Dept. of Electrical Engineering,
IIEST, Shibpur, Howrah - 711103
W.B., India.
email: seal.monojit@gmail.com
Dept. Electrical Engineering,
IIEST, Shibpur, Howrah - 711103,
W.B., India.
email: mainak.sengupta@gmail.com
Abstract —This paper deals with design, analysis and fabrication of 320 W, 5 m/s, 4-pole permanent magnet based linear synchronous machine (LPMSM). The design deals with rigorous hand calculations, analysis using standard
FEM packages and fabrication of the machine at the works of a local small machine manufacturer after procurement of imported PMs. The same will be used in a linear motor drive development research.
Index Terms —Linear permanent magnet synchronous machine, LPMSM, design optimisation, finite element method.
I. I NTRODUCTION
Linear motors have been the subject of research and development for over 100 years. Though presently only a few of such companies are known to supply linear motors across the world ( [1], [2]). However, with the increase in cost of energy since 1970’s, recent trends are focusing towards use of energy efficient drives. The availability of permanent magnets (PM) with considerable energy density and the advent of power electronic converters with digital controllers led to the development of energy efficient drive with precision in motion control. Fig.1 shows how the linear AC machines can be categorized [3].
Fig. 1.
Hierarchy chart illustrating types of linear machines
The present paper deals with the fabrication of a short primary LSM. Compared to linear IM (LIM), where sta-
Fig. 2. Single sided flat PM LSMs with slotted armature core and (a) surface PMs, (b) buried PMs. 1 - PM, 2 - mild steel pole, 3 - yoke.
tor current provides both magnetising and thrust producing component; in LPMSM, the PM produces the field flux the causing mainly the thrust producing component of stator current to be drawn from supply. Since, there is no copper loss in the rotor circuit (unlike LIM), for the same output, LPMSM will operate at much higher power factor and efficiency with consequent reduction in size and weight.
Primarily, two different types of construction are possible for LPMSM. A cross-sectional view of the first type having PMs on the surface as shown in Fig.2(a) and the other with PMs buried inside the mild steel pole as shown in Fig.2(b). In surface mounting arrangement of
LPMSM, the yoke (back iron) is made of ferromagnetic material and the direction of magnetisation of the PMs are perpendicular to the active surface. However, for buried LPMSM, the yoke is made of non-ferromagnetic material(e.g. aluminium) and the PMs are magnetised in the direction of travelling magnetic field [4].
II. B ASIC P RINCIPLES
In a PMSM the DC-field is obtained from permanent magnets (PM) instead of DC-exited electromagnets. In the present work the DC-field system is kept static while the 3-phase armature has been made the ’linor’ (moving

member). A linear synchronous motor (LSM) is a variant of the conventional synchronous motor in which the mechanical speed is the same as the speed of the linearly travelling magnetic field. Hence, the thrust (propulsion force) can be generated as an action of
•
• travelling magnetic field produced by a balanced polyphase winding energised from a balanced polyphase supply.
magnetic field produced by electronically switched d.c. windings
The part producing the travelling magnetic field is called armature (or forcer). For PM machines, the difficulty remains in the design of the PM of minimum volume and at the same time preventing demagnetisation of the
PMs. In the following sections, the design of LPMSM has been presented ( [4]–[8]).
III. D ESIGN AND ANALYSIS OF LPMSM
A. Initial specification and selection of main dimensions
The nominal specifications of the machine are given in Table.I. An efficiency of η = 0.85 and fundamental p.f.
cos Φ = 0.9 have been taken as targeted performance indices. This gives efficiency-power factor product ( η.cos
Φ ) as 0.765. The present prototype has been developed using the existing lamination of the already made developed LIM in our laboratory. This has an advantage of reduction of overall cost since the major cost involved is the cost of die and tooling of the machine.
Rated primary current I
1 connection), is given by (assuming Y -
I
1
= √
V A
3 .V
L
= √
420
3 .
100
= 2 .
41 A
Therefore, VA transferred across air-gap (S elm
), is
325.86 VA. The pitch factor (k p 1
) is 1. Distribution factor
(k d 1
) is given by, k d 1
= sin [ Q q s
.sin
[ Q
/ 2 .m
1
]
/ 2 .m
1
.q
s
] sin (
Y
/ 2 .
w c
τ
) = 1
Winding factor ( k w 1 is found to be, Φ m
) = k p 1
X k d 1
= 0.8 mWb.
= 1 and flux per pole
After repeated iterations and considering appropriate design constraints, the following values are obtained shown in Table II. Designing the effective length of armature magnet (L i
) is a little involved as it considers
:-
1) Designing of high density machine for reducing the cost of magnet.
2) Prevent demagnetisation of the magnets.
3) Cheap availability of magnets of standard size.
After iterations, the value of L i is obtained as 36 mm and it matches well with our requirements.
Design parameter
Specific magnetic loading B av
Magnitude of transverse
(T) line current, A my
(Ac/m)
B mz
.A
my product (TA/m)
Output co-efficient, σ p
(VAs/m 3 )
Value
0.445
25862
18103
9052
TABLE II
O BTAINED VALUES OF B mz
, A my
, B mz
.A
my
AND σ p
Synchronous speed v s
Number of primary phases m
1
Operating line voltage
Operating frequency
V
L f
Number of poles
Rated power
Air-gap length
P
P m g
5 m/s
3
100 V
50 Hz
4
320 W
2 mm
TABLE I
T ARGETED SPECIFICATIONS OF THE L INEAR PMSM
B. Initial calculation steps
Following Table.I, one may find that the
•
•
Pole pitch ( τ ) = 50 mm
Transverse length of primary (L
τ
) = 200 mm
Volt-Ampere (VA) rating of the machine,
P m
V A =
η.cosφ
= 418 .
3 V A ' 420 V A
No-load induced e.m.f. at rated speed as obtained when excited by PMs (without armature reaction) is, E f
= 45V [4].
C. Determination of Magnet size
Determination of PM size is most critical to the entire design exercise. Designing of permanent magnet involves considering the effect of demagnetisation ATs and availability of appropriate magnet. An optimum design will ensure reduced cost. However, at the same time for lagging load currents the PMs should not get demagnetised beyond the allowed limit. The magnet has been designed considering the average air-gap flux density, B av
= 0.445 T. Applying Ampere’s circuital law to the closed flux line in Fig.3, we have the total ampere-turns required in the magnetic circuit is nearly
1960 AT (considering B-H characteristics of NdFeB, N-
35 at temperature 100
0
C). Leakage and fringing flux are neglected [9].
So, magnet thickness is given by, l m
=
T otalAT
H m
= 5 .
774 mm ' 6 mm

(a) Double layer winding arrangement
Fig. 3.
LPMSM magnetic circuit
The dimensions of the procured magnetic tablet is
12mm X 12mm X 3mm, orientation is along thickness of 3mm.
TABLE III
C ALCULATED VALUES OF ELECTRICAL PARAMETERS OF LPMSM
Electrical parameters (per phase) Values
Length of mean turn (L mt
)
Primary resistance (r
1
)
Slot leakage reactance (X
1 l
)
0.267 m
3.52
2.13
Ω
Ω
Overhang leakage reactance (X
1 ov
) 1.20
Ω
Differential leakage reactance (X
1 d
) 11.48
Ω
11.47
Ω Armature reactance (X a
)
Primary leakage reactance (X
1
)
( = X
1 l
+ X
1 ov
+ X
1 d
) 14.81
Ω
(b) Winding arrangement for the one phase of LPMSM. S
A end and F
A is the finishing end.
is the starting
Fig. 4.
D. Selection of turn per phase
The transverse current density, A my
We have,
2
√
2 m
1
I
1
N
1
A my
=
τ P is 25862 A/m.
(1) where, N
1 is number of primary turns/phase.
Here, total number of slots (z
1
) and slots per pole per phase (q s
) are 12 and 1 respectively. Solving (1), N
1 is nearly 254 which gives number of conductors/phase/slot
(N sl
) as 127. Current density of primary conductors (J
1
) is assumed as 6 A/mm 2 , which gives diameter of the conductor (d) as 0.813 mm (corresponding to SWG 21).
E. Estimation of Electrical Parameters
F. Winding arrangement
12
Slot per pole per phase = = 1. A double layer
4 × 3 full-pitched winding consideration is used.
N o.of slots 12
Coil span = = = 3.
N o.of poles 4
The double layer winding arrangement in the respective slots and the winding chart for one phase is shown in (Fig.4(a)) and (Fig.4(b)) respectively.
G. Calculation and design validation using standard
FEM packages
The LPMSM is analysed using standard FEM package. The no-load induced e.m.f. at rated speed obtained when excited by PMs (without armature reaction) of the three respective phases is shown in Fig.5(a). The induced e.m.f. reads 50 V which is with corelation with the hand-calculated value of 46 V. The flux linkages of the three phases are shown in Fig.5(b). The relation between induced e.m.f. and flux linkage and of the same phase is shown in Fig.5(c). It is clearly seen that the induced e.m.f. is leading the flux linkage by 90 o . The magnetic field density and the flux lines at 1ms at a distance of 5mm from initial position is shown in Fig.6(a) and
Fig.6(b) respectively. The magnetic field in the air gap has a maximum value of 0.8T which is in excellent corelation with the calculated value. The overall design data sheet of the above 320 W, 4 pole, 3φ , rated speed of 5 m/s LPMSM is shown in Table.IV.
H. Fabrication of LPMSM
The designed LPMSM at the works of a local small machine manufacturer after procurement of imported
PMs. Fig.7(a) and fig.7(b) shows armature stampings and
SS-short primary of the LPMSM after winding arrangement. The procured magnet dimensions are shown in fig.7(c). The dimensions of the procured magnetic tablet is 12mm X 12mm X 3mm, orientation is along thickness of 3mm.

(a) Three phase no-load induced e.m.f. in the air-gap at rated speed of 5 m/s when excited by PMs
(a) Magnetic field density in air-gap, core, back-iron along with magnet at Position
= 5 mm, Time = 0.001 sec from initial position
(b) Three phase flux linkage of the LPMSM at rated speed of 5 m/s
(b) Flux lines in air-gap, core, back-iron along with magnet at Position = 5 mm,
Time = 0.001 sec from initial position
Fig. 6.
(c) Variation of flux linkage and induced voltage of Phase A
Fig. 5.
TABLE IV
D ESIGN DATA OF THE FABRICATED LPMSM
Design Data
Number of coils
Number of turns per coil
Wire diameter
Tooth width
Slot width
Length of armature (or linor/forcer)
Material of armature
Air-gap
PM material
PM height
PM face area
Value
12
65
0.813 mm
6.66 mm
10 mm
200 mm laminated steel
M-45 0.5 mm thick
2 mm
NdFeB, B r
= 1.21 T
3 mm
144 mm 2
Fig.8(a) shows the diagram of the yoke. Here, all dimensions are measured in ’mm’. A provision has been made for starting the motor as LIM first and then switching to LPMSM. Fig.8(b) shows the wooden base over which the back-iron, magnet and aluminium will be placed.
IV. C ONCLUSIONS
In this paper design and fabrication of a 3Φ , 4 pole,
320 W, 5 m/s surface mounted LPMSM has been done.
For ease of fabrication and for cost reduction the design starts with the available stampings used previously for fabrication of LIM which prototype exists in the laboratory ( [6], [10]). The design has been optimised and verified with the help of standard FEM packages. The linor has been fabricated and winding has been completed. The yoke (track) is fabricated with NdFeB N-35 grade permanent magnets. The fabricated LPMSM may

(a) Armature stamping of the LPMSM
(a) Design of track (yoke) of the LPMSM. All dimensions are in ’mm’.
(b) SS short primary of the LPMSM
(b) Wooden base for the yoke with PMs, Al sheet and back iron
Fig. 8.
(c) Dimension of unit NdFeB N-35 grade procured PMs
Fig. 7.
be used various advanced control speed drive for fast dynamic response and maximum reliability. Predicted values obtained from conventional analytical calculations are validated through FEM packages at different conditions. The predicted values and the experimented values are found to be in excellent correlation with each other.
V. A CKNOWLEDGMENTS
The authors wish to thank COE (MDAMD), IIEST,
Shibpur and TEQIP-II for their support. The authors acknowledge Mr.Kaushik Pyne and the entire staff of
G.E. Motors for their technical support in fabricating the motor. The authors also acknowledge the support received from the colleagues in the Advanced Power
Electronics Lab and particularly Mr. N. Dutta, Project
Technical Assistant, APE Lab, Dept. of EE and the authorities of IIEST, Shibpur towards this work.
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