energies
Article
Linear Hybrid Reluctance Motor with High
Density Force
Jordi Garcia-Amorós
Departament d’Enginyeria Electrònica, Elèctrica i Automàtica, Universitat Rovira i Virgili,
43007 Tarragona, Spain; jordi.garcia-amoros@urv.cat; Tel.: +34-977-559-695
Received: 20 September 2018; Accepted: 16 October 2018; Published: 18 October 2018
Abstract: Linear switched reluctance motors are a focus of study for many applications because of
their simple and sturdy electromagnetic structure, despite their lower thrust force density when
compared with linear permanent magnet synchronous motors. This study presents a novel linear
switched reluctance structure enhanced by the use of permanent magnets. The proposed structure
preserves the main advantages of the reluctance machines, that is, mechanical and thermal robustness,
fault tolerant, and easy assembly in spite of the permanent magnets. The linear hybrid reluctance
motor is analyzed by finite element analysis and the results are validated by experimental results.
The main findings show a significant increase in the thrust force when compared with the former
reluctance structure, with a low detent force.
Keywords: linear switched reluctance machine; finite element analysis; PM-assisted; thrust-force
performance
1. Introduction
Currently, there are many applications that use hydraulic or pneumatic drives that are being
substituted by linear electric actuators in manufacturing industries and robotic systems because of their
more stable, precise, and controllable force, along with a higher energy efficiency [1]. In this context,
reluctance machines present good environmental behavior due to their high efficiency and inherent
ease of assembly and dismantling [2]. For these reasons, among others, there are several studies
that have focused on new magnetic structures [3–5], in order to enhance their force performance [6]
and increase force density by adding permanent magnets [7–14]. As an example, linear switched
reluctance motors (LSRM) and linear permanent magnet synchronous motors (LPMSMs) have been
proposed for propelling a ropeless elevator [15,16], for an automotive suspension system [17], and for a
linear generator in direct drive wave-power converter [18]. Up to now, LPMSMs have a higher power
density and efficiency when compared with LSRMs, despite their inherent detent or cogging force,
which can be reduced or eliminated by applying several techniques [19,20]. Many current research
papers deal with developing and optimizing linear motors in order to increase power density and
efficiency [21–23].
With this aim, this work presents and analyzes a four-phase LSRM, whose novelty is in the mover.
A series of vertically magnetized permanent magnets (PMs) are inserted into the slots of the mover of
the LSRM. The resulting actuator is analyzed by finite element analysis (FEA) and a prototype was
built and tested. The FEA results and the experimental results are in good agreement and reveal an
approximately 100% increase in the peak thrust force; a moderate ripple factor operating in single
pulse; and a relative low detent force, about 10% of peak thrust force. The results obtained anticipate
an interesting actuator for high force density applications, such as those cited above.
Energies 2018, 11, 2805; doi:10.3390/en11102805
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Energies 2018, 11, x FOR PEER REVIEW
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2. Linear Hybrid Reluctance Motor Structure and Operation Principle
Energies 2018, 11, 2805
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LSRMs
are classified according to the relation between the planes that contain the flux
lines and
the axis of movement. Longitudinal flux LSRM is when these planes are parallel, and transverse flux
Linear
Hybrid
Motor Longitudinal
Structure and Operation
Principle
LSRM is 2.when
they
are Reluctance
perpendicular.
flux LSRM
may be tubular or flat, with single or
double side LSRMs
for theareflat
case. according
The LSRM
has
two between
main parts:
thethat
active
part,
the
classified
to the
relation
the planes
contain
the which
flux linescontains
and
the
axis
of
movement.
Longitudinal
flux
LSRM
is
when
these
planes
are
parallel,
and
transverse
flux
concentrated windings, also called primary part; and the passive or secondary part, made of an empty
LSRM is when they are perpendicular. Longitudinal flux LSRM may be tubular or flat, with single
slotted iron
structure. This work focuses on the double-sided longitudinal flux LSRM, referred to
or double side for the flat case. The LSRM has two main parts: the active part, which contains the
from now
on as LSRM.
concentrated windings, also called primary part; and the passive or secondary part, made of an empty
Theslotted
proposed
structure
iswork
shown
in Figure
1. The ironlongitudinal
lamination
is theto same
iron structure.
This
focuses
on the double-sided
fluxstructure
LSRM, referred
from as that
of a conventional
four-phase double-sided longitudinal flux LSRM (see Figure 1 in grey), the
now on as LSRM.
The
proposed
structure
shown
in Figure
1. The iron in
lamination
structure
is theFrom
same as
thatreluctance
of
modelling, simulation, and
testisof
which
are reported
the work
of [24].
this
double-sided
flux
LSRM
Figure 1 in grey),
the modelling,
structure,a conventional
a series of four-phase
permanent
magnets longitudinal
type NdFeB
N32
(in(see
black/white,
see Figure
1) have been
simulation, and test of which are reported in the work of [24]. From this reluctance structure, a series of
placed in
the secondary slotted lamination. The PMs are vertically magnetized following the
permanent magnets type NdFeB N32 (in black/white, see Figure 1) have been placed in the secondary
arrangement
in Figure
1. Each
phase magnetized
has four coils
per pole
connectedshown
in series,
in such
slottedshown
lamination.
The PMs
are vertically
following
the arrangement
in Figure
1. a way
that onlyEach
onephase
fluxhas
path
produced.
The main
dimensions
of the
(active
part)
are the pole
fouriscoils
per pole connected
in series,
in such a way
thatprimary
only one flux
path is
produced.
main width
dimensions
the primary
(active𝑐part)
are the pole length l p , pole
widththe
b p , and
slot width
length 𝑙𝑝The
, pole
𝑏𝑝 ,ofand
slot width
defines
primary
pole pitch
𝑝 , the sum of which
c p , the sum of which defines the primary pole pitch τp = b p + c p . For the secondary (passive) part, the
𝜏𝑝 = 𝑏𝑝 + 𝑐𝑝 . For the secondary (passive) part, the pole dimensions are the length 𝑙𝑠 , the width 𝑏𝑠 ,
pole dimensions are the length ls , the width bs , the slot width cs , and the mover pole pitch, defined as
the slot width
𝑐 , and the mover pole pitch, defined as 𝜏 = 𝑏𝑠 +
𝑐 . The magnet dimensions are the
τs = bs +𝑠cs . The magnet dimensions are the length lm and𝑠 width
bm . 𝑠The stack lamination width is
length 𝑙𝑚denoted
and width
as LW . 𝑏𝑚 . The stack lamination width is denoted as 𝐿𝑊 .
Figure 1. Longitudinal flux linear hybrid reluctance motor (LHRM) arrangement.
Figure 1. Longitudinal flux linear hybrid reluctance motor (LHRM) arrangement.
Figure 2 shows the LHRM operating principle in which the four coils of phase A are colored in
Figure
2 shows
theblue
LHRM
operatingthe
principle
in which
four
ofside
phase
Acurrent
are colored in
red and
blue, the
side represents
current entering
the the
paper
andcoils
the red
is the
flowing
out
of
the
paper.
The
red
line
of
Figure
2a
represents
the
main
flux
line
(Φ
)
of
phase
at current
+
red and blue, the blue side represents the current entering the paper and the Ared
side isAthe
pole-alignment position, when it is fed with a positive current (I A+ ). When phase A current is inverted
flowing out
of the paper. The red line of Figure 2a represents the main flux line (Φ𝐴+ ) of phase A at
(I A− ), (see Figure 2b) the blue line represents the main flux line at the same aligned position. In both
pole-alignment
position, when it is fed with a positive current (Iforce
). When
phase A current is inverted
cases, a significant force appears at pole alignment positions. The 𝐴+
is to the right FX,A+ when the
(I𝐴− ), (seecurrent
Figure
the blue line represents the main flux line at the same aligned position. In both
is I2b)
A+ , and to left FX,A− when the current is I A− . This phenomenon does not appear in an
cases, a significant
appears
alignment
positions.
The force is to the right 𝐹𝑋,𝐴+ when the
LSRM, whereforce
the force
is nullat
at pole
aligned
and unaligned
pole positions.
current is I𝐴+ , and to left 𝐹𝑋,𝐴− when the current is I𝐴− . This phenomenon does not appear in an
LSRM, where the force is null at aligned and unaligned pole positions.
Energies 2018, 11, 2805
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(a)
(a)
(b)
Linear hybrid
reluctance
motor
main
fluxpaths.
paths. (a)
AA
excited
withwith
I A+ , positive
force force
Figure 2. Figure
Linear2.hybrid
reluctance
motor
main
flux
(a)Phase
Phase
excited
IA+ , positive
FX,A+ . (b) Phase A excited with I A− , negative force FX,A− .
FX,A+ . (b) Phase A excited with IA− , negative force FX,A− .
The LSRM propulsion force versus position x and current i, (F ( x, i)) has the same direction
(right/left) in the interval x ∈ [0, τS /2], and for whatever current sign. In the LHRM, the propulsion
force is null at the unaligned pole positions, or when the stator poles are aligned with any of the PM
poles (N/S) for any current, see Figure 3a,c. The LHRM propulsion force has a positive direction
(left to right) in the interval x ∈ [0, τS ](b)
, (see Figure 3b) and a negative direction (right to left) in the
interval
x ∈2. [Linear
τS , 2·τhybrid
Figure 3d).
Thismain
implies
a current
sign A
dependency
the
LHRMforce
over the
Figure
motor
flux paths.
(a) Phase
excited withof
IA+
, positive
S ] (see reluctance
propulsion
force.
FX,A+ . (b)
Phase A excited with IA− , negative force FX,A− .
(a)
(b)
(c)
(d)
Figure 3. Linear hybrid reluctance motor operating principle. (a) Unaligned mover position. x = 0 mm,
1
FX = 0. (b) Aligned position. x = 2·𝜏𝑠 mm, FX > 0. (c) Unaligned position. x = 𝜏𝑠 mm, FX = 0. (d)
3
Aligned position. x=2 · 𝜏𝑠 mm, FX < 0.
(a)
(b)
(c)
(d)
The LSRM
propulsion
force versus
position xprinciple.
and current
i, (𝐹(𝑥, 𝑖))
has the same direction
Figure
Figure 3.
3.Linear
Linearhybrid
hybridreluctance
reluctance motor
motor operating
operating principle. (a)
(a) Unaligned
Unaligned mover
mover position.
position. xx ==00mm,
mm,
1
[
]
1, and
(right/left) inFFthe
interval
𝑥
∈
0,
𝜏
/2
for
whatever
current
sign.
In
the
LHRM,
the
=
0.
(b)
Aligned
position.
x
=
·
𝜏
mm,
F
>
0.
(c)
Unaligned
position.
x
=
𝜏
mm,
F
=
0.
(d) propulsion
𝑆
position. x = 2 2mm,
XX = 0. (b)
𝑠 FX > 0.
X (c) Unaligned position. x = τs mm, F𝑠X = 0. (d)
X Aligned
3
3
position.
x = 2 ·τs x=
mm,·pole
<positions,
0. FX < 0.
force is null at
the unaligned
or when the stator poles are aligned with any of the PM
Aligned
position.
𝜏F𝑠X mm,
2
poles (N/S) for any current, see Figure 3a and 3c. The LHRM propulsion force has a positive direction
LSRM
propulsion
andand
current
i, (𝐹(𝑥, 𝑖))
has the same
direction
[0, 𝜏𝑆versus
], (see position
(left to right)The
in the
interval
𝑥 ∈ force
Figure x3b)
a negative
direction
(right
to left) in the
(right/left) in the interval 𝑥 ∈ [0, 𝜏𝑆 /2], and for whatever current sign. In the LHRM, the propulsion
interval 𝑥 ∈ [𝜏𝑆 , 2 · 𝜏𝑆 ] (see Figure 3d). This implies a current sign dependency of the LHRM over the
force is null at the unaligned pole positions, or when the stator poles are aligned with any of the PM
propulsion
force.
poles
(N/S) for any current, see Figure 3a and 3c. The LHRM propulsion force has a positive direction
Energies 2018, 11, 2805
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In summary, the LHRM is, similar to the LSRM, a position dependent machine, so an encoder is
necessary to operate this actuator, along with an H-bridge inverter, which has to be used instead of the
asymmetric bridge converter because of its current sign dependence.
3. Mathematical Model Equations
The presence of the PM allows one to split the total phase flux linkage (ψ) as the sum of the flux
due to the phase-current (ψi ) and the PMs flux-linkage (ψPM ), as follows:
ψ( x, i ) = ψi ( x, i ) + ψPM ( x, i )
(1)
The electrical phase circuit equation is as follows:
dψ
= V − R· I
dt
(2)
where I, V, and R are the phase current, voltage, and resistance, respectively. Expressing the phase-current
flux linkage as the product of the phase inductance and the current, that is: ψi (i, x) = L(i, x)· I, and
combining Equations (1) and (2), it yields the electrical circuit equation of the LHRM given by
the following:
dI
dL
dψPM
−1
−1
= −L
R + v·
·I + L · V −
(3)
dt
dx
dt
In which the mover velocity is denoted as v. The motion equation neglecting friction is given
as follows:
dv
Fx + Fd = M·
+ Fl
(4)
dt
where Fx is the electromagnetic force, Fd is the detent force, Fl is the load, and M is the mover mass.
The instantaneous electromagnetic force (Fx ) is computed from the differential change of co-energy
respect to position for a given phase current, as follows:
m
Fx =
∑
k =1
∂
∂x
I
Z
0
ψ( x, ik )·dik
(5)
where m is the number of phases. This set of Equations (1)–(5) performs the dynamic and static
behavior of the LHRM, which can be implemented in MATLAB-Simulink software for their solution
as in LSRM.
The apparent power per phase, SVA or volt-ampere requirement per phase, is defined as the
product of peak voltage (Vp ) and peak current (Ip ) multiplied by the number of switching devices
per phase (n). From the area of the energy conversion loop (W), the average output power is given
as follows:
2 ·W
Pout =
·u
(6)
τs ·k d b
where k d is the magnetic duty cycle factor defined as k d = 2· xo f f /τs . The ratio between the power
output and the apparent power or W/VA ratio is given by the following:
Pout
2 ·W
·u
=
SVA
n·τs ·k d ·Vp · I p b
(7)
4. Finite Element Analysis Results
The electromagnetic propulsion force is obtained from a 2D-FEM solver [25]. It uses the weighted
Maxwell stress tensor technique [26], which is one of the most reliable approaches for force and
torque computations [27]. It consists of computing the Maxwell stress tensor over a set of concentric
surfaces of thickness δ and contour Γ(δ) wrapping the mover (see Equation (8)), with ny being a
Energies 2018, 11, 2805
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normal unit vector in the y-direction; and Bx and By are the magnetic field density in the x and y
directions, respectively.
Z Z
LW
1 δ
Fx =
·ny · Bx · By ·dΓ·dδ
(8)
δ 0 Γ ( δ ) µ0
Energies 2018, 11, x FOR PEER REVIEW
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The main dimensions of the FEM model of LHRM shown in Figure 4 are reported in Table A1, see
Appendix A. Figure 4 shows the flux lines obtained from the FEA for the zero current excitation phase.
phase. This
position (see Figure 4) is set as the initial position x = 0 mm, with this position being
This position (see Figure 4) is set as the initial position x = 0 mm, with this position being equivalent
equivalent
toposition
the position
in3c,
Figure
is,left
thephase
upper
left phase
poleanis aligned
to the
shownshown
in Figure
that is,3c,
thethat
upper
A primary
poleAisprimary
aligned with
with anS–N
S–Nmagnet.
magnet.
Figure 4.
Two-dimensional-finite
element
fluxplot
plot
𝐼𝐴 I=
𝐼𝐵 I=
𝐼𝐶 I=
Figure
4. Two-dimensional-finite
elementanalysis
analysis (FEM)
(FEM) flux
forfor
IA =
B =
D 𝐼=
C =
𝐷 0=at0, at x = 0
x
=
0
mm.
mm.
The electromagnetic force is evaluated for a sequence of even positions in the interval x ∈ [0, 2·τs ]
Theand
electromagnetic
force
is density
evaluated
for
even2 . positions
in the
thesame
interval 𝑥 ∈
for a set of constant
current
values
J ∈a[±sequence
5, ±10, ±15of
The LSRM has
] A/mm
2
[0, 2 · 𝜏𝑠 iron
] and
for a setand
of constant
currentmagnets.
density values J ∈ [± 5, ± 10, ± 15] A/mm . The LSRM
laminations
coils, but without
Asiron
can be
observed, there
twobut
forcewithout
profiles for
the LHRM (see Figure 5); one for positive
has the same
laminations
andare
coils,
magnets.
current
feeding
(continuous
line,
see
Figure
5)
and
one
for
(discontinuous
As can be observed, there are two force profiles forthe
thenegative
LHRMcurrent
(see Figure
5); oneline).
for positive
The LHRM force profiles are substantially higher than in the LSRM. The main FEM comparison results
current feeding (continuous line, see Figure 5) and one for the negative current (discontinuous line).
obtained from phase A are summarized in Table 1.
The LHRM force profiles are substantially higher than in the LSRM. The main FEM comparison
results obtained from phase A are summarized in Table 1.
LHRM phase A+
LHRM phase ALSRM phase A
60
60
40
40
20
20
0
0
-20
-20
-40
-40
-60
-60
-80
-80
0
5
10
15
20
25
30
0
x (mm)
5
10
15
20
25
30
x (mm)
(a)
80
PM-LSRM phase B+
PM-LSRM phase BLSRM base phase B
80
F X (N)
F X (N)
80
(b)
LHRM phase C+
80
LHRM phase D+
[0, 2 · 𝜏𝑠 ] and for a set of constant current density values J ∈ [± 5, ± 10, ± 15] A/mm . The LSRM
has the same iron laminations and coils, but without magnets.
As can be observed, there are two force profiles for the LHRM (see Figure 5); one for positive
current feeding (continuous line, see Figure 5) and one for the negative current (discontinuous line).
The LHRM force profiles are substantially higher than in the LSRM. The main FEM comparison
Energies 2018, 11, 2805
6 of 14
results obtained from phase A are summarized in Table 1.
LHRM phase A+
LHRM phase ALSRM phase A
60
60
40
40
20
20
0
PM-LSRM phase B+
PM-LSRM phase BLSRM base phase B
80
F X (N)
F X (N)
80
0
-20
-20
-40
-40
-60
-60
-80
-80
0
5
10
15
20
25
30
0
5
10
x (mm)
(a)
20
25
30
(b)
80
LHRM phase C+
LHRM phase CLSRM phase C
80
60
LHRM phase D+
LHRM phase DLSRM phase D
60
40
40
20
F X (N)
20
F X (N)
15
x (mm)
0
0
-20
-20
-40
-40
-60
-60
-80
-80
0
5
10
15
20
25
30
0
5
10
x (mm)
15
20
25
30
x (mm)
(c)
(d)
Figure 5. FEM propulsion force comparison results for linear switched reluctance motor (LSRM) and
LHRM at J = ±15 A/mm2 . (a) Phase A. (b) Phase B. (c) Phase C. (d) Phase D.
Table 1. Two-dimensional-finite element analysis (FEM) comparison results for the linear hybrid
reluctance motor (LHRM) and linear switched reluctance motor (LSRM).
Phase-A, (IA =2.95 A)
1
Average force (N) for FX,A > 0
Average force (N) for FX,A < 0 1
Positive peak force (N)
Negative peak force (N)
1
LHRM
LSRM
∆FX,A (%)
42
−43.2
99.1
−90
23.1
−23.1
35.2
−35
82
87
181
157
The average force is computed for positive and negative semi-periods.
The phase-force profiles are shifted τs mm when feeding with positive or negative phase current,
that is, FX ( x + τS , − I ) = FX ( x, I ), as can be seen in Figure 5. Table 2 shows the comparison results
between phases, when feeding with a positive current density of J = +15 A/mm2 (I = +2.95 A), along
with the cogging force values whose force profile is depicted in Figure 6. As is usual in the linear
machines, the border phases (i.e., phases A and D) are expected to have slightly different values
because of the loss of magnetic symmetry in the borders.
Table 2. Phase comparison LHRM main results.
J =15 A/mm2 , (I=2.95 A)
FX,A+
FX,B+
FX,C+
FX,D+
FCogging
Average force (N) for FX > 0
Average force (N) for FX < 0
Positive peak force (N)
Negative peak force (N)
42
−43.2
99.1
−90
45.7
−42.7
96.4
-94.6
42.9
−45.5
94.8
−96.2
42
−42
90.1
−99
2.93
−2.91
8.8
−8.8
0
Average force (N) for 𝐹𝑋 <
0
Positive peak force (N)
Energies 2018, 11, 2805
Negative peak force (N)
42
45.7
42.9
42
2.93
−43.2
−42.7
−45.5
−42
−2.91
99.1
−90
96.4
-94.6
94.8
−96.2
90.1
−99
8.8
−8.8
7 of 14
Figure
6. Coggingforce
force FEM
Figure
6. Cogging
FEMresult.
result.
The force profiles shown in Figure 5 are depicted together in Figure 7a. From this figure, an
The activation
force profiles
shown in
are
depicted
in Figure(to
7a.left,
From
an
phase-sequence
forFigure
positive5(to
right,
x > 0) ortogether
negative movement
x < 0)this
can figure,
be
activationdeduced.
phase-sequence
for
positive
(to starting
right, xfrom
> 0)x or
movement (to
left, xmust
< 0) can be
For obtaining
a positive
thrust
= 0 negative
mm, the phase-activation
sequence
[B+,
C−, D+, A+,
B−, C+, Dthrust
−, A−,starting
B+...], and
for a xnegative
thrust,
it must be [D−, A−,sequence
B+, C−, must
deduced.beFor
obtaining
a positive
from
= 0 mm,
the phase-activation
D+,
A+,
B
−
,
C+,
D
−
...].
The
curve
resulting
from
wrapping
the
force
peaks
(see
Figure
7a,
red
thick
be [B+, C-, D+, A+, B-, C+, D-, A-, B+...], and for a negative thrust, it must be [D-, A-, B+, C-,
D+, A+, Bline) is the total propulsion force when the motor phases are excited following the above-mentioned
, C+, D-...]. The curve resulting from wrapping the force peaks (see Figure 7a, red thick line) is the
positive sequence for a flat current waveform and without overlapping phase currents. The optimal
total propulsion
when
the motor
phases
areinexcited
following
thethe
above-mentioned
Energies
2018,force
11,interval
x FOR
PEER
7 of 14 positive
conduction
forREVIEW
phase
A is also
depicted
Figure 7a,
in which for
LHRM dimensions
sequencegiven
for ina Table
flat A1
current
without
overlapping
phase
are [8.75,waveform
12.75 mm] forand
A+, and
[24.75, 28.75
mm] for −A.
Figurecurrents.
7b shows theThe
totaloptimal
2
given
in
Table
A1
are
[8.75,
12.75
mm]
for
A+,
and
[24.75,
28.75
mm]
for
−A.
Figure
7b
shows
the
total
propulsion
force
positive
fordepicted
the currentin
densities
J ∈ in
±10, ±for
15] A/mm
.
[±5,
conduction
interval
forfor
phase
A thrust
is also
Figureof7a,
which
the LHRM
dimensions
propulsion force for positive thrust for the current densities of J∈ [±5, ±10, ±15] A/mm2.
110
80
100
60
90
80
40
70
F X (N)
F X (N)
20
0
-20
60
50
40
-40
30
-60
A+
B+
C+
D+
A-
B-
C-
D-
-80
20
10
0
5
10
15
x (mm)
(a)
20
25
30
0
J=5A/mm
0
5
10
2
J=10A/mm
15
2
J=15A/mm
20
2
25
30
x (mm)
(b)
Figure
±15
A/mm22,, all
Figure7.7.FEM
FEMresults.
results.(a)
(a)J J== ±
15 A/mm
all phases
phases propulsion
propulsionforce,
force,total
totalpropulsion
propulsionforce
force(red
(red
thick
∈ [±5,5,±±
±]. 15].
thickline)
line)and
andconduction
conductioninterval
intervalfor
forphase
phaseA.
A.(b)
(b)Total
Totalpropulsion
propulsion force
force at
at JJ ∈
10,10,
±15
Inorder
orderto
toassess
assessthe
thedemagnetization
demagnetizationofofthe
thepermanent
permanentmagnets,
magnets,the
theairgap
airgapflux
fluxdensity
densityhas
has
In
been
drawn
in
the
y-direction,
which
is
the
PM-magnetization
direction,
and
then
comparing
these
been drawn in the y-direction, which is the PM-magnetization direction, and then comparing these
fielddistributions
distributionswith
withzero
zerocurrent
currentand
andwhen
whenexciting
excitingphase
phase A.
A.
field
ThePM
PM operating
operating point
point
where
the the
permeance
of the
circuitcircuit
meets
The
pointisisdefined
definedasasthethe
point
where
permeance
ofmagnetic
the magnetic
the
magnet
BH
characteristic.
The
irreversible
demagnetization
occurs
when
the
PM’s
flux
density
meets the magnet BH characteristic. The irreversible demagnetization occurs when the PM’s flux
decreases
under magnet
BH-characteristic
knee value.
N32 For
grade,
residual
is 1.2 T at
density
decreases
under magnet
BH-characteristic
kneeFor
value.
N32the
grade,
the induction
residual induction
◦
◦
◦
◦
◦
the℃
knee
are values
0.3 T atare
60 0.3
C, 0.4
at 80
T at
C, and
is201.2CTand
at 20
andvalues
the knee
T atT60
℃, C,
0.40.5
T at
80100
℃, 0.5
T at0.6
100T at
℃,120
and C.
0.6 T at
120 ℃.
The critical points for phase A are found when the propulsion force reach its peak values, which
occurs at mover positions of 6 mm and 28 mm for JA = −15A/mm2, and at mover positions of 10 mm
and 22 mm for JA = + 15A/mm2 (see Figure 7a). The points analyzed are at mover positions of 22 mm
and JA = 15A/mm2, and mover at 28 mm and JA = −15A/mm2 (see Figure 8). The PM critical areas are
field distributions with zero current and when exciting phase A.
The PM operating point is defined as the point where the permeance of the magnetic circuit
meets the magnet BH characteristic. The irreversible demagnetization occurs when the PM’s flux
density decreases under magnet BH-characteristic knee value. For N32 grade, the residual induction
Energies
11, 2805
is 1.2 T2018,
at 20
℃ and the knee values are 0.3 T at 60 ℃, 0.4 T at 80 ℃, 0.5 T at 100 ℃, and 0.68 of
T 14
at
120 ℃.
The critical points for phase A are found when the propulsion force reach its peak values, which
The critical points for phase A are found when the propulsion
force reach its peak values, which
occurs at mover positions of 6 mm and 28 mm for JA = −15A/mm2, and at mover positions of 10 mm
occurs at mover positions of 6 2mm and 28 mm for JA = −15A/mm2 , and at mover positions of 10 mm
and 22 mm for JA = + 15A/mm (see Figure 7a). The points analyzed are at mover positions of 22 mm
and 22 mm for JA 2= +15A/mm2 (see Figure 7a). The points analyzed
are at mover positions of 22 mm
and JA = 15A/mm , and mover at 28 mm and JA = −15A/mm2 (see Figure 8). The PM critical areas are
and JA = 15A/mm2 , and mover at 28 mm and JA = −15A/mm2 (see Figure 8). The PM critical areas are
highlighted (see Figure 8a,b). The By(x,J) distribution field is computed along the airgap red line
highlighted (see Figure 8a,b). The By (x,J) distribution field is computed along the airgap red line shown
shown in Figures 8a,b, with the variable x being the position over this line, and J being the current
in Figure 8a,b, with the variable x being the position over this line, and J being
the current density,
density, whose values are zero in all phases J = 0, and 𝐽 = 𝐽𝐴 = ±2 15 A/mm2 (see Figures 8c and 8d
whose values are zero in all phases J = 0, and J = J A = ±15 A/mm
(see Figure 8c,d in black/red lines,
in black/red lines, respectively). The results reveal that PM would be demagnetized when operating
respectively). The
results reveal that PM would be demagnetized when operating at JA = 15 A/mm2 at
at JA = 15 A/mm2 at mover position of 22 mm (see Figure 8c), and for magnet temperature
exceeding
mover position of 22 mm (see Figure 8c), and for magnet temperature exceeding 80 ◦ C.
80 °C.
Energies 2018, 11, x FOR PEER REVIEW
(a)
(c)
(b)
8 of 14
(d)
Figure8.8.FEM
FEMresults
resultsforfor
the
of the
density.
By field
for mover
22 and
mm
Figure
the
ByBcomponent
of the
fluxflux
density.
(a) B(a)
y field
for mover
at 22 at
mm
y component
2 . (b) B field for mover at 28 mm and feeding phase A at
2. (b) By
and feeding
=
+15
A/mm
feeding
phasephase
A at JA
A =at
+ J15
A/mm
field
for
mover
at
28
mm
and
feeding
phase
A
at
J
A
=
−15
y
A
2 . (c) B distribution field along the airgap, see red line in Figure 8a, for J = 0 and
JA = −2.15
A/mm
(c)A/mm
By distribution
y field along the airgap, see red line in Figure 8a, for J = 0 and JA = 15 A/mm2.
JA B
=y 15
A/mm2 . field
(d) Balong
field
theinairgap,
inJAFigure
8b at J2. = 0 and
(d)
distribution
the airgap,
seealong
red line
Figure see
8b atred
J = line
0 and
= −15 A/mm
y distribution
2
JA = −15 A/mm .
5. Experimental Results
5. Experimental Results
In order to validate the FEM results, an LHRM prototype (see Figures 9b and 9c) was built and
In order to validate the FEM results, an LHRM prototype (see Figure 9b,c) was built and tested,
tested, with the main dimensions shown in Table A1. The experimental setup (see Figure 9a) consists
with the main dimensions shown in Table A1. The experimental setup (see Figure 9a) consists of a
of a system for positioning the mover at a given position and a load cell for measuring the static thrust
system for positioning the mover at a given position and a load cell for measuring the static thrust force.
force. The force is measured in each millimeter, in the range 𝑥 ∈ [0, 2 · τ𝑆 ], which means 32 measures
The force is measured in each millimeter, in the range x ∈ [0, 2·τS ], which means 32 measures for the
for the 6 current densities J∈ [±5, ±10, ±15]. Considering the four phases, the total number of
6 current densities J ∈ [±5, ±10, ±15]. Considering the four phases, the total number of measures is
measures is 4 x 6 x 32 = 768. These results are compared with the FEM results in Figures 10–13. The
4 × 6 × 32 = 768. These results are compared with the FEM results in Figures 10–13. The experimental
experimental results are in agreement with the FEM results, which validates the FEM simulation
results are in agreement with the FEM results, which validates the FEM simulation results.
results.
of a system for positioning the mover at a given position and a load cell for measuring the static thrust
force. The force is measured in each millimeter, in the range 𝑥 ∈ [0, 2 · τ𝑆 ], which means 32 measures
for the 6 current densities J∈ [±5, ±10, ±15]. Considering the four phases, the total number of
measures is 4 x 6 x 32 = 768. These results are compared with the FEM results in Figures 10–13. The
Energies
2018, 11, 2805
9 of 14
experimental
results are in agreement with the FEM results, which validates the FEM simulation
results.
(a)
(b)
(c)
Energies
11, x FORprototype.
PEER REVIEW
9 of 14
Figure2018,
LHRM
(a) Experimental
(b) LHRM
frontal
Moverassembly.
magnets
Figure
9.9.LHRM
prototype.
(a) Experimental
setup.setup.
(b) LHRM
frontal view.
(c)view.
Mover(c)
magnets
assembly.
Figure 10. Experimental vs. FEM simulation phase-force results for J = ± 5 A/mm . 2
Figure
10. Experimental vs. FEM simulation phase-force results for J = ±5 A/mm .
2
Energies 2018, 11, 2805
Figure 10. Experimental vs. FEM simulation phase-force results for J = ± 5 A/mm2.
Energies 2018, 11, x FOR PEER REVIEW
10 of 14
10 of 14
Figure
Experimentalvs.
vs.FEM
FEM simulation
simulation phase-force
results
forfor
J = J±= 10
A/mm
. 2.
Figure
11. 11.
Experimental
phase-force
results
±10
A/mm
2
2.
2.
Figure
Experimentalvs.
vs.FEM
FEM simulation
simulation phase-force
results
forfor
J = J±= 15
A/mm
Figure
12. 12.
Experimental
phase-force
results
±15
A/mm
Energies 2018, 11, 2805
11 of 14
Figure 12. Experimental vs. FEM simulation phase-force results for J = ± 15 A/mm2.
Figure13.
13.Experimental
Experimental vs.
vs. FEM
Figure
FEM simulation
simulationcogging
coggingforce
forceresults.
results.
6. 6.
Conclusions
Conclusionsand
andDiscussion
Discussion
From
results,the
theoperating
operating
principle
profiles
are validated
and
Fromthe
theexperimental
experimental results,
principle
andand
forceforce
profiles
are validated
and this
enables
thethe
linear
hybrid
reluctance
motor
(LHRM)
as a good
candidate
for applications
with high
this
enables
linear
hybrid
reluctance
motor
(LHRM)
as a good
candidate
for applications
with
force
density.
Unlike
LSRM,
thisthis
machine
needs
to to
operate
through
a afour-phase
full-bridge
high
force
density.
Unlike
LSRM,
machine
needs
operate
through
four-phase
full-bridge
converter,
ordertotosupply
supplythe
thephase
phase current
current with the
thethe
mover
converter,
inin
order
the appropriate
appropriatesign.
sign.AsAsininLSRM,
LSRM,
mover
position
and
currentsmust
mustbe
beacquired;
acquired; therefore,
therefore, aa linear
areare
required
position
and
currents
linearencoder
encoderand
andcurrent
currentsensors
sensors
required
implementing
a force
control. This force control can be designed for mitigating the force ripple
forfor
implementing
a force
(see
Energies
2018, 11, x FOR
PEERcontrol.
REVIEW This force control can be designed for mitigating the force ripple
11 of 14
Figure 7b) by adjusting the currents waveform [28], and thus the force can remain almost flat to its
(see Figure
7b) for
by adjusting
the currents
maximum
value
each current
density. waveform [28], and thus the force can remain almost flat to
its From
maximum
value
for
each
current
density.
the point of view of the cogging
force (see Figure 13), this presents a series of peaks of about
2 , whichforce
the force
pointat
ofJ view
of the cogging
(see Figurevalue.
13), this
presents
a series
of peaks
of
10% of From
the peak
= 15 A/mm
is a reasonable
Further
research
should
be done
2, which is a reasonable value. Further research should be
about
10%
of
the
peak
force
at
J
=
15
A/mm
to eliminate cogging force by phase-shifting, or by a sensitivity analysis in the pole’s proportions and
done to
eliminate cogging force by phase-shifting, or by a sensitivity analysis in the pole’s
number
of phases.
proportions and number of phases.
The LHRM actuator presented in this paper is conceived as a servomotor used in manufacturing
The LHRM actuator presented in this paper is conceived as a servomotor used in manufacturing
lines or precision positioning applications whose velocity is relatively low (ub < 2 m/s) and where the
lines or precision positioning applications whose velocity is relatively low (ub < 2 m/s) and where the
force control is required. For this reason, a typical hysteresis current control is adopted, which is robust
force control is required. For this reason, a typical hysteresis current control is adopted, which is
and fast [29], being the current controlled around a reference value (Iref ), and whose ripple depends on
robust and fast [29], being the current controlled around a reference value (Iref), and whose ripple
thedepends
hysteresis
range. The shape of the controlled current and voltage are shown in Figure 14, and it
on the hysteresis range. The shape of the controlled current and voltage are shown in Figure
is characterized
by the turnby
on/off
positions
(see Table
3) Table
and by
current,current,
the value
14, and it is characterized
the turn
on/off positions
(see
3) the
andreference
by the reference
the of
which
directly
to the
desired
force. force.
valueisof
which linked
is directly
linked
to thepropulsion
desired propulsion
−1−1
Figure14.
14.Current
Currentand
andvoltage
voltage waveforms
waveforms simulation
×1010
; voltage×10×1 ).
Figure
simulationresults
results(current
(current ×
; voltage
1
10 ).
Table 3. Turn on/off phase excitation.
Excited Phase
A+
Turn on Position, 𝒙𝒐𝒏
8.5 mm
Turn off Position, 𝒙𝒐𝒇𝒇
12.5 mm
Energies 2018, 11, 2805
12 of 14
Table 3. Turn on/off phase excitation.
Excited Phase
Turn on Position, xon
Turn off Position, xoff
A+
B+
C+
D+
A−
B−
C−
D−
8.5 mm
28.75 mm
16.75 mm
4.5 mm
24.5 mm
12.75 mm
0.75 mm
20.5 mm
12.5 mm
0.5 mm
20.25 mm
8.75 mm
28.5 mm
16.5 mm
4.25 mm
24.25 mm
The inherent fault tolerance of the reluctance machines and thus of LSRMs is preserved in the
LHRM, because once the damaged phase is removed, the LHRM keeps operating at a new diminished
force, as can be inferred from Figure 7a.
The motor is easily assembled despite having to put permanent magnets in the mover slots (see
Figure 9c), because flux lines attach the PM to the magnetic structure (see Figure 4) and there are no
repulsion forces.
The thermal aspect is also good because PMs are in the secondary (passive) part, which allows
high current densities in the primary (active) part for intermittent operation.
From all the findings reported above, this novel structure of linear hybrid reluctance motor can be
an interesting option in applications, which requires a high thrust force for intermittent duty cycles,
such as in manufacturing industries and robotic systems.
Funding: This research was funded by the Spanish Ministerio de Economia, Industria y Competitividad, under the
Grant DPI2016-80491-R (AEI/FEDER, UE).
Conflicts of Interest: The author declare no conflict of interest.
Appendix A.
Table A1. LHRM prototype main dimensions and rated values.
Parameter
Symbol
Primary pole width
Primary slot width
Primary pole length
Secondary pole width
Secondary slot width
Secondary pole length
Mover height
Magnet width
Magnet height
Stack width
Air gap length
Phase wire diameter
Number of wires per pole
Rated voltage
Rated current
Rated power
Rated force
Rated speed
Duty cycle
Magnetic steel grade
Insulation grade
Duty type
Permanent Magnet
bp
cp
lp
bs
cs
ls
lst
bm
lm
LW
g
d
Nph
Ub
Ib
Pb
FX
ub
DC
Value
6 mm
6 mm
30 mm
7 mm
9 mm
7 mm
30 mm
8 mm
6.5 mm
30 mm
0.5 mm
0.5 mm
180
120 V
3A
150 W
90 N
1.5 m/s
0.4
FeV 270/50 HA
B-Class ∆T = 80 ◦ C
S3
NdFeB32
Energies 2018, 11, 2805
13 of 14
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© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).