- Email: [email protected]
Hybrid stator-pole switched reluctance motor to improve radial force for bearingless application
Energy Conversion and Management 52 (2011) 1371–1376
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Hybrid stator-pole switched reluctance motor to improve radial force for bearingless application Huijun Wang a,⇑, Dong-Hee Lee b, Tae-Hub Park b, Jin-Woo Ahn b a b
College of Instrument Science and Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China Department of Electrical and Mechatronics Enigineering, Kyungsung University, 314-79, Daeyeon-Dong, Nam-Gu, Busan 608-736, South Korea
a r t i c l e
i n f o
Article history: Received 11 November 2008 Received in revised form 14 September 2010 Accepted 22 September 2010 Available online 20 October 2010 Keywords: Switched reluctance motor Bearingless
a b s t r a c t A novel hybrid stator-pole switched reluctance motor (HSPSRM) to improve radial force for bearingless application is presented in this paper. The proposed motor can generate a constant suspending force independent of rotor position only using small current excitation. And torque control can be naturally decoupled form suspending force control. Measured data and the results of numerical analysis are given to evaluate the motor structure. In the numerical analysis, the finite element method (FEM) is employed due to the highly nonlinear nature of the motor. A prototype hybrid stator-pole SRM is manufactured and tested in the experimental studies. The obtained test and simulation results show that the hybrid statorpole SRM structure has a constant suspending force, which can be controlled independent from torque control. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction Switched reluctance motor (SRM) has superior performance under special environments, because of their inherent advantages characteristics such as fault tolerance, robustness, low cost and possible operation in applications of high temperature or in intense temperature variations [1,2]. Moreover, SRM has a good feature as bearingless or self-bearing motor, which is characterized by integration of electrical motor and magnetic bearings. Generally, a significant amount of magnetic attraction force is generated in radial direction. This is because that SRM has a short air–gap length in order to produce rotational reluctance torque effectively. It is quite possible to take advantage of this inherent large magnetic attraction force to suspend the rotor shaft. Currently, there are several approaches to generate radial force for suspending the rotor shaft according to winding layer number such as double-layer winding with 12/8-pole structure [3], singlelayer winding with 8/6-pole structure [4] and single-layer winding with 12/8-pole structure [5,6]. However, they are based on sophisticated electronic control strategy with conventional SRM structure. The electronic approach is based on selecting an optimum combination of separated control of each stator pole winding. It is complicated to implement the controller due to the required number of windings and computations. Moreover, it should be noted that torque control and radial force control cannot be decoupled
⇑ Corresponding author. Tel.: +86 10 82338120; fax: +86 10 82338701. E-mail address: [email protected] (H. Wang).
in the general SRM structure, since torque and radial force are the nonlinear functions of simultaneous current and rotor position. Therefore, the operating point has to be selected in compromise between torque and radial force, regions of generating torque and radial force cannot be fully utilized. In order to solve the above problems, this paper presents the construction, numerical analysis and experimental results of a hybrid stator-pole switched reluctance motor (HSPSRM) to improve suspending force and realize naturally decoupling control of torque from radial force control. This paper explains the analytical model of radial force of SRM in Section 2 and the topology of the proposed HSPSRM structure and its basic operating principles in Section 3. The results of the FEM and measurements are shown in Section 4. Section 5 presents some conclusions. 2. Analytical model of general SRM structure Fig. 1 shows the schematic diagram of a general 8/10-pole SRM. The polarities of stator poles are alternating, so that proper magnetic loops can be established. Once phase current is established and maintained in the stator, the rotor teeth will be attracted into aligned position. The attraction force can be divided into tangential and radial components relative to the rotor. The tangential force is converted into the rotational torque. Considering this attraction force produced by one stator pole and one rotor pole firstly, a schematic illustration of the attraction force is shown in Fig. 2. The flux passes through the overlap area as well as the non-overlap area due to the fringing effect. When ignoring the core saturation, the inductance can be expressed as [5]:
0196-8904/$ - see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.09.035
1372
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
Radial force
Radial force generating region
Inductance Torque generating region 0
θ1
θ2
θ3
θ4
Torque
Fig. 3. Inductance, torque and radial force of conventional SRM.
Fig. 1. Conventional 8/10-pole SRM.
Radial force
Rotor tooth
r
Torque
θ0 i
Stator tooth
θ u0 g Fig. 2. Attraction force produced by one stator and rotor poles.
L¼
l0 N2 Lstk Rh0 2g
Fig. 4. Proposed HSPSRM.
þ N2 K f hu0
ð1Þ
in which, l0 is the permeability of the air, Kf is a constant for the fringing inductance, N is the number of coil turns, Lstk is the motor stacking length, R is the rotor radius, g is the air gap length, h0 and hu0 are the overlapping and the non-overlapping angle, respectively. When ignoring the saturation, the radial force F and torque T in this pole can be approximately explained as [1]:
F¼
1 2 dL i 2 dx
ð2Þ
T¼
1 2 dL i 2 dh
ð3Þ
When neglecting the fringing effect, radial force can be simplified as:
F
l0 N2 i2 Lstk Rh0 2g 2
ð4Þ
The above equation shows that the amplitude of suspending force is approximately proportional to the square of the excitation current in the radial force winding. It is inversely proportional to the square of air–gap length. Besides, it is a function of the rotor position. The radial force enhances with the increase of overlapping area between stator pole and rotor pole. When using the conventional SRM structure for bearingless applications, conducting region selection of stator winding requires tradeoff between torque and radial force as shown in Fig. 3. The region from h1 to h3 is to generate torque. Region from h2 to h4 is to generate radial force. Overlap area between torque and radial force generating regions is from h2 to h3. Ideally, it is best
Fig. 5. Suspending control principle.
for motor to operate in this overlap region as shown in hatched part, where enough torque and radial force can be generated at the same time. However, overlap region is very narrow due to the inherent principle of torque and radial force in general SRM structure. Accordingly, both regions for producing torque and radial force cannot be utilized very well. This also means either of torque or radial force can be increased with the expense of larger current value, which results into higher copper loss and thermal problem. 3. Description of the proposed HSPSRM The proposed HSPSRM structure consists of one 8-pole stator and 10-pole rotor. Different from conventional SRM, there are
1373
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376 Table 1 Main parameters of prototype motor. Parameter
Value
Number of stator poles Number of rotor poles Pole arc of stator for torque (°) Pole arc of stator for radial force (°) Pole arc of rotor (°) Length of axial stack (mm) Outer diameter of stator (mm) Inner diameter of stator (mm) Yoke thickness of stator (mm) Length of air gap (mm) Inner diameter of rotor (mm) Yoke thickness of rotor (mm)
8 10 18 36 18 40 112 62 10 0.25 18 9.7
Fig. 6. FEM model of proposed HSRSRM.
(a) Stator
(b) Rotor
Fig. 9. Prototype motor stator and rotor of proposed HSPSRM.
Fig. 7. Flux linkage of radial force winding vs. position and current.
Fig. 10. Experimental setup for the HSPSRM.
Fig. 8. Flux linkage of toque winding vs. position and current.
two types of the poles on the stator as shown in Fig. 4. One is the torque pole such as A1, A2, B1 and B2, which mainly produces rotational torque. The other is the radial force pole such as Px1, Px2, Px3 and Px4, which mainly generates the radial force to suspend rotor and shaft. At the same time, pole arc of radial force is one pole pitch of rotor for producing continuous radial force. Windings on the pole A1 and pole A2 are connected in series to construct torque winding A, and windings on the pole B1 and pole B2 are connected in series to construct torque winding B. Windings on poles Px1, Px2, Px3 and Px4 are independently controlled to construct four radial force windings in x and y directions.
Fig. 5 shows the control principle of the suspending force. From this figure, when rotor has eccentric displacement in the positive ydirection, only current i2 will be turned on and other radial force windings on the poles of Px1, Px3 and Px4 are turned off. Consequently, the radial force in the negative y-direction is generated. Current i2 can be regulated until rotor is in the balanced position. Using same method, if rotor has eccentric displacement in positive x-direction at the same time, only winding Px3 needs to be turned on and current i3 is regulated to make rotor return to its zero eccentric position. According to (2), the radial force of the suspending winding in the proposed structure can be expressed as follows:
F
l0 N2 i2 Lstk Rbr 2g 2
ð5Þ
1374
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
When the suspending current is fixed, the radial force is constant. As for the torque of the radial force winding, the value is approx zero due to the constant overlapping area between the radial force pole and the rotor teeth. Based on above two points, it is obviously that the proposed structure can reduce the complexity of control strategy and realize the decouple control between radial force and torque compared with existing structure. Therefore, torque region and radial force generating regions can be fully utilized. Due to the saturation effects of the material, the design procedure of HSPSRM is somewhat complex. The magnetic reluctance variation with position and current plays an important role in the motor performance. Thus, the accurate information of the inductance or flux linkage distribution for different excitation current values and rotor positions is necessary for accurately evaluating the motor performance [7]. In the mean time, the SRM operates under highly saturated conditions. So, the FEM can be used to obtain the magnetic vector potential values in the presence of complex structure and nonlinear effect [8]. Moreover, these magnetic vector potential values can be processed to obtain the important parameters such as flux distribution and inductance. The whole HSPSRM motor including windings, stator and rotor is modeled by the FEM as shown in Fig. 6. In the FEM analysis, by changing the rotor position within one pole pitch and current, inductance, flux linkage, static torque and radial force can be achieved with respect to different excitation current and rotor positions. The excitation current levels are selected to be from 0.5 A to 5 A with 0.5 A step. The flux linkage–current relationship of radial force winding and torque winding vs. current and position obtained from the FEM are shown in Figs. 7 and 8, respectively. In order to verify the validity of the proposed structure, a HSPSRM prototype motor is designed. The stator and rotor are pressed with M19 steel sheets. The main mechanical parameters of the proposed structure motor are shown in Table 1. Fig. 9 shows stator and rotor designed for the prototype system.
Fig. 11. Comparison of the FEM and measured flux linkage values for torque winding.
4. Experimental results Fig. 12. Comparison of the FEM and measured flux linkage values for radial force winding.
Fig. 10 shows the experimental setup of the prototype HSPSRM for inductance Test. The protecting bearing at suspension terminal is replaced by a conventional ball bearing. When the rotor position is determined, the rotor is fixed by a mechanical setup.
in which, br is the rotor pole arc. Therefore, the radial force of the proposed structure is almost independent from rotor position.
Power Supply Spd_cmd
Σ
+
+ Σ iA(B)_cmd actual speed PI
DSP TMS320F2812 x_cmd
+
Σ
PID
Fx_cmd
-
PI
PWM
Asymmetric Converters
Bearingless SRM
iA(B) Speed Estimation
Current Command
ix_cmd ix
Encoder
Current Controller Demux
y_cmd
+
Σ -
PID
Fy_cmd
iy Current Current Command iy_cmd Controller
i x (y)
actual displacement x actual displacement y
Fig. 13. Control block diagram for proposed structure.
Demux
Actual Displacements
1375
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
250 [μ m] 0.0
Displacement in the y-direction
250 [ μm] 0.0
Displacement in the x-direction
3000 [rpm] 2000
Motor speed
1.25
Torque winding current iA
[A] 0.0 Fig. 14. Experimental configuration.
Radial force winding current iy
2.0 [A] 0.0
Radial force winding current ix
Figs. 11 and 12 show the flux linkages of torque winding and radial force winding at various positions for the different currents. From the above two figures, it can be seen that different from the conventional type, radial force of proposed structure almost can be kept constant at any position for the same excitation current. This can be derived from its flux linkage profile. This means when using the proposed HSPSRM, a larger and wider radial force can be obtained only by small excitation current. However, in the conventional type, radial force changes with the position for the same current obviously as shown in Fig. 11. In order to get enough radial force, excitation current has to be increased, which also results into high thermal problem. In the meantime, there is a strong coupled relation between torque and radial force in the conventional type. So, increase in current will result into torque ripple. Accordingly, a large speed ripple will happen. Fig. 13 shows the control block diagram for the proposed structure. Eccentric displacements of rotor in both directions are measured by the non-contact eddy current sensors with the 16 V to 0 output voltage with respect to 1–0 mm displacement. And these two detected displacement signals can be feedback for radial position control. A PI type controller is adopted to regulate the motor speed to the desired value. PWM duty ratio can be obtained from PI controller. Combining with current rotor position detected from encoder, in-coming phase and off-going phase can be determined. Further, speed can be adjusted by turning on and turning off of corresponding torque winding switches according to PWM duty ratio. Rotor radial displacements can be regulated with two independent close-loop displacement controllers, one for x- and the other for y-direction, respectively. These two PID controllers generate the
0.0
Fig. 16. Experimental result in motor speed variation.
desired radial force commands (Fx_cmd and Fy_cmd). Then, two radial force windings are selected and there currents, i.e. ix_cmd and iy_cmd, are also calculated. Further more, actual current values of selected radial force windings can be controlled through hysteresis method according to these two current command signals. The above control algorithms are realized using a TI TMS320F2812 DSP. Fig. 14 shows the experimental configuration. A weight load is directly applied on the shaft in the radial direction. Fig. 15a and b shows the rotor eccentric displacements and radial force winding currents in x- and y-direction, respectively, in static condition. There is a radial force loads with the value of about 0.6 kgf on each direction. The motor speed command is set to be zero. x_cmd and y_cmd are set to be zero for keeping the rotor position in the center. It can be seen that the rotor moves to its balanced position immediately after the controller was applied. Fig. 16 shows the result with speed change from 2000 rpm to 3000 rpm. It can be seen that when speed step happen, torque winding currents increase suddenly. However, radial force winding currents almost keep constant during the speed variation. Rotor is also kept at the balanced position. Therefore, radial force control can be independent from the torque control when using proposed structure, which can reduce control complexity largely.
250
250 Displacement in the y-direction
Displacement in the x-direction
0.0 [μ m] -250
-250
Radial force in the x-direction
10.0
10.0
Radial force in the y-direction
0.0 [Ν ]
Radial force winding current ix
Time
[Α] 2.5
(a) x-direction
1.0 [sec]
0.0 [ μ m]
0.0 [Ν ]
Radial force winding current iy
2.5 0.0 [Α]
0.0
0.0
5.0 [sec]
Time
0.0
Time
(b) y-direction Fig. 15. Radial force and air–gap displacement at static condition.
1.0 [sec]
1376
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
5. Conclusions In this study, a novel hybrid stator-pole switched reluctance structure is proposed. A prototype motor has been constructed. The analysis and experimental results show that the proposed motor structure has a wider and larger radial force generating region by a small excitation current. And torque control can be naturally decoupled from radial force control when compared to the conventional structure. Therefore, radial force control can be independent from the torque control when using proposed structure, which can reduce control complexity largely. Acknowledgment This work is supported by the Fundamental Research Funds for the Central Universities (YWF-10-03-015), China. References [1] Miller TJE. Switched reluctance motors and their control. Oxford: Oxford University Press; 1993.
[2] Ferhat Daldaban, Nurettin Ustkoyuncu. Multi-layer switched reluctance motor to reduce torque ripple. Energy Convers Manage 2008;3:974–9. [3] Takemoto M, Chiba A, Akagi H, Fukao T. Radial force and torque of a bearingless switched reluctance motor operating in a region of magnetic saturation. In: Proceeding of record IEEE industry applications society annual meeting; 2002. p. 35–42. [4] Li Chen, Wilfried Hofmann. Analytically computing winding currents to generate torque and levitation force of a new bearingless switched reluctance motor. In: Proceeding of the 12th international power electronics and motion control conference; 2006. p. 1058–63. [5] Feng-Chieh Lin, Sheng-Ming Yang. An approach to producing controlled radial force in a switched reluctance motor. IEEE Trans Ind Electron 2006;54(4):2137–46. [6] Feng-Chieh Lin and Sheng-Ming Yang. Instantaneous shaft radial force control with sinusoidal excitations for switched reluctance motors. In: Proceeding of the IEEE industry applications society annual meeting, Seattle; 2004. p. 424– 43. [7] Lindsay JF, Arumugam R. Magnetic field analysis of a switched reluctance motor with multi-tooth per stator pole. In: Proceeding of the institute of electric engineering; 133(6): p. 347–53. [8] Omekanda AM, Broche C, Renglet M. Calculation of the electromagnetic parameters of a switched motor using an improved FEM–BIEM application to different models for the torque calculation. IEEE Trans Ind Appl 1997;33(4):914–8.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Hybrid stator-pole switched reluctance motor to improve radial force for bearingless application Huijun Wang a,⇑, Dong-Hee Lee b, Tae-Hub Park b, Jin-Woo Ahn b a b
College of Instrument Science and Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China Department of Electrical and Mechatronics Enigineering, Kyungsung University, 314-79, Daeyeon-Dong, Nam-Gu, Busan 608-736, South Korea
a r t i c l e
i n f o
Article history: Received 11 November 2008 Received in revised form 14 September 2010 Accepted 22 September 2010 Available online 20 October 2010 Keywords: Switched reluctance motor Bearingless
a b s t r a c t A novel hybrid stator-pole switched reluctance motor (HSPSRM) to improve radial force for bearingless application is presented in this paper. The proposed motor can generate a constant suspending force independent of rotor position only using small current excitation. And torque control can be naturally decoupled form suspending force control. Measured data and the results of numerical analysis are given to evaluate the motor structure. In the numerical analysis, the finite element method (FEM) is employed due to the highly nonlinear nature of the motor. A prototype hybrid stator-pole SRM is manufactured and tested in the experimental studies. The obtained test and simulation results show that the hybrid statorpole SRM structure has a constant suspending force, which can be controlled independent from torque control. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction Switched reluctance motor (SRM) has superior performance under special environments, because of their inherent advantages characteristics such as fault tolerance, robustness, low cost and possible operation in applications of high temperature or in intense temperature variations [1,2]. Moreover, SRM has a good feature as bearingless or self-bearing motor, which is characterized by integration of electrical motor and magnetic bearings. Generally, a significant amount of magnetic attraction force is generated in radial direction. This is because that SRM has a short air–gap length in order to produce rotational reluctance torque effectively. It is quite possible to take advantage of this inherent large magnetic attraction force to suspend the rotor shaft. Currently, there are several approaches to generate radial force for suspending the rotor shaft according to winding layer number such as double-layer winding with 12/8-pole structure [3], singlelayer winding with 8/6-pole structure [4] and single-layer winding with 12/8-pole structure [5,6]. However, they are based on sophisticated electronic control strategy with conventional SRM structure. The electronic approach is based on selecting an optimum combination of separated control of each stator pole winding. It is complicated to implement the controller due to the required number of windings and computations. Moreover, it should be noted that torque control and radial force control cannot be decoupled
⇑ Corresponding author. Tel.: +86 10 82338120; fax: +86 10 82338701. E-mail address: [email protected] (H. Wang).
in the general SRM structure, since torque and radial force are the nonlinear functions of simultaneous current and rotor position. Therefore, the operating point has to be selected in compromise between torque and radial force, regions of generating torque and radial force cannot be fully utilized. In order to solve the above problems, this paper presents the construction, numerical analysis and experimental results of a hybrid stator-pole switched reluctance motor (HSPSRM) to improve suspending force and realize naturally decoupling control of torque from radial force control. This paper explains the analytical model of radial force of SRM in Section 2 and the topology of the proposed HSPSRM structure and its basic operating principles in Section 3. The results of the FEM and measurements are shown in Section 4. Section 5 presents some conclusions. 2. Analytical model of general SRM structure Fig. 1 shows the schematic diagram of a general 8/10-pole SRM. The polarities of stator poles are alternating, so that proper magnetic loops can be established. Once phase current is established and maintained in the stator, the rotor teeth will be attracted into aligned position. The attraction force can be divided into tangential and radial components relative to the rotor. The tangential force is converted into the rotational torque. Considering this attraction force produced by one stator pole and one rotor pole firstly, a schematic illustration of the attraction force is shown in Fig. 2. The flux passes through the overlap area as well as the non-overlap area due to the fringing effect. When ignoring the core saturation, the inductance can be expressed as [5]:
0196-8904/$ - see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.09.035
1372
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
Radial force
Radial force generating region
Inductance Torque generating region 0
θ1
θ2
θ3
θ4
Torque
Fig. 3. Inductance, torque and radial force of conventional SRM.
Fig. 1. Conventional 8/10-pole SRM.
Radial force
Rotor tooth
r
Torque
θ0 i
Stator tooth
θ u0 g Fig. 2. Attraction force produced by one stator and rotor poles.
L¼
l0 N2 Lstk Rh0 2g
Fig. 4. Proposed HSPSRM.
þ N2 K f hu0
ð1Þ
in which, l0 is the permeability of the air, Kf is a constant for the fringing inductance, N is the number of coil turns, Lstk is the motor stacking length, R is the rotor radius, g is the air gap length, h0 and hu0 are the overlapping and the non-overlapping angle, respectively. When ignoring the saturation, the radial force F and torque T in this pole can be approximately explained as [1]:
F¼
1 2 dL i 2 dx
ð2Þ
T¼
1 2 dL i 2 dh
ð3Þ
When neglecting the fringing effect, radial force can be simplified as:
F
l0 N2 i2 Lstk Rh0 2g 2
ð4Þ
The above equation shows that the amplitude of suspending force is approximately proportional to the square of the excitation current in the radial force winding. It is inversely proportional to the square of air–gap length. Besides, it is a function of the rotor position. The radial force enhances with the increase of overlapping area between stator pole and rotor pole. When using the conventional SRM structure for bearingless applications, conducting region selection of stator winding requires tradeoff between torque and radial force as shown in Fig. 3. The region from h1 to h3 is to generate torque. Region from h2 to h4 is to generate radial force. Overlap area between torque and radial force generating regions is from h2 to h3. Ideally, it is best
Fig. 5. Suspending control principle.
for motor to operate in this overlap region as shown in hatched part, where enough torque and radial force can be generated at the same time. However, overlap region is very narrow due to the inherent principle of torque and radial force in general SRM structure. Accordingly, both regions for producing torque and radial force cannot be utilized very well. This also means either of torque or radial force can be increased with the expense of larger current value, which results into higher copper loss and thermal problem. 3. Description of the proposed HSPSRM The proposed HSPSRM structure consists of one 8-pole stator and 10-pole rotor. Different from conventional SRM, there are
1373
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376 Table 1 Main parameters of prototype motor. Parameter
Value
Number of stator poles Number of rotor poles Pole arc of stator for torque (°) Pole arc of stator for radial force (°) Pole arc of rotor (°) Length of axial stack (mm) Outer diameter of stator (mm) Inner diameter of stator (mm) Yoke thickness of stator (mm) Length of air gap (mm) Inner diameter of rotor (mm) Yoke thickness of rotor (mm)
8 10 18 36 18 40 112 62 10 0.25 18 9.7
Fig. 6. FEM model of proposed HSRSRM.
(a) Stator
(b) Rotor
Fig. 9. Prototype motor stator and rotor of proposed HSPSRM.
Fig. 7. Flux linkage of radial force winding vs. position and current.
Fig. 10. Experimental setup for the HSPSRM.
Fig. 8. Flux linkage of toque winding vs. position and current.
two types of the poles on the stator as shown in Fig. 4. One is the torque pole such as A1, A2, B1 and B2, which mainly produces rotational torque. The other is the radial force pole such as Px1, Px2, Px3 and Px4, which mainly generates the radial force to suspend rotor and shaft. At the same time, pole arc of radial force is one pole pitch of rotor for producing continuous radial force. Windings on the pole A1 and pole A2 are connected in series to construct torque winding A, and windings on the pole B1 and pole B2 are connected in series to construct torque winding B. Windings on poles Px1, Px2, Px3 and Px4 are independently controlled to construct four radial force windings in x and y directions.
Fig. 5 shows the control principle of the suspending force. From this figure, when rotor has eccentric displacement in the positive ydirection, only current i2 will be turned on and other radial force windings on the poles of Px1, Px3 and Px4 are turned off. Consequently, the radial force in the negative y-direction is generated. Current i2 can be regulated until rotor is in the balanced position. Using same method, if rotor has eccentric displacement in positive x-direction at the same time, only winding Px3 needs to be turned on and current i3 is regulated to make rotor return to its zero eccentric position. According to (2), the radial force of the suspending winding in the proposed structure can be expressed as follows:
F
l0 N2 i2 Lstk Rbr 2g 2
ð5Þ
1374
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
When the suspending current is fixed, the radial force is constant. As for the torque of the radial force winding, the value is approx zero due to the constant overlapping area between the radial force pole and the rotor teeth. Based on above two points, it is obviously that the proposed structure can reduce the complexity of control strategy and realize the decouple control between radial force and torque compared with existing structure. Therefore, torque region and radial force generating regions can be fully utilized. Due to the saturation effects of the material, the design procedure of HSPSRM is somewhat complex. The magnetic reluctance variation with position and current plays an important role in the motor performance. Thus, the accurate information of the inductance or flux linkage distribution for different excitation current values and rotor positions is necessary for accurately evaluating the motor performance [7]. In the mean time, the SRM operates under highly saturated conditions. So, the FEM can be used to obtain the magnetic vector potential values in the presence of complex structure and nonlinear effect [8]. Moreover, these magnetic vector potential values can be processed to obtain the important parameters such as flux distribution and inductance. The whole HSPSRM motor including windings, stator and rotor is modeled by the FEM as shown in Fig. 6. In the FEM analysis, by changing the rotor position within one pole pitch and current, inductance, flux linkage, static torque and radial force can be achieved with respect to different excitation current and rotor positions. The excitation current levels are selected to be from 0.5 A to 5 A with 0.5 A step. The flux linkage–current relationship of radial force winding and torque winding vs. current and position obtained from the FEM are shown in Figs. 7 and 8, respectively. In order to verify the validity of the proposed structure, a HSPSRM prototype motor is designed. The stator and rotor are pressed with M19 steel sheets. The main mechanical parameters of the proposed structure motor are shown in Table 1. Fig. 9 shows stator and rotor designed for the prototype system.
Fig. 11. Comparison of the FEM and measured flux linkage values for torque winding.
4. Experimental results Fig. 12. Comparison of the FEM and measured flux linkage values for radial force winding.
Fig. 10 shows the experimental setup of the prototype HSPSRM for inductance Test. The protecting bearing at suspension terminal is replaced by a conventional ball bearing. When the rotor position is determined, the rotor is fixed by a mechanical setup.
in which, br is the rotor pole arc. Therefore, the radial force of the proposed structure is almost independent from rotor position.
Power Supply Spd_cmd
Σ
+
+ Σ iA(B)_cmd actual speed PI
DSP TMS320F2812 x_cmd
+
Σ
PID
Fx_cmd
-
PI
PWM
Asymmetric Converters
Bearingless SRM
iA(B) Speed Estimation
Current Command
ix_cmd ix
Encoder
Current Controller Demux
y_cmd
+
Σ -
PID
Fy_cmd
iy Current Current Command iy_cmd Controller
i x (y)
actual displacement x actual displacement y
Fig. 13. Control block diagram for proposed structure.
Demux
Actual Displacements
1375
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
250 [μ m] 0.0
Displacement in the y-direction
250 [ μm] 0.0
Displacement in the x-direction
3000 [rpm] 2000
Motor speed
1.25
Torque winding current iA
[A] 0.0 Fig. 14. Experimental configuration.
Radial force winding current iy
2.0 [A] 0.0
Radial force winding current ix
Figs. 11 and 12 show the flux linkages of torque winding and radial force winding at various positions for the different currents. From the above two figures, it can be seen that different from the conventional type, radial force of proposed structure almost can be kept constant at any position for the same excitation current. This can be derived from its flux linkage profile. This means when using the proposed HSPSRM, a larger and wider radial force can be obtained only by small excitation current. However, in the conventional type, radial force changes with the position for the same current obviously as shown in Fig. 11. In order to get enough radial force, excitation current has to be increased, which also results into high thermal problem. In the meantime, there is a strong coupled relation between torque and radial force in the conventional type. So, increase in current will result into torque ripple. Accordingly, a large speed ripple will happen. Fig. 13 shows the control block diagram for the proposed structure. Eccentric displacements of rotor in both directions are measured by the non-contact eddy current sensors with the 16 V to 0 output voltage with respect to 1–0 mm displacement. And these two detected displacement signals can be feedback for radial position control. A PI type controller is adopted to regulate the motor speed to the desired value. PWM duty ratio can be obtained from PI controller. Combining with current rotor position detected from encoder, in-coming phase and off-going phase can be determined. Further, speed can be adjusted by turning on and turning off of corresponding torque winding switches according to PWM duty ratio. Rotor radial displacements can be regulated with two independent close-loop displacement controllers, one for x- and the other for y-direction, respectively. These two PID controllers generate the
0.0
Fig. 16. Experimental result in motor speed variation.
desired radial force commands (Fx_cmd and Fy_cmd). Then, two radial force windings are selected and there currents, i.e. ix_cmd and iy_cmd, are also calculated. Further more, actual current values of selected radial force windings can be controlled through hysteresis method according to these two current command signals. The above control algorithms are realized using a TI TMS320F2812 DSP. Fig. 14 shows the experimental configuration. A weight load is directly applied on the shaft in the radial direction. Fig. 15a and b shows the rotor eccentric displacements and radial force winding currents in x- and y-direction, respectively, in static condition. There is a radial force loads with the value of about 0.6 kgf on each direction. The motor speed command is set to be zero. x_cmd and y_cmd are set to be zero for keeping the rotor position in the center. It can be seen that the rotor moves to its balanced position immediately after the controller was applied. Fig. 16 shows the result with speed change from 2000 rpm to 3000 rpm. It can be seen that when speed step happen, torque winding currents increase suddenly. However, radial force winding currents almost keep constant during the speed variation. Rotor is also kept at the balanced position. Therefore, radial force control can be independent from the torque control when using proposed structure, which can reduce control complexity largely.
250
250 Displacement in the y-direction
Displacement in the x-direction
0.0 [μ m] -250
-250
Radial force in the x-direction
10.0
10.0
Radial force in the y-direction
0.0 [Ν ]
Radial force winding current ix
Time
[Α] 2.5
(a) x-direction
1.0 [sec]
0.0 [ μ m]
0.0 [Ν ]
Radial force winding current iy
2.5 0.0 [Α]
0.0
0.0
5.0 [sec]
Time
0.0
Time
(b) y-direction Fig. 15. Radial force and air–gap displacement at static condition.
1.0 [sec]
1376
H. Wang et al. / Energy Conversion and Management 52 (2011) 1371–1376
5. Conclusions In this study, a novel hybrid stator-pole switched reluctance structure is proposed. A prototype motor has been constructed. The analysis and experimental results show that the proposed motor structure has a wider and larger radial force generating region by a small excitation current. And torque control can be naturally decoupled from radial force control when compared to the conventional structure. Therefore, radial force control can be independent from the torque control when using proposed structure, which can reduce control complexity largely. Acknowledgment This work is supported by the Fundamental Research Funds for the Central Universities (YWF-10-03-015), China. References [1] Miller TJE. Switched reluctance motors and their control. Oxford: Oxford University Press; 1993.
[2] Ferhat Daldaban, Nurettin Ustkoyuncu. Multi-layer switched reluctance motor to reduce torque ripple. Energy Convers Manage 2008;3:974–9. [3] Takemoto M, Chiba A, Akagi H, Fukao T. Radial force and torque of a bearingless switched reluctance motor operating in a region of magnetic saturation. In: Proceeding of record IEEE industry applications society annual meeting; 2002. p. 35–42. [4] Li Chen, Wilfried Hofmann. Analytically computing winding currents to generate torque and levitation force of a new bearingless switched reluctance motor. In: Proceeding of the 12th international power electronics and motion control conference; 2006. p. 1058–63. [5] Feng-Chieh Lin, Sheng-Ming Yang. An approach to producing controlled radial force in a switched reluctance motor. IEEE Trans Ind Electron 2006;54(4):2137–46. [6] Feng-Chieh Lin and Sheng-Ming Yang. Instantaneous shaft radial force control with sinusoidal excitations for switched reluctance motors. In: Proceeding of the IEEE industry applications society annual meeting, Seattle; 2004. p. 424– 43. [7] Lindsay JF, Arumugam R. Magnetic field analysis of a switched reluctance motor with multi-tooth per stator pole. In: Proceeding of the institute of electric engineering; 133(6): p. 347–53. [8] Omekanda AM, Broche C, Renglet M. Calculation of the electromagnetic parameters of a switched motor using an improved FEM–BIEM application to different models for the torque calculation. IEEE Trans Ind Appl 1997;33(4):914–8.