Sunday, April 19, 2009



Linear induction motors (LIM) are used in many different applications, from slow moving sliding doors to high-speed trains around the world. Anything that requires linear motion will require a LIM. The primary goal is to analyze a small laboratory sized single sided linear induction motor (SLIM) for educational aid.

The idea of a LIM had been suggested in 1895 and was first developed by an English Electrical Engineer, Eric Laithwaite. He spent the rest of his career investigating these special machines. His colleagues are currently designing a launch system with linear motors, which is a more efficient alternative to the rockets used to launch spacecrafts.

Lim operates on the same principle as the conventional rotary motor. The rotary motor is cut out and laid flat to from the equivalent lim. Nothing has changed; only the direction of motion has changed.

Conventional motor Linear motor

This report describes the basic concept and control of linear induction motor. The stator winding and reaction plate design are very important.


1.1 Objective and goals: -

The aim of this report is to understand a basic of linear induction motor for educational purposes. The main goal of this report is to study of linear induction motor.

1.2 Overview of report: -

The report is divided up into several chapters. The chapters follow each other logically to explain the overview of LINEAR INDUCTION MOTOR.

Chapter 1: Provides an introduction to the report, defines the objectives and goals.

Chapter 2: This chapter is the literature review, which provides a working knowledge of the LIM, gathered from various resources.

Chapter 3: Explains the operating properties associating with LIM.

Chapter 4: Describes the various effects regarding LIM.

Chapter 5: Describes the control of Linear Induction Motor.


This chapter includes a working knowledge of the linear induction motor, its characteristics, and types of linear induction motor.

2.1 History: -

The idea of a linear induction motor had been suggested in 1895, and was first developed by an English Electrical Engineer, Eric Laithwaite. Laithwaite discovered that it is possible to arrange two linear motors back to back, to produce a continuous oscillation without the use of any switching devices. In 1946, the first large scale linear motor was built by westinghhouse corporation, which was an aircraft launcher. This is no new technology regarding LIM, but merely designed in a different form. Only the way it produces motion and shape is changed.

2.2 Application: -

Wherever straight-line motion or reciprocating forces are needed, the lim is superior to provide such service. They are typically used in applications where accurate positioning is not required. The linear induction motor has proven itself in many unusual applications, ranging from a small sliding door right to steam catapults used on aircraft carriers. Table illustrates some typical application where LIM are used.

Fig 2.1 Linear machine

Typical Application.

  • Sliding Doors
  • Sewage Distributors
  • Automated Warehousing
  • Aluminium can propulsion
  • Crane drives
  • Stage curtain movement
  • Mixer stirrer drives
  • Scrap sorting movement
  • Revolving doors
  • Baggage handling
  • Flat circular motors
  • Linear accelerators
  • Flexible manufacturing systems
  • Personal rapid transport system
  • Ship test tank drives
  • Bogie drives
  • Turntable drives
  • Target movement
  • Steel tube movement
  • Wire winding
  • Slewing drives
  • Sheet metal movement
  • Pallet drives
  • Research machines
  • Automated postal systems
  • Multi motor in track systems
  • Theme park rides
  • Extrusion pullers
  • Robotic systems
  • People movers
  • Lover profile drives
  • Conveying systems
  • Airport carousels

2.3 Linear induction motor: -

A linear induction motor is basically a rotating squirrel cage induction motor opened out flat. Instead of producing rotary torque from a cylindrical machine it produces linear force from a flat one. Depending on the size and ratings of the LIM, they can produce thrust up to several thousands Newton. The speed of the LIM is determined by the winding design and supply frequency.

Conceptually all types of motors can have possible linear configurations (dc induction, synchronous, and reluctance). The dc motor and synchronous motor require double excitation (field and armature). This makes the hardware application rather complex. The reluctance motor produces poor thrust, since it has no secondary excitation. It can be seen why most of the attention is diverted to linear induction motors.

Linear induction motors can have various configurations: the air gap can be flat or cylindrical, and the flux can be longitudinal or transverse. A lim can be either a short primary or a short secondary lim, depending on whether the primary or the secondary is the shorter. In each case, either the primary or the secondary can be the moving member. Finally, the motor can either be single sided or a double sided. This report will be concerned with designing a sho0rt primary (moving member), flat air gap, longitudinal flux and single sided motor.

Fig 2.2 LIM with transverse flux.

2.4 Operation: -

The linear motor operates on the same principal as a rotary squirrel cage induction motor. The rotary induction motor becomes a linear induction motor 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 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 stator coils becomes unreasonable.

When supplying an ac current to the coils, a traveling magnetic wave is produced. Swapping the phases reverse the direction of travel. Currents induced in the reaction plate by the traveling magnetic wave create a secondary magnetic field. It is not necessary to kept 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.

2.5 LIM Components: -

The LIM consists of two main components.

1) 3-phase coil assembly:

The coil assembly consists of a 3-phase winding that is wound into a steel lamination stack. 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 coil assembly will require some form of mounting to ensure stability during operation. The single sided configuration consists of a single coil assembly that is used in conjunction with an aluminium or copper plate backed by a steel reaction plate. The coil assembly can be directly connected to the ac line for single speed applications.

2) Reaction plate: -

A suitable reaction plate is required for proper operation of the LIM. The reaction plate is made from standard steel, aluminium, and or copper. For single sided operation, the required reaction plate consists of a .125” [3 mm] thick aluminium or a .080” [2 mm] thick copper plate that is backed by a .25” [6mm] thick ferrous steel plate. The steel plate can be omitted put the force will be dramatically reduced.

Fig 2.3 Reaction Plate


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 two are basically identical to one another. The equations formulated for rotary machines can be applied directly to LIMs with a few minor adjustments.

3.1 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 by:

Vs=2pf (3.1)

Vs = 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-pitch width.
To further clarify, consider two machines where the radii are R and 2R respectively (Figure 3.1a). The rotational field speed for is w0 for both of them, while the linear speeds are different.

FIG 3.1: Linear and rotary corresponding gap sizes: a) Effective radius R: b) Effective radius 2R: c) travel length 2JR: d) travel length 4JR

For case (a), for case (b)

Vs = w0R vs = 2 w0R
= 2ÿfR = 4ÿfR
=2f* pole pitch =2f* pole pitch.

For each one cycle of current the field travels two pole pitches. In figure 3.1 (b), the pole pitch is twice that of figure 3.1 (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.

3.2 SLIP: -

The slip formula of LIM is identical to conventional rotary machine. The slip is defined as, “ slip (s) of an induction motor is the difference between the synchronous speed and rotor speed, expressed as a percentage (or per unit) of synchronous speed.” The per unit of slip can be expressed by
S = (vs-v)/vs.


S = slip.
Vs = synchronous linear speed [m/s].
V = speed of rotor (or stator) [m/s].

3.3 FORCES: -

The main forces involved with the LIM are thrust, normal and lateral. Thrust is what this Report 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 the orientation of the stator.

Fig 3.2 Forces associated with LIMs.

3.3.1 THRUST: -

Under normal operation, the LIM develops a thrust proportional to the square of the applied voltage (Figure 3.3), and this reduces as the slip is reduced similarly to that of an induction motor with a high rotor resistance.

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 3.4.

Fig 3.3 Thrust - line voltage characteristic

Fig 3.4 Air gap on thrust and current characteristic.
The amount of thrust produced by a LIM is as follows.

F = Pr/Vs


F = thrust [N].
Pr = power transmitter to the rotor [w].
Vs = linear synchronous speed [m/s].

The equivalent circuit of the LIM is exactly the same as of a conventional 3-phase rotary machine. The power output is as follows:

Power output = 3(I1) 2 Rs/s (1-s) W

Referring to equation, if F is the amount of thrust produced in newtons and vs is the linear synchronous speed in m/s then:

Fvs = 3(I1) 2 Rs/s (1-s)

If the iron loss is very small, thus:

Power output = power input - 3(I1) 2 Rp

The power input can be approximately related to the mechanical input of the machine.

Fig 3.5 LIM Equivalent Circuit.

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 is placed asymmetrically between the two stators. This force tends to center the reaction plate. A small displacement of the reaction plate from the center is directly proportional to the displacement.

In a SLIM configuration in which there is a rather large net force between the primary and secondary. This is because of the fundamental asymmetrical topology. At synchronous speed, the force is an attractive force and its magnitude is reduced as the speed is reduced. At certain speeds the force will become repulsive, especially at high frequency operation.
Fig 3.6 Normal Force in LIM

Lateral force moves in the y-direction as shown in figure. These occur due to the asymmetric positioning of the stator in a LIM. Any displacement from 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 track is sufficient to eliminate small lateral force.


Induction motors draw current from its primary source and then transfer 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 reactances of the primary and the secondary circuit are not essential. The energy conversion efficiency can be improved as the mutual reactance Xm of the motor is increased and the secondary circuit resistance R2 is decreased. The goodness factor is G = Xm/ R2 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

G = (2Ffp2)/(prrg)
= (m0/prr) * vs (p/g).

f = source frequency.
p = pole pitch of the primary winding.
rr = surface resistivity of the secondary conduction sheet.
g = air gap.
m0 = permittivity of free space.
Vs = linear synchronous speed.

From above formula, it can be seen that a linear motor 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 loadings. 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 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 an therefore the ratio (p/g) are reduced as frequency is increased. Low frequency motors therefore perform much better than high frequency ones.


Since the length of the LIM does not join up upon itself, one might think that when the flux reaches the end of the stator, there must be a delay before it returns to restart once more at the beginning. In fact, this is not the case. The traveling waves of flux produced by the LIM, move smoothly from one end of the stator to the other. Figure 3.7 shows the movement of flux from left to right in a 2-pole LIM. At the extremities A and B of the stator, the flux cuts off sharply. No matter how fast the N or S pole disappears at the right, it builds up again at the left.
Figure 3.7: shape of the magnetic field created by a 2- pole, 3-phase linear stator, over one complete cycle. The successive frames are separated by an interval of time equal to 1/6 cycle.

This chapter describes the various effects of LIM. These effects must be minimized as much as possible when designing LIM, so that they do not drastically affect performance. Some effects can be eliminated while others are unavoidable.


One obvious difference between LIM and conventional rotary machines is that the fact that LIM has ends. This means that the traveling 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. 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 fig 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. 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.
Fig 4.1 Normal flux density distribution in LIM.
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 machine.”


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 center due to the edge effect, and the dip is more obvious at higher slips.

Fig 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.

Conventional rotary machine has a 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 the magnetizing current is also higher. There is a rather large leakage flux that further reduces the operating power factor. The gap density is less than for the rotary counterpart, and consequently iron losses form a smaller part of the total loss.

Figure shows the effect of air gap to the attraction force. Figure 4.3 and Figure 4.4 shows the effect of air gap on thrust and line current.
Fig 4.3 Attraction/ air gap characteristics.
Fig 4.4 Effect of air gap on thrust and line current.

Following are the name of various methods by which we can control the speed of linear induction motor.

1. Variable frequency variable voltage method.

2. Direct torque and flux control method.

3. Vector control method.

All above methods are similar to Induction Motor with small modification and same equations can be applied to Linear Induction Motor.

1 comment:

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