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第 25 卷 第 5 期 中 国 电 机 工 程 学 报 Vol.25 No.5 Mar. 2005
2005 年 3 月 Proceedings of the CSEE ©2005 Chin.Soc.for Elec.Eng.
文章编号：
0258-8013 (2005) 05-0098-06
中图分类号：
TM341
文献标识码：
A
学科分类号：
470
⋅
40
一种新型混合转子结构无轴承电动机
磁悬浮力的矢量控制
王凤翔
1
，王宝国
1
，徐隆亚
2
(1. 沈阳工业大学电气工程学院，辽宁省 沈阳市 110023；
2. 美国俄亥俄州立大学电气工程系，美国俄亥俄州 哥伦布市 43210 ）
LEVITATION FORCE VECTOR CONTROL OF A NOVEL BEARINGLESS MOTOR
WITH HYBRID ROTOR STRUCTURE
WANG Feng-xiang
1
, WANG Bao-guo
1
，XU Long-ya
2
(1. School of Electrical Engineering, Shenyang University of Technology, Shenyang 110023, Liaoning Province,
China; 2. Department of Electrical Engineering, Ohio-State University, Columbus, 43210, Ohio-State USA)
ABSTRACT: Bearingless motors have the advantage of
without mechanical wear and noise. The electromagnetic torque
and levitation force for rotor rotation and suspension are
generated by the motor itself. Based on the comparative study
of toque and magnetic levitation force for a bearingless motor
with different rotor structures by means of finite element
analysis, this paper presents a new hybrid rotor structure, which
has the advantages of both permanent magnet rotor and
induction rotor. The proposed bearingless motor can not only
produce larger electromagnetic torque and levitation force but
also provide a way to realize decoupling control
of levitation
force through current vector orientation. A control system of the
proposed bearingless motor with hybrid rotor structure based
on DSP TMS320C32 and Xilinx CPLD has been set up. The
vector control strategy of levitation force has been implemented.
The tested results show that the proposed motor design and
control strategy of the novel bearingless motor are feasible.
KEW WORDS: Electric machiinery; Bearingless motor;
Hybrid rotor;
Current vector orientation; Decoupling control
of levitation force
摘要：无轴承电机具有无机械磨损和噪声等优点，其转子旋
转和悬浮的电磁转矩和磁悬浮力皆由电机本身产生。在对不
同转子结构转矩和磁悬浮力进行有限元对比分析的基础上，
该文提出了一种兼有永磁式和感应式转子共同优点的新型
基金项目: 国家自然科学基金项目(59977014)。
Project Supported by the National Natural Science Foundation of China
(59977014).
混合转子结构。该电机不仅能产生大的电磁转矩和磁悬浮
力，而且提供了通过电流矢量定向实现悬浮力解耦控制的途
径。基于数字信号处理器 DSP （TMS320C32）和复杂可编
程逻辑芯片 CPLD（Xilinx），构建了混合转子无轴承电机的
控制系统，实现了悬浮力矢量控制策略。试验结果表明该文
所提出的新型无轴承电机的设计与控制策略是可行的。
关键词
：电机；无轴承电动机；混合转子；电流矢量定向；
悬浮力解耦控制
1 INTRUDUCTION
Magnetic bearings have been widely used due to
their advantages of without mechanical wear and
noise. A bearingless motor is an electromotor without
bearings of any kind, conventional or magnetic. Its
innovation is that the magnetic forces for the rotor
suspension are generated by the motor itself and not
by the separated magnetic bearings [1]. To generate
torque and levitation force, specially designed stator
and rotor structures are needed. Various rotor
structures may be used for a bearingless motor
design [2-5]. In the previous work, some stator and
rotor structures are introduced [2-3, 6-9]. However,
there is not a rotor structure, which has the good
capability of producing both torque and levitation
force [10].
Based on the comparative study of toque and
第 5 期 王凤翔等： 一种新型混合转子结构无轴承电动机磁悬浮力的矢量控制 99
magnetic levitation force for a bearingless motor with
different rotor structures (cage rotor, reluctance rotor,
surface mounted permanent magnet rotor and internal
permanent magnet rotor) by means of finite element
analysis, this paper presents a new hybrid rotor
structure, which can provide the motor with better
torque and levitation force control performance. A
new vector control strategy of levitation force is also
proposed based on the derived levitation force model.
2 COMPARISON OF DIFFERENT ROTOR
STRUCTURES
The structure of a bearingless motor is similar to
conventional AC machines. In order to provide torque
and levitation force, the stator has two sets of stator
windings with different pole numbers. All the
brushless rotor structures of AC machines can be used
for the bearingless motor. However, the question is
what kind of rotor structure is better from the point of
view to produce more torque and magnetic levitation
force. Therefore, it is necessary to make a comparative
study of torque and levitation force for the different
rotor structures as shown in Fig. 1
(a) Cage rotor (b) Reluctance rotor
(
c) Surface mounted PM rotor (d) Internal PM roto
r
图 1 无轴承电机的转子结构
Fig. 1 Rotor structures of bearingless motor
By using finite element method (FEM), the
calculated levitation forces versus the levitation force
winding current for a bearingless motor with four
rotor structures are as shown in Fig. 2. The operation
condition is as follows: the motor has a uniform air
gap of 0.6 mm and the torque winding has a fixed
current of 0.45 A. From Fig. 2, it can be seen that the
cage rotor and reluctance rotor bearingless motor have
the maximum and minimum levitation force
respectively, and the capability of producing levitation
force for the two types of PM rotor has no much
difference. The calculated electromagnetic torque for
different rotor structures under the same operation
condition is as shown in Fig.3. The comparison shows
that the PM rotor bearingless motors can produce
more electromagnetic torque than the cage and
reluctance rotor motors.
Current of levitation winding /A
Levitation force / N
Reluctance Rotor
Cage rotor
Surface PM rotor
Internal PM roto
r
20
16
12
8
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
图 2 不同转子结构悬浮力比较
Fig. 2 Comparison of levitation forces for different rotor
structures
0
0.002
0.004
0.006
0.008
0.010
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Surface PM rotor
Internal PM rotor
Reluctance Rotor
Ca
g
e roto
r
Torque / Nm
Current of levitation winding / A
Torque/N
⋅
m
图 3 不同转子结构转矩比较
Fig. 3 Comparison of torque for different rotor
structures
3 A NOVEL HYBRID ROTOR STRUCTURE
The comparison from Fig. 2 and Fig. 3 shows that
the surface mounted PM rotor would be the preferred
rotor structure of the bearingless motor since it has the
largest torque and larger levitation force in compare
with other rotor structures. This conclusion is deduced
from the case without eccentricity between the stator
and rotor. However, there is always somewhat
eccentricity between the rotor and stator for the
practical operation due to various reasons. If the air
gap is not uniform, some additional magnetically
attractive force will be produced on the side having
smaller air gap[4-5]. The calculated radial forces by
means of FEM for different rotor position
100 中 国 电 机 工 程 学 报 第 25 卷
displacements are as shown in Fig. 4. It can be seen
from Fig. 4 that the radial force increases linearly with
respect to the rotor position displacement. In order to
make the rotor back to the center position, sufficient
current of the stator levitation force winding should be
applied. Unfortunately, the air gap flux density
produced by the levitation force winding current is
much smaller than that produced by the permanent
magnets, and it is difficult to make the rotor back to
the center position by increasing the levitation force
winding current.
8.0
6.0
4.0
2.0
0
0 0.04 0.08 0.12 0.16 0.20
Rotor position displacement / mm
Radial force / N
图 4 偏心产生的径向力
Fig. 4 Radial force due to eccentricity
A proposed novel rotor structure of bearingless
motor in this paper is as shown in Fig.5. Two
additional rotor cores are added to the PM rotor to
increase the capability of producing levitation force.
This hybrid rotor structure has the advantages of both
PM rotor and cage rotor.
Fig.6 shows the calculated radial force
characteristics versus current applied to the levitation
force winding for different rotor structures under the
same rotor displacement of 0.05mm from the center
position. The four curves in Fig. 6 are related to the
different cases.
g
0
g
c
l
0
l
c
l
c
Permanent
magnets
Additional
rotor core
Non-magneti
c
l
c
L
0
g
c
g
0
l
c
图 5 一种新型无轴承转子结构
Fig. 5 A new rotor structure of bearingless motor
0 0.4 0.8 1.2 1.6
0
0.4
0.8
1.2
1.6
2.0
Pure PM rotor
2l
c
=15mm,g
c
=1.0mm
2l
c
=15mm,g
c
=0.8mm
2l
c
=10mm,g
c
=0.5mm
Rotor position displacement/mm
Radial force/N
g
0
=1.0mm
图 6 不同转子结构径向力比较
Fig. 6 Comparison of radial forces for different rotor
structures
From the comparison of four curves it can be
seen that the radial force can not be compensated by
only increasing the levitation winding current for pure
PM rotor (curve 1), and using additional rotor core
and decreasing air gap of additional rotor core are the
effective way to compensate the radial force (curve 2
through 4).
4 LEVITATION FORCE VECTOR CONTROL
The new structure bearingless motor has a 4-pole
3-phase torque winding and 2-pole 2-phase levitation
force winding. The 3-phase torque winding can be
equivalent as a 2-phase winding. If the 2-pole and
4-pole windings are supplied with symmetrical
2-phase AC voltage having the same frequency, the
phase currents of the two windings in x-y stationary
frame can be expressed as follows:
44 4
cos( )
xm
iI t
ω
ϕ
=+ (1)
44 4
sin( )
ym
iI t
ω
ϕ
=+ (2)
22 2
cos( )
xm
iI t
ω
ϕ
=+ (3)
22 2
sin( )
ym
iI t
ω
ϕ
=+ (4)
The 4-pole and 2-pole winding currents will
produce air gap magnetic fields respectively. By
means of Maxwell stress tensor method, the radial
force on the rotor surface can be calculated [11]. By
integrating the force along with the rotor surface, the
resultant x- and y- direction forces can be expressed as
follows:
42 4 2
[cos()]
xmm
FkII
ϕ
ϕ
=− (5)
42 4 2
[sin( )]
ymm
FkII
ϕ
ϕ
=− (6)
The coefficient k is determined by the following
equation:
第 5 期 王凤翔等： 一种新型混合转子结构无轴承电动机磁悬浮力的矢量控制 101
014 2
2
0
4
rl N N
k
g
μ
π
= (7)
where N
4
and N
2
are the equivalent turns of the 4-pole
and 2-pole winding per phase; r, l
1
and g
0
are the inner
radius of stator, additional stack length and air gap
length respectively. Using (1) through (4), the x- and
y- direction forces can be expressed as
42 42
[ ]
x
xx yy
Fkii ii=+ (8)
42 42
[ ]
yyxxy
Fkii ii=− (9)
It can be seen from (8) and (9) that the levitation
forces in x-and y-direction can be calculated using the
instantaneous stator currents. However, the force in x-
(or y-) direction depends upon all the winding currents.
From the point of view to simplify the control, it is
desirable to decouple the mutual effect of the winding
currents between the x- and y-directions [12].
The phase currents in x-y frame can be
transformed into the new variables in a d-q rotating
reference frame. The schematic diagram of the
relationship between the stationary x-y reference
frame and rotating d-q reference frame is as shown in
Fig. 7. The relationship of the variables between the
two reference frames can be expressed as follows:
44
44
22
22
cos sin 0 0
sin cos 0 0
00cossin
00sincos
qy
dx
qy
dx
ii
θθ
ii
θθ
ii
θθ
θθ
ii
⎡⎤ ⎡⎤
−
⎡⎤
⎢⎥ ⎢⎥
⎢⎥
⎢⎥ ⎢⎥
⎢⎥
=
⎢⎥ ⎢⎥
⎢⎥
−
⎢⎥ ⎢⎥
⎢⎥
⎢⎥ ⎢⎥
⎣⎦
⎣⎦ ⎣⎦
(10)
If the d- axis is chosen as the direction of current
vector
i
4
as shown in Fig. 7, the angle
θ
can be
determined as
θ
= atan (i
4y
/i
4x
). After locking the
d-axis to the direction of vector
i
4
, the current
variables in d-q reference frame will become constant
because the current vector
i
4
and i
2
have the same
angular frequency. Equation (10) can be expressed as
4
44
2242
242
2
0
sin( )
cos( )
q
dm
qm
m
d
i
iI
iI
I
i
ϕϕ
ϕϕ
⎡⎤
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
=
⎢⎥
⎢⎥
−−
⎢⎥
⎢⎥
−
⎢⎥
⎣⎦
⎣⎦
(11)
Using the new variables, the expression of levitation
forces can be simplified as
42
x
dd
Fkii= (12)
42ydq
Fkii=− (13)
It is apparent that the levitation force control can
be easily realized through controlling the current
vector
i
2
in the synchronous rotational frame based on
(12) and (13). The levitation force component F
x
can
be generated by setting i
2d
= I
2m
and i
2q
= 0. In the
same way, the levitation force component F
y
can be
generated by setting i
2q
= I
2m
and i
2d
= 0.
q
y
i
2
d
i
4
x
i
4x
i
4
y
0
θ
图 7 静止 x-y 坐标与旋转 d-q 坐标系统之间的关系
Fig. 7 Relationship between stationary x-y and rotating
d-q reference frames
The generation progress of the levitation force
during the variation of the winding current and
magnetic field can be illustrated clearly by Fig. 8,
which shows the instantaneous current vector
positions, magnetic field distribution and direction of
the resultant levitation force for different intervals. It
can be seen that although the rotating speeds of
current vector
i
2
and i
4
are the same, the rotating
speeds of the magnetic fields produced by these two
winding currents are different due to the different pole
numbers of the two windings. As the result, the
magnetic field distribution is not the same for different
F
ω
t
=0
ω
t
=
π
/2
F
ω
t
=
π
F
ω
t
=3
π
/2
F
q
d
X
YY
0
i
2
i
4
q
q
q
d
d
d
0
0
0
X
X
Y
Y
Y
i
2
i
4
i
2
i
4
i
4
i
2
X
图 8 不同时刻的电流矢量、磁场分布与合成磁悬浮力
F
ig. 8 Current vector, magnetic field distribution and
levitation force for different intervals
102 中 国 电 机 工 程 学 报 第 25 卷
interval. However, the same resultant levitation force
can be obtained by controlling the current vector
i
2
and
i
4
based on the proposed control strategy.
5 EXPERIMENTAL RESULTS
A control system of the proposed bearingless
motor with hybrid rotor structure based on DSP
TMS320C32 and Xilinx CPLD has been set up. The
proposed vector control scheme is shown in Fig. 9.
The motor speed is controlled by the open-loop speed
controller based on the speed command
n
*
. There are
two closed loops for the rotor levitation control. The
rotor position loop and the current loop of the
levitation winding are used as the outer loop and inner
loop respectively. After taking the reference frame
transformation, the outputs of the rotor position loop
are used as the current loop commands
i
*
2d
and i
*
2q
.
图
9
混合转子无轴承电机控制系统原理框图
Fig. 9 System control block diagram of a bearingless motor with hybrid rotor
Bearingless
motor
i
4y
i
4x
－
i
2
y
i
2
x
v
2q
v
2d
θ
x
*
y
*
PD
PD
PI
PI
θ
=
arctan(i
4y
/i
4x
)
abc-xy
VSI
Inverter
Speed
controller
i
*
2d
i
*
2q
i
2d
i
2q
xy- dq
VSI
Inverter
xy-abc
θ
n*
dq-xy
Rotor position
sensing
+
+
i
2x
i
2y
－
－
－
xy-dq
The vector control strategy of levitation force
described above has been implemented. Fig. 10 and
11 show the tested rotor position displacements at
the speed of 750 r/min without and with the vector
control of levitation forces respectively. The top two
traces of each figure are the
x- and y-direction rotor
displacements detected by the eddy-current sensors.
The bottom trace shows the rotor displacement as a
20ms/div
50μm/div
50
μ
m/di
v
x
-direction
y
-direction
x
y
50μm/div
图 10 未加悬浮力控制时的转子位移轨迹
Fig. 10 Rotor displacement trace without levitation force
control
space vector. Fig. 10 shows that the rotor movement
is large and restricted by the touch down bearing for
lack of levitation force control. Under the vector
control, the rotor displacements become smaller and
the rotor suspension is realized as shown in Fig. 11.
20ms/div
50
μ
m/di
v
50μm/div
x
-direction
y
-direction
x
y
50μm/div
图 11 加悬浮力控制时的转子位移轨迹
Fig. 11 Rotor displacement trace with levitation force
control
6 CONCLUSION
The proposed hybrid rotor structure of a
第 5 期 王凤翔等： 一种新型混合转子结构无轴承电动机磁悬浮力的矢量控制 103
bearingless motor can not only produce larger
electromagnetic torque and levitation force but also
provide a way to realize levitation force control
through current vector orientation. The tested results
on the prototype machine show that the proposed
motor design and control strategy of the novel
bearingless motor are feasible.
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收稿日期：2004-12-24。
作者简介：
王凤翔（1938-）男，教授，博士生导师，研究方向为特种电机及
其控制、电力电子与能量转换；
王宝国（1960-）男，博士，副教授，研究方向为特种电机及其控
制；
徐隆亚 (1955-) 男, 博士，美国俄亥俄州立大学教授，研究方向为
电机设计与控制、电力电子与电力传动。
