# Electric Traction Motor: Linear Induction Motor

## Linear Induction Motor

A linear induction motor is a special type of induction motor that gives linear motion instead of rotational motion, as in the case of a conventional motion. In case of linear induction motor, the movement of field and movement of the conductors are linear.

## Construction and Working of Linear Induction Motor

A linear induction motor consists of a three-phase distributed field winding placed in the slots and the secondary winding is nothing but a conducting plate made up of either copper or aluminium as shown in Figure-1.

The field system of the linear induction motor may be either of following two types −

• Single Primary System

• Double Primary System

## Single Primary System

A single primary system is shown in Figure-2. In the single primary field system of the linear induction motor, a ferromagnetic plate is placed on the other side of the copper plate and it is necessary to provide low reluctance path for the magnetic flux.

When the primary winding is excited by three-phase AC supply, then according to the principle of mutual inductance, the induced currents are flowing through the secondary and ferromagnetic plate. The main drawback of the single primary system is that the ferromagnetic plate is energized and attracted towards the primary winding causes to unequal air-gap between primary and secondary windings.

## Double Primary System

Figure-3 shows the double primary system of a linear induction motor. In the double primary system, the drawback of single primary system that is unequal air-gap between primary and secondary is eliminated. In the double primary system, two primary windings are placed on both the sides of secondary winding.

Now, when three-phase primary winding is excited by giving three-phase AC supply, a magnetic field is developed which rotates at synchronous linear speed 𝑉𝑆. This linear synchronous speed is given by,

$$\mathrm{\mathit{V_{s}\mathrm{\: =\: }\mathrm{2}\, \tau f\: }\: meter\: per \: sec}$$

Where,

• 𝝉 is the pole pitch in meters, and

• 𝒇 is the supply frequency in Hertz.

From the above equation, it can be seen that in case of a linear induction motor, the synchronous speed is not the function of number of poles in the motor but it depends upon the pole pitch and the supply frequency.

The flux developed by the field winding pulls the rotor in the direction of the magnetic field linearly, which will reduce the relative speed between the magnetic field and the rotor plate. If the speed of the rotor plate and the speed of the magnetic field become equal, then the magnetic field would be stationary when viewed from the rotor plate.

If the speed of the rotor plate becomes greater than the speed of the magnetic field (or linear synchronous speed), then the direction of the force would be reversed which results in regenerative braking.

In case of linear induction motor, the slip is given by the following expression −

$$\mathrm{Slip,\mathit{s\mathrm{\: =\: }\frac{V_{s}-V}{V_{s}}}}$$

Where, 𝑽 is the actual speed of the rotor plate.

The torque-speed characteristics or tractive effort characteristics of a linear induction motor is shown in Figure-4.

Thus, the tractive effort produced by the linear induction motor is given by,

$$\mathrm{\mathit{F_{t}\mathrm{\: =\: }\frac{P_{r}}{V_{s}}}}$$

Where, 𝑃𝑟 is the actual power supplied to the rotor.

## Advantages of Linear Induction Motor

The chief advantages of the linear induction motors from the view point of electric traction are as −

• Linear induction motors are simple in construction.

• The maximum speed of the linear induction motors is not limited due to the centrifugal forces.

• Linear induction motors have better power to weight ratio.

• The initial cost of linear induction motor is low.

• The maintenance cost of the linear induction motor is also low.

## Disadvantages of Linear Induction Motor

The disadvantages of the linear induction motors include the following −

• Linear induction motors require high cost for providing collector system.

• Linear induction motors draw high currents because of the large air-gap, thus, they have poor efficiency and low power factor.

## Applications of Linear Induction Motor

Some of the applications of the linear induction motors are listed below −

• Linear induction motors find application in high speed rail traction.

• Linear induction motors are widely used in trolley cars and metallic belt conveyors.

• Linear induction motors are also used to drive electro-magnetic pumps.