Report Consist a general knowledge about linear induction motor construction, principle, application etc.

1. LINEAR INDUCTION MOTOR AND ITS APPLICATIONS
A
Seminar report
In partial fulfilment
For the award of the degree of
Master of Technology
In
Department of Electrical Engineering
(With specialization in Power Electronics and Electrical Drives)
Under the guidance of: Submitted by:
Dr. Dinesh Birla (Professor) Ajit Singh Rajawat
Dr.Vivek Shrivastav (Associate Professor) Roll No. 14/922
Dept. of Electrical Engineering M.Tech. 3rd
SEM
Rajasthan Technical University (P.E.E.D)
Rajasthan Technical University, Kota
Department of Electrical Engineering

2. Candidate's Declaration
I hereby declare that the work , which is being presented in the Seminar Report, entitled
"Linear Induction Motor and its applications" in partial fulfilment for the award of Degree
of "Master of Technology" in Department of Electrical Engineering with Specialization in
Power Electronics and Electrical Drives, University is a record of my own investigations
carried under the guidance of " Dr. Dinesh Birla (Professor)" and " Dr.Vivek Shrivastav (Associate
Professor) " Department of Electrical Engineering , RTU, Kota.
I have not submitted the matter presented in this seminar report anywhere for the award of
any other degree.
Ajit Singh Rajawat
Roll No. 14/922
M.Tech. 3rd
sem
(P.E. & E.D)
RTU, Kota
Under the guidance of:
Dr. Dinesh Birla (Professor)
Dr.Vivek Shrivastav (Associate Professor)
Dept. of Electrical Engineering
Rajasthan Technical University, Kota

3. ACKNOWLEDMENT
It would be a great pleasure to write a few words, which would although not suffice as the
acknowledgment of this long cherished effort, but in the absence of which this report would
necessarily be incomplete. So these words of acknowledgment come as a small gesture of
gratitude towards all those people, without whom the successful completion of this project
would not have been possible.
Firstly, I would like to express deep gratitude towards my guide Dr. Dinesh Birla (Professor) and
Dr.Vivek Shrivastav (Associate Professor) Department of Electrical Engineering, RTU, Kota who
gave their valuable suggestions, motivation and the direction to proceed at every stage. They
are like a beam of light for me. Their kind guidance showed me the path of life and is
unforgettable. Also special thanks and due regards extends to, DR. D.K. Sambhriya (Associate
Professor of Electrical engineering Dept.) for they extended towards their valuable guidance,
indispensable help and inspiration at times. In appreciation I offer them my sincere gratitude.
Last but not least I would to thank the department of Electrical Engineering, RTU, Kota. This
seminar work has been greatly assisted by the corporation of Library staffs and Lab staffs that
provided full support and facilities. It would have been impossible for me to complete the work
without their valuable guidance and prompt cooperation
Date Ajit Singh Rajawat

4. ABSTRACT
Nowadays, Linear Induction Motors are widely used, in many industrial applications including
transportation, conveyor systems, actuators, material handling, pumping of liquid metal, and
sliding door closers, etc. with satisfactory performance. The most obvious advantage of linear
motor is that it has no gears and requires no mechanical rotary-to-linear converters. This report
provides a technical review of a linear induction motor with rotary motors, linear motors
frequently run on a three-phase power supply and can support very high speeds. However, there
are end effects which reduce the force, and it's often not possible to fit a gearbox to trade off
force and speed. Linear induction motors are thus frequently less energy efficient than normal
rotary motors for any given required force output. linear induction motor (LIM) is an
alternating current (AC), asynchronous linear motor that works by the same general principles
as other induction motors but is typically designed to directly produce motion in a straight line.
Characteristically, linear induction motors have a finite length primary or secondary, which
generates end effects, whereas a conventional induction motor is arranged in an endless loop.
As Compared to rotary induction motor, the linear requires a larger air gap. Consequently the
magnetizing current is large, & therefore PF, Efficiency are low.

5. LIST OF FIGURES
Name Page No.
Fig 2.1 Geometry of single sided LIM (Linear induction Motor) 4
Fig 2.2 Geometry of double sided LIM 5
Fig 2.3 3- coil Assembly 6
Fig 2.4 Secondary winding of LIM 7
Fig 2.5 Conventional induction motor & linear induction motor 7
Fig 2.6 Radius of a rotary induction motor and length of a LIM 9
Fig 3.1 Actual slot before winding 14
Fig 3.2 Single layer winding configuration for a 4 pole, 3 phase, 1 slot per pole per phase,
LIM 15
Fig 3.3 Flux distribution and back-iron density of a single layer winding 16
Fig 3.4 Fractional-pitch, Double layer winding for a 4 pole, 3 phase, 1 slot per pole per
phase LIM whose coil span is one-third the pole pitch 17
Fig 3.5 Fractional pitch, Double layer winding for a 4 pole, 3 phase, 7/6 slot per pole per
phase LIM whose coil span is two-thirds the pole pitch 17
Fig 3.6 Full-pitch, double layer winding for a 5 pole, 3 phase, 1 slot per pole per phase LIM
18
Fig 4.1 Normal flux density distribution of LIM 19
Fig 4.2 Edge effect of LIM 20
Fig 4.3 Linear and rotary gap sizes: (a) effective radius (b) effective radius 2R 22
Fig 4.4 Forces 23
Fig 4.5 Thrust Line voltage characteristics 23
Fig 4.6 Air gap or thrust & current characteristics 24
Fig 4.7 LIM circuit 25
Fig 4.8 Normal forces in LIM 26
Fig 4.9 Application of LIM 27

6. CONTENTS
ACKNOWLEGMENT
ABSTRACT
LIST OF FIGURES
Chapter 1 INTRODUCTION OF LINEAR INDUCTION MOTOR 1-3
2.1 History of LIM 1
1.2 About LIM 2
1.3 Future aspects of LIM 2
Chapter 2 CONSTRUCTION AND OPERATING PRINCIPAL OF LIM 4-10
2.1 Construction of LIM 4
2.2. Parts Associated with LIM 5
2.2.1 Stator of LIM 5
2.2.2 Rotor of LIM 6
2.3 Operating principal of LIM 7
2.4 Mathematical Expression for LIM 8
Chapter 3 DESIGN OF LIM 11-19
3.1 Design parameter of LIM 11
3.1.1 Air gap 11
3.1.2 Pole pitch 11
3.1.3 Number of poles 12
3.1.4 Secondary surface resistivity 12
3.1.5 Primary core 12
3.1.6 The goodness factor 13

7. 3.2 Construction of LIM 14
3.2.1 Stator 14
3.2.2 Reaction Plate 14
3.3 Winding Configuration of LIM 15
3.3.1 Single Layer Windings 15
3.3.2 Double Layer Windings 16
Chapter 4 Various Effects in LIM 19-28
4.1 Effects in LIM 19
4.1.1 End Effect 19
4.1.2 Edge Effect 20
4.1.3 Gap Effect 20
4.2 Properties of LIM 21
4.2.1 Linear Synchronous Speed 21
4.3 Forces 21
4.3.1 Thrust 23
4.3.2 Normal 25
4.3.3 Lateral 26
4.4 Application of LIM 26
4.5 Advantage of LIM 27
4.6 Disadvantage 27
CONCLUSION AND FUTURE ASPECTS 29-30
BIBLIOGRAPHY 31
REFERENCES 32-33

8. 1
CHAPTER-1
INTRODUCTION OF LINEAR INDUCTION MOTOR (LIM)
1.1 History of LIM
The history of linear electric motors can be traced back at least as far as the 1840s, to the work
of Charles Wheatstone at King's College in London, but Wheatstone's model was too inefficient
to be practical. A feasible linear induction motor is described in the US patent 782312 (1905
inventor Alfred Zehden of Frank furtam Main), for driving trains or lifts. The history of linear
induction motors extends as far back as the 19th century. Although these machines have been
practically forgotten for the last 30 or 40 years, there appears to be a genuine revival of interest
in them. The fascinating history of these “unrolled” motors and their theory of operation are
discussed in this seminar report. A few Years just after the discovery of RIM (Rotary induction
motor) principle in 1890 came LIM (Linear induction motor). The idea of the linear induction
motor is probably contemporary with the invention of the rotating field machine by Tesla,
Dolivo-Doborovolsky, and Ferrari sometime after 1885. However, some authors give other
dates for the discovery. [1,2]
Nicola Tesla invented the induction motor in 1888. The first patent in linear induction motors
was obtained by the mayor of Pittsburg in 1895. The first electromagnetic gun was undoubtedly
Birkeland’s cannon of 1918, again a reluctance device, but possibly the first tubular motor
using a row of simple coils energized in sequence with DC. In 1946, Westinghouse built a full-
scale aircraft launcher, the “Electropult”, which was an induction motor with a moving
primary. It was this machine that inspired E.R.Laithwaite to begin his own work on linear
motors in the 1950’s, since when there have been rapid advances in linear induction machines
for producing standstill forces, for propelling high-speed vehicles and as accelerators for
producing kinetic energy. [3]
The basic concept behind linear device consist a rotary machine which is to be cut along a
radial plane & unrolled so that the primary member then consists of a single row of coils in
slots in a laminates steel core. For low speed applications both flat and tubular linear induction
motors (TLIM) are suitable. The single-sided linear induction motor (SLIM) is by far the most
widely used linear motor.
The German engineer Hermann Kemper built a working model in 1935. In the late 1940s,
Professor Eric Laithwaite of Imperial College in London developed the first full size working

9. 2
model. In a single sided version, the magnetic field can create repulsion forces that push the
conductor away from the stator, levitating it, and carrying it along in the direction of the moving
magnetic field. Laithwaite called the later versions of it magnetic river. These versions of the
linear induction motor use a principle called transverse flux where two opposite poles are
placed side by side. This permits very long poles to be used, which permits high speed and
efficiency. [1,2]
1.2 About LIM
A flat or single-sided LIM i.e., a SLIM, is obtained by the imaginary process of “cutting” and
“unrolling” a rotary induction motor. In practice, the primary or stator of a LIM consists of a
rectangular slotted structure formed by a stack of steel laminations. Within the slots of the
primary stack are laid the poly-phase windings to produce the linearly traveling magnetic field,
just like the rotating magnetic field in a rotary induction motor, produced by the poly-phase
stator windings. The secondary of the LIM, or rotor, which is an aluminium sheet (or copper),
with or without a solid back iron plate, completes the magnetic circuit and creates the magnetic
flux linkage across the air gap. This in turn induces a voltage on the conductive wall, which
generates an eddy current in the conducting outer layer of the secondary. The interaction
between the eddy current and the changing electromagnetic field generates electromagnetic
thrust on the plate in the longitudinal direction of the motor. [4,5]
1.3 Future Aspects of LIM
Linear motors potentially have unlimited applications. Linear induction motors (LIM’s) alone
have found application in the following general areas: conveyor systems, material handling and
storage, people movers, liquid metal pumping, accelerators and launchers, machine tool
operation, airport baggage handling, opening and closing drapes, operation of sliding doors and
low and medium speed trains. Linear induction motor have potential to revolutionize how we
travel. The trains themselves are less costly and noisy than conventional trains and they require
less maintenance due to their levitation eliminating most of the friction [4].
Maglev trains use far less energy than conventional trains and emit no pollutants. High speeds
allow for maglev trains to be a realistic alternative to flying, and they can help reduce air and
road congestion as more people are moving around the world. So far LIM has been controlled
with few classic controllers in future various latest control methodologies are upcoming which
will have effective control of LIM in terms of the efficiency and performance of the machine.

10. 3
The U.S. Navy plans to start launching future naval fixed aircraft using linear induction motor.
The scientists are changing the shape of stator to flat, and the vehicle is too used in place of the
rotor. This vehicle will move in straight line and will achieve high acceleration quickly. [6]

11. 4
CHAPTER-2
CONSTRUCTION AND OPERATING PRINCIPAL OF LIM
2.1 Construction of LIM
A Linear Induction motor (LIM) is a special type of induction motor which gives linear motion
instead of rotational motion, as in the case of conventional induction motor. It operates on the
principle of which a conventional induction motor operates. In contrast with its rotary
counterpart, a LIM may have a moving primary (with a fixed secondary) or a moving secondary
(the primary being stationary). In stator of LIM act as primary and rotor acts as secondary. LIM
can be a short primary or short secondary, depending on whether the primary or secondary is
shorter. In each case, either primary or the secondary can be the moving member in our project,
secondary is short. In addition, the LIM may have two primaries face to face to obtain a double-
sided LIM (DLIM shown in Figure 2.2). If the LIM has only one primary, it is called as single
sided LIM [3]
LIM are of two types:
1. SLIM(Single Sided Linear Induction Motor)
2. DLIM(Single Sided Linear Induction Motor)
Below figure 2.1 gives the brief construction of SLIM
Fig 2.1 Geometry of single sided LIM

12. 5
A flat or single-sided LIM i.e., a SLIM, is obtained by the imaginary process of “cutting” and
“unrolling” a rotary induction motor. In practice, the primary or stator of a LIM consists of a
rectangular slotted structure formed by a stack of steel laminations. Within the slots of the
primary stack are laid the poly-phase windings to produce the linearly traveling magnetic field,
just like the rotating magnetic field in a rotary induction motor, produced by the poly-phase
stator windings. The secondary of the LIM, or rotor, which is an aluminium sheet (or copper),
with or without a solid back iron plate, completes the magnetic circuit and creates the magnetic
flux linkage across the air gap. This in turn induces a voltage on the conductive wall, which
generates an eddy current in the conducting outer layer of the secondary. The interaction
between the eddy current and the changing electromagnetic field generates electromagnetic
thrust on the plate in the longitudinal direction of the motor. [4,5]
The secondary of the LIM is normally conducting plate made of either copper or aluminium in
which interaction currents are induced. In a single primary system a Ferro magnetic plate is
usually placed on the other side of the conducting plate to provide a path of low reluctance to
the main flux. However the ferromagnetic plate gets attracted towards the primary on
energization of the field and this causes unequal gap length on the two sides of the conducting
plate. Depending on the size and ratings of LIM they can produce thrust up to several thousand
Newton’s .The speed of the LIM is determined by winding design and supply frequency.
Conceptually all types of motors have possible linear configurations (dc, induction
synchronous and reluctance).The dc motor and synchronous motor requires double excitation
(field and armature). [5,6]
Fig 2.2 Geometry of double sided LIM
2.2 Parts Associated with LIM
2.2.1 Stator of LIM:-

13. 6
Linear Induction Motor consists of 3 phase windings that are wound on a steel laminated core.
These laminations are insulated from one another with very fine materials such as paper or
adhesive glue. The entire assembly can be encapsulated with thermally conductive epoxy for
insulation and stability. The core will require some mounting to ensure its stability during
operation. The core is provided with semi enclosed slots to house the conductors. The single
sided configuration consists of a single coil assembly that is used in conjunction with
aluminium or copper plate which may be backed with either steel or iron plate if necessary
shown in figure 2.3. The coil assembly can be directly connected to A.C lines for single speed
application.
Fig 2.3 3-ɸ coil assembly
2.2.2 Rotor of LIM:-
It is made up of non-magnetic and highly conductive material. The easiest way to build up this
secondary circuit is by use of aluminium plate as it is cheap and easy to handle. If the thickness
of aluminium plate is small the conducting plate will get hot, if it is too big the 10 air gap
would be large and the efficiency of the machine goes low. The plate may be little bit wider
than primary iron to allow the current closing its path outside the active area. The induced field
is maximized by backing up the reaction with the iron plate, this plate serve to amplify the
magnetic field produced in the coil [4].The reaction plate is used as secondary shown in the
figure 2.4.

14. 7
Fig 2.4 Secondary winding of LIM
2.3 Operating Principal of LIM
The LIM operates on the same principal as a rotary squirrel cage induction motor. The rotary
induction motor becomes a LIM when the coils are laid out flat; the reaction plate in the LIM
becomes the equivalent rotor. This is made from a non-magnetic highly conductive material.
The induced field can be maximized by backing up, the reaction plate with an iron plate
(conducting sheet). The iron plate serves to amplify the magnetic field produced in the coil.
The air gap between the stator and the reaction plate must typically be very small, much smaller
than the allowable gap for the synchronous motor, otherwise the amount of current required
for the stator coils becomes unreasonable. When supplying an AC current to the coils, a rotating
magnetic field is produced as showed in the figure 2.5. Currents induced in the reaction plate
by the rotating magnetic field create a secondary magnetic field. It is not necessary to keep the
field of motion synchronized to the position of the reaction plate, since the second field is
induced by the stator coil. A linear thrust is produced with the reaction between these two
fields.
Fig 2.5 Conventional Induction Motor & Linear Induction Motor

15. 8
The principle of operation of a LIM is the same as that of a rotary induction motor. A linear
Induction motor is basically obtained by opening the rotating squirrel cage induction motor and
laying it flat. This flat structure produces a linear force instead of producing rotary torque from
a cylindrical machine. LIMs can be designed to produce thrust up to several thousands of
Newton’s. The winding design and supply frequency determine the speed of a LIM. The basic
principle of LIM operation is similar to that of a conventional rotating squirrel-cage induction
motor. Stator and rotor are the two main parts of the conventional three phase rotary induction
motor. The stator consists of a balanced poly-phase winding which is uniformly placed in the
stator slots along its periphery. The stator produces a sinusoidally distributed magnetic field in
the air-gap rotating at the uniform speed 2ω/p, with ω representing the network pulsation
(related to the frequency f by ω= 2πf) and p the number of poles. The relative motion between
the rotor conductors and the magnetic field induces a voltage in the rotor. This induced voltage
will cause a current to flow in the rotor and will generate a magnetic field. The interaction of
these two magnetic fields will produce a torque that drags the rotor in the direction of the field.
This principle would not be modified if the squirrel cage were replaced by a continuous sheet
of conducting material.
2.4 Mathematical Expression for LIM
From the induction motor principle explained above, we obtain a linear motor if we imagine
cutting and unrolling the motor, as shown in Figure 2.5, causing the motor to have a linear
motion. Instead of rotating flux, the primary windings now create flux in a linear fashion. The
primary field interacts with the secondary conductors and hence exerts a force on the
secondary. Generally, the secondary is made longer than the primary to make maximum use of
the primary magnetic field.
As stated earlier, there should be relative motion between the conductor and the magnetic lines
of flux, in order for a voltage to be induced in the conductor. That’s why induction motors,
normally operate at a speed Vr that is slightly less than the synchronous velocity Vs. Slip is the
difference between the stator magnetic field speed and the rotor speed. Consider a conventional
rotary motor, it is possible to lay a section of the stator out flat without affecting the shape or
speed of the magnetic field. Hence, the flat stator would produce a magnetic field that moves
at constant speed. The linear synchronous speed is given
𝑉𝑠 =
2. 𝜔. 𝑅
𝑝
(2.1)
Where
v= linear synchronous speed [m/s]

16. 9
p = width of one pole-pitch [m]
f = frequency [Hz]
It is important to note that the linear speed does not depend upon the number of poles but only
depend on the pole-pitch width. By this logic, it is possible to for a 2-pole linear machine to
have the same linear synchronous speed as that of a 6-pole linear machine, provided that they
have the same pole-pitch width.
Slip is the relative motion needed in the induction motor to induce a voltage in the rotor, and
it is given by
𝑆 =
𝑉𝑠−𝑉𝑟
𝑉𝑠
(2.2)
The SLIM synchronous velocity Vs is the same as that of the rotary induction motor, given by
𝑉𝑠 =
2.𝜔.𝑅
𝑝
= 2. 𝑓. 𝝉 (2.3)
Where, R is the stator radius of the rotary induction motor, as shown in Figure 2.6. It is
important to note that the linear speed does not depend upon the number of poles but only on
the pole pitch.
Fig 2.6 Radius of a rotary induction motor and length of a LIM

17. 10
The parameter τ is the distance between two neighbouring poles on the circumference of the
stator, called pole pitch, defined as
𝝉 =
2.𝜋.𝑅
𝑝
(2.4)
The stator circumference of the rotary induction motor, 2πR, in (2.5) is equal to the length of
the SLIM stator core, Ls as shown in figure 2.6.Therefore, the pole pitch of a SLIM is
𝝉 =
2.𝜋.𝑅
𝑝
=
𝐿 𝑠
𝑝
(2.5)
If the velocity of the rotor is Vr, then the slip of a SLIM can be defined as
𝑆 =
𝑉𝑠−𝑉𝑟
𝑉𝑠
(2.6)
The air-gap shown in Figure 2.6 (b) is the clearance between the rotor wall and the SLIM stator.
When comparing the properties of the LIM to the properties of the conventional rotary motor,
these are the properties of the LIM to the properties of the conventional rotary motor, these can
be applied directly to LIMs.

18. 11
CHAPTER-3
DESIGN OF LIM
3.1 Design Parameters of LIM
The design parameters of LIM are
• Air gap
• Pole pitch
• Number of poles
• Secondary surface resistivity
• Primary core
• The goodness factor
3.1.1 Air Gap:-
The length of the air gap is very important parameter in machine design. A large air gap requires
a large magnetizing current and results in a smaller power factor. In the case of an LIM, exit-
end zone losses increase with a larger air gap. Also, output force and efficiency decrease when
the design incorporates a large air gap. The goodness factor is inversely proportional to the air
gap. Using the goodness factor concept, machine design can be optimized, since for a low-
speed LIM, to a certain extent, the larger the goodness factor, the better the machine. Thus, it
is clear that the air gap should be as small as is mechanically possible
3.1.2 Pole Pitch:-
For larger goodness factor, the pole pitch should be as large as possible. Note that the pole
pitch (𝝉p) is squared in the expression goodness factor. However, too large pole pitch results in
increased back iron thickness, which could tremendously increase the weight of the LIM. Also,
if pole pitch increases, efficiency decreases, resulting in less active length of conductor
(conductor in the slot) to the total length of the conductor (conductor in the slot plus the end
connections). As known, end connections serve no useful purpose and can produce very high
leakages and losses. Synchronous speed (Vs ) is related to frequency and pole pitch as follows:
𝑉𝑠 = 2. τ 𝑝. 𝑓1 𝑚/𝑠

19. 12
Thus, for a given frequency, the pole pitch alone determines the synchronous speed of the
machine .For a given machine length, a large pole pitch results in a smaller number of poles,
which is usually not desired.
3.1.3 Number of Poles:-
End effects are reduced with an increase in the number of poles, in the LIM. This is because
more poles tend to share the constant end-effect a loss between them, resulting in a better
performing machine. Thus, it would be advantageous to have a machine with a large number
of poles.
3.1.4 Secondary Surface Resistivity:-
The secondary thickness and the material play an important role in the performance of a LIM.
The thicker secondary, the larger goodness factor. In case of a nonferrous secondary, a thicker
material results in a larger air gap, which is undesirable. For nonferrous secondary’s, then, the
thickness must be small, but strong enough to withstand the magnetic-forces present. In ferrous
secondary’s, the air gap is independent of material thickness. However, a thicker secondary
results in larger starting currents. As a result, the thickness chosen depends on the starting
current limitations rather than the desired increase in the goodness factor.
The secondary material is as effective as thickness on secondary resistivity. Therefore,
the lower resistivity improves the goodness factor and also gives less secondary loss. But low
resistivity results in a shower decay of the end-effect travelling wave which reduces the output.
Thus, a compromise between goodness factor and secondary resistivity is necessary. Of the
two homogeneous materials, ferromagnetic material has the advantage of high permeability,
which means less magnetising current; but a disadvantage is the strong magnetic pull between
the primary and the secondary [2]. A nonferrous but electrically conducting material reduces
this large magnetic pull, but when the permeability of air gap is low, magnetising currents are
very large. A composite secondary of both ferrous and nonferrous materials combines the
advantage of each (high permeability and reduced magnetic pull) and appears to be the best
secondary electromagnetically. Cost considerations are not included in our discussions.
3.1.5 Primary Core:-
The variations in stator core design also affect the performance of a LIM. Given a constant
cross-sectional area of copper in the slot, a machine with narrower teeth produces more force
and has better efficiency and a better power factor than a machine with wider teeth. This is
because a machine with narrower teeth has lower primary and secondary leakage reactance that
results in a smaller secondary time constant. A smaller time constant produces an end-effect
travelling wave of smaller magnitude, and this leads to larger machine output. To determine

20. 13
the narrowest tooth width, the flux density in the tooth must be considered, tooth saturation
setting the limit on the narrowest tooth
3.1.6 Goodness Factor:-
Induction motors draw current from its primary source and then transfers it to the secondary
circuit crossing the air gap by induction. The difference between the power transferred across
the air gap and the rotor losses is available as the mechanical energy to drive the load. In
prospective of energy conversion, the primary resistance and the leakage reactance’s of the
primary and the secondary circuit are not essential. The energy conversion efficiency can be
improved as the mutual reactance of the motor is increased and the secondary circuit resistance
is decreased. The goodness factor is for a basic motor. As the value of G increases, the
performance of the machine gets better.
The goodness factor for a linear motor can be defined as:
)(*)(
2 0
2
0
g
p
V
g
fp
G s
rr 



 (4.1)
Where
f = source frequency
p =pole pitch of primary winding
r = surface resistivity of the secondary conducting sheet
g = air gap
0 = permittivity of free space
Vs= linear synchronous speed
From the equation, it can be seen that a LIM is a better energy conversion device at high
synchronous speeds and also when the ratio (p / g) is large. This can be explained in terms from
a more fundamental point of view. For example, a linear motor, just like any other
electromagnetic device, has an inherent force density limitation imposed on it by the design
constraints of electric and magnetic loading [4]. With the resulting thrust limitations, high
power for a given sized of motor is only possible at very high speeds. When the ratio (p / g) is
small, the primary leakage flux is large, and consequently the effective magnetic coupling is
reduced and the LIM shows poor performance. The air gap is determined by mechanical
considerations and hence, for a given linear synchronous speed, the pole pitch and therefore
the ratio (p /g) are reduced as frequency is increased. Low-frequency motors therefore perform
much better than high-frequency ones.

21. 14
3.2 Construction of LIM
3.2.1 Stator:-
The core manufacturing process started with purchasing of various lamination sheets of steel
alloys basically CRGO material used for core manufacturing. These lamination sheets are
painted with thinner to clean them from any oil or dust which might have accumulated over
storage time. Each of lamination sheets is handled with care because without cleaning process
the glue will not properly stick to one another to finally form a laminated core. Now according
to the design specification cuts the lamination sheet into required shapes as per the slot length
and width and number of slots so required. The height of the core depends upon the number of
stakes put together to form the core. After cutting of the laminations is done the vendor prepares
a necessary DYE or JIG for particular job. The following fig. gives us a better idea of JIG or
DYE. The stator must be designed as accurately as possible and this is possible with help of a
jig device only. The Jig lines each lamination into the correct slot, forming a neat layer. Each
layer is glued together with an adhesive glue or spray. Once 10 layers are filled up on the jig
with the glue, they are compressed firmly to ensure an even distribution of the glue. Finally all
the layers are glued together and compressed to form the stator as shown in the figure 5.4. Here
it can be seen that the slots are to be securely insulated to prevent from any short circuiting of
the winding so as to avoid short circuit due to overheating.
Fig 3.1 Actual slot before winding
3.2.2 Reaction Plate:-
The reaction plate design can consist of either a solid or laminated design. To further improve
the performance, the reaction plate is coated with conduction sheet of either copper or
aluminium. In case of SLIM configuration, the secondary component is an important segment
of the LIM magnetic circuit. The SLIM performance is greatly degraded if the reaction plate is
solid instead of laminations. With laminated plate, the eddy current carried by the laminations
and the resulting ohmic losses and the thrust are both small enough to be ignored. The amount
of thrust produced by the SLIM will depend on the permeability of the reaction plate; lower

22. 15
permeability will result in lower thrust and poor power factor. There is no particular design
consideration for reaction plate, but for standard operation it is to be noted that the length of
the reaction plate should be equal or more than the addition of the width of the core and the
pole pitch of the primary winding.

p
WW cs
2
 (4.2)
Where,
Ws= width of secondary,
Wc = width of core,
p = pole pitch
Now as far as the manufacturing process is concerned, the process is not a difficult job as that
of the stator construction. The aluminium plate of the necessary width, thickness and length is
designed. We have gone for an aluminium plate of the thickness about 0.5mm, which is
sufficient enough for flux linkage through it.
3.3 Winding Configurations of a LIM
There are many winding arrangements possible for a LIM. Prominent among them are the
single layer, double layer and the triple layer winding configurations. This report shows the
feasibility of single layer and double layer winding configurations in LIM’s.
3.3.1 Single layer windings:-
The number of coils in a single layer winding is one-half the number of slots available, because
each coil side completely occupies one slot. Each slot contains one coil side only in a single
layer winding configuration, as shown in Fig 3.2.
Fig. 3.2 Single layer winding configuration for a 4 pole, 3 phase, 1 slot per pole per phase, SLIM
The approximate flux density distribution of single layer windings is obtained by adding the
contribution of all three phases A, B, C as shown in fig 3.3.

23. 16
Figure 3.3: Flux distribution and back-iron density of a single layer winding.
These are quite generally used in small single phase motors because of their convenience in
coil assembly. Single layer windings also eliminate the need for coil-coil insulation in slots
since there is only one coil per slot.
3.3.2 Double Layer windings
The armatures of nearly all synchronous generators and motors, and most induction motors
above a few kilowatts, are wound with double-layer windings. In a double layer winding, there
are two sets of windings of different phases placed in the same slot, except the end slots, as
shown in Fig 3.4 .Each coil has two sides. The end of each coil or its second coil side is placed
below the start of the adjacent coil or its first coil side. This ensures that the windings are placed
identically with respect to each other. This winding configuration results in a balanced
arrangement with all three phases carrying the same amount of current. The number of turns in
each coil and the parallel arrangements depends on the supply current and the size of each slot.
It is possible to construct a winding with a coil pitch less than the pole pitch. When the span
from centre to centre of the coil, which constitutes a phase belt, is less than the pole pitch, the
winding as a whole is said to be a fractional-pitch winding.

24. 17
Fractional pitch windings are extensively used, particularly with two layer windings because
they reduce harmonics in the voltage wave and produce a more nearly sinusoidal current
waveform than with full-pitch windings. They also give a saving in the amount of copper used
in the overhang and the greater stiffness of the coils due to shorter end connections. The
fractional-pitch, double layer winding having a coil pitch equal to one-third the pole pitch is
shown in the Figure 3.4.
Fig 3.4: Fractional-pitch, Double layer winding for a 4 pole, 3 phase, 1 slot per pole per phase SLIM
whose coil span is one-third the pole pitch.
Figure 3.5 illustrates a fractional-pitch double layer winding for a 3 phase, 4 pole,
7/6 slots per pole per phase SLIM whose coil span is two-thirds the pole pitch. It can be seen
that this winding configuration needs 14 slots compared to 12 slots in the previous arrangement
as shown in Figure 3.4.
Fig 3.5: Fractional pitch, Double layer winding for a 4 pole, 3 phase, 7/6 slot per pole per phase SLIM
whose coil span is two-thirds the pole pitch.
The full-pitch, double layer winding arrangement for a 5 pole, 3 phase, 1 slot per pole per
phase SLIM can be as shown in figure 3.6. The approximate flux density distribution is also

25. 18
shown by summing up the flux produced by individual phases. The back-iron density is also
shown.
Figure 3.6 Full-pitch, double layer winding for a 5 pole, 3 phase, 1 slot per pole per phase SLIM
The advantages and disadvantages of these windings are related to the manufacturing costs
and the capacity for producing an air-gap field distribution approaching a purely sinusoidal
wave. The double layer winding utilizes double the number of coils than a single layer
winding but it produces a very good forward traveling wave of fewer harmonics components
than its counterpart. Thus, there is a trade-off between cost and performance in choosing the
type of winding for a SLIM. In high-thrust applications, the double layer winding is most
suitable. In general, it may be said that modern practice favours the double-layer winding
except where the slot openings would be large compared with the length of the air-gap, as in
high voltage induction motors.

26. 19
Chapter 4
VARIOUS EFFECTS IN LIM
4.1 Effects in Lim
4.1.1 End Effect:-
One obvious difference between LIM and conventional rotary machines is that the fact that
LIM has ends. This means that the travelling magnetic field cannot join up on itself, and
introduces end effects. The end effects can result in characteristics that are much different from
rotary machines.
The end effect is clearly exhibited in the form of a non-uniform flux density distribution along
the length of the motor [6,7]r. For a LIM supplied with a constant current, typical variation of
the normal flux density with slip and position along the length is illustrated in Figure 4.1. With
constant primary current, its magnetizing component and consequently the air gap flux
decreases as the load component increases with increasing slip. This is true for any induction
motor, with or without end effect [2,3]. For a given slip, the flux density builds up along the
LIM length, beginning with a small flux density at the entry end. Depending on the length of
penetration of the entry-end- effect-wave, the flux density may not even reach the nominal
level that would be found in a motor without end effect.
Figure 4.1 Normal flux density distribution of LIM

27. 20
The theoretical evaluation of these effects is much too complicated to explain, but the results
can be stated fairly simply. Laithwaite states that, if the total number of pole-pitches on the
shorter member (either short stator or short rotor) exceeds four, the additional effect of the
transients due to the edges is likely to be so small that it can be neglected, except in large,
powerful machines.
4.1.2 Edge Effect:-
The edge effect is generally described as the effect of having finite width for a linear motor.
This effect is more evident with lower values of width-to-air gap ratio. Figure 4.2 illustrates
the variation of the normal flux density in the transverse direction. The figure shows a dip at
the centre due to the edge effect, and the dip is more obvious at higher slips.
Figure 4.2 Edge effect in LIM
As a result, the edge effect will increase the secondary resistivity, lateral instability due to the
uneven secondary overhangs and a reduction in performance.
4.1.3 Gap Effect
Conventional rotary machine has a very small air gap, in the order of 2mm or less. This allows
a high gap flux density. For LIM, the air gap can be as large as 5cm for one operating on a
traction system. The magnetic circuit reluctance is much higher for large air gaps, in which th

28. 21
e magnetizing current is also higher. There is a rather large leakage flux that further reduces
the operating power factor [5]. The gap density is less than for the rotary counterpart, and
consequently iron losses form a smaller part of the total loss.
4.2 Properties of Lim
This chapter describes the various properties associated with LIM. When comparing the
properties of the LIM to the properties of the conventional rotary motor, these are the properties
of the LIM to the properties of the conventional rotary motor, these can be applied directly to
LIMs
4.2.1 Linear Synchronous Speed:-
Consider a conventional rotary motor, it is possible to lay a section of the stator out flat without
affecting the shape or speed of the magnetic field. Hence, the flat stator would produce a
magnetic field that moves at constant speed. The linear synchronous speed is given
p
f
Ns
120
 (4.1)
Where
Ns= linear synchronous speed [m/s]
p = width of one pole-pitch [m]
f = frequency [Hz]
It is important to note that the linear speed does not depend upon the number of poles but only
depend on the pole-pitch width. By this logic, it is possible to for a 2-pole linear machine to
have the same linear synchronous speed as that of a 6-pole linear machine, provided that they
have the same pole-pitch width.
4.3 Forces
The main forces involved with the LIM are thrust, normal and lateral. Thrust is what this thesis
interested in and its relationship with the other adjustable parameter the normal force is
perpendicular to the stator in the z direction. Lateral forces are side forces that are undesirable,
due to the orientation of the stator. Under normal operation, the LIM develops a thrust
proportional to the square of the applied voltage and this reduces as the slip is reduced similarly
to that of an induction motor with a high rotor resistance. The amount of thrust produced by a
LIM is as follows:
s
r
V
P
F  (4.2)

29. 22
Where,
F=thrust [N],
Pr=power transmitted to the rotor [W],
Vs=linear synchronous speed [m/s]
Fig 4.3 Linear and rotary gap sizes: (a) effective radius (b) effective radius 2R
For case (a) for case (b)






polepitchf
fR
R
Vs
*2
2
0








polepitchf
fR
R
Vs
*2
4
2 0


For each one cycle of current the field travels two pole pitches. In Figure 4.3(b), the pole pitch
is twice that of Figure 4.3(a). The results clearly indicate that linear synchronous speed does
not depend on the number of poles, but depend on the pole pitch.
To increase the linear synchronous speed of the LIM, the designer could either:
(a) Design a longer pole pitch.
(b) Increased the supply frequency.

30. 23
The main forces involved with the LIM are thrust, normal and lateral (Figure 4.4). Thrust is
what this thesis is interested in, and its relationship with the other adjustable parameters. The
normal force is perpendicular to the stator in the z-direction. Lateral forces are side forces that
are undesirable, due to orientation of the stator.
Figure 4.4 Forces
4.3.1 Thrust:-
Under normal operations, the LIM develops a thrust proportional to the square of the applied
voltage (Figure 4.4), and this reduces as the slip is reduced similarly to that of an induction
motor with a high rotor resistance [3].
Figure 4.5 Thrust line voltage characteristics

31. 24
The air gap for a typical LIM machine is 2mm, variations up to ±20% are considered
acceptable. The effect of the air gap on thrust and current line is shown in (Figure 4.5).
Figure 4.6 Air gap on thrust and current characteristics
The amount of thrust produced by a LIM is as follows
s
r
V
P
F  (4.3)
Where
F=thrust [N],
Pr=power transmitted to the rotor [W],
Vs=linear synchronous speed [m/s]
The equivalent circuit of the LIM shown in figure 3.2.5 is exactly the same as of a conventional
3-phase rotary machine. The power output is as follows:
)1()(3outputPower
'
2
1
'
s
s
R
I
s
 Watt (4.4)

32. 25
Referring to equation, if F is the amount of thrust produced in Newton’s and is the linear
synchronous speed in m/s, then:
)1()(3FV
'
2
1
'
s s
s
R
I
s
 watt (4.5)
If the iron loss is very small, thus:
pRI 2
1
'
)(3-inputPoweroutputPower 
The power input can be approximately related to the mechanical input of the machine
Figure 4.7 LIM circuit
4.3.2 Normal:-
In a double-sided linear induction motor (DLIM) configuration, the reaction plate is centrally
located between the two primary stators. The normal force between one stator and the reaction
plate is equal and opposite to that of the second stator. Therefore, the resultant normal force is
zero. A net normal force will only occur if the reaction plate (secondary) is placed
asymmetrically between the two stators. This force tends to centre the reaction plate. A small
displacement of the reaction plate from the centre is directly proportional to the displacement.
In a SLIM configuration in which this seminar report is based on, there is a rather large net
force between the primary and secondary. This is because of the fundamental asymmetrical
topology. Figure 4.8 shows the variation of the normal force with speed and frequency of
primary current. At synchronous speed, the force is an attractive force and its magnitude is

33. 26
reduced as the speed is reduced. At certain speeds the force will become repulsive, especially
at high-frequency operation.
Figure 4.8 Normal force in LIM
4.3.3 Lateral:-
Lateral force moves in the y-direction as shown in Figure 4.4. These occur due to the
asymmetric positioning of the stator in a LIM. Any displacement from the central positioning
will result in an unstable system. Generally, small displacements will only result in very small
lateral force. At high frequency operation, the lateral force can be become quite chaotic. A set
of guided mechanical wheel tracks is sufficient to eliminate small lateral force.
4.4 Application of LIM
Application of LIM as follows:
1. Transportation(Low & Medium Speed trains)
2. Sliding Doors Closure(Malls, Metros)
3. Pumping of Liquid metal
4. Conveyor systems
5. People movers
6. Accelerators and launchers
7. Airport baggage handling

34. 27
8. Material handling and storage
4.9 Application of LIM
4.5 Advantage of LIM
Advantage of LIM as Follows:
1. Direct Electromagnetic Force
2. Economical & Cheap Maintenance
3. Easy Expansion for any linear motion of system topology
4. Exact Positioning in closed loop system
4.6 Disadvantage of LIM
Disadvantage of LIM as Follows:
1. Power factor and efficiency are less than of rotary motors because of a ratio of large
air gap between inductors and pole pitch.
2. Extra vibrations with distortions can be noticed because of uncompensated normal
force.

35. 28
3. The longitudinal end effect reduces power factor and efficiency. This can be noticed
only with fast speed and small pole number motors.

36. 29
CONCLUSION & FUTURE ASPECTS
Conclusion
In this seminar report, a detailed study of the design of the LIM was performed and compared
with that of a comparable CIM design. The main objective of this project was to formulate the
design equations of the LIM and then develop a user-interactive computer program for its
design. The equivalent circuit model of the LIM was studied in order to obtain the performance
equations for thrust and efficiency. It can be concluded that the air-gap plays a very important
role in the performance of the LIM. The air-gap needs to be as small as possible to have a better
thrust and efficiency. Another crucial design parameter is the thickness of rotor outer layer
which is aluminium. As the thickness of the aluminium sheet is increased thrust also increases
along with the length of magnetic air-gap which is undesirable. Hence, care should be taken in
choosing the best value for aluminium thickness which yields maximum thrust at a reasonable
efficiency. The number of poles in the stator was the last parameter that was varied to observe
the SLIM performance curves. By increasing the number of poles, the end effects are reduced,
which is good for the SLIM performance. At the same time thrust is increased but at the expense
of efficiency. Hence, there is a trade-off between the thrust and the efficiency with increasing
number of poles.
So, from the parametric evaluation which in performed in Chapter 5, it can be concluded that
the input parameters like the length of physical air-gap, the thickness of aluminium sheet and
the number of poles play a vital role in the performance parameters, thrust and efficiency.
Therefore, care should be taken in choosing these parameters. Based on our target values of
rotor velocity and thrust, these parameters should be chosen which gives the best possible thrust
closest to the target value at a decent value of efficiency.
Future Aspects
This study of LIM neglected several issues like end effects and edge effects, which will affect
the performance of the LIM. There are some improvements which can be implemented in the
design of LIM for better analysis. Some suggestions for future study are as follows:
1. Improving the equivalent circuit model of the LIM by introducing various realistic factors
like end effects, edge effects, air-gap leakage fluxes and skin effects due to finite plate
thickness.

37. 30
2. Use the finite element method (FEM) analysis instead of equivalent circuit model for
determining the LIM performance.
3. Detailed study must be done regarding the layout of stator windings by building a laboratory
model of the LIM. Improvements to the proposed model can be suggested by trying different
winding configurations.
4. The LIM is designed and analysed in its steady state only. The transient behaviour of the
LIM is not analysed in this study.

38. 31
BIBLIOGRAPHY
 www.ieeexplore.org
 www.wikipedia.org
 www.google.com
 www.digitallibrary.edu.pk
 www.encyclopedia.org
 www.academia.org

39. 32
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