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Rotor Design for Sensorless Position Estimation in
Permanent-Magnet Machines
Rafal Wrobel, Alan S. Budden, Dan Salt, Derrick Holliday, Phil H. Mellor,
Andrei Dinu, Parmider Sangha, and Mark Holme
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 9, SEPTEMBER 2011
Page(s): 3815 - 3824
學生:馮謙詠
指導老師:王明賢
NCKU Servo Control Lab / Electric Motor Technology Research Center
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Outline
1.Abstract
2.Introduction
3. Design Considerations
a. Manufacturing Considerations
4. FE Design
a. FE Modeling
b. Saliency Analysis
5.Conclusions
6.References
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Abstract
A high-frequency injection sensorless rotor position estimation algorithm is
incorporated directly into the finite element design process to realize a
permanent-magnet (PM) machine that is suited to zero- and low-speed
sensorless control.
The machine design is tightly constrained by an existing stator assembly, only
enabling the redesign of the replacement PM rotor.
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Introduction
Sensorless position estimation in PM machines is reliant upon the existence of
a measurable electrical parameter that is related to rotor position. When the
machine is operating at speed, the electromotive force (EMF) generated across
the machine supply terminals provides a suitable rotor-position dependent
quantity .
When the rotor is stationary or operating at low speed, however, no rotorposition-dependent parameter is readily available, and more complex methods
that typically depend upon detection of the machine’s rotor dependent
inductance profile are used .
Typically, a PM machine may exhibit some degree of magnetic saliency which
will cause a rotor-position-dependent variation in the inductance of the stator
windings.
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Design Considerations
This machine comprises a concentrated wound stator with 1.5 slots per pole
and a uniformly magnetized rotor with NdFeB magnet segments bonded to the
surface of a magnetically permeable steel hub, as shown in Fig. 1.
The interior PM (IPM) rotor topology exhibits more favorable saliency
characteristics and was therefore chosen as the basis for the development of a
new rotor.
Fig. 1. Baseline concentrated wound surface magnet topology.
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Manufacturing Considerations
To simplify manufacture, the proposed rotor would use soft magnetic
composite (SMC) pole pieces with rectangular PMs arranged in between a
“spoke” pattern.
The proposed rotor design is shown in Fig. 2, where the composite pole pieces
and PMs are bonded to a nonmagnetic steel hub and the structure is secured
using a thin sleeve.
Fig. 2. Proposed IPM arrangement.
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FE Design
The manufacturing considerations described in Section 3-a dictate that torque
and magnetic saliency are key design parameters.
In addition, the predefined stator structure and air gap and the proposed rotor
structure and materials limit the design variables to the depth and width of the
rectangular magnet segments.
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FE Modeling
The magnet depth is expressed in terms of the ratio of the inner dimension Rm
to the outer radius R , and the width is expressed as the ratio of an angle  m
subtended by the magnet to the pole pitch  p , as shown in Fig. 2. These
quantities are represented in the set of dimensionless parameters x, as shown in
(7), which is used to specify the motor structure used in the FEM analysis
  m Rm 
 , 
  p R 
(7)
Torque is calculated using the coenergy method shown in (8), where W is the
magnetic coenergy, Θ is the angle defining the relative position between the
rotor and the stator, and ΔΘ is the angular rotation between field solutions
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FE Modeling
Note that (10) is the inverse of the more usual definition of the saliency ratio
and reflects the inverse saliency that is characteristic of the IPM machine
xi 
L 
q i
Ld i
.
(10)
Both the torque and saliency ratio calculations are repeated for different values
of x, with target values of Ti T = 1 to ensure the correct torque performance
and xi= 1.1, 1.2, 1.3, . . . , 2.5 to ensure a degree of rotor saliency that is
suitable for sensorless control.
The FE analysis incorporates an objective function, defined in (11), which
seeks to minimize the error between the calculated and target values of torque
and saliency
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FE Modeling
Fig. 4 shows that, in general, the torque developed by the
motor increases as  m  p (magnet width) increases and as
R m Rr (magnet depth) decreases. The saliency surface,
shown in Fig. 5, is more complex and shows no simple trend
in relation to changes to m  p and R m Rr .
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FE Modeling
Table I presents the target torque and
saliency ratio values and the
corresponding values resulting from the
FE design process which are also
highlighted on the surface plots of
Figs. 4 and 5. It is important to note that the
saliency ratios shown in Table I result from
calculation at a fixed rotor position
and that, beyond the limits of
 m  p = 0.73 and  m  p = 0.93, none of
the resulting rotor versions meets the design
specification.
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Saliency Analysis
Fig. 9. Estimated rotor position for rotor version 1.
Fig. 11. Estimated rotor position for rotor version 14.
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Manufacture Of Rotor Version3
Fig. 14. IPM rotor version 3. (a) Rotor components. (b) Assembled rotor prior
to the addition of the containment sleeve.
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Conclusion
A high-frequency injection sensorless position estimation algorithm has been
directly incorporated into the FE design procedure for an IPM machine,
resulting in a machine that exhibits the required electrical characteristics while
being tailored for sensorless control.
The design was highly constrained such that the rotor was required to fit
within an existing stator and to produce the same torque as the original motor
The experimental results verify the machine performance and operation under
the control of an injection-based sensorless rotor position strategy.
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Thanks for your attention.
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