Advanced
Sensitivity Analysis of Geometrical Parameters of a Switched Reluctance Motor with Modified Pole Shapes
Sensitivity Analysis of Geometrical Parameters of a Switched Reluctance Motor with Modified Pole Shapes
Journal of Electrical Engineering and Technology. 2014. Jan, 9(1): 136-142
Copyright © 2014, The Korean Institute of Electrical Engineers
  • Received : February 04, 2013
  • Accepted : July 06, 2013
  • Published : January 01, 2014
Download
PDF
e-PUB
PubReader
PPT
Export by style
Article
Author
Metrics
Cited by
TagCloud
About the Authors
M. Balaji
Dept. of Electrical and Electronics Engineering, SSN College of Engineering, India. (kamarajv@ssn.edu.in)
S. Ramkumar
Corresponding Author: Dept. of Electrical and Electronics Engineering, SSN College of Engineering, India. (balajim@ssn.edu.in)
V. Kamaraj
Dept. of Electrical and Electronics Engineering, RMD Engg College of Engineering, India. (ramme04@gmail.com)

Abstract
A major problem in Switched Reluctance Motor (SRM) is torque ripple, which causes undesirable acoustic noise and vibration. This work focuses on reducing the undesirable torque ripple in SRM by modifying stator and rotor geometry. This paper presents a comparative study on torque ripple minimization in SRM with modified pole shapes such as stator pole taper, stator pole face with non-uniform air gap and pole shoe attached to rotor pole. Further this paper presents a detailed sensitivity analysis of the effect of different geometrical parameters that alter the pole face shapes on the performance of SRM. The analysis is performed using finite-element method considering average torque and torque ripple as performance parameters. Based on the analysis, a design combining stator pole taper with non-uniform air gap is proposed to improve the torque characteristics of SRM. The dynamic characteristics of the proposed design are simulated and the results show satisfactory reduction in torque ripple.
Keywords
1. Introduction
There has been growing research interest towards the design and development of SRM for variable speed applications [1 - 2] . The primary disadvantage of an SRM is the higher torque ripple compared with conventional machines, which contributes to acoustic noise and vibration. The origin of torque pulsations in an SRM is due to highly non-linear and discrete nature of torque production mechanism. Torque pulsations are most significant at commutation instants when torque production mechanism is being transformed from one active phase to another [3] . Two different approaches are considered for torque ripple minimization in SRM. One is to pursue a motor geometry which reduces torque ripple and the other is to manipulate motor current [4 , 5] to improve the performance. It is to be noted that even if electronic torque ripple reduction techniques are used, it is desirable to look for an optimum geometry for inherent improvement [6] . SR motors normally have three operating modes; low speed mode, chopped current mode at medium speeds and high speed mode. The effect of torque ripple is most significant at low speeds where torque variations considerably affect instantaneous speed of the shaft. At higher speeds, inertia of the rotor helps to reduce these speed variations and hence vibration. At low speed, torque ripple is significant, and the overlap of the phase current may be assumed negligible. Further the phases are assumed to turned on and off at rotor position corresponding to the intersections of the torque characteristics [3] . The effect of different design parameters on torque ripple in SRM and the design approaches to minimize torque ripple have been discussed in detail by Iqbal Husain. The sensitivity of geometrical parameters on the performance of SRM has been described in the literature [7 - 11] . In [10] , the sensitivity of the stator and rotor pole arcs is studied to determine optimum pole arc configuration to minimize torque ripple. From the literature it is evident that the torque output and torque ripple of SRM are sensitive to stator and rotor pole arcs and their selection is a vital part of SRM design process.
In recent years a lot of research has been directed towards reducing the undesirable torque ripple in SRM by modifying stator and rotor geometry. Several attempts have been made to study the effect of special pole shapes on the torque profile and torque ripple characteristics of SRM [12 - 16] . In these methods the basic idea for torque ripple minimization comes from the fact that the torque profile and the exciting current profile, is a function of the inductance profile when the exciting voltage profile and the switching time for each phase are fixed [16] . While studying the effect of modified geometry on the performance of SRM due consideration should be given to both average torque and torque ripple, since improvement in torque ripple may result in degradation of average torque. Hence a detailed sensitivity study of the design parameters that alter the pole shapes on average torque and torque ripple needs to be performed. This paper intends to address this by presenting a sensitivity analysis of geometrical parameters on the performance of SRM with modified pole shapes such as stator pole taper [15] , stator pole face with non-uniform air gap, pole shoe attached to rotor pole [16] .
2. Performance Analysis of SRM with Modified Pole Shapes
The structure of 8/6 SRM is shown in Fig. 1 . The initial design details of the motor are given in Appendix 1. For each design modification average torque and torque ripple are calculated by modeling and simulation using Finite Element Analysis (FEA) based CAD package MagNet.
PPT Slide
Lager Image
Structure of SRM
Average torque is computed by the following equations
PPT Slide
Lager Image
PPT Slide
Lager Image
PPT Slide
Lager Image
where I represents the rated phase current, L a represents the inductance at the fully aligned position and L u represents the inductance at the complete unaligned position.
Torque ripple is evaluated from the torque dip present in the static torque characteristics [6] and is given by
PPT Slide
Lager Image
where T max is the maximum torque determined from the peak of the static torque characteristics and T min is the torque at the intersection instants.
In order to validate FEA modeling, a prototype SRM was subjected to static measurements to determine the flux linkage current characteristics. For this purpose, an experimental setup comprising a motor, and position encoder was used. The components of the experimental setup are shown in Fig. 2 . The experimental method [17 , 18] makes use of the voltage equation as the basis for determining the magnetization characteristics of the machine. When a voltage pulse is applied to one of the phases of SRM with all other phases open, its voltage equation is given by
PPT Slide
Lager Image
Experimental setup to determine flux linkage vs. current characteristics
PPT Slide
Lager Image
where V is the instantaneous voltage across the phase winding, R is the resistance and i is the current. The flux linkage is given by
PPT Slide
Lager Image
The flux-linkage can be determined for different values of current by using the Eq. (6). The general practice is to apply a voltage pulse to the stator winding by clamping the rotor to a known position. The current rises up to a steady state level, and then the voltage is turned off, de-energizing the stator winding. Throughout this time, integration takes place to determine the instantaneous flux-linkage as a function of current and position. The current and voltage waveforms recorded while the rotor was locked at aligned position are shown in Fig. 3 . Table 1 shows a comparison of the flux-linkage by measurement and FEA methods at discrete points to evaluate the correlation between the results. The flux linkages obtained by FEA show higher values than those of experimental values. However the difference is small. Inspite of the same physical dimensions of the motor, differences are inevitable due to measurement errors in the experiment and tolerances in the numerical computation. The closeness of the results have confirmed and validated the FEA model.
PPT Slide
Lager Image
Waveforms recorded at aligned position
Comparison of Flux-linkage
PPT Slide
Lager Image
Comparison of Flux-linkage
- 2. 1 SRM with tapered stator pole
The tapered stator pole model [15] is shown in Fig. 4 . The ratio ‘ a’ between the enlarged stator pole arc at the base (β S1 ) and the initial constant width stator pole arc at the base (β S ) is varied from 1 to 2 keeping β S constant. Increasing ‘ a’ has the effect of increasing the overall area of the cross section, leading to a decrease in the reluctance of the stator pole sections. This in turn reduces the total reluctance of the machine and increases the flux for the given mmf resulting in higher inductances and average torques [2] . The effect of tapering is evident near aligned position. There is a considerable increase in the inductance and its slope near aligned position. This is evident from the phase inductance characteristics shown in Fig. 5 . This results in a rectangular torque vs. rotor position characteristics as shown in Fig. 6 . As a result of rectangular torque vs. rotor position characteristics there is considerable reduction in torque ripple.
PPT Slide
Lager Image
SRM with tapered stator pole
PPT Slide
Lager Image
Inductance profile with stator pole taper
PPT Slide
Lager Image
Torque characteristics with stator pole taper
The average torque and torque dip for different pole taper angles are summarized in Table 2 . From the table it is clear that there is improvement in the average torque and reduction in torque ripple with tapered stator pole configuration.
Average torque and torque dip for various pole taper ratios
PPT Slide
Lager Image
Average torque and torque dip for various pole taper ratios
- 2. 2 Stator pole face with non-uniform airgap
For optimizing the torque profile of SRM by changing the inductance profile, the most significant parameter is the air gap profile between the stator and rotor poles. SRM with a modified air gap profile [16] is shown in Fig. 7 . The design parameter θ varies the air gap profile when the rotating direction of the rotor is clockwise. In this design the air gap becomes narrower as the rotor pole overlaps with the stator pole. This results in a flatter inductance profile near aligned position which results in reduced torque dip. The performance of the machine is analyzed by varying the design parameter θ from 0 to 2 degrees.
PPT Slide
Lager Image
SRM with non-uniform air gap profile
The inductance profile and torque vs rotor position characteristic is shown in Figs. 8 and 9 respectively. From the figures it is evident that inductance value is reduced with increase in θ which in turn results in reduced torque. However the shape of the torque vs. rotor position characteristics is almost rectangular, which has the advantage of reducing torque ripple.
PPT Slide
Lager Image
Inductance profile of stator pole face with non-uniform air gap
PPT Slide
Lager Image
Torque characteristics of stator pole face with non-uniform air gap
The torque dip variation for different values of θ is shown in Fig. 10 . The torque dip is minimum for the design with θ=1. 2deg. The average torque and torque dip for different angles are summarized in Table 3 . It is evident that by modifying the air gap profile there is considerable reduction in torque ripple. But due consideration should be given to the fact that the average torque of the machine with modified air gap profile is reduced when compared to the initial design.
PPT Slide
Lager Image
Torque dip variations with design parameter θ
Average torque and torque dip for various values of θ
PPT Slide
Lager Image
Average torque and torque dip for various values of θ
- 2. 3 SRM with pole shoe attached to rotor pole
SRM model with pole shoe attached to the lateral side of the rotor pole [16] is shown in Fig. 11 . As the rotor moves from unaligned to aligned position the introduction of pole shoe changes the inductance profile at the unaligned positions which in turn controls the rising torque profiles and reduces torque ripple. The inductance profile of SRM with different pole shoe angle α is shown in Fig. 12 .
PPT Slide
Lager Image
SRM with Rotor pole shoe
PPT Slide
Lager Image
Inductance profile of SRM with rotor pole shoe
The electromagnetic torque vs rotor position characteristic is shown in Fig. 13 . The average torque and torque dip for different pole shoes are summarized in Table 4 . From the table it is clear that the introduction of rotor pole shoe reduces torque ripple with less variation in average torque.
PPT Slide
Lager Image
Torque characteristics of SRM with rotor pole shoe
Average torque and torque dip for various values of α
PPT Slide
Lager Image
Average torque and torque dip for various values of α
- 2. 4 SRM with stator pole taper and Non-uniform air gap
SRM structure with tapered stator and non-uniform air gap is shown in Fig. 14 . From the above analysis it is evident that the SRM design with modified air gap profile produces less torque ripple when compared with other configurations. However there is considerable reduction in average torque. SRM design with a tapered stator pole results in higher average torque when compared with other configurations. Hence a design based on stator pole taper with non-uniform air gap is proposed.
PPT Slide
Lager Image
SRM with stator pole taper and non-uniform air gap
This results in a flatter torque vs. rotor position characteristics near aligned position as shown in Fig. 15 . The average torque and torque dip for different pole taper angles are summarized in Table 5 . From the table it is clear that there is improvement in the average torque and reduction in torque ripple with the proposed design configuration.
PPT Slide
Lager Image
Torque characteristics of tapered stator model with non-uniform air gap
Average torque and torque dip for various values of pole taper angle and θ
PPT Slide
Lager Image
Average torque and torque dip for various values of pole taper angle and θ
The dynamic torque characteristics of the machine is analysed using a drive circuitry [19] as shown in Fig. 16 . The characteristics with a taper angle 1. 4 and θ=0. 5deg with load torque 1Nm is shown in Fig. 17 . The characteristics of the initial design is shown in Fig. 18 . The results are summarized in Table 6 . From the table it is evident that torque ripple is reduced in the proposed design.
PPT Slide
Lager Image
Drive circuitry for dynamic analysis
PPT Slide
Lager Image
Dynamic torque characteristics of tapered stator model with non-uniform air gap
PPT Slide
Lager Image
Dynamic torque characteristics of initial design
Performance characteristics of initial and proposed design
PPT Slide
Lager Image
Performance characteristics of initial and proposed design
3. Conclusion
This paper has investigated the influence of geometrical parameters that alter the pole face shape on the torque profile of SRM. Considering average torque and torque ripple to be optimizing factors, the following results pertaining to the geometrical parameters involved in the study could be useful
  • a) There is considerable improvement in average torque and reduction in torque ripple for the structure with stator pole taper. An increase in pole taper angle increases the average torque and reduces torque ripple.
  • b) Considerable reduction in torque ripple is achieved with SRM design incorporating rotor pole shoe while the average torque produced is almost the same for different pole shoe angle.
  • c) Stator pole face with non-uniform air gap produces minimum torque ripple. There is an optimum angle for which the torque ripple is minimum. However average torque produced by the design is reduced.
  • d) Stator pole taper design with non-uniform air gap shows significant improvement in average torque with considerable reduction in torque ripple. For the 8/6 SRM configuration considered in this work the pole shape design with pole taper angle 1. 4 deg and air-gap angle 0. 5 deg produces minimum torque ripple without compromising the average torque.
The analysis reported will aid the designer in choosing the bounds of design variables to determine optimum design by applying multi-objective optimization.
BIO
M. Balaji He received the B. E Degree in Electrical and Electronics Engineering from Annamalai University, M. E Degree in Power Electronics & Drives from Anna University and Ph. D degree from Anna University. His areas of interest include Electrical Machines and Drives.
S. Ramkumar He received the B. E Degree in Electrical and Electronics Engineering from Bharathiar University, M. E Degree in Power Electronics & Drives from Anna University and Ph. D degree from Anna University. His areas of interest include Electric Drives, Power converters and intelligent control of power converters.
V. Kamaraj Dr. V. Kamaraj is working as Professor in the Department of EEE in SSN College of Engineering, Kalavakkam, TamilNadu, India. His areas of interest include Electrical Machines and Drives.
References
Miller T. J. E 1993 “Switched reluctance motor and their control” Magna Physics Oxford
Krishnan R. 2001 Switched Reluctance Motor Drives: Modeling, Simulation, Analysis, Design and Applications CRC press Boca Raton
Husain I. 2002 “Minimization of Torque Ripple in SRM drives” IEEE Trans. Industrial Electronics 49 (1) 28 - 39    DOI : 10.1109/41.982245
Husain I. , Ehsani M. 1996 “Torque Ripple Minimization in Switched Reluctance Motor Drives by PWM Current Control” IEEE Transactions on Power Electronics 11 (1) 83 - 88    DOI : 10.1109/63.484420
Shaked N. T. , Rabinovici R. 2005 “New Procedures for Minimizing the Torque Ripple in Switched Reluctance Motors by Optimizing the Phase-Current Profile” IEEE Transactions On Magnetics 41 (3) 1184 - 1192    DOI : 10.1109/TMAG.2004.843311
Sahin F. , Erta H. B. , Leblebicioglu L. 2000 “Optimum geometry for torque ripple minimization of switched reluctance motors” IEEE Tranactions on Energy Conversion 15 (1) 30 - 39    DOI : 10.1109/60.849113
Arumugam R. , Lindsay J. F. , Krishnan R. 1988 “Sensitivity of pole arc/pole pitch ratio on switched reluctance motor performance, ” in Conf. Rec. IEEE IAS Annu. Meeting Pittsburgh, PA 1 50 - 54
Faiz J. , Finch J. W. 1993 “Aspects of design optimization for switched reluctance motors, ” IEEE Trans. Energy Convers. 8 (4) 704 - 713    DOI : 10.1109/60.260984
Murthy S. S. , Singh B. , Sharma V. K. 1998 “Finite element analysis to achieve optimum geometry of switched reluctance motor, ” in Proc. IEEE TENCON 2 414 - 418    DOI : 10.1109/TENCON.1998.798204
Sheth N. K. , Rajagopal K. R. 2003 “Optimum pole arcs for a switched reluctance motor for higher torque with reduced ripple, ” IEEE Trans. Magn. 39 (5) 3214 - 3216    DOI : 10.1109/TMAG.2003.816151
Sahraoui H. , Zeroug H. , Toliyat H. A. 2007 Switched Reluctance Motor Design Using Neural-Network Method with Static Finite Element Simulation IEEE Transactions on Magnetics 43 (12) 4089 - 4095    DOI : 10.1109/TMAG.2007.907990
Nabeta S. I. , Chabu I. E. , Lebensztajn L. , Corrêa D. A. P. , DaSilva W. M. 2008 “Mitigation of the torque ripple of a switched reluctance motor through a multi-objective optimization.” IEEE Trans. Magnetics 44 (6) 1018 - 1021    DOI : 10.1109/TMAG.2007.915137
Moallem M. , Ong C. -M. , Unnewehr L. E. 1992 “Effect of Rotor Profiles on the Torque of a Switched-Reluctance Motor” IEEE Transaction on Industry Applications 28 (2) 364 - 369    DOI : 10.1109/28.126743
Sheth N. K. , Rajagopal K. R. 2004 “Torque profiles of a switched reluctance motor having special pole face shapes and asymmetric stator poles” IEEE Transactions on Magnetics 40 (4) 2035 - 2037    DOI : 10.1109/TMAG.2004.829841
Neagoe C. , Foggia A. , Krishnan R. 1997 “Impact of pole tapering on the electromagnetic torque of the switched reluctance motor” IEEE International conference on Electric Machines and Drives WA1/2.1 - WA1/2.3
Choi Yong Kwon , Yoon Hee Sung , Koh Chang Seop 2007 “Pole-shape optimization of a switched-reluctance motor for torque ripple Reduction” IEEE Transactions on Magnetics 43 1797 - 1800    DOI : 10.1109/TMAG.2006.892292
Ramanarayanan L. , Panda D. 1996 “Flux-linkage characteristics of switched reluctance motor, ” in Power Electronics, Drives and Energy Systems for Industrial Growth, Proceedings of the 1996 International Conference on 1 281 - 285
Balaji M. , Kamaraj V. 2011 “Optimum Design of Switched Reluctance Machine for Electric Vehicle Applications using Chaotic Particle Swarm Optimization” International Review of Electrical Engineering 6 (2) 770 - 776
www.infolytica.com