of a 180 kW medium-speed inductionmotor with solid rotor are speed motor is ... induction motors is becoming increasingly popular, especially, performance ...
Rotor Materials for Medium-Speed Solid-Rotor Induction MotorS T. Aho, V. Sihvo, J. Nerg, J. Pyrhonen Lappeenranta University of Technology, Department of Electrical Engineering P.O.Box 20 53851 LAPPEENRANTA, FINLAND Abstract- The effects of different solid-rotor materials on the motor performance are studied. The performance characteristics of a 180 kW medium-speed induction motor with solid rotor are analyzed using two-dimensional finite element method. A set of fictitious and realistic ferromagnetic materials, the mechanical properties of which satisfy the requirements of high-speed operation, were used in the calculations. It is shown that the highest torque is reached with a material having high saturation magnetic flux density and good electrical conductivity. It is also shown that in order to achieve efficient operation of the motor the rotor resistive losses should be minimized,
I. INTRODUCTION The use of high power variable speed electrical drives with induction motors is becoming increasingly popular, especially, in high pressure pumps, high speed gas compression systems and in small energy conversion units. The reason why solidrotors are utilized in high-speed applications is that by making the rotor and the rotor shaft from a single solid piece also results in an increased ability to withstand mechanical and thermal stresses caused by the high circumferential velocity of the rotor. In electrical high-speed machines which are rotating at higher speeds than it is possible to direct-on-line, a mechanical gearbox is replaced by an electrical frequency converter. The idea is that the load machinery is attached directly on the motor shaft. This eliminates the losses of a gearbox. Furthermore, the use of a high-speed machine offers possibility of a full speed control with the accuracy of electrical adjustable speed controller that outperforms any of the mechanical alternatives. Although the smooth solid-rotor construction offers superior properties from the mechanical and fluid dynamical point of view, its electromagnetic properties are unsatisfactory, i.e. the rotor resistance is high and the slip dependent Joule losses become excessive. A remarkable performance improvement m the electromagnetic properties of a solid-rotor can be achieved by axially slitting the cross-section of the rotor. By such a way, better flux penetration into the rotor can be achieved. Although the slitting of the rotor has a desired influence on the electromagnetic performance and on the rotor eddy current losses, the drawback of such an axial slitting is that it lowers the mechanical strength of the rotor and increases the manufacturing costs of the motor. It is obvious that nominal mechanical stresses at the root of the teeth, calculated e.g. in
1 -4244-0743-5/07/$20.OO ©2007 IEEE
[1], should not exceed the yield strength of the material with a suitable safety factor. Thus, even though the rotor of a highspeed motor is manufactured from a solid single piece of metal, the
.l... of tthe .rotor materials to withstand high forces due to ability
the high circumferential forces has to be considered with a
special care. The most commonly chosen solid-rotor core material is low carbon steel, such as Fe52 that contains 1.5 00 manganese, to
increase the mechanical strength. The mechanical strength of the low carbon steel is often high enough for medium-speed applications, but unfortunately the resistivity is quite high thus resulting in relatively large slip and increased rotor losses. The effects of the solid rotor core material on the motor performance characteristics were experimentally studied in [2]. The results obtained from experimental analysis indicated that the highest torque may be reached with a material having high saturation magnetic flux density and good electrical conductivity. However, a wider range of different solid-rotor materials should be included in comprehensive analysis. The main objective of this paper is to numerically analyze the effects of different ferromagnetic materials on the electromagnetic performance characteristics of a 180 kW solidrotor induction motor. In order to cover a wide range of electromagnetic material property combinations numerous fictitious ferromagnetic rotor core materials were created. Furthermore, a set of realistic ferromagnetic iron alloys satisfying the mechanical requirements set by the high-speed operation are included in the analysis.
II. ROTOR CONSTRUCTION AND METHOD OF ANALYSIS The effect of a ferromagnetic solid-rotor material on the performance characteristics of a two-pole, three-phase, 180 170 Hz induction motor with a slitted solid-iron rotor was calculated using two dimensional fiite element analysis. Numerical calculations were carried out to evaluate the influence of different ferromagnetic rotor core material parameters on the motor performance characteristics. In order to cover wide range of possible material property combinations 64 different fictitious ferromagnetic rotor core materials were created. The varied electromagnetic material properties were initial relative permeability, saturation flux density and resistivity. The magnetization characteristics of each of the materials were described as a single valued magnetization
kW,
525
(-t
curve. The motor performance was also analyzed with eight L> 2k , k =1- tanh (3) realistic iron alloys, which can be found in practice. The same stator and rotor geometries were used in all the calculations in order to achieve comparable results. The analyzed rotor was a slitted solid-rotor with an equal slit depth where is the rotor pole pitch and L is the rotor length. All the and with straight slits. The cross-section of the solid-rotor FEM calculations were performed using FluxA2DT software induction motor and the main parameters of the motor analyzed package from CEDRAT. are given in Fig. 1. M
Number of poles Number of phases Rated output power [kW]
3
III. EFFECT OF THE FICTITIOUS FERROMAGNETIC ROTOR CORE
2 180
Outerdiametereofuhe st [[] 1740200 Inner diameter of the stator [mm] CoNumber ofstatorslots [4880 Outer diameter of tHe rotor [mm] 195 Number of rotor slits 34 Width of the rotor slit [mm] 3
j~ 'AJ_l
Depth ofthe rotor slit [mm] 40
Fig. 1. Cross-section and the main parameters of the studied solid-rotor
induction motor.
The performance characteristics of the solid-rotor induction machine were evaluated using a two-dimensional, non-linear time-stepping finite-element analysis of the magnetic field, i.e. magnetic saturation, skin effect and the motion of the rotor with respect of the stator are taken into account. The circuit equations were used to model the sinusoidal power supply as well as to take the effect of the stator end fields into account in the calculations. The circuit equations and the electromagnetic field are solved together. The electromagnetic field of the motor in the Cartesian plane can be described in terms of magnetic vector potential A as
VvVA+u
(8A A =, -
a~9Jt ~
(1)
MATERIALS ON THE MOTOR PERFORMANCE The effect of the relative permeability of the solid-rotor core material on the performance characteristics of the solid-rotor induction machine was numerically studied. In order to obtain the results in a wide range of permeability, the initial relative permeability of rotor core material was varied from 50 to 8000. It must be noticed that the varied relative permeability was the initial relative perneability at the origin of the corresponding materials magnetization curve, i.e. the magnetization curve of each virtual material is a combination between a straight line and of an arctangent function. According to results obtained from the numerical calculations shown in Figs. 2 and 3, the initial relative permeability of the solid rotor core material has only a very minor effect on the electromagnetic torque production and on the power factor of the motor. Considerable changes were not obtained until the relative permeability was as low as 50. This phenomenon can be explained due to the fact that the rotor core of the highspeed solid-rotor induction machine is always highly saturated even in the normal operation area, i.e. the motor operates normally far beyond the linear region of the material's magnetization curve and, therefore, the relative permeability of the rotor material is naturally very low. This result supports the idea of using the limiting non-linear theory used by Agarwal in [7]. According to this significant conclusion the initial relative permeability in the subsequent presentation for the fictitious materials is set to be a constant value of 2000.
where v is magnetic reluctivity, ais electrical conductivity, t is time and J is the current density. In order to take the end winding effects of the stator into account equation (1) is coupled with a circuit equation q u = Ri+L di dt (2) ew dt dt ~7 where u and i are the voltage and the current of the winding, R is the resistance of the winding, qis the flux linkage associated with the two-dimensionally modeled magnetic field and Lew is the end-winding inductance, representing the part of flux linkage, which is not included in Vw In the two-dimensional finite element calculations the rotor end effects can be taken into account by modifying the rotor equivalent resistivity by the end-factor. The end-factor k depending on the geometry of a solid-rotor can be defined as [3]
526
1.75
-
1.501.25 1.00
Relativepermeability
.....800 6000 4000
0.75
- -2000 1000 500
0.50 0.25
-
o.oo 0.00
0.25
0.50
0.75
1.00
1.25
1.50
250
1.75
2.00
Slip [%] Fig 2. Effect of the initial relative permeability on the electromagnetic torque as a function of slip. The resistivity of the material was set to 30 ,uQm. The
strto lxdniywsstt au f20T
0.75-
motor can not be avoided. However, according to Fig. 5, the
0.70
higher the saturation flux density of the rotor core material, the
0.65-
0.60 0.55 0.50
better the power factor, especially, when the motor is operating at a low slip. As well as in case of electromagnetic torque production, the reasonable saturation flux density value is
-
,80.40 -
pennebility ~~~~~~~~~~~Relaive ~ ~~ ~ ~ ~ ~~~~~~-8000 -6000
above 1 .25 T. 0.75-
0.40
~~~~0.35 Po 0.30 -4000 0.25 -- -2000 0.20- 1000 0.15 --500 0.10 0.05 0.000.00 0.25 0.50 0.75
0
07 0.650.60 0.55 0.50
250 50 ~0.45
0.401.00
1.25
1.50
1.75
2.00
Fig 3. Effect of the initial relative permeability on the power factor as a function of slip. The resistivity of the material was set to 30 m. The saturation flux density was set to value of 2.0 T.
0.20
smooth solid-rotor issolid-rotor extremely low and the magnetic flux and the torque producing eddy-currents are concentrated on the very surface layer of the rotor thus saturating the surface of the rotor. In Fig. 4, the effect of the saturation flux density on the electromagnetic torque can be seen while the saturation flux density was varied form 0.50 T to 2.25 T. The results indicate that the saturation flux density seems to have only a minor effect on the generated electromagnetic torque and on the
power factor above the value of 1.25 T. When the saturation flux density is around 1.25 T the rotor surface and the roots of the rotor teeth reach their maximum magnetic flux carrying capabilities and thus the torque producing fundamental magnetic flux flow in the rotor teeth is restricted. 2.00
Saturation flux density
2.25 T
1.75
2.00 T
1.75 T
a)
T
o.oo
0.00
0.25
1.00
Slip [%]
1.25
10[XQ
1.25
L
0.50
1.00
0.25
o 0.75
;
0.00 1.00 Slip
[%]
1.25
2.00
.....cm +
tQcm 20 [tQcm 3~~~~~~~~~~~~~~~~~0
0.75-
0.75
5
1.75
The electrical resistivity of the rotor core material has a considerable effect on the performance characteristics of a solid-rotor induction motor. Fig. 6 reveals that the lower the resistivity of the solid rotor core material, the higher electromagnetic torque is achieved at the same slip. This is due to the fact that the lower the resistivity of the solid rotor core material, the higher the induced torque producing eddycurrents on the rotor teeth. When the rotor resistive losses, i.e. rotor Joule losses, are considered, the nominal operation point of the solid-rotor induction motor should occur at a low value of slip. This is because the rotor Joule losses are proportional to the per-unit slip value. It should be noted in Fig. 7 that with a low resistive rotor material the power factor of the motor falls rapidly while the per unit slip increases.
0.50 T
0.50
1.50
,uQm and the initial relative permeability was set to value of 2000.
o
0.25
0.75
Resistivity
4.0 T
0.00
0.50
Fig 5. Effect of the saturation flux density of the rotor core material on the power factor as a function of slip. The resistivity ofthe material was set to 30
loT1.75
E>j) 1.00
225 T 2.00 T T
1.25 T 1.00 T
1.25T
1.25
-nty
0.10 4 0.05 -
andthemagnticfluxand
i lo extremely
0 35
-1.75
T 0.15 ---.1.50
As a result of the skin effect, induced eddy currents at the surface of the ferromagnetic, electrically conducting rotor core material tend to push the induced magnetic field to the outer layer of the rotor. Thus, the depth of penetration into the smooth
o
0.3020.25
Slip [%]
1.50
1.75
2.00
0.50
0.25
Fig 4. Effect of the saturation flux density of the rotor core material on the o oo electromagnetic torque as a function of slip. The resistivity of the material was set to 30 ,uQm and the initial relative permeability was set to value of 2000.
Since in solid-rotor the rotor core is used as well as a current and magnetic flux carrying circuit, the poor power factor of the
527
-
60.Qcm 80 iQcm/
-
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Slip [%o]
Fig 6. Effect of the electrical resistivity of the rotor core material on the power
factor as a function of slip. The saturation flux density ofthe rotor material was 2 T and the initial relative permeability was set to a constant value of 2000.
low resistivity and high initial permeability. Unfortunately pure iron has inadequate mechanical properties, such as hardness and tensile strength. The tensile strength of pure iron is only around 150 MPa. Pure iron material is also very expensive and hence unpractical. Therefore, it has to be doped with some other element in order to gain better mechanical properties. Improving mechanical properties of iron is not a difficult thing to do, because most elements increase the strength of iron. But it is a task of very challenging kind to do the doping without
0.75
070.6
0.60
0.55 0.50
0.45-
°0.45 Ct ,Z 0.40-
a) 0.35
0.30
c
~
//
-
-
Resistivity /
iQcm
1 [tQcm ¢ ~ ~~~~~~~~~~~~ /10 ~~~ 0.30 ~~~~~~~2 -20 [Qcm
30 tQcm
0.25 -
0.20 0.15 0.10 -
--A--40 iQcm
sarfcniffpoete
50-4Qcm 60[tQcm 80 tQcm
0.05
0.00
S
0.00
0.25
0.50
0.75
1.00 1.25 Slip [%]
1.50
1.75
2.00
Fig 7. Effect of the electrical resistivity of the rotor core material on the power factor as a function of slip. The saturation flux density ofthe rotor material was 2 T and the initial relative permeability was set to a value of 2000. Please notice that the rated slip varies as a function ofthe resisitivity, e.g. the rated slip for the 10 gQcm material is about 0.4 %, which may be seen in Fig. 6.
In Fig. 8, the effect of the saturation flux density and electrical resistivity on the electromagnetic output power (shaft power + friction losses) of the motor is show when the per-unit slip was 1.0 per cent. The electromagnetic torque of the motor can be determined at points where the saturation flux density and resistivity curves are intersecting. According to curves shown in Figs. 2-7, the resistivity is the most dominating electromagnetic parameter affecting the performance of the motor. As it is shown in Fig. 8, the low value of the flux density saturation value can easily be compensated with a material having a lower value of electrical resistivity. Reversed compensation, i.e. compensation of high resistivity with high value of saturation flux density, is not possible. lux 1z; *j 1O slip= 1.00
sacrificig the electromagnetic properties of iron. With low doping rates, every alloying element, even the ones with lower resistivity than that of iron, increases the resistivity of the alloy. Saturation flux density, on the other hand, will decrease rather rapidly when the doping rate is increased. This will happen with every common element except cobalt. Also platinum and everyee pt platinum rhodium icrease the steel saturation flux density r5], but due to their extremely high price, these two elements are far beyond reach for electrical machine engineers. The electromagnetic properties of alloys analyzed in this study are listed in Table 1.
A. Carbon Steel Alloys Carbon steel, such as Fe52, is a metal alloy containing carbon. It is the most common form of steel used as a solidrotor core material. In fact, this is a conventional structure steel used widely in industry and constructions. Low-carbon steel, such as C15, has a carbon-content up to 0.30 wt. 00 and is therefore neither extremely brittle nor ductile. Carbon is added to iron, because even with low doping rate, it significantly improves the mechanical properties of the alloy. The hardness can be further increased by the addition of manganese. However, carbon increases resistivity and decreases saturation flux density rather rapidly. Therefore, the carbon content must be rather low in order to maintain decent electromagnetic
properties. B. Fe-Si and Fe-Ni Alloys The addition of silicon increases the resistivity and decreases the saturation flux density of iron, which both are undesired consequences. On the other hand, the addition of silicon increases the relative permeability of the material. The tensile strength is also increased and is at best, when the doping rate is approximately 4 00.
Ferromagnetic alloys containing nickel,
R
c$R
are
usually stronger
and harder than most of steels. A high alloying percent of Rnickel R gives an alloy a good permeability and low resistivity, but at the same time low saturation flux density. Low nickel content alloy has a high saturation flux density, but very low permeability at the same time.
0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00
Fig. 8. Effect of the saturation flux density and electrical resistivity on the
electro magnetic torque ofthe motor when the slip was 1.0 %.
C. Maraging Steel Maraging steel can be used as a rotor material in high-speed applications where extreme tensile strength is required.
IV. ANALYZED REALISTIC FERROMAGNETIC MATERIALS The base material in a high-speed rotor body is iron. It has good electromagnetic prop erties, high saturation flux den sity,
Maraging steel is one example of special steels that are extremely hard and resistant to corrosion. The iron content in tealyi ut o,i hscs 9w.0.Tedpn emntinhscaenlueikl,obtadmlyeu.
Electromagnetic torque pu
528
TABLE 1. ELECTROMAGNETIC AND MECHANICAL PARAMETERS OF THE FERROMAGNETIC ALLOYS STUDIED. Saturation flux Initial Relative Tensile strength, Tensile strength, Density References Ferromagneti alloy CompositiResistivity Composion cm] density [T] permeability yield [MPa] ultimate [MPa] [kg/m3]
Ferromagnetic alloy Carbon Steel Fe52
C Mn
0,55 1,6
Low carbon Steel C15 Maraging Steel Vascomax C250
C Mn Al C Co Mo
0.12-0.18 0.3 - 0.6 0,1 0,03 8,5 3,25
Fe-Cu Alloy
Fe-Si Alloy Silicon Steel M36 Consumet
~~~F
Si C
2,2 0,01
Si C
0,15 0,02
Fe-Co Alloy
25,7
1,9
-1000
300
520
7,87
Measured at LUT
> 97.5 99.13-99.58
15,9
1,9
-1000
330
440
7,87
18,5 0,1
49,0
1,9
500
1800
-2200
8,00
MatWeb www.matweb.com Measured at LUT
Cu
5
11,0
1,6
-1000
424
-
7,92
Measured at LUT
~~~Fe
95
41,0
2,04
1485
300
390
7,75
[61
13,0
2,15
190
345
7,86
40,0
2,4
400
800
8,15
Ni Si Ti Zr
Mn Al Fe Mn V
C Mn
0,02
0,5
0,09
0,2 0,01
0,25 0,3
--97 0,15 0,1
99 5 ~~~ ~~~Fe
V Co
Supermendur
Fe-Ni Alloy High Permeability 49
0,2
Si V Fe Fe
2 49
~~~~Fe49
Si
Ni Fe
0,35 48 51
*1000 800
[7]
Carpenter
www.cartech.com
[71
Carpenter
www.cartech.com
48,2
1,5
Also chromium is widely used in extremely hard, corrosionresistant alloys. Maraging steel is a martensitic steel alloy, which is extremely hard, but it is lacking of toughness and may be quite brittle. As a result of high portion of nickel, the electrical resistivity of Maraging steel is relatively high. D. Fe-Co Alloys As was mentioned earlier, cobalt is the only affordable alloying element, which can increase the saturation flux density of iron. The maximum saturation flux density can be achieved with approximately 35 wt. 00 of cobalt. Typically iron-cobalt alloys also include vanadium. Adding only 2 wt. /0 of vanadium can significantly increase the mechanical properties and workability of the alloy. Moreover, vanadium has only the
6500
255
545
8,18
Carpenter
www.cartech.com
operation of a solid-rotor induction motor. According to Fig. 9, the highest output power of the motor at the rated slip can be achieved with a rotor manufactured of some low-resistivity material. Such materials can be found e.g. from the Fe-Cu and Fe-Si alloys. Also the low carbon steel C15 offers efficient operation capability with low slip values. To achieve the rated output power with a rotor made of low resistive material, the
slip-dependent Joule losses remain at reasonable levels. 400
-FeCu 350 --FeS/Consumet
L 300 G 2
F,52
FeCo
FeNi
150 E. Fe-Cu Alloys 100 Copper, is a very tenacious element and thus it increases the L 50 mechanical properties of iron. At room temperature copper has 0 the highest electrical conductivity of any metal except pure 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 silver. The effect of copper on the resistivity of the alloy is Slip [%] quite minor. Copper as an alloying element decreases the Fig 9. The effect of the solid-rotor material on the saturation flux density, but not as much as silicon, though. As a torque as a fufnction of slip.generated electro-magnetic downside of Fe-Cu alloy, doping iron with copper is a very difficult process and thus iron-copper alloys are commercially Even though the tensile strength of the Maraging steel is hardly, if at all, available. Copper is considered usually as a superior, the high electrical resistivity ruins the electromagnetic contamination in steels and thus Fe-Cu materials may not be properties of the material and thus the slip tends to be manufactured using the same equipment as other steels. increased. The high tensile strength of the Maraging steel may be utilized by increasing the rotor diameter and thereby V. RESULTS AND CONCLUSIONS boosting the electromagnetic torque production. It might also The results obtained from the finite element calculations be a good alternative in a rotor carrying a cage winding in the indicate that large variations in machine operation occurred solid core material. The tensile strength of the Fe-Co alloy is when using different realistic solid-rotor core materials. Fig. 9 significantly higher than it is in the case of a Fe52 alloy. reveals that alternative rotor core materials to be used instead However, similarly as in case of Maraging steel, Fe-Co alloy of the commonly chosen low carbon steel Fe52 can be found. suffers from a high electrical resistivity. Low per-unit slip related to the produced output power is In Fig. 10, the power factor ofthe motor as afunction of slip essential in order to have a non-saturated and efficient with different ferromagnetic rotor core materials is illustrated. U
529
It can be seen that in order to achieve an acceptable power factor, the solid-rotor core material should have a low value of electrical resistivity and a high saturation magnetic flux density. This phenomenon is emphasized at the low slip values, However, when the power factor is considered as a function of axial output power, as it is shown in Fig. 1 1, the effect of the rotor core material is negligible,
surface losses, the solid-rotor surface could be coated with a thin layer of ferromagnetic material having high surface impedance i.e. the coating material has a high permeability and a high electrical resistivity. Another possibility is to coat the rotor with a thin highly conductive non-magnetic material layer made e.g. of copper. This alternative is, however not discussed here in detail.
0.80
7.00- U1 Total loss ~~~~~~~~~~~~~~~~~~6.50
0.70
* Surface loss D- Resistive loss
6.005.50
0.50
~~~~~~~~~~~~~~5.00-
FeCu
~~~~~~~~~~~~FeSi/Consumet
0.40
4.50-
'4
~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.30
~~~~4.00-
'0 3.50-
0.20
0
eIM 6P FeNi
0.10
~Maraging 0.00
0.25
0.50
0.75
1.00
1.25
1.50
3.002.50-
2.001.50-
2.00
1.75
1.00
Slip [Oo]
0.50-
Fig 10. Effect of the solid-rotor material on the power factor as a function of
00
slip.
FeC
Resistivity [pQcm] Saturtion flux denity [T] Relative perebility
0.90
Outputpower[kW]
0.80
Rottiospeed[rpm]
-
0.70
11.0 1.6 1000 180 10156
eS
15
13.0 T 2.15 1000 j 180 10147
15.9 1.9 1000 180 10144
~~~~~~~~~~~~ ~~~~~ ~ ~~~~~~ ~~0.660.52~ 9~.~07Slip[%]0.43 24.100.550.66 0.66 S~tator1hasurn[kW]
Power~~~~~~~ ~~~~~~~~
A
~
fato
2.05
.~~~~~~ 0.50
-~~~~~~~~~~~~~~~~~~- FeCu
Roo reitvels kW] ls [kW]
0.55 1.49
~~~~~~oorsrfc ~~
0.70
0.81
F5
2. 1.9 1000 10 10099 0.99
0.66
24.39
1.27
eC
400 2.4 800 180 10033 1.64
0.65
14
3.0
2.8
Fe-Si
Fe-Ni
482 49.0 41.0 1.5 2.04 1.9 1485 500 6500 180 180 10031 10008 1.66
0.66
31473
2.08
1.88
0.670.66
Marging
180 9992 2.04
46.08 3.6
2.42
2.64
1.09 1.0211 1.3 .9 1.2 7 1.45
-~~~~~(- FeSi/Consumet ~~~~~~~Fig 12. The effect of the solid-rotor material on the rotor losses.
0.40
--C15
---Fe52 FeCo
0.30
0.20-FeSi/M36
0.10
0.00
1 0
50
100
150
200
AKOLDMN AKO LDMN
FeNi
250
300
350
This work was supported by Academy of Finland and Finmnish Agency for Technology and Innovation (TEKES).
F~~~~~~~~~~Mrgigunding 400
45(
Axial power [kW] Fig 11. Effect of the solid-rotor material on the power factor as a function of axial output power.
RFRNE
[1]
RFRNE T. Aho, J. Nerg, J. Sopanen, J. Huppunen and J. Pyrhonen, "Analyzing the Effect of the Rotor Slit Depth on the Electric and Mechanical Performance of a Solid-Rotor Induction Motor," Review of Electrical Engineering (IREE), vol. 1, no.
Besides the electro magnetic torque production capability, the resistvity olid roto rtor core mterialhas matrial hs an ffect n the4, theInternational resistiity ofthe the sold pp. 516-525, 2006. J. Pyrhonen, "The High Speed Induction Motor: Calculating the electrical efficiency of the motor, as well. In order to have a [2] Effects of Solid Rotor Material on Machine Characteristics," Acta good electrical efficiency, the rotor of a solid-rotor induction Scandinavica, Electrical Engineering Series no. 68, machineshould machineshould rovidelow resstivitypaths resstivitypaths or the the nducedPolytechnica nducedDiss. LUT, Lappeenranta, 1991. R.L. Russel and K. H. Norsworthy, "Eddy current and wall losses in fundamental harmonic eddy-currents. This can be achieved [3] screened induction motors," Proc. IEE, vol. 105 A, no. 20, 1958, with rotor material having a low resistivity and a moderate o
cre
an
n
or
saturaion saturaion fuxfux denity. denity.
een inFig. ss it cn cn be een
163-173. thelowerpp. [4] Agarwal, P., D., "Equivalent Circuits and Performance Calculations
2, thelower
the resistivity of the solid-rotor core material, the lower the
rotor fundamental resistive losses.
[5]
Hoee,the rotor surface losses to high However, frequency air [] ~ ~~ ~ ~ due ~~ ~~~~~~~~~~[]
gap harmonics are strongly dependent on the surface impedance of the rotor. The increase in the rotor core material
conductivity decreases the surface impedance of the rotor thus
[7]
of Canned Motors". AIEE trans. 1960, pp 635 - 642.
R. M. Bozort, Ferromagnetism, John Wiley & Sons, Hoboken, New
Jersey, E. P. Wohlfarth (ed.), Ferromagnetic Materials: A Handbook on the Properties of Magnetically Ordered Substances, vol. 2, Elsevier Science Publishers, Amsterdam, Netherlands, 1986. ISBN 0-4442003. ISBN 0-7803-1032-2.
853 12-X.
Ame-ricann S,ocietyi for Mettals, Meltals Handbook, vol. 1 Prnoprtiesv
