Recent Developments of Electrical Drives - Part 31 ppt

298 Choi et al.
Figure 3. Dynamic constraints between dynamic capability and required motional profiles.
Design strategy using dynamic constraints
In principle, dynamic capability shown in (1) should be at least larger than Force-Speed
relation of required trajectory shown in (2). This relation is showninFig. 3, where static and
dynamic capability and the required motional trajectory are compared. Particularly between
two forces from maximum voltage and current respectively, the smaller one could be the
final dynamic capability, which is based on (1). Therefore, heavy-line in Fig. 3 indicates
the final capability of PMLSM, which should be larger than motional profile, and this
conclusion gives effective design criteria referred as dynamic constraints. Therefore, it is
reasonable that only dynamic capability at the velocity of v
1
,v
2
,v
max
should be larger
than the required one, which is summarized as follows.
< Constraint 1;v = v
1
, J = J
max
, a = a
max
>
3
2
K
e
C
1

+
√
C
2
−C
3
R
2
s
+ (π/τ)
2
L
2
s
v
2
>> ma
max
+ Bv
1
+ F
l
(3)
< Constraint 2;v = v
2
, J = 0, a = a
max
>
3
2

K
e
min

C
1
+
√
C
2
−C
3
R
2
s
+ (π/τ)
2
L
2
s
v
2
, I
max

>> ma
max
+ Bv
2
+ F

l
(4)
< Constraint 3;v = v
max
, J =−J
max
, a = 0 >
3
2
K
e
C
1
+
√
C
2
−C
3
R
2
s
+ (π/τ)
2
L
2
s
v
2
>> 0 (5)

In (3), the dynamic constraints only from voltage limitation are considered, because the
other constraints from maximum input current can be neglected due to the same kind
of constraints in (4). In practical application, it is not fixed which one between dynamic
capability and the force from maximum input current has larger value. Thereby, at velocity
of v
2
in (4), both of them must be satisfied at the same time, where dynamic capability
(J = 0, a = a
max
) and static capability (J = 0, a = 0) show little difference which can
be verified through (1). In constraints 3, it is sufficient to judge whether motor has an
III-1.1. Design and Manufacturing of Steel-Cored PMLSM 299
ability to produce the force or not. However, constraints 3 can be replaced by other different
constraint like ∂ F
e,max
/∂v >> ∂ F
e
(v)/∂v (at v = v
2
) which means that, if the slope of
dynamic capability is larger than that of required motional profile at v = v
2
(slope < 0),
constraint 3 at v = v
max
is satisfied by itself. However, this constraint is so strict that a lot
of combination of design variables could fail to be selected even though they could survive
through constraint 3. Therefore, it is reasonable to apply constraint 3 at design procedure,
and then check the force margin in the interval of v
2

<v<v
max
after work.
In addition to three basic constraints, such a relations as v
max
= V
max
/K
e
and another
constraint, C
2
>> C
3
, should be obeyed also in all of dynamic constraints.
Meanwhile,majordifferencebetweenconstraints from conventional staticcapabilityand
proposed dynamic capability would be noticed at v = v
1
and v = v
2
. Although the properly
designed machinecan satisfy constraintsgiven bystatic capability, requiredmotional profile
cannot be realized due to the dynamic constraints, especially at v = v
1
(at v = v
2
, there
is little difference due to the zero jerk). Since discontinuous force change at v = v
1
and

v = v
2
results purely from jerk and acceleration, high accelerating PMLSM used in short
traveling displacements should be designed along the dynamic constraints.
Defined design parameters in (1) will be τ, K
e
, R
s
, L
s
which are strongly regulated
by dynamic constraints, and used as decision criteria to the combination of the design
variables judging that the dynamic constraints are fully satisfied, i.e. designed machine can
be driven successfully satisfying the required motional profile. Actually, sensitivity to the
design parameter variance is most serious to τ and K
e
relatively than R
s
, L
s
which are
occasionally neglected in simplified design flow. Accordingly, in addition to the dynamic
constraints, more generalized design consideration at the primary stage should be done
focusing on the influence of τ and K
e
, which makes entire design process performing more
effectively.
Generalized design consideration and determination of design variables
In Fig. 4, the point where the maximum output power could be generated will be near
v = V

max
/K
e
/2 (half to the no-load velocity). Likewise, the maximum required mechanical
power exists at v = v
2
, therefore a design basis should be oriented as v
2
≈ V
max
/K
e
/2(K
e2
Figure 4. Generalized design schematic diagram (K
e1
> K
e2
> K
e3
).
300 Choi et al.
45
40
35
30
25
20
15
10

45
40
35
30
25
20
15
10
5
45
40
35
30
25
20
15
10
5
45
40
35
30
25
20
15
10
5
0.10
0.15
0.20

0.25
0.30
0
K
e
= 10
R
s
L
s
L
s
L
s
L
5
R
s
R
s
R
s
(5956)
K
e
= 30
(11461)
K
e
= 20

K
e
= 39
(13769)
(1070)
tt
t
t
0.0
0.0
0.5
1.0
1.5
2.0
0
2
4
6
8
10
0.2
0.4
0.8
1.0
1.2
1.4
1.6
0.0
0.2
0.4

0.6
0.8
1.0
1.2
1.4
1.6
0
0
2
4
6
8
10
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
0.6
Figure 5. Admissible design combination vs. K

e
(where V
max
= 160 V, I
max
= 150 A, m = 37 kg,
B = 100 N/(m/s), F
l
= 50 N, a
max
= 20 m/s
2
, V
max
= 4 m/s, J
max
= 3,000 m/s
3
).
model in Fig. 4). However, if required input current (I
s
= F
e,max
/(1.5K
e
)) is considered,
K
e1
model needs smaller current (I
s1

) than K
e2
model (I
s2
), which could be also interpreted
as better efficiency. In conclusion, EMF coefficient, K
e
[V/(m/s)], should be designed at
least in the interval as follows.
V
max
/v
max
≤ K
e
≤ V
max
/(2v
max
) (6)
Another sensitive design parameter, pole pitch (τ ), should be defined from the magnetic
combination (four poles and three coils) and the manufacturing feasibility. One module
length τ
m
corresponding to 4τ and 3τ
c
(where, τ
c
is coil pitch) should be multiplied
with 12, which has validated itself compared with the other combinations. Hence, its mini-

mum andmaximum sizeare stronglyrestrictedbythe manufacturingfeasibilityand thecost.
Acceptable τ
m
range for relatively larger power in continuous operation is approximately
from 36 mm (τ = 9 mm) to 180 mm (τ = 45 mm).
In Fig. 5, distribution of design combination vs. K
e
is shown, and if it is applied to Fig.
4, K
e
= 20 corresponds to K
e2
model manifesting the best design point from a viewpoint
of size-effectiveness and usefulness in application. As K
e
increases, better efficiency (lower
input current) can be realized, and near the no-load speed (K
e
= 39), dynamic constraints
strongly restrict the design combinations in the speed range of v
2
≤ v ≤ v
max
. Particularly,
the number of admissible design combination is maximum at the K
e
= 20, which means
the possibility to implement the machine successfully is highest at the best design point.
Design parameters (τ, K
e

, R
s
, L
s
) are electrically and magnetically composed of the
designvariablesexpressingthe machinedimension,hence thedesignprocess willbedone by
changing the design variables and checking the validity of sets of the design variables under
III-1.1. Design and Manufacturing of Steel-Cored PMLSM 301
Figure 6. Optimal design flowchart.
the criteria proposed by dynamic constraints. Particularly, pole pitch (τ ) will be sufficient to
represent the moving-directional (longitudinal) design aspects, because coil pitch and one
module-length are also determined accordingly. Then, the other variables including pole
pitch can be summarized as air-gap length (g
0
), height of magnet (h
m
), height of slots (S
h
)
(or number of turns in slots), which are flexible to the normal direction. With the proposed
design variables, the optimization method can be applied to the design process under the
constraints such as dynamic constraints, the maximum mover length, and the maximum
machine height, which are shown in Fig. 6 as a flowchart.
Detent force reduction
Theoretically, the detent force is the resultant one of two different reaction forces, i.e. the
core detent force and the teeth detent force. The core detent force is the existing force
between the permanent magnets and the primary core, which has a large period equal to the
pole pitch. Whereas, the teeth detent force between the permanent magnets and the primary
teeth has a relatively small period, the greatest-common-divider (GCD) of the pole pitch
and the tooth pitch (τ

c
, same with coil pitch)
Reduction of core detent force
Reduction of the core detent force can be done by giving the core a suitable length in order
to cancel the core detent force at both end cores each other by adjusting the phase difference
between the two core detent forces, and by reforming the edge of the core to minimize the
reluctance variation. To begin with, making the geometric length such that the two forces
at both end cores cancel each other can be effective, which could be realized by adjusting
the electrical phase difference as follows [5].
θ = (2k −1)π, (7)
where k is integer.
302 Choi et al.
The other candidate is reforming the edge of core, which is induced from avoiding a
rapid reluctance change when the mover approaches or leaves the magnets.
Reduction of teeth detent force
The teeth detent force, the main component to be reduced, not only occupies the total detent
force up to 80%, but also is frequently produced along the motion track. Feasible ways to
minimize the teeth detent force based on the practical utilization are chamfering the teeth
edges and skewing the magnet. Firstly, chamfering the teeth edge, which is a similar idea to
core chamfering, intends to make abrupt the reluctance changes minimal due to the sharp
tooth edge. The other one, skewing the permanent magnet which is similar in principle to
rotary machines, can remove theteethdetent force outstandingly. Theoptimized skew-angle
should be determined through the following relation.
Skew-angle =
GCD(τ,τ
c
)
2
1
τ

180 [Electrical degree] (8)
Equation (7)manifests the electrical30
◦
in fourpoles and threecoils combination. However,
this is so small one in a mechanical length. In case of τ = 45 mm, mechanical skew-length
correspondent to skew-angle (electrical 30
◦
) is 7.5 mm.
Investigation on reduction result
Fig. 7 shows the reduction of the detent force.
The peak detent force of conventional model is about 300 N. But the peak value is
reduced to 150 N after applying the chamfering and the skew, about 5% of the continuous
thrust force. The detent force pattern has many harmonics because the width of magnet is
very large and many teeth affect same magnet. In this case the effect of the skew is not so
notable.
Figure 7. Detent force reduction by proposed methods.
III-1.1. Design and Manufacturing of Steel-Cored PMLSM 303
Figure 8. Manufactured PMLSM.
Design, manufacturing, and testing
The designed steel-cored PMLSM is manufactured and tested. The picture of the manufac-
tured PMLSM is presented in Fig. 8 and specifications of the designed machine are listed
in Table 1.
The magnetic flux distribution and air-gap flux density are shown in Figs. 9 and 10. In
this model, very large input current is needed to get large thrust force, so that sufficient
amount of iron core should be secured to avoid magnetic saturation.
The stroke of the linear motor is 1,000 mm and the maximum force/continuous force is
15,000 N/3,000 N. This motor can run up to 4 m/s under the input voltage of 220 V and the
maximum current of 300 A.
Table 1. Design specification of sample steel-cored PMLSM
Specification Dimension

General (with water cooling) Voltage/current 220 V/41 A
Stack length 200 mm
Magnet height 9 mm
Magnet width 41 mm
Stator (NdFeB, 45 H) Pole pitch 45 mm
Slot width 22 mm
Tooth height 30 mm
Tooth width 38 mm
Mover (coil size = 1.2 Ø) No of turns 90 per coil
Coil connection 3 parallel
Chamfering 10 × 6mm
304 Choi et al.
Figure 9. Magnetic flux density distribution.
The dynamic capability of the designed PMLSM is shown in Fig. 11 and the capability
curve has force margin about 500 N.
By using the load cell, the thrust force is measured and the input current is measured
with the current probe and the oscilloscope.
Fig.12showsthemeasured current-thrust force curve. Thegraph showsvery good linear
relation of the input current to the thrust force. The continuous thrust force is generated
with the input current of 58 A and the maximum thrust force with the input current of 305 A
is 15,890 N, which satisfies the objective output. Over 300 A region, the linearity of the
curve is broken, because it is the highest available measuring value of the current probe.
The thrust force constant resulting from the measured curve is 54.81 [N/A] and EMF
constant is 36.54 V/(m/s). The measured results have a good agreement with calculated
thrust force constant 51.53 [N/A] and EMF constant is 34.35 V/(m/s).
The measured input current is shown in Fig. 13 when the motor is operated with the
maximum speed. The pole pitch of the machine is 90 mm and the pitch of the measured
Length mm
Bn. Tesla
0

−2
−1
0
1
2
50 100 150 200 250 300
Figure 10. Air-gap flux density distribution.
III-1.1. Design and Manufacturing of Steel-Cored PMLSM 305
Figure 11. Running characteristics of designed motor.
Figure 12. Current-thrust force curve.
Figure 13. Measured input current.
306 Choi et al.
current wave form is 22.6 ms. Therefore the moving speed can be calculated and the result
is 3.98 m/s. Because the stroke is short, very large acceleration is needed to achieve the
speed of 4 m/s. In addition, the power capability of the testing building is not sufficient, so
that the resultant speed is not over 4 m/s. If long stroke or better power source is available,
the machine can achieve the speed of 4 m/s.
Conclusion
In this paper, steel-cored permanent magnet linear synchronous motor for large thrust force
and high speed operation is designed, manufactured, and tested. The machine is analyzed
by finite element method considering dynamic and static constraints. The designed model
is optimized to reduce force ripples and to avoid magnetic saturation.
Test machine is manufactured and the measured result of EMF constant shows good
agreement with designed one. Thrust force characteristic shows good linearity and the
measured maximum thrust force is over 15,000 N, the objective value. The measured max-
imum velocity is 3.98 m/s. The performances of the designed motor can guarantee the
objective large thrust force and high speed.
References
[1] T. Sebastian, V. Gangla, Analysis of induced EMF waveforms and torque ripple in a brushless
permanent magnet machine, IEEE Trans. Ind. Appl., Vol. 32, No. 1, pp. 195–200, 1996.

[2] T. Yoshimura, H.J. Kim, M. Watada, S. Torii, D. Ebihara, Analysis of the reduction of detent
force in a permanent magnet linear synchronous motor, IEEE Trans. Magn., Vol. 31, No. 6, pp.
3728–3730, 1995.
[3] D.L.Trumpher, W J. Kim,M.E. Williams,Design andanalysis frameworkfor linearpermanent-
magnet machines, IEEE Trans. Ind. Appl., Vol. 32, No. 2, pp. 371–379, 1996.
[4] S Y. Jung, H K. Jung, J S. Chun, Performance evaluation of slotless permanent magnet linear
synchronous motor energized by partially excited primary current, IEEE Trans. Magn., Vol. 28,
No. 2, pp. 3757–3761, 2001.
[5] N. Bianchi, S. Bolognani, F. Tonel, “Design Criteria of a Tubular Linear IPM Motor”, Proc. of
IEMDC’03, 2001, pp. 1–7.
[6] S Y. Jung, S Y. Kwak, S K. Hong, C G. Lee, H K. Jung, “Design Consideration of Steel-
Cored PMLSM for Short Reciprocating Travel Displacements”, Proc. of IEMDC’03, Vol. 2,
June 1–4, 2003, pp. 1061–1067.
[7] S Y. Jung, J K. Kim, H K. Jung, C G. Lee, S K. Hong, Size optimization of steel-cored
PMLSM aimed for rapid and smooth driving on short reciprocating trajectory using auto-tuning
niching genetic algorithm, IEEE Trans. Magn., Vol. 40, No. 2, pp. 750–753, 2004.
III-1.2. HIGH POLE NUMBER, PM
SYNCHRONOUS MOTOR WITH
CONCENTRATED COIL
ARMATURE WINDINGS
Antonino Di Gerlando, Roberto Perini and Mario Ubaldini
Dipartimento di Elettrotecnica—Politecnico di Milano Piazza Leonardo da Vinci, 32-20133
Milano, Italy
, ,
Abstract. A high pole number, PM synchronous motor is presented, employing novel two-layer,
special armature windings consisting of concentrated coils wound around the stator teeth. This kind
of machine is characterized by excellent e.m.f. and torque waveform quality: it is well suited not only
as an inverter driven motor, but also for mains feeding, self-starting, applications. In the paper, the
main features of the machine are shown, together with some design, FEM, and test results.
General features of the windings

In recent times, a large attention has grown toward the electrical machines equipped with
concentrated coils, thanks to their great constructional and functional advantages [1–12];
nevertheless, a general approach to the concentrated winding theory seems not fully de-
veloped yet. In the proposed paper, a PM machine is considered, with two-layer, armature
concentrated windings [13].
The features of this kind of machines are (see Figs. 1 and 2):
r
uniformly distributed and equally shaped magnetic saliencies of the structures (stator
teeth and rotor PMs);
r
practical equality among tooth pitch τ
t
and PM pitch τ
m
(it can be τ
m
< τ
t
or τ
m
> τ
t
,but
τ
m
= τ
t
);
r
series inverted connection of coils belonging to adjacent teeth of the same phase (contro-

verse coils).
By adopting the representation of Fig. 1 (right) to specify the winding sense of each coil
around its tooth, a typical three-phase, two-layer, winding appears as shown in Fig. 2.
Referring to Fig. 2, the following quantities and properties should be defined and con-
sidered:
r
cycle: space period (periphery portion at which bounds the faced structures show the
same mutual disposition);
S. Wiak, M. Dems, K. Kom
˛
eza (eds.), Recent Developments of Electrical Drives, 307–320.
C

2006 Springer.