The analysis and comparation of the halfcoiled shortpitch windings with different phase belt are presented in the paper. The halfcoiled shortpitch windings can supply the odd and even harmonics simultaneously, which can be applied in multiphase bearingless motor (MBLM). The space harmonic distribution of the halfcoiled shortpitch windings with two kinds of phase belt is studied with respect to different coil pitch, and the suitable coil pitch can be selected from the analysis results to reduce the additional radial force and torque pulse. The two kinds of halfcoiled shortpitch windings are applied to the five and sixphase bearingless motor, and the comparation from the Finite Element Method (FEM) results shows that the winding with 2π/
m
phase belt is fit for the five phase bearingless motor and the winding with π/
m
phase belt is suitable for the six phase bearingless motor. Finally, a five phase surfacemounted permanent magnet (PM) bearingless motor is built and the experimental results are presented to verify the validity and feasibility of the analysis. The results presented in this paper will give useful guidelines for design optimization of the MBLM.
1. Introduction
Various types of bearingless motors have been successfully applied to multiple areas, such as flywheel energy storage systems, semiconductor, pumps and mixers in medical industry, etc
[1

4]
. It is benefited from its advantages as like noncontact bearing capability and no mechanical friction and lubricants.
Based on the theory of the electromagnetic field, the nonuniform magnetic field in machine airgap produces the magnetic force, which can support the rotor shaft in the airgap. Hence, the uniform magnetic field in the airgap should be broke for the rotor levitation. So far, there are mainly two kinds of methods to work it out. One is that the additional set of conditional windings is wound on the stator core with the main windings
[5

8]
. It needs two sets of inverters to supply the currents to the torque and suspensionwinding respectively. This configuration is clear and easily control. However, this machine has larger size of outer diameter as compared to the conventional motor with mechanical bearings. The other one is that single set of multiphase winding is embedded in the stator core. The advantage of this winding configuration is that it has simpler construction and needs single multiphase inverter.
Many approaches have been proposed with the single set of multiphase windings. A splitphase configured winding was proposed based on the conventional three phase induction motor
[9

11]
. The system can be implemented with a smaller airgap and consequently smaller steady state current. However, it is difficult to obtain better control performance. A bridge configured winding was proposed for multiphase bearingless motors (MBLM) in
[12
,
13]
. It offers relatively low power loss and is possible to be extended to other multiphase machines. However, the isolated multiple singlephase inverters are required to provide the levitation currents. Additionally, a main motor winding structure with middlepoint current injection was proposed in
[14]
. The flux density of only one side of airgap changes with the current injection, and the other side remains unchanged. Thus, the current requirement is low. However, the control system also requires two sets of threephase inverters to build asymmetric fields.
An induction bearingless motor with sixphase halfcoiled shortpitch windings powered by single sixphase inverter was proposed in
[15]
. This winding configuration uses the multiphase winding character of multiple orthogonal
d

q
planes to obtain equivalent torque windings and suspension windings simultaneously. Then the different current sequences are injected to give odd and even harmonic orders of magnetic field. Except the former advantages, the MBLM possesses relatively low power losses and capability of faulttolerant operation
[16]
.
The torque and suspension performance of the MBLM depend on the configuration of the halfcoiled shortpitch winding, and it is necessary to study its characters for the design optimization of the MBLM. Following on the preliminary results in
[17

19]
, the winding optimization for the MBLM can maximize the winding utilization rate for the torque performance and reduce the additional radial force for the suspension performance.
The halfcoiled shortpitch windings with 2π/
m
 and π/
m
phasebelt are investigated in the paper, which are applied to the five and sixphase bearingless motor. The mathematical model of the halfcoiled shortpitch winding with 2π/
m
 and π/
m
phasebelt is analyzed. Then the space harmonic distribution of the two types of windings with respect to different coil pitch is studied, and the analysis and comparation for the five and sixphase bearingless motor by Finite Element Method (FEM) are provided. Finally, the static and dynamic experiment on a five phase surfacemounted permanent magnet (PM) bearingless motor is presented to verify the validity of the analysis.
2. Analysis of Halfcoiled Shortpitch Windings with Different Phase Belt Applied in Five Phase Bearingless Motor
 2.1 Mathematical model of halfcoiled shortpitch winding with 2π/m and π/mphasebelt
In the bearingless motor, it is necessary to obtain two magnetic fields with a difference of polepair numbers equal to one to generate suspension force
[20]
. It means that both odd and even fields are needed simultaneously. The halfcoiled shortpitch winding, which is defined as the winding with the coils under half pole, can meet the requirement. The halfcoiled shortpitch winding with 2π/
m
phase belt is shown in
Fig.1
. There is only two phases in
Fig. 1
, which contains two coils respectively.
Halfcoiled shortpitch winding with 2π/m phase belt
The winding function of the halfcoiled shortpitch windings with single coil is shown in
Fig. 2
, which can be written as
Winding function of halfcoiled shortpitch winding with single coil
where
ϕ
is the spatial angle,
v
is the space harmonic order,
α
_{1}
is the angle between the adjacent slots,
y
_{1}
is the coi l pitch,
N
is the number of turns per slot,
N_{v}
is the magn itude of the
v
th space harmonic.
Hence, it is possible to plot the diagram of winding function of phase
a
based on (1), which is shown in
Fig. 3
. And the general winding function can be written as (2).
Winding function of halfcoiled shortpitch winding with 2π/m phase belt
where
q
_{1}
is the number of coils per phase.
The halfcoiled shortpitch winding with π/
m
phase belt is shown in
Fig. 4
. Each phase winding is divided into two coil groups. They are embedded in the up and downside of the slot respectively, which forms two kinds of coil pitch
y
_{1}
and
y
_{2}
.
Halfcoiled shortpitch winding with π/m phase belt
The winding function of phase
a
is shown in
Fig. 5
. And the general winding function of halfcoiled shortpitch winding with π/
m
phase belt can be written as (3).
Winding function of halfcoiled shortpitch winding with π/m phase belt
where
q
_{2}
is the number of coils per coil group.
 2.2 2π/mphase belt
A 30slot fivephase bearingless motor with halfcoiled shortpitch winding is shown in
Fig. 6
. The winding is 2π/
m
phase belt, which is 72
^{o}
in this bearingless motor. The coil numbers of each phase
q
_{1}
is equal to six in the bearingless motor. All the phase windings are star connected.
Five phase winding with 72^{0} phase belt
The coil pitch
y
_{1}
is equal to ten in
Fig. 6
. The phase winding function is shown in
Fig. 7.(a)
based on (2). In addition, the magnitude of each space harmonic can be obtained by FFT, which is shown in
Fig. 7(b)
. It is seen that the magnitudes of the first and second space harmonic are larger than those of other space harmonics. Especially, the third space harmonic is almost zero.
Phase winding function with y_{1} =10(One turn per coil)
Furthermore, the distribution of the magnitude of each space harmonic with respect to different coil pitch can be also acquired following on the same method as shown in
Fig. 8
. According to the analysis results in
[18]
, the third space harmonic can generate the additional radial force, which should be reduced by adjusting the coil pitch. It is seen that each space harmonic changes periodically with respect to the coil pitch. When the coil pitch is equal to ten, the magnitude of the third space harmonic
N
_{3}
reaches the minimum value. At this point, the magnitude of the first space harmonic is equal to 3.10, which is sin(π/3) times of the maximum value of
N
_{1}
and the magnitude of the second space harmonic is equal to 1.27, which is sin(2π/3) times of the maximum value of
N
_{2}
.
Space harmonic distribution of five phase bearingless motor with 72^{0} phase belt (One turn per coil)
 2.3 π/mphase belt
The five phase bearingless motor with π/
m
phase belt is shown in
Fig. 9
. The winding is 36
^{o}
phase belt, and all of the windings are star connected. Each phase winding is divided into two coil groups, and coil number of each group
q
_{2}
is equal to three. The up and downside coil groups have the same coil pitch
y
_{1}
, and the best choice for
y
_{1}
is 3
q
_{2}
, which is equal to nine in
Fig. 9
. In addition, the coil pith
y
_{2}
is equal to fourteen in
Fig. 9
.
Five phase winding with 36^{0} phase belt
It is possible to generalize the winding function method to the fivephase winding with π/
m
phase belt as shown in
Fig. 10.a)
. The magnitude of each space harmonic can be obtained by FFT, which is shown in
Fig. 10(b)
. It is seen that the magnitudes of the first and second space harmonic are larger than those of other space harmonics, and the third space harmonic reaches its minimal value. In addition, since the fivephase windings are symmetric, the fifth space harmonic will be cancelled out.
Phase winding function with y_{2} =14 (One turn per coil).
Since the coil pitch
y
_{1}
is constant, the space harmonic changes with respect to the coil pitch
y
_{2}
as shown in
Fig. 11
. When the coil pitch
y
_{2}
is equal to 3
q
_{2}
, which means that
y
_{2}
is the same with
y
_{1}
, the space harmonics reach their maximum value simultaneously. Furthermore, when the coil pitch
y
_{2}
is equal to fourteen, the third space harmonic reaches the minimum value. In addition, the magnitudes of the first and second space harmonic are equal to 2.63 and 0.86 respectively at this point. Hence, the utilization rate of this winding is lower than that of the five phase bearingless motor with 72
^{o}
phase belt.
Space harmonic distribution of five phase bearingless motor with 36^{0} phase belt (One turn per coil).
 2.4 FEM analysis for two types of fivephase bearingless motor
The analysis results are verified in a fivephase surfacemounted PM bearingless motor with the parameters shown in
Table 1
by FEM.
Parameters of a fivephase surfacemounted PM bearingless motor
Parameters of a fivephase surfacemounted PM bearingless motor
The axes of the magnetic pole of permanent magnet and the phase winding are coincident, and the unit torque and suspensioncurrent with same phase angle are injected into the five phase winding. The airgap flux density of torque and suspensionfield are obtained as shown in
Fig. 12
. It is seen that the axes of the two torque fields are not coincident, and the phase difference is equal to π/6. The reason is that the axis of the winding with π/
m
phase belt is compounded by two coil groups, the phase difference of which is π/3 in
Fig. 9
. Moreover, the axes of the two suspension fields are not coincident either, and the phase difference is equal to π/3. In addition, the magnitudes of the torque and suspensionfield of the winding with 2π/
m
phase belt are larger than that of the winding with π/
m
phase belt because of the higher winding utilization rate of the former one.
Airgap flux density of the torque field and suspension field with unit curren.
The suspension force with respect to different suspension current values is analyzed by FEM as shown in
Fig. 13
. It is seen that the suspension force is proportional to the suspension current. In addition, the suspension force constants, which is defined as the suspension force with respect to unit current, are 42.68N/A and 29.20N/A respectively. It shows that the winding with 2π/
m
phase belt can produce larger suspension force than that of windings with π/
m
phase belt with same current value. Hence, the winding with 2π/
m
phase belt is more suitable for the five phase bearingless motor.
Suspension force of the two types of five phase bearingless motor.
3. Six Phase Bearingless Motor with Different Phase Belt
 3.1 2π/mphase belt and π/mphase belt
For the convenience of comparation, the six phase bearingless motor possesses the same parameters with the former fivephase bearingless motor as shown in
Table 1
, except that the number of stator slot is equal to 36. The six phase bearingless motor with 60
^{0}
and 30
^{0}
phase belt is shown in
Fig. 14
. And all of the phase windings are star connected. Following on the same method in the previous section, the space harmonic distribution with respect to different coil pitch is presented as shown in
Fig. 15
.
Six phase halfcoiled shortpitch winding
Space harmonic distribution of six phase bearingless motor (One turn per coil)
According to the analysis results presented in
[15]
, the fourth space harmonic can generate the additional radial force, which should be reduced by adjusting the coil pitch in the sixphase bearingless motor. In
Fig. 15.a)
, when the coil pith
y
_{1}
is equal to nine, the magnitude of the fourth space harmonic
N
_{4}
reaches the minimum value. Meanwhile, the magnitude of the first space harmonic is equal to 2.58, which is sin(π/4) times of the maximum value of
N
_{1.}
And the magnitude of the second space harmonic reaches the maximum value 1.59.
In
Fig. 15(b)
, it is interesting to note that the magnitude of the fourth harmonic is eliminated with respect to any value of coil pitch
y
_{2}
. Hence, when
y
_{2}
is equal to 3
q
_{2}
, which means that it is the same with coil pitch
y
_{1}
, the magnitudes of the first and second harmonics can reach the maximum value at the same time. And they are equal to 2.67 and 1.83 respectively. Since the winding distribution coefficient increases, the utilization rate of the winding is improved by 1.035 and 1.15 times than that of the six phase bearingless motor with 60
^{o}
phase belt.
 3.2 FEM analysis for two types of sixphase bearingless motor
The above two sixphase bearingless motors are analyzed by FEM as shown in
Fig. 16
. The results show that the axes of the two torque fields are coincident, which is same for the two suspension fields. In addition, the magnitudes of the torque and suspensionfield of the winding with π/
m
phase belt are a little larger than that of the winding with 2π/
m
phase belt.
Airgap flux density of the torque field and suspension field with unit current
In addition, the suspension force with respect to different suspension current values is analyzed by FEM as shown in
Fig. 17
. The suspension force constants of the six phase winding with π/
m
 and 2π/
m
phasebelt are 42.17N/A and 48.45N/A respectively. It shows that the winding with π/
m
phase belt can produce larger suspension force than that of windings with 2π/
m
phase belt under the same current value. Hence, the winding with π/
m
phase belt is more suitable for the six phase bearingless motor.
Suspension force of the two types of six phase bearingless motors
The characters of the four types of the halfcoiled shortpitch windings are summarized in
Table 2
. It is seen that the halfcoiled shortpitch winding with 2π/
m
phase belt is fit for fivephase bearingless motor and the winding with π/
m
phase belt is suitable for sixphase bearingless motor. In addition, although the six phase bearingless motor with π/
m
phase belt has better suspension performance than that of the five phase bearingless motor, the five phase bearingless motor with 2π/
m
phase belt has the advantages as more compact construction, better torque performance and less power devices, which is more suitable for industry application.
Characters of the halfcoiled shortpitch windings for five and sixphase bearingless motor
Characters of the halfcoiled shortpitch windings for five and sixphase bearingless motor
4. Prototype and Experimental
A fivephase surfacemounted PM bearingless motor prototype is shown in
Fig. 18
. The parameters of the structure are the same as those of the FEM model as shown in
Table 1
. And its winding configuration adopts the halfcoiled shortpitch winding with 2π/
m
phase belt as shown in
Fig. 6
. The bottom of the rotor shaft is held by the spherical roller bearing. And there is a gap of 0.3mm between the top shaft and auxiliary bearing for rotor suspension. There are two eddycurrenttype gap sensors to measure the rotor displacement.
Five phase bearingless motor prototype
To verify the validity of the analysis results by FEM, it is necessary to measure the suspension force constant in the experiment. Firstly, the magnetic pole of PM is located on the
α
axis in the space by injecting little exciting current, and the rotor is maintained at standstill. Then the rotor is suspended by injecting the suspension currents. After that, the external force is applied on the
α
 and
β
axis of the rotor shaft respectively. And the corresponding suspension currents are changed by adjusting the values of the applied force as shown in
Fig. 19
. It is seen that the applied force is proportional to the suspension current. And the suspension force constant is equal to 32.21N/A in
Figs. 19(a)
and 33.67N/A in
Fig. 19(b)
, which is in basic agreement with the FEM results in
Fig. 13
. The error between the analysis result and measurement could result from the manufacture errors, magnetization of the permanent magnet and so on, which is acceptable in the industry application.
Suspension force vs. suspension current
Based on the measured suspension force constant, the suspension and acceleration experimental results are shown in
Fig. 20
. In the initial acceleration stage, the rotor rotates around the auxiliary bearing and the suspension currents stay in zero. After injecting the suspension current, the rotor moves to the center quickly and suspension currents
i
_{d2}
and
i
_{q2}
are in a shape adjusting to maintain the rotor radial displacement variations
α_{r}
and
β_{r}
less than 50 μm, which successfully certify the feasibility of the MBLM.
Suspension and acceleration experiment result
5. Conclusion
This paper analyzes the harmonic distribution of the halfcoiled shortpitch windings with different phase belt and its application in the multiphase bearingless motor (MBLM). The selection of the coil pitch is very important to optimize the torque performance and reduce the harmful space harmonic for the stable suspension of the rotor shaft. Consequently, the analysis and comparation results by FEM show that the winding with 2π/
m
phase belt is fit for five phase bearingless motor and the winding with π/
m
phase belt is proper for six phase bearingless motor. And the five phase halfcoiled shortpitch winding with 2π/
m
phase belt is proved to be more suitable for the MBLM in the industry application. The results presented in this paper provide a theoretical foundation for the further study of the design optimization of the MBLM.
Acknowledgements
This work was supported by the National Basic Research Program of China under Grant No. 2013CB 035604 and the National High Technology Research and Development Program of China under Grant N0. 2011 AA11A101.
BIO
Bingnan Li He received the B.S. and M.S. degrees from the College of Electrical Engineering, Shenyang University of Technology, Shenyang, China, in 2006 and 2009, respectively. He is currently working toward the Ph.D. degree from the College of Electrical Engineering, Zhejiang University, Hangzhou, China. His research interests are in multiphase theory, multiphase bearingless machines and drives.
Jin Huang He received the B.S. degree from the College of electrical engineeering, Zhejiang University, Hangzhou, China, in 1982, and the Ph.D. degree in electrical engineering from the National Polytechnic Institute of Toulouse, Toulouse, France, in 1987, respectively. From 1987 to 1994, he was an associate Professor in College of Electrical Engineering, Zhejiang University, China. He is currently Professor of Zhejiang University. He is engaged in research on electrical machine, AC drives, multiphase machine and condition monitoring of electrical machines.
Wubin Kong He received a B.S. degree from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2009, where he is currently working toward the Ph.D. degree. His research interests are in multiphase machines and drives.
Lihang Zhao He received a B.S. degree from the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2011, where he is currently working toward the Ph.D. degree. His research interests are in parameter identification of AC motor.
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