where - range of working wheel diameters (, page 175).

We accept .

Working circle diameter

(7.2)

Power scale

Reactive current section length

Active current length

Bars on a chart

(7.7)

(7.8)

7.2 Performance characteristics

We calculate the performance characteristics in the form of Table 1.

Table 1 - Induction motor performance characteristics

Conditional convoy	Output power in fractions











cos0.080.500.710.800.830.85


P, W1564.75172520622591.53341.74358.4

, %13,5486,8891,6492,8893,0892,80

8. Maximum torque

Variable part of the stator coefficient with a trapezoidal semi-closed slot

Saturation-dependent component of the stator leakage conductance coefficient

Variable part of the rotor coefficient with oval closed slots

(8.3)

Saturation-dependent component of the rotor leakage conductivity coefficient

Rotor current corresponding to maximum torque (9-322)

(8.7)

Equivalent circuit impedance at maximum torque

Impedance of equivalent circuit at infinitely large slip

Equivalent equivalent circuit resistance at maximum torque

Maximum torque ratio

Slip at maximum torque

(8.12)

9. Initial starting current and initial starting torque

1 Active and inductive resistances corresponding to the starting mode

Rotor cage bar height

Reduced rotor bar height

We accept the coefficient (, Figure 9-23).

Estimated depth of current penetration into the rod

Width of the rod at the calculated depth of current penetration into the rod

(9.4)

Cross-sectional area of the rod at the calculated current penetration depth

(9.5)

Current displacement ratio

Active resistance of the cage rod at 20 0C for starting mode

Active resistance of the rotor winding at 20 0C, reduced to the stator winding, for starting mode

We accept the coefficient (, Figure 9-23).

Rotor slot leakage conductivity coefficient at start-up for an oval closed slot

Dissipation conductivity coefficient of the rotor winding at start-up

Motor leakage inductive reactance dependent on saturation

Motor leakage inductive reactance independent of saturation

(9.12)

Active short-circuit resistance at start-up

9.2 Initial starting current and torque

Rotor current when starting the engine

Impedance of the equivalent circuit at startup (taking into account the phenomena of current displacement and saturation of leakage flux paths)

Inductive reactance of equivalent circuit at start-up

Active component of the stator current at start-up

(9.17)

Reactive component of the stator current at start-up

(9.18)

Stator phase current at start-up

Multiplicity of initial starting current

(9.20)

Active resistance of the rotor at start-up, reduced to the stator, at the design operating temperature and L-shaped equivalent circuit

(9.21)

Multiplicity of initial starting torque

10. Thermal and ventilation calculations

1 Stator winding

Losses in the stator winding at the maximum permissible temperature

where is the coefficient (, page 76).

Conditional internal cooling surface of the active part of the stator

The air flow that can be provided by the outdoor fan must be greater than the required air flow. This condition is met.

Air pressure developed by an external fan

Conclusion

In this course project, an asynchronous electric motor of the basic design was designed, with a height of the rotation axis h = 250 mm, degree of protection IP44, with a squirrel-cage rotor. As a result of the calculation, the main indicators for an engine of a given power P and cos were obtained, which satisfy the maximum permissible value of GOST.

The designed asynchronous electric motor meets GOST requirements both in terms of energy indicators (efficiency and cosφ) and starting characteristics.

Engine type Power, kW Rotation axis height, mm Weight, kg Rotation speed, rpm Efficiency, % Power factor, Moment of inertia,

2. Kravchik A.E. and others. Asynchronous motor series 4A, reference book. - M.: Energoatomizdat, 1982. - 504 p.

3. Design of electrical machines: textbook. for electromechanical And electricity. specialties of universities / I. P. Kopylov [etc.]; edited by I. P. Kopylova. - Ed. 4th, revised and additional - M.: Higher. school, 2011. - 306 p.

Application. Drawing up a specification

Designation	Name	Note

	Documentation

1.096.00.000.PZ	Explanatory note
1.096.00.000.СЧ	Assembly drawing



	Stator winding
	Rotor winding
	Stator core
	Rotor core
	Terminal box

	Rym. Bolt

	Ground bolt

	Fan
	Shroud Fan
	Bearing

Design of an asynchronous motor with a squirrel-cage rotor. Coursework: Design of an asynchronous motor with a squirrel-cage rotor Design an asynchronous motor with a squirrel-cage rotor

5.4 Air gap magnetic voltage F d:

6. Operating parameters

(conductors are secured with a groove cover).

7. Calculation of losses

Power scale:

Submitting your good work to the knowledge base is easy. Use the form below

Electrical machines

Course project

“Design of an asynchronous motor with a squirrel-cage rotor”

Technical specifications

Design an asynchronous three-phase motor with a squirrel cage rotor:

P = 15 kW, U = 220/380 V, 2р = 2;

n = 3000 rpm, = 90%, cos = 0.89, S NOM = 3%;

h=160 M p / M n = 1.8, M max / M n = 2.7, I p / I n = 7;

design IM1001;

IP44 protection;

cooling method IC0141;

climatic version and placement category U3;

insulation heat resistance class F.

operating mode S1

Determination of basic geometric dimensions

1. First select the height of the rotation axis according to Fig. 8.17, and (hereinafter all formulas, tables and figures from) h = 150 mm.

From the table 8.6 we take the nearest smaller value h = 132 mm and a = 0.225 m (D a is the outer diameter of the stator).

2. Determine the internal diameter of the stator:

D=K D D a =0.560.225=0.126 (m)

K D - proportionality coefficient, determined according to table. 8.7.

3. Pole division

m

where 2p is the number of pole pairs.

4. Determine the estimated power:

P = (P 2 k E)/(cos)

k E - the ratio of the EMF of the stator winding to the rated voltage, determined from Fig. 8.20, k E = 0.983

- Efficiency of an asynchronous motor, according to Fig. 8.21,a, = 0.89, cos = 0.91

P 2 - power on the motor shaft, W

P = (1510 3 0.983) / (0.890.91) = 18206 (W)

5. Determine electromagnetic loads (preliminarily) according to Fig. 8.22, b:

Linear load (ratio of the current of all turns of the winding to the circumference) A = 25.310 3 (A/m)

Induction in the air gap B= 0.73 (T)

6. We select the preliminary winding coefficient depending on the type of stator winding. For single-layer windings k O1 = 0.95 0.96.

Let's take k O1 = 0.96.

7. The estimated length of the air gap is determined by the formula:

= P / (k V D 2 k O 1 AB)

k B is the field shape coefficient, preliminarily taken equal to

kV = / () = 1.11

- synchronous angular speed of the motor shaft, rad/s, calculated by the formula

rad/s

where 1 is the supply frequency, Hz

= 18206 / (1.110.126 2 3140.9625.310 3 0.73) = 0.19 (m)

8. Check the relation = / . It should be within the range of 0.19–0.87, determined from Fig. 8.25:

= 0,19 / 0,198 = 0,96

The obtained value is higher than the recommended limits, therefore we accept the next largest from the standard series (Table 8.6) height of the axis of rotation h = 160 mm. We repeat the calculations according to paragraphs. 1-8:

D a = 0.272 (m) P = (1510 3 0.984) / (0.910.89) = 18224 (W)

D = 0.560.272 = 0.152 (m) A = 3410 3 (A/m)

= (3,140,152) / 2 = 0.239 (m) B = 0.738 (T)

= 18224 / (1.110.152 2 3140.963610 3 0.738) = 0.091 (m)

= 0,091 / 0,239 = 0,38

Calculation of windings, slots and stator yoke

Definition Z 1 , 1 And sections wires windings stator

1. We determine the limiting values ​​of tooth division 1 according to Fig. 6-15:

1 max = 18 (mm) 1 min = 13 (mm)

2. The limit values ​​for the number of stator slots are determined by the following formulas

We accept 1 = 36, then q = Z 1 / (2pm), where m is the number of phases

q = 36 / (23) = 6

The winding is single-layer.

3. We finally determine the tooth division of the stator:

m = 1410 -3 m

4. Find the number of effective conductors in the groove (preliminarily, provided that there are no parallel branches in the winding (a = 1)):

u =

I 1H is the rated current of the stator winding, A, and is determined by the formula:

I 1H = P 2 / (mU 1H cos) = 1510 3 / (32200.890.91) = 28.06(A)

u= = 16

5. We accept a=2, then

u= au = 216 = 32

6. We get the final values:

number of turns in a winding phase

linear load

Vehicle

flow

Ф = (1) -1

1. We determine the limiting values of tooth division 1 according to Fig. 6-15:

2. The limit values for the number of stator slots are determined by the following formulas

Values A and B are within acceptable limits (Fig. 8.22b)

cross-sectional area of bare wire q EL = 1.118 mm 2

cross-sectional area of the effective conductor q EF = 1.1182 = 2.236 (mm 2)

Cross-sectional area of the groove for placing conductors:

cross-sectional area of gaskets S PR = 0

cross-sectional area of body insulation in the groove

The obtained value of k3 for mechanized winding installation is excessively high. The fill factor should be in the range of 0.70 - 0.72 (from Table 3-12). Let's reduce the fill factor by increasing the cross-sectional area of the groove.

Let's take B Z1 = 1.94 (T) and B a = 1.64 (T), which is acceptable, since these values exceed the recommended ones by only 2.5 - 3%.