Improving the Efficiency of Squirrel Cage Motors-elmotorer Beaktande 803970

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IMPROVING THE EFFICIENCY OF SQUIRREL CAGE

INDUCTION

MOTORS: TECHNICAL AND ECONOMICAL

CONSIDERATION

INTRODUCTION

There are several methods of decreasing the energy consumption in electrical machines, for

example: reorganising the production lines, using adjustable ac-drives choosing the motor size

correctly and decreasing the losses of machines. The first three are mainly dependent on the

processes used in industry, but the fourth is both up to industry and motor producers.

Purchasing motors as cheaply as possible might not be the optimum solution for the whole

company in all cases. Especially in three shift industry where a great deal of the motors run

7000 - 8000 hours a year it might be wiser to buy more expensive motors with better

efficiency and thus decrease the motor energy costs. The decreased losses in industry also

lead to lower power transmission losses, reduction in the need for cooling and lower power

reservation costs.

2 LOSSES IN INDUCTION MACHINES

Maximising motor efficiency is equivalent to minimising motor losses. Motor losses consist

of ohmic-, iron- and mechanical losses. Fig. 1 shows the sharing of losses in a standard 2-pole

4 kW motor. These losses are explained in more detail in the following sections.



Fig. 1. Losses in a standard 2-pole 4 kW motor 2.1 Iron Losses

The main factors of iron losses are the hysteresis losses and the eddy current losses. The

hysteresis losses depend on the magnetic properties of the iron used and the eddy current

losses on the lamination thickness τ , frequency f , flux density B and the resistivity ρ lam of the

iron. Iron losses occur all over the iron and they are a function of (local) flux density and

frequency. In addition, there are also harmonic losses which mainly occur on teeth and iron

surfaces and are caused by harmonics in the flux density.

2.1.1 Hysteresis losses

The area inside the hysteresis loop represents hysteresis losses in the material. The increasing

of the amount of silicon in iron reduces the area of the hysteresis loop. Silicon decreases the

friction between the Weiss domains, but also impairs to some degree the saturation fluxdensity. The losses correspond also to the frequency f .

2.1.2 Fundamental eddy current losses in lamination

The alternating magnetic flux creates electro motive forces (emf) inside the material it flows

through. These emfs fluctuate at the same speed as the flux and similarly create eddy currents

normal to the flux path, i.e. the eddy currents circle around the flux. The eddy current power

loss can be presented as follows [2]

. (1)It can be seen from Eq. (1) that there are several factors that affect the eddy current losses, but

usually the outer dimensions of the motor, flux density and the frequency are constants and so

there are only two variable factors left. The thickness of the lamination seems to have the

strongest influence in eddy current losses. Some problems arise if the plate is very thin. First

it is very difficult to manufacture and handle and second the filling factor becomes small

because at least one side of the laminated plate has a non magnetic insulation layer which

prevents eddy currents from travelling between the plates. Another possibility is to increase

the resistivity of the plate. One way of achieving this is to add some silicon to the iron [3]. In

small motors magnetic materials with quite poor properties are us when considering power

losses.

2.1.3 Harmonic eddy current losses

There are two main causes of harmonics in the air-gap flux density distribution of the machine



when used with a sinusoidal supply: the permeance harmonics and the winding harmonics.

Air gap permeance function generates flux density fluctuations on the rotor surface. These

flux density fluctuations induce high frequency eddy currents that generate losses on the

surface of the rotor.

One method to flatten the permeance function is to use some semi-magnetic material to close

the stator slot opening. The purpose of the slot-wedge is to lead the flux under the slotopening. The magnetic properties of the wedge should be somewhere between stator iron and

air and its electric conductivity should be low. Choosing the material is a question of

optimisation between the power factor of the machine and harmonic losses on the rotor

surface. Increasing the permeability of the slot-wedge flattens the permeance function, but

also increases slot leakage flux. The effect of the slot-wedge, compared with a normal slot

opening is presented in Fig. 2 [4].

a) b)

Fig. 2. a) Flux plot in a normal semi-closed stator slot section. b) Flux plot in a stator slot

section as a result of using a wedge made of Aluminium-Iron dust (8 w-% of Al) impregnated

with epoxy resin.

Since the windings of induction machines are usually placed in stator slots and cannot thus be

spread smoothly over the stator inner surface we get, in addition to permeance harmonics,

winding harmonics, too. The ordinals of the winding harmonics ν in an ms-phase winding are

, (2)

where g 1 is any positive or negative integer. The stator winding factor for the harmonic ν, ξ sω

in an ms-phase winding is [5]



, (3)

The ratio ws/τ p describes the deviation of the coil span ws from the pole pitch τ p and Qs is the

number of stator slots. Two different winding types are used in different test motors, a full

pitch winding ws/τ p = 1 and a short pitch two layer winding ws/τ p = 5/6. Two layer windings

have not usually been used in small machines, but they could be a good way to reduce the

effect of the harmonics, even though they are more difficult to manufacture than single layer

windings.

Actually the ratio ws/τ p = 5/6 happens to give an overall minimum for the harmonic content of

the three-phase stator winding magneto motive force (mmf).

2.2 Winding lossesThe stator windings are usually made of enamelled copper wires and the rotor cage of cast

aluminium. The main winding losses are caused by the fundamental and harmonic currents,

but also skin and proximity effects contribute to the losses.

The stator winding dc-resistance Rs as a function of temperature T is

, (4)

where l s is the length of the stator winding, Asb is the cross-section area of a stator bar and Cu

is the resistivity of copper (1.72 10-8 m at 20 °C) and the coefficient of resistivity is = 410-3°K-1. As can be seen from Eq. (4) there are four parameters that affect the stator dc-

resistance. If the material and the temperature are not changed the conductor cross-section

area can be increased or the length of the winding decreased. Both acts decrease the stator

resistance. But these also affect several other factors.

One factor that affects the ohmic losses of the stator is the obligatory slot insulation. The

insulation, made normally of polyester, takes more than 10 % of the effective slot area in

small motors. For example using 0.15 mm thick polyimid instead of 0.30 mm thick polyester

would make it possible to increase the conductive area and decrease the coil resistance both

by about 8 %.

The calculation of the rotor resistance is much more complicated than that of the stator.

Because of the shape of the ring, the current path on the outer part of the ring is much longerthan in the inner part. This leads to unequal current density in the ring. Levi [6] presents an

equation for calculating the rotor resistance Rr per phase

. (5)

The resistance of a rotor bar Rrb can be calculated by Eq. (4) Rotor end ring equivalent

resistance is approximately



, (6)where Aer is the average cross-section area of the end ring and the average path length in the

ring is

. (7)

Qr is the number of rotor slots. The squirrel cage is usually made of aluminium. If the end

rings and rotor bars were made of copper the rotor resistance would be only 63 % of the

original which means that the rotor ohmic losses would drop correspondingly. Because the

casting of copper is difficult, the copper rotor cage with short-circuit rings would require other production techniques and thus increase the production costs. This is the main reason why this

technique has not been used in small motors.

Both iron and winding losses are greatly affected by the size of the motor. Usually an energy

optimal motor is larger than the present standard motors.

2.3 Mechanical losses

In small induction machines the mechanical losses are usually about 10 % of the total losses.

The main factors that affect on windage losses are the rotors peripheral velocity, the

smoothness of the rotor and stator surfaces and the length of the air-gap. The smaller the air-

gap, the bigger the windage losses and also the permeance harmonic losses presented earlier,

but on the other hand increasing the air-gap increases the need for magnetising current. The

air-gap length has to be optimised between these three factors. The earlier mentioned stator

semi-magnetic slot-wedges smoothen the stator surface, and thus also decrease the windage

losses.

2.4 Summary of the actions that can improve the efficiency

The summary of the actions that can improve the efficiency of induction motors is presented

in table I.

Table I. Summary of the actions that can improve the efficiency of induction motors.

LOSS POSSIBLE

DESIGN

CHANGES

POSITIVE

EFFECTS ON

LOSSES ADVERSE

EFFECTS

STATOR LOSSES

- Ohmic loss I 2 R

1. Increase amount

of copper wire in

slot.

2. Increase stator

slot size & amount

of copper wire in

slot.

3. Decrease length

of coil extensions.

1. - 3. Decreased

stator resistance R.

1. -2. Difficult to

build, increased

costs.

3. Possible increase

of inrush current &

difficult to build.

May increase iron

losses.

ROTOR LOSSES

- Ohmic loss I 2 R

1. Increase flux

density in air gap.2. Increase rotor bar

1. Decrease in slip

& resulting ohmiclosses.

1. Increased inrush

current.2. -3. Possible



/ end ring size.

3. Increase rotor bar

/ end ring

conductivity.

2. - 3. Decreased

ohmic losses.

increase of inrush

current & decrease

of starting torque.

IRON LOSSES

- Hysteresis losses

- Fundamental eddy

current losses in

lamination

- Harmonic eddycurrent losses

1. Change to better

lamination steel.

2. Decrease

lamination steel

thickness.

3. Improve

coreplating /

annealing processes.

4. Use a semi-

magnetic slot-

wedge

5. Increase the airgap length

6. Modify the shape

of the slot opening

7. Use two layer

windings instead of

single layer

windings

1. Decreased

hysteresis losses.

2. - 3. Decreased

fundamental eddy

current losses.

4. - 6. Decreased

permeance

harmonics7. Decreased

winding harmonics.

1. - 2. Increased

costs & reduce

available of

materials.

3. Increased cost

and usage of energy.

4. Increased costs.

5. Increases the

magnetising current6. - 7. Difficult to

build, increased

cost.

MECHANICAL

LOSSES- Windage losses

- Friction losses

1. Optimise the fan

design2. Optimise bearing

selection.

1. Reduced

operatingtemperatures.

2. Reduced friction

losses.

1. Can increase

noise levels. May

result in

unidirectional fans.2. May affect noise

level or impose

speed or bearing

loading restriction.

STRAY LOAD

LOSSES

1. Insulate rotor

bars.

2. Increase air gap

length

3. Eliminate rotor

skew.4. Strand depth.

5. Transposed turns.

1. Reduced bar to

lamination current.

2. Reduced high

frequency surface

losses.

3. Reduction in W r .4. - 5. Reduced eddy

currents.

1. Increased costs.

2. Reduced power

factor

3. May increase

noise level & affect

speed torquecharacteristics.

4. - 5. Difficult to

build, high cost.

3 TEST MOTORS AND RESULTS

In order to evaluate that it is economically reasonable to produce induction motors with better

efficiency, Lappeenranta University of Technology (LUT) has examined methods and costs ofincreasing the efficiency of small squirrel cage induction motors. As an example we have



manufactured several versions of a 4 kW two-pole induction motor and compared them with a

standard 4 kW motor called later as a reference motor. The construction of the motors is

shown in Table II. These changes are explained in more detail in the following chapters.

Table II. The construction of the test motors

Motorno.

Construction

(4 kW, two pole ( p = 1), 400 V motors,Qs = 36, Qr = 28 Dd = 104 mm, Dr =

103.2 mm, Dex = 180 mm )

1 Standard motor

- ls = 0.082 m

- motor core material DK-70, 0.63 mm,

- full pitch winding

2 Standard motor + semi magnetic slot-

wedge

3 Standard motor with 5/6 short pitch

winding

4 Modified construction

- ls = 0.120 m

- motor core material CK-37, 0.50 mm,

- full pitch winding

5 Modified construction as motor no. 4

- W = 5/6 τ p

6 Modified construction as in motor no. 4

- rotor end ring material copper

7 Modified construction as in motor no. 4- end ring material copper + Fe.

3.1. Stator material

In the initial 4 kW standard motor the iron losses were about 13 % of the total losses at

nominal load. Almost 80 % of these occurred in the stator yoke. Only about 11 % of the rotor

losses were iron losses. That makes 1.5 % of the total losses, so it does not seem to be very

economical to try to reduce them. Replacing the 0.63 mm DK-70 (3.1 W/kg, 50 Hz, 1 T) with

0.50 mm CK-37 (1.45 W/kg, 50 Hz, 1 T) reduces the stator iron losses and results in an 1 %-

unit improvement for the efficiency at the nominal point.

3.2 The semi-magnetic slot-wedge

Despite the effect of the permeance harmonics which are assumed to be quite small in a

machine with laminated rotor the effect of a slot wedge was examined. Slot openings in one

of the standard motors were filled with a mixture of Aluminium-Iron powder (8 w-% of Al)

and epoxy resin.

3.3 Winding

A standard stator was equipped with a 5/6 short pitch two layer winding. The effect of

winding harmonics at low slip, which is the normal operating area, was rather small.

3.4 The stator core length

As mentioned earlier the ohmic losses were the most noticeable in the standard motor. When

searching for a practical modification one of the starting assumptions is to keep the shaft

height constant. This means that the diameter of the motor can not be change, which leaves

the core length the only possible varying dimension. In order to get the best possible



efficiency, we had to find an optimum between the iron ( P Fe) and ohmic losses ( P el), in other

words to change the core length so that

. (8)The electro motive force (emf) E in a non saturated machine is

, (9)

where s is the angular velocity of the voltage supply, N s is the total number of the turns in

series per stator phase, is the peak value of the flux density in the air-gap,

p is the pole pitch and l sc is the length of the stator core.

The standard motor was tested with different voltages. These tests proved that the best power

factor - efficiency combination was reached at nominal voltage (U ph = 230 V). This means

that the flux density for this material was suitable. The flux density as well as the emf and the

angular velocity are held constant in the calculations what leads to an equation between two

constructions

. (10)

If the structure of the winding is not changed, the pole pitch and the winding factor ξ can be

eliminated and so

. (11)

Thus if the length of the stator core is increased, the number of stator bars can be decreased

and if the shape and the dimensions of the slot cross-section area are unchanged, the cross-

section area of the stator bars ( Asb) can be increased. As Eq. (11) shows, the total length of the

stator coil in the slots (l cs) does not change, but the total length of the stator coil ends ( l ce)

corresponds only with the number of the bars. So if the coil span is constant the total length of

the stator winding decreases

, (12)where l se is the average length of one conductor in one stator end.

3.5 Resistances

The stator winding dc-resistance was presented earlier in Eq. (4) as a function of temperature

T . Both the decreased length of the stator winding and the increased conducting area of the

stator bars decrease the stator ohmic losses. If the temperature remains unchanged the new

resistance of the stator is

. (13)



The length of the rotor core should be the same as the length of the stator core what increases

both the length of the rotor bars and the rotor bar resistance ( Rrb). The resistance of the end

rings ( Rre) remains the same. The new rotor resistance is

, (14)

where rr is the ratio of rotor end ring resistance to total rotor resistance. The transformation

ratio az for referring one rotor phase reactances and resistances to the stator in a squirrel cage

machine is [7]

. (15)

Both the number of phases (ms) and the number of rotor bars or rotor phases (Qr ) are constant.

r1 is the rotor skew leakage factor. The decrease in the rotor resistance from the stator side

corresponds to the square of the transformation ratio or the number of the stator bars

, (16)

where Rr1´ is the original rotor resistance seen from the stator.

While the flux density, the axial cross-section area, materials and the emf are set to be

unchanged the iron losses change corresponds to the ratio of the stator core lengths

. (17)

4 THE ENERGY OPTIMAL MOTOR

If high efficiency and a constant shaft height are the only criteria when choosing the motor for

a certain drive, we are able to calculate the optimal length of the stator stack by using the

equations presented in the previous chapter. From calculations it can be seen in Fig. 3 that theoptimum stack length is about 0.185 m. A better motor electrical steel (for example CK-37)

still increases the optimum stack length. The problem with the increased stack length is that

while ohmic losses diminish, the power factor deteriorates. This increases the need for current

and decreases the advantage of diminished resistances.



Fig. 3. The calculated electrical losses as a function of stator core length.

Fig. 4. The calculated electrical efficiency and power factor as a function of stator core

length

There were several reasons that led to the chosen stack length (lsc = 0.12 m) for the test

motor. First, as stated earlier one of the requirements was that the existing motor could be

replaced directly with the new one. Secondly, the increment of the stack length 0.12 mm leads

to a considerable deterioration of the power factor while the improvement of the efficiency

remains quite small.4.1 The measurements

To evaluate the effects of the changes made, all motor configurations were tested in

laboratory. The load tests were made with sinusoidal supply.

The measured efficiencies of the motors are presented in Fig. 5. which shows a remarkable

increase in the efficiencies of motors 4, 5, 6 and 7 compared to the initial motor. It should be

noticed that the efficiency is much better throughout the whole presented scale and that the

peak of the efficiency curve is very flat.



Fig. 5. The measured efficiencies of different test motors

The calculated loss components of the standard and test motor 4 at the rated load are

compared in Fig. 6.

Fig. 6. The calculated loss components for the standard and test motor 4 at rated power

As can be seen in table III, the starting current of some high efficiency versions is higher than

the standards allow. The starting current of the best motor, however, is reduced to a level

accepted also by the NEMA standard. This reduction of the starting current is mainly due to

the changes in the rotor construction that increase the locked rotor resistance and reactance.

Table III. Some motor data measured with sinusoidal supply.

Motor number 1 2 3 4 5 6 7

Efficiency at 4 kW output / % 85.3 85.9 85.4 90.6 91.4 91.8 89.0

Best efficiency / % 86.7 87.4 87.1 90.9 91.7 92.1 90.2

I st / I N (rotor locked, coldmotor)

6.9 7.1 7.7 10.9 10.4 8.7 8.0



Power factor at 4 kW output 0.914 0.912 0.915 0.860 0.840 0.856 0.77

Slip at 4 kW output / % 4.42 4.45 4.36 2.31 2.31 1.85 2.15

5 REDUCING HIGH EFFICIENCY INDUCTION MOTOR

STARTING CURRENT

The disadvantage of decreasing losses is that the starting current can get higher than the

standards allow as a result of the decreased starting impedance Z . The reduction of the ohmic

losses decreases stator and rotor resistances and the reduction of iron losses by using silicon

has made the values of the leakage reactance X s and X ́ r somewhat lower at starting than at

normal speed. This is because the relatively high rotor and stator current during starting may

saturate portions of the iron in the rotor and stator teeth in the leakage-flux paths.

At starting the slip s = 1 and therefore the magnetising impedance Z m is high compared to the

rotor impedance Z r. By using the values of the equivalent circuit and line-to-line voltage U we

get a good approximation of the line current I st at starting

, (18)

where Rs is the stator winding resistance, Xss is the stator leakage reactance, R´ r is the rotor

resistance and X´sr is the rotor leakage reactance referred to the stator. When the motor is

operating at normal speed (i.e., at a slip of about a few percentages), the line current is

limiting mostly by the magnetising impedance.The reduction of the starting current or the increase in the starting impedance without large

changes the running values can be done by taking advantage of the skin effect which increases

the conductor impedance. This idea is normally used in double-squirrel-cage and deep-bar

motors.

The skin effect means an uneven current distribution in a current carrying conductor. The total

current density distribution in a conductor determines its dynamic impedance which is the

result from system operating frequencies, conductor's shape and the electromagnetic

properties of the materials used.

The equation for skin effect can be derived from Maxwell´s equations. If it is assumed that the

end ring leakage flux Φ has only a component normal to the conductor cross-section and the

current density J has only a component tangential to the conductor, the skin effect can bederived from Ampere´s law as:

(19)

where J is the sectional current density, σ the electrical conductivity, L the tangential length

of the conductor and ∆Φ the leakage flux of the conductor. The leakage flux of the conductor

can be expressed as follows:

(20)



where µ 0 is the permeability, ht the height of the conductor, b p the cross-sectional width of the

conductor and i the sectional current.

At starting the frequency of the rotor currents is relatively high so the influence of uneven

current distribution both in the rotor bars and end-rings increases thus the rotor impedance.

Skin effect appears mainly in the rotor bars which are surrounded by the ferromagnetic rotor

core. In order to increase the skin effect in the rotor end rings the end rings were partlysurrounded by iron. This was done by adding extra ferromagnetic rings beside the aluminium

end ring and modifying the shape of rotor end-rings.

The idea of sophisticated squirrel-cage end ring area design has been know a long time. One

of the earliest inventions about this has been made in year 1926 by K. L. Hansen and W. J.

Oesterlein, Milwaukee, Wis. (Fig. 7a). Since those days more advanced inventions have been

patented like starting disk in 1981 by Gabor Kovacs, Budapest, Hungary (Fig. 7b) or squirrel-

cage rotor having end rings of double structure in 1980 by Makio Sei, Nakaminato, and Kunio

Miyashita, Hitachi, both in Japan (Fig. 7c).

a) b) c)

Fig. 7. a) Self-starting induction motor patent, b) Squirrel-cage rotor having starting disc, c)

Squirrel-cage rotor having end rings of double structure

Referring to Eq. (20) the dimensions of the end-ring shape that affect the skin effect are the

radial depth h and the axial length b.To maximise the skin effect the radial depth of the end-ring should be as high as possible and

the end-ring should be made of copper, whose electrical conductivity is higher that of

aluminium. The axial length b of the end-ring should also be as small as possible because it

increases the leakage flux Φ through the conductor

The task of the extra ferromagnetic rings around the aluminium end ring is to decrease the

reluctance in the leakage flux path and thus increase the leakage flux. To reduce iron losses,

the ferromagnetic rings were made of lamination sheets.

6 THE COSTS OF INCREASING THE EFFICIENCY

When the core length of a machine is changed the amount of the materials and the work

needed in production changes too (Fig. 8). The amount of electrical steel in a motor is

comparable to the core length. In the rotor, the aluminium rotor bars also correspond to the

stack length, but the short circuit rings remain unchanged. For this reason the slope of

aluminium is lower than that of iron. As was previously seen the amount of conductors in one

slot can be reduced when the stack length is increased and the air-gap flux density is kept

constant. This means that the "useless" part (length) of coils at stack ends is reduced. If the

cross section area of one conductor were unchanged, the total amount of copper could be

decreased. To reduce ohmic losses, the cross section area of each conductor is increased in

such a way that the filling factor of a slot remains about the same.



Fig. 8. The change in the amount of the materials as a function of the stator and rotor core

lengths

The only change in manufacturing costs is caused by the motor electrical steel processing,

which is relative to the stack length. The work needed in winding the machine, casting,

composition and testing are constant. The price for the decreased power losses is presented in

Fig. 9.

Fig. 9. Increased production cost of the 4 kW test motors divided by the decreased losses.

The manufacturing costs are based on a research [8] made for a 2 hp motor. In that study, 65

% of the total production costs were due to the materials and 35 % due to the other costs. Inthe calculations above, the other costs are assumed to increase 2.5 % for each increased 10 %

of the stack length. The material prices used in the calculations are: Cu 30 FIM/kg, Al 20

FIM/kg, DK-70 3.50 FIM/kg and CK-37 5.10 FIM/kg.

7 CONCLUSIONS

If only the rise in the production costs is considered, the payout period of the investment for

example with 5000 h annual usage time is less than a year.

From the results reached we can notice that the harmonic field effects in small inductionmotors are quite insignificant, especially around the nominal point. It seems that the short



pitch winding, which is much more complex to manufacture than the normal full pitch

winding, is not economical, at least not with sinusoidal supply or when the number of slots

per pole and phase is large (6 in our axample). Instead of that, the semi-magnetic slot-wedge,

which could quite easily be joined with the slot insulation at the slot opening, might be a

useful alternative. Anyway, the most important factors in the motors' efficiency are the correct

dimensioning of the cores and the motor electrical steel used. However the reduction of lossesincludes some problems. First, the resistance and reactance values diminish, which causes an

increased starting current when the motors that are directly connected to the network are used

periodically.

The reduction of the starting current without changing the running values very much can be

done by using either deep slot rotors or by modifying the rotor end rings as in motor 7. Both

of these actions would increase the production costs to some extent, but not remarkably.

REFERENCES

[1] T. Jokinen, Reduction of Losses in Electrical Machines and Transformers. Helsinki

University of Technology/Laboratory of Electromechanics. Report nr. 17 (in Finnish), 1983.

[2] L. W. Matsch, J. D. Morgan, Electromagnetic and Electromechanical Machines. New

Mexico/USA. Harper & Row, Publishers Inc, 1986, p.51.[3] C. Heck, Magnetic Materials and their Applications, London, Butterworth, 1974, 770 p.

[4] J. Pyrhönen, P. Kurronen, Research on Solid-Rotor Induction Machines, part 1. Research

report EN B-73 Lappeenranta University of Technology, 1991, 24 p. (in Finnish)

[5] K. Vogt, Elektrische Maschinen, Berechnung rotierender elektrischer Maschinen. Dritte

bearbeitete Auflage, Berlin, Veb Verlag Technik, 1983, 500 p.

[6] E. Levi, Polyphase Motors; A Direct Approach to Their Design. New York/USA: John

Wiley & Sons, 1984. 438 p.

[7] R. Richter, Elektrische Maschinen, Volyme IV. Die Induktionsmaschinen.

[8] Tucci, C. L., Lang, J. H., Tabors, R. D., Kirtley, J. L. 1994. A Simulator of the

Manufacturing of Induction Motors. IEEE Transactions on Industry Applications, Vol. 30 ,

No 3, pp 578 - 584.

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Improving the Efficiency of Squirrel Cage Motors-elmotorer Beaktande 803970