Linear induction motor

A 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 primary or secondary length, which generates end-effects, whereas a conventional induction motor is arranged in an endless loop. Despite their name, not all linear induction motors produce linear motion; some linear induction motors are employed for generating rotations of large diameters where the use of a continuous primary would be very expensive. As with rotary motors, linear motors frequently run on a three-phase power supply and can support very high speeds. However, there are end-effects that reduce the motor's force, and it is 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. LIMs, unlike their rotary counterparts, can give a levitation effect. They are therefore often used where contactless force is required, where low maintenance is desirable, or where the duty cycle is low. Their practical uses include magnetic levitation, linear propulsion (as a mass driver, and linear actuators. They have also been used for pumping liquid metals.

History 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 US patent 782312 (1905; inventor Alfred Zehden of Frankfurt-am-Main), and is for driving trains or lifts. 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 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 the direction of the moving magnetic field. Laithwaite called the later versions a 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, and thus permits high speed and efficiency.

Construction A linear induction motor's primary typically consists of a flat magnetic core (generally laminated) with transverse slots that are often straight cut with coils laid into the slots, with each phase giving an alternating polarity so that the different phases physically overlap. The secondary is frequently a sheet of aluminium, often with an iron backing plate. Some LIMs are double sided with one primary on each side of the secondary, and, in this case, no iron backing is needed. Two types of linear motor exist: a short primary, where the coils are truncated shorter than the secondary, and a short secondary, where the conductive plate is smaller. Short secondary LIMs are often wound as parallel connections between coils of the same phase, whereas short primaries are usually wound in series. The primaries of transverse flux LIMs have a series of twin poles lying transversely side-by-side with opposite winding directions. These poles are typically made either with a suitably cut laminated backing plate or a series of transverse U-cores.

Principles

In this electric motor design, the force is produced by a linearly moving magnetic field acting on conductors in the field. Any conductor, be it a loop, a coil, or simply a piece of plate metal, that is placed in this field will have eddy currents induced in it thus creating an opposing magnetic field in accordance with Lenz's law. The two opposing fields will repel each other, creating motion as the magnetic field sweeps through the metal.

n s = 2 f s / p {\displaystyle n_{s}=2f_{s}/p}

where fs is supply frequency in Hz, p is the number of poles, and ns is the synchronous speed of the magnetic field in revolutions per second. The travelling field pattern has a velocity of:

v s = 2 t f s {\displaystyle v_{s}=2tf_{s}}

where vs is velocity of the linear travelling field in m/s, and t is the pole pitch. For a slip of s, the speed of the secondary in a linear motor is given by

v r = ( 1 − s ) v s {\displaystyle v_{r}=(1-s)v_{s}}

Forces

Thrust

The drive generated by linear induction motors is somewhat similar to conventional induction motors; the drive forces show a roughly similar characteristic shape relative to slip, albeit modulated by end effects. Equations exist for calculating the thrust of a motor.

End effect Unlike a circular induction motor, a linear induction motor shows 'end effects'. These end effects include losses in performance and efficiency that are believed to be caused by magnetic energy being carried away and lost at the end of the primary by the relative movement of the primary and secondary. With a short secondary, the behaviour is almost identical to a rotary machine, provided it is at least two poles long but with a short primary reduction in thrust that occurs at low slip (below about 0.3) until it is eight poles or longer. However, because of end effects, linear motors cannot 'run light' -- normal induction motors are able to run the motor with a near synchronous field under low load conditions. In contrast, end effects create much more significant losses with linear motors.

Levitation

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