[ieee 2014 students conference on engineering and systems (sces) - allahabad, india...

Abstract-- In this paper the effect of various rotor core materi-

al for high speed Solid Rotor Induction Motor (SRIM) have been analyzed. A comparative study, regarding the performance of high speed SRIM on variation of various material properties has been made. It has been observed that a material with good elec-trical conductivity gives efficient operation. The effect of end ring length of SRIM has also been analyzed. A considerable variation in torque has been observed on variation in end ring length for 180 kW, 10200 rpm high speed SRIM. It was seen that the rotor with smaller end ring provided better torque but with lower power factor. The efficiency was also increased with smaller end rings.

Index Terms— End ring length, high speed, Saturation densi-ty, Solid Rotor Induction Motor (SRIM), Torque.

I. INTRODUCTION ITH noteworthy growth in the field of frequency con-verter technology, it has become viable to utilize varia-

ble speed technology of different AC motors to a broad range of applications. Multiphase induction motor with a solid rotor has tremendous advantages over traditional cage induction motor regarding simplicity and mechanical strength. Maximum rotational speed of a revolving machine is con-strained by the mechanical stress caused by very high circum-ferential velocity of the rotor and critical frequencies caused by the dynamics of the rotor. Thus an extremely rugged design for rotor construction is needed at high and medium speed operations. Design of a laminated cage rotor introduces the difficulty in keeping the laminated layers tightly together at-tached to the shaft at elevated rotor speeds. Constructing rotor and rotor shaft from a single piece of ferromagnetic steel has also resulted in an increased ability to withstand mechanical and thermal stress caused by high angular velocity of the rotor. This robust solid rotor becomes the better option compared to the laminated rotor structure. Solid rotor offers various mechanical and thermal advantag-es at high circumferential velocity. These rotors are the strongest possible ones and maintain balance even at elevated speeds. Solid rotor induction motor when used at very high

Gaurav is a research scholar with the Department of Electrical Engineer-

ing, Motilal Nehru National Institute of Technology, Allahabad-211004, India (e-mail: [email protected]).

Sarika Kalra and Vineeta Agrawal are with the Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad-211004, India (e-mail: [email protected], [email protected]).

978-1-4799-4939-7/14/$31.00 ©2014 IEEE

speed provide better mechanical strength and better balance with reduction in vibration and fluctuations.

Traditionally a mechanical gearbox was earlier used which is now replaced by the electrical frequency converter. Use of electrical frequency converters with load directly attached to it helps in reduction of losses due to the gearbox. Furthermore, this mechanism provides full speed control of the drive in a much efficient way. While the smooth solid-rotor construction provide better results in mechanical and fluid dynamics point of view, the electromagnetic property of this rotor are not de-sirable, i.e. the rotor resistance is high and the losses are in-creased which are dependent on slip. Numerous researches are made in order to enhance the electromagnetic property of the solid rotor among which axially slitting the cross section of the rotor proves out to be major enhancement for soli-rotor structure. Axial slit provides better flux penetration into the rotor core, thus generating better electromagnetic torque. Slit-ting of rotor improves the electromagnetic torque but the me-chanical strength of the smooth solid rotor is compromised at a higher manufacturing cost. Not only the rotor construction is a prime issue while designing a high speed induction motor but the material being used for the rotor construction also needs to be analyzed carefully. It is to be noted that mechani-cal stress at the base of the rotor teeth should always be less than the yield strength of the material being used for the rotor construction [1].

Another way of enhancing the performance of the solid-rotor induction motor is by welding of high conductive end rings together with the rotor iron at the rotor end, thus reduc-ing the apparent resistance of the solid-rotor [2]. In general aluminum or copper is basically used as an end ring material in high and medium speed machine. Centrifugal and thermal stresses are the limiting factor in determining the material for end ring structure. Also, addition of the end ring reduces the mechanical strength of the entire rotor structure, to eliminate this shortcoming the rotor is constructed from a single piece of ferromagnetic material without any end rings. Low carbon steel is usually used as solid-rotor core materi-al, Fe-52 that contains 1.5% Manganese, so as to increase its mechanical strength. Low carbon steel have sufficient strength for medium speed operations and applications, but its resistivi-ty is quite high thus resulting in a relatively large slip and in-creased rotor losses.

In this paper an effect of variation of material parameter and length of rotor end ring on 3-phase, 180 kW, 10150 rpm high speed induction motor is analyzed. Wide range of material has been analyzed for comprehensive study. In order to consider a wide range of electromagnetic material property, relative per-meability and conductivity has been taken. A combination of a

Rotor core material and End ring length analysis for Solid-rotor High Speed Induction Motor

Gaurav Khanduri, Sarika Kalra and Vineeta Agrawal, senior member, IEEE

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large number of fictitious ferromagnetic rotor core materials was created and analyzed. It has been observed that a material with good electrical conductivity gives efficient operation. Further it has been observed that the smaller length of the end ring gives a better electromagnetic performance. To evaluate the effect of end ring length on the performance of the motor, analysis was done in ANSYS RMxprt software.

II. MOTOR CONSTRUCTION AND METHOD OF ANALYSIS Two dimensional finite element analyses is used to deter-

mine the effect of various ferromagnetic solid-rotor material for two poles, three phase 180kW, 170Hz induction motor. Entire analysis was made using ANSYS RMxprt and electro-magnetic Maxwell 2D software. Mathematical calculations and analysis was made to assess the influence of different ro-tor material parameters on performance characteristics of the motor. In order to make a comparative study for rotor core material and end ring length, similar geometries of stator, rotor and core were considered. Each material with a unique magne-tizing curve was taken into account. The cross section of the motor under analysis is given below in Fig.1. Table I shows the design parameters of the studied motor.

Fig. 1 Cross section of solid-rotor induction motor.

TABLE I DESIGN PARAMETERS OF STUDIED MOTOR

No. of poles 2 No. of phases 3 Rated output power(kW) 180 Rated frequency(Hz) 170 Outer diameter of stator(mm) 400 Inner diameter of stator(mm) 200 Core length(mm) 280 No. of stator slots 48 Outer diameter of the rotor(mm) 195 No. of rotor slits 34 Width of the rotor slit(mm) 3 Depth of the rotor slit(mm) 40

Two dimensional, non linear, time stepping finite element

analysis of magnetic field have been used in measuring the performance characteristics of the solid-rotor induction motor. Rotation of the rotor with respect to stator, magnetic saturation

and skin effect are taken into account. To consider the effect of the stator end field as well as to design the sinusoidal power supply to the motor in the calculation, circuit equations were used. The electromagnetic field and circuit equations are solved simultaneously. The electromagnetic field of the motor in Cartesian plane can be explained in terms of magnetic vec-tor potential, A as

1

Where, σ is electrical conductivity, t is time, ν is magnetic

reluctivity, and J is current density. In order to consider the end winding effect of a stator into account, equation (1) is paired to circuit equation, 2

Where, u and i are voltage and current of the winding, R is

the resistance of winding, Ψ is the flux linkage associated with two-dimensionally modeled magnetic field and Lew is end winding inductance, representing the part of flux linkage which is not included in Ψ. Ferromagnetic materials used mostly for the construction of the solid-rotor are low carbon steel, Fe52 is one of the most commonly used. Mechanical properties of a solid-rotor are satisfactory but the electromagnetic properties must be veri-fied. As a consequence of low conductivity and saturation of solid-rotor material, the rotor losses tend to be high and power factor low. Electromagnetic properties can be enhanced by axial slitting of the rotor [1]. Soldering or welding electrically high conductive end rings together with rotor iron at the end of rotor helps in considerable reduction in apparent resistance of solid rotor. Copper and aluminum are generally used as end ring material in high and medium speed machines. Introduc-tion of end ring puts on a limitation on the rotating speed of high speed solid-rotor induction motor. Unfortunately these highly conducting end rings are unable to withstand the high centrifugal force due to high circumferential velocity, thus in such a case the rotor is made of one single piece of ferromag-netic material without end rings. Highly conductive end ring have a substantial effect on the solid-rotor induction motor performance. A three Dimensional finite element analysis is required in order to determine three dimensional effect of the current distribution in the end region. But due to the highly computing problem this 3D rotor end effect has to be modeled in 2D, by modifying the rotor effective resistivity by end fac-tor K [2]. 1 2 tanh 2 3

Where, τ is the rotor pole pitch and L is the rotor length. The electromagnetic torque calculation, in applied FEM

based analysis is dependent on the principle of virtual analy-sis. The electromagnetic torque T is calculated as a partial

differential of magnetic co-energy with respect to virtual angular displacement δθ. Electromagnetic torque T is calcu-lated as a surface integration over the air-gap finite element in two dimensional cases. . . 4

Where V is the volume studied, H is magnetic field intensity and B is the magnetic flux density.

III. END FACTOR FOR SOLID ROTOR In case of solid-rotor induction motor the main electromag-

netic field problem is three dimensional eddy currents, solu-tion to these eddy currents with analytical equations proves out to be a very tough task. Skin effect phenomenon compels the rotor current to flow on the outer rotor surface. Axial slits in the rotor structure forces the rotor current to flow axially in the stator stack region. Skin effect forces the current to flow at the end ring surface. Considering that the flow of current in both active region and the end ring region is identical, long end ring increases the path of flow of current from one pole to another thus increasing the apparent resistance of the rotor. The current follows a circumferential path in the end region. Fig. 2 shows the assumed curved path [2].

Fig. 2 Assumed circular path of current in high speed solid-rotor induction motor.

Resolving and considering three dimensional effects in 2D space requires the development of equations and constants, the end effect factor being a major one. Rotor equivalent resistiv-ity ρ is increased by an end factor K in case of solid-rotor without any end rings. There are several end ring factors de-rived by various authors. Modifying the rotor resistance by the end factor depending on the geometry of the solid-rotor, the rotor ends can be taken under consideration while calcula-tions [4].

1 2 tanh 2 5

Where is the pole pitch and L the rotor length. In analysis and conclusions made in [5], it is assumed that the current density in rotor is confined in a thin shell around

the rotor. The end factor for smooth non slitted rotor is given by,

11 2 6

Where , L is rotor length, g is air gap length.

It was concluded that the end factor depends on inner and outer diameter and pole pair of rotor in [6]. The end factor is given as, 2 1 DD1 DD 1 DD 7

Where D is rotor outer diameter, D is rotor inner diameter p is the pole pair number. In case of slitted solid rotor inner di-ameter D can be defined according to the rotor slit depth as follows, D D 2y 8 Where, y is the depth of rotor slitting. As seen from equa-tion (7) the end factor is independent of rotor length, hence remains constant irrespective of any rotor length. A formula is derived in [7] that defines end factor which reduces rotor equivalent conductivity 9

Where L is the rotor length and is average rotor radius. In [8] the end factor is described as follows 12 4 tanh 10

Where and are 1 tanh 11

11

Where and represents end region thickness and resis-tivity, is slit depth and is cylindrical shell region resistiv-ity. As mentioned earlier, while determining 2-D analysis for solid-iron rotor, the conductivity of the solid material needs to be corrected using an end-effect correction factor k. 12

In almost all of the studies made by various authors [4]-[8], while calculating the end-effect correction factor for 2-D

analysis in case of solid-iron rotor, the correction factor was considered to be independent of the rotor angular frequency. This assumption proved to be inadequate as seen in [11]. Thus an effort was made so as to introduce the effect of rotor angu-lar frequency, and a modified end effect factor was derived as

[12], given by 13 Where [5] is given by

1 tanh1 tanh tanh 14

is the pole pitch, l is half of the active stator stack length

and is length of rotor end beyond the active stator stack. Introduction of correction factor (13), set to reduce the conductivity of the rotor material as a function of angular frequency 1 15 Where c adaptation coefficient and is angular frequency of penetrating field. As seen in (15), it is derived from the fact that, as Agar-wal’s depth of penetration is inversely proportional to square root of rotor angular frequency [9] 16 Value of is considered to be unity for lower values of speed, as gives correct results at lower values of speed [12]. Furthermore, it was seen that there is a need to decrease the correction factor at a much faster speed with de-crease in conducting surface , hence a better corrective factor dependent on the angular frequency of the rotor is pro-posed [12]. 1 17 this, rotor angular frequency correction factor was found to give best possible results in 2-D analysis.

IV. VARIATION IN PARAMETERS OF FICTITIOUS FERROMAGNETIC MATERIAL AND ITS EFFECT ON ROTOR

PERFORMANCE Varying performance of the solid-rotor induction motor on

variation in relative permeability of the solid-rotor core ma-terial is numerically studied. To study the variation a wide range of relative permeability was considered, initial relative permeability ranging from 40 to 9000.

According to the results obtained from the calculations in Fig. 3 and Fig. 4, it is seen that considerable change in the motor performance was not achieved for low relative permea-bility. This calculation result does fully satisfy the phenome-

non that for a high speed solid-rotor induction motor in which the rotor core is highly saturated even in the optimal operation region i.e. motor does not operate in the linear region of the materials magnetizing curve, thus the relative permeability of the rotor is naturally low. In accordance with result, the rela-tive permeability of the material being used in the further study is considered to be constant 2000.

Fig. 3 Speed versus power factor curve of studied motor with variation in relative permeability.

Fig. 4 Speed versus torque characteristics of studied motor with variation in relative permeability.

To determine the effect of change in electrical conductivity

of the material, the rotor core materials with conductivity ranging from 2 10 to 6 10 were analysed. It was seen that material with large electrical conductivity produces higher operating torque. The reason for better electromagnetic torque is, as the eddy current could easily penetrate into the rotor core with better conductivity and produce larger electromagnetic torque. Since the rotor resistance or joule losses are propor-tional to the slip, the optimal operating point of the solid-rotor induction motor occur at a low value of slip, provided the ro-tor resistive losses are considered. It can be seen from Fig. 6, that though the rotor with higher conductivity provide better operating torque but the power factor at same value of slip is decreased. Thus resistivity or conductivity of the material be-ing used in solid rotor construction plays a vital role in en-hancing the performance characteristics of induction motor. Designing of rotor with good conductivity gives better operat-ing torque at higher values of slip for the motor.

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Fig. 5 Speed versus torque characteristics of studied motor with variation in conductivity of rotor core material.

Fig. 6 Power factor versus speed curve for studied motor with variation in conductivity of rotor core material.

To determine the effect of rotor end ring iron length on the output performance characteristics of solid-rotor high speed induction motor, a set of end ring length was considered. End ring length was varied from 0mm to 60mm. It was found from the results that the rotor with short end ring length gave better electromagnetic torque than the rotor with longer end ring length.

Fig. 7 Torque versus speed characteristics with variation in end ring length.

All the speed versus torque characteristics made in ANSYS software is shown in Fig. 7 with all studied end ring lengths. Results depict that apparent resistivity of the rotor is very sen-sitive to variations in electrical angular frequency of the rotor. As it was assumed in Fig. 2 that apparent resistivity is higher for longer rotor end rings. Shorter the end ring length better is the torque produced, and if the maximum torque generating capability at maximum measured load is taken, the betterment in torque can be as high as 6 to 8 percent with short end rings and at higher values of slip this phenomenon is enhanced.

The power factor is defined as the ratio between the amounts of real power supplied to the total apparent power used. A higher value of power factor implies better and effec-tive use of electrical energy. While considering the perform-ance of solid-rotor induction motor the poor power factor of the motor cannot be neglected. Analysing the results for the variation in end ring length in the power factor versus speed characteristics in Fig. 8 it is seen that the rotor with longer end ring length shows slightly better power factor at higher values of slip. This can be analysed as higher apparent rotor resis-tance and thus higher rotor losses. Where in rotor with smaller end ring length, the torque generation is better with respect to higher end length with lower rotor losses and thus power fac-tor is slightly lower. But the effect of rotor end length on power factor is very less.

Fig. 8 Measured power factor versus speed characteristics for various values of end ring length. Efficiency versus output power for the test motor is shown in Fig. 9. The curve reveals that the efficiency of the motor increases with reduction in end ring length. Variation in end ring length shows variation in efficiency as high as 1 to 2 percent, thus utmost care must taken while designing end ring length. Although highest efficiency was obtained in rotor with no end rings but for all practical purpose the end ring of rotor is inevitably needed in order to assure a rigid rotor body con-struction in high speed operations.

Fig. 9 Efficiency versus output power with variation in end ring length.

V. CONCLUSION It was seen that variation in properties of material being

used for solid rotor construction has effect on motor charac-

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teristics. Relative permeability of the material has very mi-nor effect on motor performance. The conductivity of the rotor material has significant effect on the motor characte-ristics material with higher electrical conductivity produces higher electromagnetic torque. Rotor end ring length does play a vital role in enhancing solid-rotor induction motor characteristics. End ring iron with smaller length shows bet-ter torque.

VI. REFERENCES [1] J. Huppunen, “High speed solid-rotor induction motor- Electromagnetic

calculation and design,” Acta University No.197, Diss. LUT, Lapperanta, 2004.

[2] T.Aho, J. Nerg, and J. Pyrhönen, “Experimental and finite element analysis of solid rotor end effect,” IEEE-ISIE,International Symposium on Industrial Electronics, pp. 1242-124, 2007.

[3] T. Aho, J. Nerg, J. Sopanen, J. Huppunen, and J. Pyrhönen, “Analyzing the effect of rotor slit depth on electric mechanical performance of solid-rotor induction motor,” IREE Vol. 1 no. 4 pp. 516-525, 2006.

[4] R. L. Russell, and K. H. Norsworthy, “Eddy current and wall losses in screened rotor induction motors,” Proc. IEE, Vol 105A, no. 20, pp. 163-173, 1958.

[5] H. Yee, “Effects of finite length in solid rotor induction machines,” Proc. IEE, Vol. 119, no. 8, pp. 1025-1031, 1971.

[6] P. H. Trickey, “Induction motor resistance ring width,” Trans. Am. Inst. Elect. Eng., Vol 55, pp. 144-150, 1936.

[7] D. O’Kelly, “Theory and performance of solid-rotor induction and hysteresis machines,” Proc. IEE, Vol 119, No.9, pp. 1301-1308, 1972.

[8] I. Wooley, and B.J. Chalmers, “End effects in unlaminated rotor induction machines,” Proc. IEE, Vol. 120, no. 6, pp. 641-646, 1973.

[9] P. D. Agarwal, “Equivalent circuit and performance calculation of canned motors,” AIEE trans., pp 635-642. 1960.

[10] T. Jokinen, and A. Arkkio, “High speed AC motors,” in Proc. conf Power Electronics, Industrial Drives, Power Quality, Transaction Systems (SPEEDAM), pp B5-9 - B5-14, 1996.

[11] K. Yamazaki, and Y. Watanade, “Interbar bar current analysis of induction motor using 3-D finite element methode considering lamination of rotor core,” IEEE Trans. Magn., vol. 42, no. 4, pp. 1287-1290, 2006.

[12] J. Pyrhönen, J. Nerg, P. Kurronen, and U. Lauber, “High-Speed High-Output Solid-Rotor Induction-Motor technology fro Gas compression,” IEEE Trans. On Industrial Electronics, vol. 57, no. 1, pp. 272-280, 2010.

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